Math Homework Questions & Answers Archive

Determine whether the geometric series is convergent or divergent. sum from n=1 to infinity of (10^n)/((-8)^(n-1)) If it is convergent, find its sum. (If the quantity diverges, enter Diverges.)

Which expression has the greatest value when (x=3) ? (2 x^3) (2 x^3+5) ((2 x)^3) ((x-1)^3)

Déterminer la fraction irréductible p / q (avec q>0) dont le développement décimal est p/q = 0.1 297 = 0.1297297297 ... Quels sont les entiers p et q ? p= Nombre q= Nombre

T T F f f t T F T t t t T F F t t f F T T f f t F T F f f t F F T t f t F F F t f t C. What are the conditions that make the compound statement false? A. No such conditions exist to make the statement false. B. The statement is false when p and r have the same truth values. C. The statement is false when r is true and p and q are false. D. The statement is false when p is true and q and r are false. E. The statement is false when p is false and q and r are true.

Factor completely. 121 c^4 - 44 c^2 + 4

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. [ (x+3)^2+y^2=25 ] The center is □ . (Type an ordered pair. Simplify your answer.)

√36x^3y^9

Give one pair of supplementary angles and one pair of vertical angles shown in the figure below.

Consider the vectors u=(1,1,1), v=(2,1,-1). Answer the following questions, (a) Find a unit vector in the direction of v. (b) Find u · v. (c) Find u+v. (d) Find the angle between u and v.

Grade 5 Using Models to Explore x +; Lesson 9 Standard NC.S.MD. 5 Special Delivery Ms. Hale ordered supplies for her new classroom. According to the information she uses to track the shipping, the combined volume of her packages is 210 cubic feet. When the packages (in the shape of rectangular prisms) arrive, she finds them stacked on her front porch and challenges her son to find the volume and dimensions of the separate prisms using only the information she gives him. Use the following information to determine the volume and dimensions of each package: - The side lengths are all whole numbers. - The packages have the same height. - The volume of Package 2 is half the volume of Package 1. - Package 1 has a base of 20 square units.

Four tour buses depart the terminal on the same day. The itinerary of the first bus takes 4 days; it takes 10 days for the second bus, 12 days for the third bus, and it takes 20 days for the fourth bus. Assuming that another tour begins the same day that the bus returns to the terminal, how many days will it take until all four buses return to the terminal on the same day?

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 3x^2+7x<6 Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution is . A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.

The bar graph shows that life expectancy, the number of years newborns are expected to live, in a particular region has increased dramatically since ancient times. Find the percent increase in average life expectancy of the region from the Stone Age to 2016.

Solve the following exponential equation. 2^x=3 Select the correct choice below and, if necessary, fill in the answer box. A. The solution is (Round to four decimal places as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

Find the x-intercept of -6x-3y=30 Write your answer in the form (x, 0), no spaces

Refer to the results of the accompanying study. Complete parts (a) through (e) below. B. The mean is very close to the sample mean, 306/659, not the mean found in part (b). The standard deviation though is very close the theoretical standard deviation from part (b). C. These values are very close to the theoretical values from part (b). D. The mean is very close to the theoretical mean from part (b), but the standard deviation does not seem to follow the theoretical standard deviation from part (b). (d) Describe the shape of the distributions of outcomes from the simulation in part (c). Compute n p(1-p) where p=0.5 (the proportion stated in the null hypothesis). Based on this result is the distribution of p̂ approximately normal? Since n p(1-p)= 164.75 10 and the sample size is less than 5% of the population size (assuming the TV personality has made at least the necessary number of predictions, which is a reasonable assumption), the distribution of the sample proportion, p̂, is approximately normal. (e) Use the normal model to find P(p̂ ≤ 0.464), where 0.464=306/659, the sample proportion of correct predictions made by the TV personality. P(p̂ ≤ 0.464)=

In the past month, Ryan has had five pizzas delivered. He kept a record of how long it took to get the pizzas: 20 minutes, 28 minutes, 35 minutes, 40 minutes, and 25 minutes. If the sixth time he orders pizza, it takes 95 minutes, how will this affect his data? a.) It will have little to no effect on both the mean and the median. b.) It will have little to no effect on the median, but it will make the mean a less useful measure of center. c.) It will make both the mean and the median less useful measures of center. d.) It will have little to no effect on the mean, but it will make the median a less useful measure of center.

Find the greatest common factor for the list of terms. 70 x^5, 110 x^6, 60 x^8 The greatest common factor is .

Evaluate the following function at the indicated values. H(x)=2^x (a) H(-4) (b) H(0) (c) H(5)

TRUE or FALSE: The matrix A=[2 1; 6 3] is diagonalizable TRUE because the vectors [1; 3] and [2; -1] form an eigenbasis for A FALSE because det(A)=0 FALSE because A has rank 1 TRUE because the vectors and [-1; 2] and [1; 3] form an eigenbasis for A

(a) On December 1, Marvin's Corp. had three DVD players left in stock at an individual unit price of 85. During December, the following events took place: December 1: 10 DVD players were purchased at 100 each. December 15: 5 DVD players were sold at 150 each. December 31: 2 DVD players were returned by customers for 40 each. (b) Calculate the cost of goods available for sale during December using FIFO periodic inventory method, assuming that there were 20 DVD players left in stock on December 31. (c) Calculate the cost of goods sold during December using FIFO periodic inventory method.

Which of the following is NOT part of the expenditure approach to calculating GDP? Imports Labor income Exports Business investments

Let f(x)=(4.5)^x Find x such that f(x)=528.38 Round your final answer to two decimal places?

Multiply. (9z+4)(9z-4) Simplify your answer.

Consider the following rational expression. 8y^3 - 27 / 2y - 3 Determine what value(s), if any, of the variable must be excluded.

Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer.

Graph y=-x^3-3x^2

Adding rational expressions with different Subtract. [ frac74-frac53 d ] Simplify your answer as much as possible.

If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.01, what are the odds against a direct hit? A. 100 to 1 B. 99 to 1 C. 98 to 1 D. 1 to 100

The inverse of matrix (A) is given. [ A^-1 = left[ beginarraylll 3 2 1 1 1 2 1 2 1 endarray right] ] Use the inverse to solve for (X). [ AX = left[ beginarrayr 3 -1 2 endarray right] . ] [ X = left[ beginarrayc endarray right] ]

Find the equation of the tangent line to f(x)=(x-1)^8 at the point where x=2.

For a standard normal distribution, find: P(z>1.51) Express the probability as a decimal rounded to 4 decimal places.

If the probability of a thunderstorm today is 2/9, then what is the complement or the probability of it NOT thunderstorming today? a.) 9/7 b.) 9/2 c.) 1/9 d.) 7/9

The following equation expresses a relationship in terms of one variable. Which of the following identifies the equation in terms of a different variable? P=I × I × R (or P=P^2 R) I=? a. R^2/P b. P^2/R c. sqrt(R/P) d. sqrt(P/R)

Evaluate 7+1(4+8)

Factor the polynomial. 6561-x^4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 6561-x^4 = (Type your answer in factored form. Simplify your answer.) B. The polynomial is prime.

Factor -3x^2+3x+90= (x+ ) (x+ )

Write 73 in the base-seven system. 73=□seven

Select the correct choice that completes the sentence below. If a system of linear equations in two variables has two graphs that coincide, there is/are □ solution(s) to the system.

Use the like bases property to solve the equation 2^x=16 x=

Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x)=(x^2-6x+9)/(x-5) Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. There are no relative maxima. The function has a relative minimum of at x= (Use a comma to separate answers as needed.). B. There are no relative minima. The function has a relative maximum of at x= (Use a comma to separate answers as needed.) C. The function has a relative maximum of at x= at x= and a relative minimum of (Use a comma to separate answers as needed.) D. There are no relative extrema.

Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form lim h → 0 (f(x+h)-f(x))/h occur frequently in calculus. Evaluate this limit for the given value of x and function f. f(x)=√x, x=2

Complete the row of each truth table. Use T for true and F for false. p q r r ∧ p q → (r ∧ p) --------------- T T F a b c ~b c → ~b b → a (c → ~b) ∧ (b → a) --------------------- T F T

Use the standard normal table to find the z-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. P8 The z-score that corresponds to P8 is (Round to two decimal places as needed.)

Find dy/dt for y=cos^2(4πt+3).

Find the indefinite integral. Check your result by differentiating. (Use C for the constant) ∫ v^(-1 / 2) dv

Use the quadratic formula to solve for (x). [3 x^2-6 x+2=0] Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.

Through market research, a business analyst has determined that the number N (in thousands) of units of a new video game the company can sell is a function of the price p (in dollars) of the game and is given by N=-0.07 p^2+0.8 p+86. (a) Find the ordered pair to complete the following table. Round to the nearest whole number. p N (p, N) 10 87 (10,87) 15 82 (15,82) 20 (20,) 25 62 (25,62) 30 47 (30,47) 35 28 (35,28) 40 6 (40,6) (b) Write a sentence that explains the meaning of the ordered pair (25,62) in the context of this problem. If the price of the game is , the company expects to sell games. (c) Graph the function for p between 10 and 40.

A box contains 6 green marbles and 14 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.

3/4 j-2(1/2 j+2)=1/8 j j=

Find a polynomial (f(x)) of degree 3 with real coefficients and the following zeros. [ 3,2 i f(x)= ]

A random variable is binomially distributed with n=16 and π=.40. The expected value and standard deviation of the variables are Multiple Choice 2.00 and 1.24. 4.80 and 4.00 . 6.40 and 1.96. 2.00 and 1.20.

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 90% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 240 194 181 159 157 156 148 148 148 148 What is the confidence interval estimate of the population mean μ ? million < μ < million (Round to one decimal place as needed.)

Find the derivative of the following function. f(x) = (x^3 - 7x^2 + x) / (x - 4) f'(x) =

Use the sample data below to answer the following question(s). Use a 0.05 significance level and the observed frequencies of 144 drownings at the beaches of a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely. Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1 3 2 7 14 20 37 33 16 6 2 3 Determine the value of the χ^2 test statistic.

f(x)= - if x <= 3, then -x^2 + 2x - 1 - if x > 7, then -x + 7 f(5)= Undefined

What is the product of the 2 x^3 and the 4 x^2 y-3 x y^2 ? a.) 8 x^5 y-6 x^4 y^2 b.) 8 x^5 y-3 x y^2 c.) 8 x^6 y-6 x^3 y^2 d.) 8 x^6 y-3 x y^2

Graph the given function by making a table of coordinates. f(x) = (2/3)^x Complete the table of coordinates. x -2 -1 0 1 2 y (Type integers or fractions. Simplify your answers.)

Find the value of the linear correlation coefficient (r). The paired data below consist of the temperatures (in degrees Fahrenheit) on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Temperature 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16 0 0.256 -0.210 0.196

Use the formulas developed in this section to find the area of the figure. 16in A= (Simplify your answer.)

Graph the function. y=3^(2x+2)+1 Specify the domain, range, intercept(s), and asymptote. (If an answer does not exist, enter DNE.)

Factor the following binomial completely. 81-x^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 81-x^2= B. 81-x^2 is prime.

Without using a calculator, compute the sine and cosine of 7π/4 by using the reference angle. What is the reference angle? radians. In what quadrant is this angle? (answer 1, 2, 3, or 4) sin(7π/4)= cos(7π/4)=

Use the one-to-one property of logarithms to solve. List all working and extraneous solutions. [ ln (-4 x)=ln left(x^2-3 xright) ] (Use commas to separate multiple answers, or type "NONE" if appropriate.) Solution(s): x= Extraneous: x ≠

A sample of 16 people was conducted to see how many cups of coffee (per day) people buy at star-bucks. The sample had a mean of 2.6 cups and a standard deviation of 1.5 cups. What is the margin of error (step 2 ) for a 95 percent confidence interval? Note: Round your answer to two decimal places.

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 25 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 16 flights are on time. (d) Find and interpret the probability that fewer than 16 flights are on time. (e) Find and interpret the probability that at least 16 flights are on time. (f) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time. (a) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The experiment is performed a fixed number of times. B. The probability of success is different for each trial of the experiment. C. The experiment is performed until a desired number of successes are reached. D. The trials are independent. E. Each trial depends on the previous trial. F. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. G. The probability of success is the same for each trial of the experiment. H. There are two mutually exclusive outcomes, success (plane arrives on time) or failure (plane does not arrive on time). (b) Using the binomial distribution, determine the values of n and p. n= (Type an integer or a decimal. Do not round.) p= (Type an integer or a decimal. Do not round.) (c) Using the binomial distribution, the probability that exactly 16 flights are on time is . (Round to four decimal places as needed.)

Anish works at an hourly rate of 7.50. Which of the following could NOT represent the amount of money Anish makes in one hour?

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^3-4x^2-5x+6 ; f(-3) f(-3)=

Test 4 - Chapter 4 Score: 0/17 Answered: 0/17 Question 1 A population numbers 16,000 organisms initially and grows by 1.4% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P=ab^t, where P=

Write a quadratic function f whose only zero is -7. f(x)=

Determine the measures of the angles using the diagram below. 1: 2: 3: 4:

Find the indicated area under the standard normal curve. To the left of z=-2.55 and to the right of z=2.55. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The total of the area to the left of z=-2.55 and the area to the right of z=2.55 under the standard normal curve is . (Round to four decimal places as needed.)

Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112. A university plans to award scholarships to students whose scores are in the top 4%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

(a) Find an angle θ, with 0°<θ<360°, that has the same cosine as 53° (but is not 53° ). θ= i .53 (b) Find an angle θ, with 0°<θ<360°, that has the same sine as 53° (but is not 53° ). θ= i

Evaluate the piecewise function at the given values of the independent variable. f(x) = 3x+5 if x<0 4x+6 if x ≥ 0 (a) f(-2) (b) f(0) (c) f(3) (a) f(-2)= (b) f(0)= (c) f(3)=

The letters in the word CALCULATE are arranged randomly. Write your answers in decimal form. Round to the nearest thousandth as needed. What is the probability that the first letter is U? What is the probability that the first letter is C? What is the probability that the first letter is a vowel? What is the probability that the first letter is H?

Consider statements p and q. p : We sell carrots at the market. q : We sell berries at the market. For part (a), fill in the symbolic form. For part (b), choose the descriptive form. Descriptive form Symbolic for (a) If we do not sell berries at the market, then we sell carrots at the market. (b) (Choose one) p ↔ ~q

In triangle ABC, the bisectors of angle A, angle B, and angle C cut the opposite sides onto lengths a1 and a2, b1 and b2, and c1 and c2, respectively, labeled in order counterclockwise around triangle ABC. Find the perimeter of triangle ABC for the set of values given below. a1 = 11/3, a2 = 22/3, b1 = 77/9 The perimeter is □

Problem 14.1: (7 points) A manufacturing company wants to construct a rectangular box with a square base and an open top as shown below. Suppose the box needs to have a volume of 108 cm^3. Follow the steps below to find the dimensions of the box that will minimize the surface area (and therefore minimize the cost of materials to manufacture the box). Find the dimensions that will minimize the surface area. To get full credit, you must verify your value is a local minimum with either the First or Second Derivative test. Show all steps to receive credit.

Question 10 1 pts IF ln x = 3/2, then x = e^(3/2) x = e^(2/3) x = (3/2) e x = (ln 3)/(ln 2)

A sample of college students was asked how much they spent monthly on cell phone plans. Approximate the mean for the cost. Monthly cell phone plan cost () Number of students 10.00-19.99 6 20.00-29.99 26 The mean for the cost is .

Divide using long division. State the quotient, q(x), and the remainder, r(x). (8 x^3-2 x^2-14 x-28) ÷ (2 x-4) (8 x^3-2 x^2-14 x-28) ÷ (2 x-4) = 4 x^2+6+(-4)/(2 x-4) (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)

Use the quotient rule to find the derivative of the function. f(x)=(2x-5)/(5x+8) f'(x)=

f(x)=3x^4-2x^3+74x^2-50x-25 a) Find the rational zeros of f(x), and then the other zeros. b) Factor f(x) into linear factors.

Choose the best selection for the quadrilateral with vertices at the following points: (0,0),(-2,3),(7,0),(5,3) Hint: Start by graphing the points. Distance Formula: d=sqrt((x2-x1)^2+(y2-y1)^2) A. Trapezoid B. Rectangle C. Parallelogram D. Rhombus

In a family with 2 children, the probability that all the children are girls is approximately 0.25 . In a random sample of 1000 families with 2 children, what is. the approximate probability that 220 or fewer will have 2 girls? Approximate a binomial distribution with a normal distribution. Use the table of areas under the normal curve given below. Click here to view page 1. Click here to view page 2. Click here to view page 3. Click here to view page 4. Click here to view page 5. Click here to view page 6.

Find the locations and values of all relative extrema for the function with the graph below.

Use the theoretical method to determine the probability of the following event. Sharing a birthday with another person when you both have birthdays in June. (Type an integer or a simplified fraction.)

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Fourth-degree and a single zero of -1.

Fill in the blank. A straight line satisfies the if the sum of the squares of the residuals is the smallest sum possible. residual plot empirical rule rare event rule least-squares property

f(x)=(x+9)/(x^2-81) B. There is no x-intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The y-intercept is (0,-1/9). (Type an ordered pair, using integers or fractions.) B. There is no y-intercept. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

Listed below are the numbers of cricket chirps in 1 minute and the corresponding temperatures in °F. Find the regression equation, letting chirps in 1 minute be the independent (x) variable. Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute, using the regression equation. What is wrong with this predicted temperature? Use a significance level of 0.05. Chirps in 1 min: 819, 1014, 811, 874, 1205, 793, 1082, 1199 Temperature (°F): 68.1, 82.6, 75.5, 70.5, 93, 71.2, 82.2, 91.8 The regression equation is ŷ = + + (Round the y-intercept to one decimal place as needed. Round the slope to four decimal places as needed.)

Let f(x) = cos^(-1)(cos(x)), which is valid for all x. Sketch the graph of this periodic function f. Find its period and the range of its values f(x).

What fraction of all the cards are Red or Face cards? What fraction of all the cards are neither Red nor Face cards?

A researcher who is in charge of an educational study wants subjects to perform some special skill. Fearing that people who are unusually talented or unusually untalented could distort the results, he decides to use people who scored in the middle 50% on a certain test. If the mean for the population is 100 and the standard deviation is 10, find the two limits (upper and lower) for the scores that would enable a volunteer to participate in the study. Assume the scores are normally distributed. Refer to the table of values (*) Area Under the Standard Normal Distribution) as needed. If necessary, round your answer to the nearest whole number. A volunteer with a test score between and can participate in the study.

What condition causes aluminum branch circuit wiring to be unsafe? overheating at poor connections the absence of ground wires the use of COPALUM crimp connectors wire gauges too small for amperage

Given f(x)=1/(x-4) and g(x)=4/(x-3), find the domain of f(g(x)) Domain (in interval notation):

Calculate the standard score of the given X value, X=75.1, where μ=68.3 and σ=71.8. Round your answer to two decimal places.

QUESTION 16 2.5 points Parallel Enterprises has collected the following data on one of its products. During the period the company produced 25,000 units. The direct materials quantity variance is: Direct materials standard (7 Kilogram 2 / Kilogram ) 14 per finished unit Actual cost of materials purchased 322,500 Actual direct materials purchased and used 150,000 Kilogram 50,000 unfavorable. 50,000 favorable. 22,500 unfavorable. 22,500 favorable.

Multiply the monomials. - (4 x^2 y)(-2 x y^3)(5 x^4 y^2) - (4 x^2 y)(-2 x y^3)(5 x^4 y^2) = (Simplify your answer.)

Consider the equation (4 cdot 10^-3 x=18). Solve the equation for (x). Express the solution as a logarithm in base-10. Approximate the value of (x). Round your answer to the nearest thousandth. (x approx)

2x^3 = 44x

year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 107 125 139 149 155 157 155 149 139 Determining the average rate of change of sales is important. It tells whether sales are increasing or decreasing over a time period, and at what rate. a) What was the average rate of change of annual sales between 1998 and 1999? millions of dollars/year b) What was the average rate of change of annual sales between 1998 and 2000? millions of dollars/year Give your answers as whole numbers.

Question 10 5 pts Write a formula for a linear function f whose graph satisfies the conditions. Slope: 1/3 ; y-intercept: 4 f(x)=1/3 x+4 f(x)=1/3 x-4 f(x)=-1/3 x-4 f(x)=-1/3 x+4

Evaluate the expression for s = -2. 6 + s =

A timber company in northern Georgia is harvesting pine trees to sell by the cord. A typical acre produces 13.85 cords of wood, and the company sells each cord for 19.20. How much money can the timber company expect to make from each acre of pine trees?

Find the vertical, horizontal, and oblique asymptotes, if any, of the function Q(x)=(3x^2-10x-8)/(5x^2-19x-4) Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function has one vertical asymptote, . (Type an equation. Use integers or fractions for any numbers in your answer.) B. The function has two vertical asymptotes. The leftmost asymptote is . (Type equations. Use integers or fractions for any numbers in your answers.) C. The function has no vertical asymptote.

The mean and standard deviation of a random sample of n measurements are equal to 33.2 and 3.3, respectively. a. Find a 99% confidence interval for μ if n=81. b. Find a 99% confidence interval for μ if n=324. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

56 equals 221 subtracted from the product of 66 and g

The results of a simulation of the event of tossing two fair coins 25 times is shown. What is the simulated probability of the outcome Π, where T represents tails. T H T T T H H T H H H H H H H T T H T T T T T T T H T H H H H T H T H T T H H H H H H H H H H H The simulated probability of the event T T is (Type an integer or decimal rounded to two decimal places as needed.)

Write the sentence as an equation. The product of 2 and q equals 199.

Perform long division given (x^3+3x^2-3x+1)/(x-2). Identify the quotient and remainder.

Choose the end behavior of the graph of each polynomial function. (a) f(x)=-4x^3+7x^2+3x-9 Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right (b) f(x)=-4x^6+x^4+8x^3+9x Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right (c) f(x)=2x(x-1)^2(x+3) Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right

Simplify the following polynomial by combining any like terms. 2 a b-4 a+9 a b-2 a 2 a b-4 a+9 a b-2 a=

If the probability of a child being a girl is 1/2, and a family plans to have 3 children, what are the odds against having all girls? The odds are to

An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was 420, 453, 402, 229. Compute the range, sample variance, and sample standard deviation cost of repair. The range is s^2= dollars (Round to the nearest whole number as needed.) s= (Round to two decimal places as needed.)

Given that 3 is a zero of the polynomial function (f(x)), find the remaining zeros. (f(x)=x^3-7 x^2+20 x-24) List the remaining zeros (other than 3). (Simplify your answer. Type an exact answer, using radicals and (i) as needed. Use a comma to separate answers.)

For the functions f(x) = 2 / (x + 3) and g(x) = 5 / (x - 1), find the composition f · g and simplify your answer as much as possible. Write the domain using interval notation. (f · g)(x) = Domain of f · g :

Simplify each of the following expressions as much as possible. a. 6x-2-2x b. 6x-(2-2x)

Elise and her younger brother, Reid, take turns loading the dishwasher after dinner. Because she is older, Elise loads the dishwasher 4 times for every 3 times Reid loads it. If Elise and Reid have loaded the dishwasher 84 times in all this year, how many times has Elise loaded the dishwasher?

A shop sells bags of marbles. Each bag contains to marbles. Write an expression for the total number of marbles in 5 of these bags.

Circle Relationships: Mastery Test Point O is the center of the circle in the diagram. What is m∠BOA? A. 80° B. 75° C. 70° D. 65°

Solve for (c). 8c+17=73 c=

Find the equation for the least squares regression line of the data described below. The design team at an electronics company is evaluating its new prototype for a miniature recording device. As part of this evaluation, designers at the company gathered data about competing devices already on the market. Among other things, the designers recorded the thickness of each recording device (in millimeters), x, and its maximum recording length (in minutes), y. Thickness (in millimeters) Recording time (in minutes) ------ 11.92 136 20.30 117 20.41 119 24.61 118 25.93 478 28.85 476 29.69 396 Round your answers to the nearest thousandth. y = □ x + □

Consider the following shape. Determine whether each figure has the same or the reverse orientation of the figure shown bel

Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the origin (a) If the graph is that of a function, what are its domain and range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is The range is (Type your answers in interval notation.) B. The graph is not a function. (b) If the graph is that of a function, what are its intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercepts are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

When ordering a certain type of computer, there are four choices of hard drive, five choices for the amount of memory, four choices of video card, and three choices of monitor. In how many ways can a computer be ordered? The total number of ways a computer can be ordered is .

Express in scientific notation. 38.78

Given RSTU is a rectangle with RZ = 8 and US = 2x + 6, solve for x.

For groups of 25 or more people, a museum charges 21 per person for the first 25 people and 14 for each additional person. Which function f gives the total charge, in dollars, for a group with n people, where n ≥ 25? (A) f(n)=14 n+175 (B) f(n)=14 n+525 (C) f(n)=35 n-350 (D) f(n)=14 n+21

Subtract. Write your answer as a fraction 7/8 - 1/8

The half-life of sodium-22 is 2.6 years. If there are initially 40 grams of sodium-22, find a formula that gives the amount S, in grams, remaining after t years.

Match the following descriptions to functions which meet that condition. A function, f(x) which is concave up for (a) f(x)=-x^2+3 all x values. A function, f(x) which is concave down (b) f(x)=cos(x) for all x values. A function, f(x), which is never concave (c) f(x)=e^x up or concave down (a function which has no concavity). A function, f(x), which has a point where (d) f(x)=2x+4 f'(x)=0 but no maximum or minimum values. A function, f(x), for which f'(x) will (e) f(x)=x^3 never equal 0. A function, f(x), with infinitely many (f) f(x)=3x maximums and minimums.

Suppose the lengths of human pregnancies are normally distributed with μ=266 days and σ=16 days. Complete parts (a) and (b) below. (a) The figure to the right represents the normal curve with μ=266 days and σ=16 days. The area to the right of X=280 is 0.1908. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) A. The proportion of human pregnancies that last more than 280 days is 0.1908 B. The proportion of human pregnancies that last less than days is Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) A. The probability that a randomly selected human pregnancy lasts less than days is B. The probability that a randomly selected human pregnancy lasts more than days is

A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x+35y=3,934 represents this situation. Which of the following is the best interpretation of x in this context? (A) The average number of trees per hectare in the park (B) The average number of trees per hectare in the residential area (C) The total number of trees in the park (D) The total number of trees in the residential area

A travel agent wants to estimate, with 98% confidence, the proportion of vacationers who use an online service or the Internet to make reservations for lodging. The estimate must be accurate within 4% of the population proportion. a) How many vacationers must be surveyed? b) If past industry data suggest that 10% of vacationers use an online service or the Internet to make such reservations, how many vacationers much be surveyed?

Choose the property of addition that justifies the equation. 0 = -5 + 5

Solve the inequality for (u). [ frac37 u+1>frac97-frac45 u ] Simplify your answer as much as possible.

Find a. Graph the exponential function. f(x)=2^x Plot five points on the graph of the function, and also draw the asymptote.

Fill in the blanks to complete the geometric proof. Given: angle 1 and angle 2 are supplementary angle 2 and angle 3 are supplementary Proof: angle 1 congruent to angle 3 Statements Reasons angle 1 and angle 2 Supp angle 2 and angle 3 Supp Given Definition of supplementary angles m angle 1 + m angle 2 = m angle 2 + m angle 3 m angle 1 = Subtraction Prop of Equality angle 1 congruent to angle 3

c^-1(x)=x-4

In the diagram below, AC is parallel to DG, BE is congruent to BF, and the measure of angle ABH is 73 degrees. Find the measure of angle ABE.

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(34<X<63) Which of the following normal curves corresponds to P(34<X<63)?

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.09 1 0.21 2 0.40 3 0.21 4 0.09 Is the distribution a discrete probability distribution? Why? Choose the correct answer below. A. No, because the total probability is not equal to 1. B. No, because some of the probabilities have values greater than 1 or less than 0. C. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive. D. Yes, because the distribution is symmetric.

Solve for x : 2^(3x-6)=9^(5x-5) x=

Each figure shows a triangle with one or more of its medians. Find x if RE=x-1 and GE=2x-12

Consider the following function depicted in the following graph.

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x̄=37.5 ml / kg (milliliters plasma per kilogram body weight). Assume that σ=7.60 ml / kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 34.41 upper limit 40.59 margin of error 3.09 (b) What conditions are necessary for your calculations? (Select all that apply.) σ is unknown n is large the distribution of volumes is normal the distribution of volumes is uniform σ is known

Give a vector parametric equation for the line through the point P(0,1,3) that is parallel to the line <-4,2,1-3 t> : L(t)= (Enter your answer as <x0, y0, z0>+t<a, b, c> or <x0+a t, y0+b t, z0+c t>)

Find the domain of the function. g(x) = 2x / (x^2 - 9)

Determine if the following probability experiments represent binomial experiments. If not, explain why. If a probability experiment is a binomial experiment, state the number of trials, (n), and probability of success, (p). (a) According to the Chronicle of Higher Education, there is a (59 %) probability that a randomly selected incoming first-year student will graduate from college within 6 years. Suppose that 40 incoming first-year students are randomly selected. After 6 years, each student is asked whether he or she graduated. (b) An experiment is conducted in which a pair of dice are cast until their sum is 3. The number of throws required is recorded. (a) Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer. A. Yes, because the experiment satisfies all the criteria for a binomial experiment, [ n= p= text and text integers or decimals rounded to two decimal text places as needed.) ] B. No, because the trials of the experiment are not independent because the probability of success differs from trial to trial. C. No, because the experiment is not performed a fixed number of times. D. No, because there are more than two mutually exclusive outcomes for each trial.

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is skewed right. However, records indicate that the mean time is 16.4 minutes, and the standard deviation is 4.1 minutes. Complete parts (a) through (c) below. B. Any sample size could be used. C. The normal model cannot be used if the shape of the distribution is skewed right. D. The sample size needs to be greater than 30. (b) What is the probability that a random sample of n=40 oil changes results in a sample mean time less than 15 minutes? The probability is approximately 0.0001. (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a 50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager. There would be a 10% chance of being at or below minutes. (Round to one decimal place as needed.)

The National Institute of Mental Health published an article stating that in any one-year period, approximately 27 percent of American adults suffer from depression or a depressive illness. In a survey of 100 people in a certain town, the percentage of people suffering from depression or a depressive illness was actually different than 27 percent. The sample proportion was 28%. a. Choose the correct null and alternative hypothesis. Ho: p=0.27 and Ha: p ≠ 0.27 Ho: p ≥ 0.28 and Ha: p=0.28 Ho: p ≥ 0.28 and Ha: p<0.28 Ho: p=0.28 and Ha: p>0.28 Ho: p=0.27 and Ha: p<0.27 Ho: p=0.28 and Ha: p<0.28 Ho: p=0.27 and Ha: p>0.27

Refer to Exhibit 1. The percentage of workers who took 1 - 5 sick days per month was (A) 20% (B) 60% (C) 75% (D) 120%

Simplify: (2 x^3-x+5)-(6 x^3+x^2-x+1) 8 x^3+x^2-2 x+6 -4 x^3-x^2+4 4 x^3-x^2-2 x-4 4 x^3-4

Find a general solution to the given equation for t<0. y''(t) - (3/t) y'(t) + (29/t^2) y(t) = 0

Use the Pythagorean Theorem to find the missing length in the right triangle.

G2-T1 UNIT 6 LESSON 6 Equations inequalities Systems of Equations Systems of Equations Quick Check Solve the system of equations. y = -x + 2 3x + 3y = 6 Which best describes the solution? (1 point) One solution at (0,2) There are infinitely many solutions. There are no solutions. One solution at (2/3, 8/3)

Exponents Power and quotient rules with positive exponents Simplify. (m^5 n^7 / m n^2)^5 Write your answer using only positive exponents.

log3 x = log5(x^2)^5

Multiple Choice Question Which of the following is an expression that represents sampling error? s-s^2 μ-σ X̄-s X̄-μ

Question 5(Multiple Choice Worth 5 points) (05.01 MC) At a Tasty D-Lite, there are 9 different toppings a customer can select for their frozen yogurt. How many ways can a customer choose 4 toppings? 9 * 8 * 7 * 6 9 ! 9!/(9-4)! 9!/(4!(9-4)!)

Salaries for teachers in a particular elementary school district are normally distributed with a mean of 66,400 and a standard deviation of 1,800. We randomly survey 8 teachers from that district. Find the mean and standard deviation of the distribution of sums; round to three decimal places when needed. μ∑x= σ∑x= Find the 85th percentile for the sum of the salaries of 8 teachers. Round to the nearest dollar. x=

Question 3 5 pts Find the zeros of f(x), given that one zero is k. f(x) = x^4 - 6x^3 + 3x^2 + 24x - 28 k=2 ±2, -3 ± 2i ±2, 3 ± √2 ±2, 3 ± 2i ±2, -3 ± √2 i

Seed costs for a farmer are 80 per acre for corn and 120 per acre for soybeans. How many acres of each crop should the farmer plant if she wants to spend no more than 4800 on seed? Express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Let x be the number of acres planted with corn and let y be the number of acres planted with soybeans. Choose the correct inequality below. A. 80x + 120y leq 4800, x geq 0, y geq 0 B. 80x + 120y < 4800, x geq 0, y geq 0 C. 80x + 120y > 4800, x geq 0, y geq 0 D. 80x + 120y geq 4800, x geq 0, y geq 0

Solve the system using inverse matrices. 5x - 2y = 30 x + 6y = -26

7.1) จงหาพื้นที่ผิวซึ่งเป็นส่วนหนึ่งของทรงกระบอกเชิงกลม (x^2+z^2=9) ในอัฐภาค (octant) ที่ 1 ชึ่งถูกตัดด้วยระนาบ (x=0), (x=3), (y=0) และ (y=5)

Question 23, 4.4.67 Solve the logarithmic equation. Be sure to reject any value of x that is not in Give an exact answer. log5(x) + log5(4x-1) = 1 Solve the equation. Select the correct choice below and, if necessary, fill in A. The solution set is . (Type an exact answer in simplified form. Use integers or fractions B. There are infinitely many solutions. C. There is no solution.

The 95% confidence interval for the difference between two treatment means extends from 2.50 to +5.50. Based on this information, you can conclude that there is no significant difference between the treatments at the .05 level of significance.

Express the fraction as a percent. Use bar notation, if necessary. 5 1/2 = %

Use properties of logarithms to condense the logarithmic expression. Write the expression as 1. Where possible, evaluate logarithmic expressions. 1/2(log7 x + log7 y) 1/2(log7 x + log7 y) =

Assignment 5.1: Quadratic Functions Question 11 Fill in the info below. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. y=x^2-10x+21 1. State whether the parabola opens up or down? Up Down 2. State the vertex as an ordered pair: 3. State the y-intercept as an ordered pair 4. Write the Equation of the Axis of Symmetry 5. Click on the vertex and then another point of the parabola that fits on the axes below. Clear All Draw:

Put the following inequality in interval notation: x>17 or x ≤-10

The boxplot below shows salaries for Construction workers and Teachers. Jennie makes the first quartile salary for a construction worker. Markos makes the first quartile salary for a teacher. Who makes more money? Jennie Markos How much more? 52,000

Given the function P(x)=(x-3)^2(x-7), find its y-intercept is and its x-intercepts are x1= and x2= with x1<x2 When x → ∞, y → ∞ (Input + or - for the answer) When x → -∞, y → ∞ (Input + or - for the answer)

Determine a general formula (or formulas) for the solution to the following equation. Then, determine the specific solutions (if any) on the interval [0,2 π). sin θ=0

Report the answers to the following calculations to the correct number of decimal positions. Assume that each number is precise to ±1 in the last decimal position reported. 23.40-18.2=5.2 948.75+62.45=1011.20 Answer 1: 5.2 Answer 2: 1011.20 The density of whole blood is 1.05 g/mL. A typical adult has about 5.5 L of whole blood. What is the mass in pounds of this amount of whole blood? [Answer to 1 decimal place] 12.7 lb

Find all numbers that are not in the domain of the function. Then give the domain using set notation. f(x) = (2x+18) / (4x^2+2x-2) A. 2,-1 ; x x ≠ 2,-1 B. -9,-1, 1/2 ; x x ≠ -9,-1, 1/2 C. -1/2, 1 ; x x ≠ -1/2, 1 D. 1/2,-1 ; x x ≠ 1/2,-1

Use the graph of g to find g(-10) g(-10)=

In Exercises 19-40, calculate the derivative. 19. f(x)=(x^3+5)(x^3+x+1) 20. f(x)=(1/x-x^2)(x^3+1)

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