Math Homework Questions & Answers Archive

Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a house and a car the method of sealed bids. The players' bids (in dollars) are: A B C D --------------- House 240000 239000 232000 234000 Car 30000 35000 34000 31000 The original fair share of A is worth: 68750 In the initial allocation, player A: Select an answer and Select an answer the estate After all is said and done, in the final allocation, player A: Select an answer and Select an answer the estate

Suppose you toss a coin 100 times and get 52 heads and 48 tails. Based on these results, what is the estimated probability that the next flip results in a tail? The estimated probability that the next flip results in a tail is approximately (Type an integer or decimal rounded to two decimal places as needed)

Use the Laplace transform to solve the following initial value problem: y'' - 4y' + 20y = 0 y(0) = 0, y'(0) = 4 a. Using Y for the Laplace transform of y(t), i.e., Y = Ly(t), find the equation you get by taking the Laplace transform of the differential equation b. Now solve for Y(s) = 4 / (s-2)^2 + 4^2 c. By completing the square in the denominator and inverting the transform, find y(t) = e^(2t) sin(4t)

Consider the region R between y=x^2+3, x=0, x=2, and y=0. Use the Shell Method or Disk Method to find the volume V of the solid formed by rotation R around the y-axis. (Express numbers in exact form. Use symbolic notation and fractions where needed.) V=

Factor the trinomial completely. x^2+4x-21

A population of values has a normal distribution with μ=124.1 and σ=95.8. If a sample size of n=250 is selected, find the probability that the mean of the group of 250 is less than 141.1. Round to 3 decimal places. P(X<141.1)=

Differentiate. f(x)=8 ln x f'(x)=

In the following probability distribution, the random variable x represents the number of activities a parent of a K to 5th-grade student is involved in. Complete parts (a) through (f) below. x 0 1 2 3 4 P(x) 0.202 0.147 0.233 0.128 0.290 This is a discrete probability distribution because the sum of the probabilities is 1.0 and each probability is between 0 and 1, inclusive. (b) Graph the discrete probability distribution. Choose the correct graph below. A. B. C. D.

You order some books online and get an estimated delivery date of June 1-June 9. You know you will be our of town June 4th and Sth and are a little concerned abour the package arriving when you are away. Assuming the delivery date follows a discrete uniform distribution, what is the likelihood your package will be delivered while you are out of town? Round your answer to four decimal places, if necessary.

You are only allowed to use integer exponents. - Use sqrt(...) to deal with fractional exponents. - Make sure your final answer is written as a single logarithm. a. 7 log (x)+5 log (z)-1/2 log (y)=log ((x^7 z^5)/sqrt(y)) b. 1/2 log (x)-5 log (y)-7 log (z)=log (sqrt(x)/(y^5 z^7)) c. 5/2 log (x)-7/2 log (y)-5/2 log (z)=log (sqrt(x^5)/(y sqrt(7/2) sqrt(z^5))) Hint - Do you have a sum of logarithms? Use the fact that log (a)+log (b)=log (a b). - Do you have a difference of logarithms? Use the fact that log (a)-log (b)=log (a/b). - Remember that a^(m/n)=sqrt[n](a^m).

According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.06 inches. What is the probability that the mean daily precipitation will be 0.098 inches or less for a random sample of 40 November days (taken over many years)? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Evaluate the definite integral [ int-1^2left(x^2-5 xright) d x ] using the Fundamental Theorem of Calculus, Part 2. Enter the exact answer. [ int-1^2left(x^2-5 xright) d x= ]

Write in logarithmic form. 1/9=3^(-2) The logarithmic form is □ (Use integers or fractions for any numbers in the expression.)

Graph one complete cycle of the following. Label the axes accurately. y = -2 + 4 cos(1/2 x - π/3)

Perform the indicated operations, then simplify. 7x^2 / (x^2 - 49) - 7x / (x + 7) + 7 / (x - 7)

Answer the following: a. Find the uniform continuous probability for P(X<12) for U(0,50). Note: Round your answer to 2 decimal places. Probability b. Find the uniform continuous probability for P(X>800) for U(0,1,000). Note: Round your answer to 3 decimal places. Probability c. Find the uniform continuous probability for P(26<X<58) for U(19,63). Note: Round your answer to 4 decimal places. Probability

If cos(x) = 2/7, and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimals. sin(x/2) = cos(x/2) = tan(x/2) =

A test was given to a group of students. The grades and gender are summarized below A B C Total ----------------------- Male 15 18 19 52 Female 20 10 12 42 Total 35 28 31 94 If one student is chosen at random from those who took the test, find the probability that the student was female GIVEN they got a 'C'.

Consider the following rational function. f(x) = (x+2) / (x-10) Step 2 of 2: Find equations for the horizontal or oblique asymptotes, if any, for the function.

Introduction to Exponential Functions If the Inputs change at a constant rate, which of the following are true of Linear and Exponential Functions? Check all that apply. The outputs for Exponential Functions change by Addition. The outputs for Linear Functions change by Addition. The outputs for Linear Functions change by Multiplication. The outputs for Exponential Functions change by Multiplication.

6. What is this quadrilateral's most precise name?

Determine the location of each local extremum of the function. f(x)=-x^3-9x^2-24x+1 What is/are the local minimum/minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Let A be the event of rolling a sum of 8, and let B be the event of rolling doubles. The sample space consists of all possible rolls of two dice. Since there are 6 ways to roll the first 6-sided die, and 6 ways to roll the second 6-sided die, there are 6 × 6 = elements in the sample space. Recall the addition rule of probabilities: P(A or B) = P(A) + P(B) - P(A and B) Thus, we need to find all of the values on the right hand side of that equation.

A pianist plans to play 6 pieces at a recital. In how many ways can she arrange these pieces in the program?

Calculate the standard score of the given X value, X=49.3, where μ=48 and σ=43.8 and indicate on the curve where z will be located. Round the standard score to two decimal places.

An equation is given: y = √x^2 + 4x + (-2.21)y + 4.1) Use a graphing calculator to graph the equation in the given viewing rectangle. y intercept (x, y) = x intercept (x, y) = x intercept (x, y) = Find the x- and y-intercepts from the graph. Verify your answers algebraically (from the equation). *If an answer does not exist, enter DNE.

Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec(cos^(-1) (2/x))

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. log x + log (x-2) = log 15 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

logx(25) = 2 x =

Some experts believe that 24% of all freshwater fish in a country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 250 fish tested, and 54 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with 24% dangerous fish, assuming that this is a random sample. Use a significance level of 0.05. Comment on your conclusion. State the null and alternative hypotheses. A. H0: P<0.24 Ha: P>0.24 B. H0: p=0.24 Ha: p>0.24 C. H0: p=0.24 Ha p ≠ 0.24 D. H0: p>0.24 Ha P<0.24 E. H0: p ≠ 0.24 H3: P=0.24

Which function describes the graph?

Solve the exponential equation. Express the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal approximation for the solution. e^x=20.4 What is the solution in terms of natural logarithms? The solution set is (Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the expression.)

Let S=1,2,3,4,5,6,7,8,9,10 be the universal set. Let sets A, B, and C be subsets of S, where: Set A=1,3,5,7,8 Set B=3,8,9,10 Set C=4,6,9 LIST the elements in the set A ∩ B ∩ C:

Given the function C(r)=(r-4)(r+7)(r-3) its C-intercept is its r-intercepts are

The area of the shaded region is 0.2744

Simplify the radical expression. (Use absolute value signs, if appropriate.) √[4]5 x^4 y^6

Step 2 of 5: Find the number of mushroom pizzas sold each month. Round your answer to the nearest integer.

Relation Function Not a function

Week 2 Quiz (Retake) Score: 2/5 2/5 answered Question 3 Characteristics of Polynomials For each Polynomial, identify its key characteristics. Polynomial Name Leading Coefficient Constant Term Degree 8x^7+x^6+3 Select an answer v -x+4 Select an answer v 7x^4 Select an answer v

Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows. x 0 1 2 3 4 P(x) 0.2 0.1 0.3 0.3 0.1 Part 1 of 2 (a) Compute the mean μX. Round the answer to one decimal place. μX=

The demand function for a given product is D(p)=600-p. What is the elasticity at the price p=100?

For the given functions f and g , find the indicated composition. f(x)=(x-6)/2, g(x)=2x+6 ;(g∘f)(x) A. 2x+6 B. x-3 C. x+12 D. x

Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing. f(x) = -(1/2) x^2 + 9x - 2 (a) The vertex is (Type an ordered pair, using integers or fractions.)

Solve the system of equations by the substitution method. 4x + 3y = 27 y = -(4/3)x + 9 (x, y) = ( )

If a jury pool consists of 10 men and 12 women, what is the probability of selecting a 5 person jury consisting of all females? Round your answer to the nearest whole number Probability = % (Type an integer.)

A restaurant server believes the distribution of their tips has a model that is slightly skewed to the right, with a mean of 9.60 and a standard deviation of 5.40. Complete parts a through c below. a) Explain why you cannot determine the probability that a given party will tip them at least 20. Choose the correct answer below. A. 20 is 10.40 greater than the mean, but 10.40 is greater than the standard deviation. Since this is true and all determinable values must occur within one standard deviation of the mean, the probabilities of values that far from the mean cannot be determined. B. 20 is 10.40 greater than the mean, but 10.40 less than the mean is -0.80. Since these values should have the same probability and tipping a negative amount is not possible, the probabilities of values that far from the mean cannot be determined. C. This distribution is not unimodal, meaning it has more than one mode and does not meet the conditions of the Normal model, so the probabilities of values within this distribution cannot be determined. D. This distribution is skewed, meaning it is non-symmetric and does not meet the conditions for the Normal model, so the probabilities of values within this distribution cannot be determined.

10:48 PM Sat oct 26 Section 9.3 HW Question 18 of 38 (1 point) Question Attempt: 1 of Unlimited Part 3 of 6 (c) f(√161) ≈ 2.5407 Part 4 of 6 (d) f(5 π) ≈ Part 5 of 6 (e) f(5.6 × 10^5) ≈ Part 6 of 6 (f) f(7.3 × 10^-2) ≈

Suppose you flip two coins. What is the probability of getting at most one heads? Give your answer as a reduced fraction.

Knowledge Check Question 12 Camron Joel A technical machinist is asked to build a cubical steel tank that will hold 360 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m . m

A sample of 75 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.3 pounds with a standard deviation of 0.21 pounds. The population standard deviation is known to be 0.24 pounds. Find the 98% confidence interval. Round all answers to the nearest hundredth. a. Find x̄. x̄=2.3 b. Find s and σ. Enter DNE if they are unknown. s=0.21 σ=0.24 c. Find n. n=75 d. Identify the type of confidence interval. Select an answer - e. Find the Critical Value. ? = f. Find the 98% confidence interval and complete the sentence below. Conclusion: We estimate with % confidence that the population mean time needed is between and hours.

Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)/d(x), where d(x) r(x) is the remainder. (x^3+7x^2-18x-6)/(x-2)

Simplify the expression 0.039 × 0.0084 / 0.21 × 0.078 using scientific notation and express your answer in scientific notation.

Using the given data, find the following. 28 23 9 3 16 Part: 0 / 2 Part 1 of 2 Identify the five-number summary. Round your answers to one decimal place as needed. Low = Q1= , MD = , Q3= , High =

Find and simplify the difference quotient (f(x+h)-f(x))/h, h ≠ 0 for the given function. f(x)=1/(7x) A. -(1/(7x(x+h))) B. 0 C. 1/(7x) D. -(1/(x(x+h)))

√[12]y^5 · √[6]y^5 = y^(5/6 + 5/12)

One centimeter is equivalent to inches. 2.54 0.39 1.0 0.254

The uniform, normal, and exponential distributions are all continuous probability distributions. are all discrete probability distributions. can be either continuous or discrete, depending on the data. are all the same distributions.

Consider the message "DO NOT PASS GO." Identify the number obtained after applying the encryption function f(p)=(3p+7) mod 26 to the number translated from the letters of the above message. (You must provide an answer before moving to the next part.) Multiple Choice 16-23 20-23-12 0-7-9-9 25-23 16-23 20-21-12 0-7-9-9 25-23

Simplify the expression by using a double-angle formula. (2 tan 5 theta)/(1-tan^2 5 theta)

What is the quotient of the following division problem? 16023 ÷ 25=? A. 639 r24 B. 642 r 23 C. 640 r 24 D. 640 r 23

The function f(x) is continuous on (-∞, ∞). Use the given information to sketch the graph of f. x -2 -1 0 1 2 f(x) -1 1.1 2 4 -4 Choose the correct graph of f below. A. B. C. D.

Solve the equation. First combine any like terms on each side of the equation. 3x + 7 - 2x = 16 The solution is x =

The professor of an introductory calculus class has stated that, historically, the distribution of final exam grades in the course resembles a normal distribution with a mean final exam mark of μ=61% and a standard deviation of σ=12%. (c) The top 3% of students writing the final exam will receive a letter grade of at least A in the course. To two decimal places, find the minimum final exam mark needed to earn a letter grade of at least A in the course.

Use the given function to complete parts (a) through (e) below. f(x)=x^4-1 x^2 a) Use the Leading Coefficient Test to determine the graph's end behavior. A. The graph of f(x) falls left and rises right. B. The graph of f(x) rises left and rises right. C. The graph of f(x) rises left and falls right. D. The graph of f(x) falls left and falls right: b) Find the x-intercepts. x= (Type an integer or a decimal. Use a comma to separate answers as needed.)

The graph of y=K(x) is given. (a) Write the domain of K. (b) Write the range of K.

Rationalize sqrt(3)/sqrt(2) (or sqrt(3)/sqrt(2)) Choose one · 3 points sqrt(3) sqrt(2) sqrt(6)/2 sqrt(2)/6 sqrt(6)/3 sqrt(3)/6 2/3 3/2 6

2+5 y

Multiply or divide the following measurements, Be sure each answer you enter contains the correct number of significant digits. 2.094 g/mL × 2.85 mL = 5.9 g 101.1 mol ÷ 0.35 L = 290 mol/L 2.094 cm × 5.125 cm = 10.73 cm²

QUESTION 10 Select the words that correctly completes the sentence. - To graph q(x)=x+2, we shift the graph f(x)=x because Down ; 2>0 Up ; 2>0 Down; -2<0 Up ;-2<0

On the basis of a population survey, there were 85.5 million males and 98.3 million females 25 years old or older Educational Attainment for Men and Women Educational Attainment Males (in millions) Females (in millions) Not a high school graduate (A) 14.8 14.9 High school graduate (B) 27.2 34.2 Some college, but no degree (C) 14.8 15.3 Associate's degree (D) 6.1 7.3 Bachelor's degree (E) 15.5 18.2 Advanced degree (F) 7.1 8.4 Relative Frequency (males)

Find the center and radius of the circle. Write the standard form of the equation The center of the circle is (h,k) = []

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. 7x-9y=1 -14x+18y=1 A. (x, 1/12 x) B. (x, 2/9+7/9 x) C. (-1/12, 19/108) D. ∅

Consider the following frequency table representing the scores on a test. Scores on a Test Class Frequency 30-46 11 47-63 15 64-80 13 81-97 4 98-114 12 Choose the interval that contains the score, 61.7. Answer 2 Points 30-46 47-63 64-80 81-97 98-114

Solve for x: 2/3 x-5=2 x=

A market analysis team selects 7 random volunteers to taste 5 Bacon Cheeseburgers from local restaurants. 4 from the national chain and 1 from a local diner. a. What is the probability that exactly 3 people will pick the local diner's burger? b. What is the probability that none of the people select the local diner's burger?

A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Department Labor-Hours per Ski Maximum Labor-Hours Available per Day --------- Trick Ski Slalom Ski Fabricating 9 6 216 Finishing 1 1 27 Answer parts (A), (B), and (C) below. (A) If the profit on a trick ski is 30 and the profit on a slalom ski is 50, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is The maximum occurs when trick skis and slalom skis are produced.

This question: 2 point(s) possible Add and, if possible, simplify. [ (a-5b)/(a+b)+(a+7b)/(a+b) ] (a-5b)/(a+b)+(a+7b)/(a+b)= (Simplify your answer. Type an integer or a fraction.)

Subtract. Your answer should be a polynomial in standard form. [ (-5 m^2-8)-(-3 m^2+m+2)= ]

Rationalize the denominator and simplify. 8 / √5

Sea el triángulo ABC, ¿Cuánto mide el lado AB?

The high temperature in Jackson, WY, on July 13 was 80°F. Use the formula, C=5/9(F-32), where C is Celsius degrees and F is Fahrenheit degrees, to convert 80°F to Celsius degrees. Round to the nearest tenth of a degree. 86.4°C 26.7°C 62.2°C 12.4°C

Student Homework 3.5: Exponential and Logarithmic Models Score: 18.5 / 25 10 / 13 answered Question 12 x 1 2 3 4 5 6 y 726 960 1160 1663 2116 2772 Use regression to find an exponential equation that best fits the data above. The equation has form y = a * b^x where: a =□ b =□

Match each equation in parts (a)-(i) with the sketch of its graph. (a) The correct graph for y=x^2+2 is B. (b) The correct graph for y=x^2-2 is A. (c) The correct correct graph for y=(x+2)^2 is G. (d) The correct graph for y=(x-2)^2 is I.

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write integers or simplified fractions. -10x - 3y = -9 -8x - 6y = -5 Part 1 of 2 Evaluate the determinants D, Dx, and Dy. D = □ Dx = □ Dy = □

Suppose 200 trout are seeded into a lake. Absent constraint, their population will grow by 50% a year. If the lake can sustain a maximum of 2300 trout, use a logistic growth model to estimate the number of trout after 2 years. □ trout

What are the exact values of a and b? a=5 sqrt(3), b=5 a=5, b=5 sqrt(3) a=5, b=5 sqrt(2) a=5, b=10 sqrt(3)

A quadratic function (f) is given. [f(x)=2 x^2+x-6] (a) Express (f) in standard form. [f(x)=] (b) Find its vertex and (x)-and (y)-intercept(s) of (f). (If an answer does not exist, enter DNE.) vertex [(x, y)=()] (x)-intercepts ((x, y)=) ) (smaller (x)-value) ((x, y)=()) (larger (x)-value) (y)-intercept ((x, y)=) )

Listed in the accompanying data table are student evaluation ratings of courses and professors, where a rating of 5 is for "excellent." Assume that each sample is a simple random sample obtained from a population with a a. Use the 93 course evaluations to construct a 99% confidence interval estimate of the standard deviation of the population from which the sample was b. Repeat part (a) using the 93 professor evaluations c. Compare the results from part (a) and part (b).

Find the range and standard deviation of the set of data. 12,8,7,11,17 The range is 10. (Simplify your answer.) The standard deviation is (Round to the nearest hundredth as needed.)

In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the population standard deviation is 4.5 hours. How large a sample must be selected? A. 5 B. 4 C. 19 D. 20

T = (x, y) x ∈ ℕ and y = 2x

Given the following polynomial function: p(x) = 6x^3 + x^2 + 3x + 8 According to the Rational Zero Theorem, the possible zeros for p(x) are ±(1,2,4,8)/(1,2,3,6) Substitution reveals that x = -1 is a zero of p(x). Perform synthetic division to express p(x) in the factored form given below. Find the values for a, b, c. p(x) = (x+1)(ax^2 + bx + c) a = b = c = Identify the nature of the remaining two zeros: complex, rational, irrational (type one):

Solve the given system of equations. x+y+9z=-37 x+y+5z=-21 x-8y+2z=36

Solve the following inverse function: If (f(x)=7 x+2), find (f^-1(x)).

If all the elements of set A are also elements of set B, then set A is a(n) of set B.

In Exercises 11 to 14, find the indefinite integral using the substitution (x=2 tan theta). [ int frac2 x^2(4+x^2)^2 d x ]

Find the volume of the hemisphere. Use 3.14 for π. The volume is in ^3 (Round to the nearest tenth.)

Jorge borrowed 5200 from the bank. The bank added on a finance charge of 832.00. a. What is the total amount Jorge will have to repay the bank? b. If he pays it off in 60 equal monthly payments, how much will each payment be? Round to the nearest cent. a) The total amount Jorge will have to repay the bank is (Do not round.) b) Jorge's monthly payment is (Round to the nearest cent as needed.)

Find t0.75 for T distribution with 13 degrees of freedom. t0.75= (Round the answer to 3 decimal places)

If the two triangles are similar. What is the length of x to one decimal place?

Calculate the variance of the following data: 1,2,3,3,5,6,8,9 Express your answer to 1 decimal place, with rounding.

In a sprint to the finish line, a professional cyclist travels 380 meters in 20 seconds. At that rate, how far does the cyclist travel in 3 seconds? You can use a table if it is helpful.

Write the number as a product of a real number and i. Simplify all radical expressions. sqrt(-13) sqrt(-13)= (Simplify your answer. Type your answer in the form a+bi. Type an exact answer, using radical expressions.)

Write an augmented matrix and use elementary row operations in order to solve the following system of equations. Your final matrix should be in reduced row echelon form. In order to get credit you will have to have a correct final answer as accurate steps in each row operation. (x - 5y = 7) (5x + 8y = -4) Write the augmented matrix: [ ][ ][ ] [ ][ ][ ]

A pleasant boat ride from City A to City C with a stop at City B. On the first part of the trip, from City A to City B, the boat traveled at an average speed of 12 miles per hour. The entire trip covered 100 miles. How long did the entire trip take if the two parts each took the same number of hours?

Roger Company produces beach balls and operates three shifts. Roger produces 5,000 balls per shift on shifts 1 and 2. On shift 3, the company can produce 6 times as many balls as on shift 1. Assume a 5-day workweek. Total balls in shift 1: 5,000 Total balls in shift 2: 5,000 Total balls in shift 3: 30,000 Work-days per week: 5 Work weeks per year: 52 Required: Using the information above, answer the below questions 1. How many beach balls per day are produced? 2. How many beach balls per week are produced? 3. How many beach balls per year are produced?

Let f(x) = 2x / (2x + 5) and g(x) = (13x + 15) / (2x^2 + 3x - 5). Simplify f(x) + g(x) : The values of x that need to be excluded from the domain of the sum function are

Solve: 0.24(100 x+5)=0.4(30 x+15). x=

Determine el valor de dy/dt de la pendiente de la recta tangente para la curva x=t^4+10t, y=t^10-4t^2+t en el punto t=1. (A) 0 (B) -3/2 (C) 2/3 (D) 3/2

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 78 times and recording the number of times the ball lands on green.

Solve the polynomial equation in the complex numbers. x^3 - 4x^2 - 19x - 14 = 0 x = (Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

Solve: 1/4 x + 1/2 = 5/8 x=

Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7. What is the P(E and F) ? The probability P(E and F) is (Type an integer or a decimal.)

For the equation x^2 + y^2 - 8x - 6y - 11 = 0, do the following. (a) Find the center (h, k) and radius r of the circle. (b) Graph the circle (c) Find the intercepts, if any. (a) The center is (Type an ordered pair.) The radius is r = (b) Use the graphing tool to graph the circle. (c) Find the intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using radicals as needed.) B. There is no intercept.

The following data represents the age of 30 lottery winners. 22, 28, 29, 29, 30, 32, 33, 36, 36, 37, 38, 40, 43, 46, 46, 47, 48, 51, 58, 58, 59, 59, 64, 64, 72, 73, 73, 75, 78, 82 Complete the frequency distribution for the data. Bin Frequency 20-29 30-39 40-49 50-59 60-69 70-79 80-89

Consider the following three systems of linear equations. System A System B System C -7x - 6y = -21 [A1] -5x - 3y = -6 [A2] 3x = -9 [B1] -5x - 3y = -6 [B2] x = -3 [C1] -5x - 3y = -6 [C2] Answer the questions below. For each, choose the transformation and then fill in the blank with the correct number The arrow (→) means the expression on the left becomes the expression on the right. (a) How do we transform System A into System B? × Equation [A1] → Equation [B1] × Equation [A2] → Equation [B2] × Equation [A1]+ Equation [A2] → Equation [B2] × Equation [A2]+ Equation [A1] → Equation [B1] (b) How do we transform System B into System C? × Equation [B1] → Equation [C1] × Equation [B2] → Equation [C2] × Equation [B1]+ Equation [B2] → Equation [C2] × Equation [B2]+ Equation [B1] → Equation [C1]

Quotient rule with negative exponents: Problem type 2 Simplify. 8 a^3 b^-5 c^-2 / 2 a^-8 c^6 Write your answer using only positive exponents.

Let AB and CD be parallel, and let AD and BC intersect at E. Prove that a * y = x * b. In order for a * y = x * b, what must be true about the two triangles? A. The two triangles must have three congruent angles. B. The two triangles must have equal sides and congruent angles. C. The two triangles must have at least two sides of equal length. D. The two triangles must be similar.

The function (f) is defined as follows. [f(x)=sqrt[3]x-1] Find (f(64)) and (f(-125)). [f(64)=] [f(-125)=]

A store sells notebooks for 3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y ? The value of x can be any real number, and y will be a real number. The value of x can be any real number greater than or equal to 0 , and y will be a real number greater than or equal to 0 . The value of x can be any integer, and y will be an integer. The value of x can be any integer greater than or equal to 0 , and y will be an integer greater than or equal to 0 .

Understand equivalent rational expressions: Rational Expressions Writing equivalent rational expressions with polynomial denominators Fill in the blank to make equivalent rational expressions. 4/(x+5) = [ ]/((x-9)(x+5))

Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that: a. Comic F will perform fourth. b. Comic A will perform third and Comic D will perform fourth. c. The comedians will perform in the following order: F, A, D, C, B, E. d. Comic B or Comic E will perform fourth. a. (Type a fraction. Simplify your answer.) b. (Type a fraction. Simplify your answer.) c. (Type a fraction. Simplify your answer.) d. (Type a fraction. Simplify your answer.)

Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 40% of σ. Is this sample size practical? * To be 95% confident that s is within 1% 5% 10% 20% 30% 40% 50% * of the value of σ, the sample size n should be at least 19,205 768 192 48 21 12 8 * To be 99% confident that s is within 1% 5% 10% 20% 30% 40% 50% * of the value of σ, the sample size n should be at least 33,218 1,336 336 85 38 22 14 The minimum sample size needed is . Is this sample size practical? A. No, because the sample size is excessively large to be practical for most applications. B. No, because the sample size should be as small as possible for most applications. C. Yes, because the sample size should be as large as possible for most applications. D. Yes, because the sample size is small enough to be practical for most applications.

A normal population has mean μ=9 and standard deviation σ=5. (a) What proportion of the population is less than 20 ? (b) What is the probability that a randomly chosen value will be greater than 6 ? Round the answers to four decimal places. The proportion of the population less than 20 is 0.9861. The probability that a randomly chosen value will be greater than 6 is 0.2743.

Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-1) is on the terminal side of θ. Then find the values of the six trigonometric functions for the angle. Rationalize denominators if applicable. Do not use a calculator. Choose the correct graph below. A. B. C. Select the correct choice below and fill in any answer boxes in your choice. A. sin θ= □ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Factor the trinomial by grouping. 8 x^2 + 14 x + 3 a. Find two numbers whose product is 8 * 3 = 24 and whose sum is 14. b. Write 14 x using the factors from part (a). c. Factor by grouping. a. The two numbers with a product of 24 and a sum of 14 are

The graph of 5x-2y<24 has a boundary line.

Graph the solution to the following system of inequalities. y > 5x - 3 y ≥ -2x + 5

At the end of the day, a bakery had 44 / 5 pies left over. The 6 employees each took home the same amount of leftover pie. How much pie did each employee take home? Write your answer as a fraction or as a whole or mixed number.

Find the absolute maximum and minimum values of the following function on the given set R. f(x, y) = x^2 + y^2 - 2y + 1 ; R = (x, y): x^2 + y^2 ≤ 9 What is the absolute maximum value? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The absolute maximum value is . (Simplify your answer.) B. There is no absolute maximum value.

In tests about a population proportion, po represents the (A) hypothesized population proportion (B) observed p-value (C) probability of p=p̄=0 (D) observed sample proportion

-15(6h-2/5)=□, -15 * 6h + 15 * 2/5 =

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. 3^(x+1)=3619 The solution set expressed in terms of logarithms is . 3. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use ln for natural logarithm and log for common logarithm.)

Are the ratios 2:3 and 3:4 equivalent?

A government official wanted to know if more than 90% of the residents in a region had an income that was less than 100 thousand dollars. The official randomly sampled 500 residents and found that 463 of them had an income that was less than 100 thousand dollars. The official conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of residents in the region that have an income that is less than 100 thousand dollars is greater than 90%. (a) H0: p ≤ 0.9 ; Ha: p>0.9, which is a right-tailed test. (b) Use Excel to test whether the true proportion of residents in the region that have an income that is less than 100 thousand dollars is greater than 90%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

-2+-3-[7+4(-2+5)]-4=

Solve the formula 4x + y = 3 for y.

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. log(m^-2) log(m^-2)=

Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x) and C(x) are in dollars. R(x) = 4x, C(x) = 0.01x^2 + 0.6x + 30, when x = 20 and dx/dt = 9 units per day The rate of change of total revenue is per day.

30 = -5(6n + 6)

Compute the mean and standard deviation of the random variable with the given discrete probability distribution. x P(x) -4 0.24 -1 0.14 6 0.27 8 0.26 9 0.09 Part 1 of 2 (a) Find the mean. Round the answer to three decimal places, if necessary, The mean is .

Suppose you compared 2 independent samples (groups). The first sample contained 10 people, had a mean score of 74.20, and a standard deviation of 2.20. The second sample contained 10 people, had a mean score of 73.20, and a standard deviation of 2.10. In this study, what is the calculated value of t (see section 4 b of the lecture notes, the T-Test Example for Independent Data file, and/or pages 229-231 of the Handout file)? Send just the calculated value of t; send NO WORK.

The deciles of any distribution are the points that mark off the highest and lowest 10% of the observations. How many standard deviations on either side of the mean do the deciles in a normal distribution lie? Hint: Look for a center value of 0.8015.

Fourteen jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 46% are of a minority race. Of the 14 jurors selected, 2 are minorities. (a) What proportion of the jury described is from a minority race? (b) If 14 jurors are randomly selected from a population where 46% are minorities, what is the probability that 2 or fewer jurors will be minorities? (c) What might the lawyer of a defendant from this minority race argue? (a) The proportion of the jury described that is from a minority race is (Round to two decimal places as needed.) (b) The probability that 2 or fewer out of 14 jurors are minorities, assuming that the proportion of the population that are minorities is 46%, is (Round to four decimal places as needed.) (c) Choose the correct answer below. A. The number of minorities on the jury is unusually high, given the composition of the population from which it came B. The number of minorities on the jury is unusually low, given the composition of the population from which it came. C. The number of minorities on the jury is reasonable, given the composition of the population from which it came. D. The number of minorities on the jury is impossible, given the composition of the population from which it came

(b) Find the maximum or minimum value of f. (c) Find the domain and range of f. (Enter your answers using interval notation.) domain (-∞, ∞) range

An amusement park charges an admission fee of 50 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following function. C(p)=50p What is the cost of admission for a group of 4 people? dollars

You are working with a quadratic equation and construct the following graph. Identify the vertex of the parabola: Remember that the vertex is a point! Identify the y-intercept of the parabola: Remember that the y-intercept is a point! Identify the x-intercepts: and Remember that the x-intercepts represent points on the graph! Write an equation for the axis of symmetry:

1. In comparing the means of 2 groups, the null hypothesis could state: "the population mean of Group 1 is equal to the population mean of Group 2" (T/F)? 2. If you specify that the mean score of one population is going to be significantly higher than the mean score of another population, you are making a directional research hypothesis (T/F)?

Relation 3 Domain Range b star r star n star f star u star

The Standard Normal Distribution (μ=0, σ=1) (a) Convert the x interval, 4.5<x, to a z interval. <z (b) Convert the x interval, x<4.2, to a z interval. z< (c) Convert the x interval, 4.0<x<5.5, to a z interval. <z< (d) Convert the z interval, z<-1.44, to an x interval. (Round your answer to one decimal place.) x< (e) Convert the z interval, 1.28<z, to an x interval. (Round your answer to one decimal place.) (f) Convert the z interval, -2.25<z<-1.00, to an x interval. (Round your answers to one decimal place.) <x< (9) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values. Yes. A z score of 5.00 implies that this RBC is unusually high. No. A z score of -5.00 implies that this RBC is unusually low. No. A z score of 5.00 implies that this RBC is normal.

A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 9 labor-hours for fabricating and 1 labor-hour for finishing. The slalom ski requires 5 labor-hours for fabricating and 1 labor-hour for finishing. The maximum labor-hours available per day for fabricating and finishing are 135 and 20, respectively. Find the set of feasible solutions graphically for the number of each type of ski that can be produced. If x is the number of trick skis and y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y. Write an inequality for the constraint on fabricating time. Complete the inequality below. 9x+5y ≤ 135 Write an inequality for the constraint on finishing time. Complete the inequality below. x+y ≤ 20 Are any other inequalities needed? A. Yes, x ≤ 0 and y ≤ 0 B. Yes, x ≥ 0 and y ≥ 0 C. Yes, x ≥ y D. No

Evaluate the log base 2 of 1/16. Write your answer in simplest form.

The percentage of adult height attained by a girl who is x years old can be modeled by f(x)=62+35 log (x-5) where x represents the girl's age (from 5 to 15 ) and f(x) represents the percentage of her adult height. Complete parts (a) and (b) below. a. According to the model, what percentage of her adult height has a girl attained at age 12 ? A girl has attained % of her adult height by age 12 . (Do not round until the final answer. Then round to the nearest tenth as needed.) b. Why was a logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive? A. Height increases at a steady rate, regardless of one's age. B. Height increases rapidly at a young age, stops increasing at a certain age, and then starts decreasing. C. Height increases rapidly at a young age, and then increases more slowly. D. Height increases rapidly at a young age, and continues to increase even faster as one gets older.

According to a recent survey, 74% of teens ages 12-17 in a certain country used social networks in 2009. A random sample of 140 teenagers from this age group was selected. Complete parts a through d below. a. Calculate the standard error of the proportion. σp=0.0371 (Round to four decimal places as needed.) b. What is the probability that less than 76% of the teens from this sample used social networks? P (Less than 76% of the teens from this sample used social networks) = (Round to four decimal places as needed.)

¿Cuál de las siguientes afirmaciones describe correctamente la relación entre las variables independientes y dependientes? a. La variable dependiente es aquella que tiene un efecto directo sobre la variable independiente b. La variable independiente es aquella que es afectada o influida por la variable dependiente. c. La variable independiente es aquella que causa o determina los cambios en la variable dependiente. d. La variable dependiente es aquella que puede variar en función de la variable independiente. Página siguiente

Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. (-4x^3 / y^3)^3

Determine if the graph can represent a polynomial function. If so, assume that the end behavior and all turning points are represented in the graph. (a) Determine the minimum degree of the polynomial. (b) Determine whether the leading coefficient is positive or negative based on the end behavior and whether the degree of the polynomial is odd or even. (c) Approximate the real zeros of the function, and determine if their multiplicities are even or odd.

Evaluate the function h(x) = x^4 + 5x^2 + 3 at the given values of the independent variable and simplify. a. h(3) b. h(-1) c. h(-x) d. h(3a)

Evaluate the function h(x) = x^4 + 5x^2 + 3 at the given values of the independent variable and simplify. a. h(3) b. h(-1) c. h(-x) d. h(3a) a. h(3) = (Simplify your answer.) b. h(-1) = (Simplify your answer.) c. h(-x) = (Simplify your answer.) d. h(3a) = (Simplify your answer.)

Melinda buys one raffle ticket at the Spring Fling since there is one 1000 prize, one 500 prize, and five 100 prizes. There were a total of 800 tickets sold at 10 each. Part: 0 / 2 Part 1 of 2 (a) What is Melinda's expectation? Melinda's expectation is dollars.

Suppose we know that a confidence interval is (42, 47.6). Find the error bound and the sample mean. Round to 2 places where possible. a. Mean = b. Error Bound =

Find the sum and enter your answer below. 6+2=?

Statistical methods that organize, summarize, or simplify data are called: Descriptive Inferential Statistics Variables

What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=-1.73? (Do not round your answer; compute your answer using a value from the table below.)

You wish to test the following claim ( H₁ ) at a significance level of α=0.05. H₀: μ=56.1 H₁: μ ≠ 56.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=21 with mean x̄=61.8 and a standard deviation of s=6.2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p -value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 56.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is not

∫(arcsen x)^2 dx

Solve. Write your answer in interval notation. 3x+5>8 If no solutions exists - enter No solutions. Use reduced fractions in your answer- no decimals!

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P72, the 72-percentile. This is the temperature reading separating the bottom 72% from the top 28%. P72= °C (Round answer to three decimal places)

Multiple Cholce Question Total variable cost divided by the amount of output produced is equal to: marginal cost. average total cost. average fixed cost. average variable cost.

Factor the expression. y^2+13y+36=

Rational Expressions Adding rational expressions with denominators ax-b and b-ax Subtract. 6/(8x-3) - 4/(3-8x) Simplify your answer as much as possible.

p-value = 0.347 The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1. The sample data support the claim that the population mean is not equal to 79.1. There is not sufficient sample evidence to support the claim that the population mean is not equal to 79.1.

There is a pack of four cards numbered 1 to 4. There is also a coin with one side marked as heads and the other tails. As a trial of an experiment, a card was drawn and the coin was flipped. The number (1 to 4) of the card and the side (H for heads and T for tails) of the coin from the flip were recorded. Here is a summary of the data from 550 trials. Outcome 1 H 2 H 3 H 4 H 1 T 2 T 3 T 4 T --------------------------- Number of trials 70 71 66 74 63 69 73 64 Answer each part. (a) Assuming the card was chosen at random and the coin is fair, find the theoretical probability of this event: both drawing the 1, 2, or 3 card and flipping heads, in a single trial. Round your answer to the nearest thousandth. (b) Use the data to find the experimental probability of this event: both drawing the 1, 2, or 3 card and flipping heads, in a single trial. Round your answer to the nearest thousandth. (c) Choose the statement that is true. With a large number of trials, there must be no difference between the experimental and theoretical probabilities. With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.

Fill in the blank so that the resulting statement is true. An equation that is true for all real numbers for which both sides are defined is called a(n) inconsistent equation conditional equation. identity.

The function g is defined below. g(x) = (x^2 - 2x - 48) / (x^2 + 4x - 45) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas. x =

Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean? Use the table above for the z-score, and be sure to round up to the nearest integer. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.57

Use the graph of f to estimate the local extrema. The local extrema are □ (Use a comma to separate answers as needed. Round to the nearest integer.)

The life of light bulbs is distributed normally. The variance of the lifetime is 900 and the mean lifetime of a bulb is 580 hours. Find the probability of a bulb lasting for at most 610 hours. Round your answer to four decimal places.

Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. p=509.53, r=8.3%, t=73 days

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 37 and a standard deviation of 5. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 32 and 42? ans = %

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