Math Homework Questions & Answers Archive

Détermine si les énoncés suivants sont vrais ou faux. Dans chaque cas, justifie ta réponse. a) Toutes les situations de proportionnalité sont modélisées par des fonctions. b) La relation réciproque d'une fonction qui modélise une situation de proportionnalité est une fonction de variation inverse. c) Les couples qui appartiennent à une fonction de variation inverse appartiennent aussi à la relation réciproque de cette fonction.

A retiree invests 3,000 in a savings plan that pays 4% per year. What will the account balance be at the end of the first year?

Calculate the 60th percentile of the data shown x 3 3.2 6.2 12.3 17.9 18.2 18.3 27 28.1 29.2

Given that -4 i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x^4+x^3-14 x^2+16 x-480

A stepladder is diagrammed on a coordinate plane. The base of one leg of the stepladder is at the point ( 0,0 ), the base of the other leg is 4 feet to the right, and the top of the stepladder is 5.5 feet high. a. Write a rule for function f to represent the stepladder, and state the domain. b. Another stepladder has legs 6 feet apart and is 8.25 feet high. The base of its left leg is at the point ( 0,0 ). Write a rule for function g to represent this ladder and describe it as a transformation of t. a. f(x)= (Simplify your answer. Use integers or decimals for any numbers in the expression.)

4x + 2y = 4 6x - y = 8

The circle above is tangent to both the horizontal and vertical lines. It also touches the corner of the .5 by .75 rectangle. Solve for the radius of the circle. A r ≈ 5.27 B r ≈ 8.25 C r ≈ 15.71 D r ≈ 2.57 E none of these

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. g(x) = 8x^3 - 2/3 x + 6

For the function (f(x)=-3 x^2-2 x-4), evaluate and fully simplify (f(x+h)=) (fracf(x+h)-f(x)h=)

Solve for (v). (7 v-6 v=9) (v=)□

CONTINUOUS RANDOM VARIABLES: PROBABILITY DENSITY FUNCTIONS 1. Weight Gain The graph shows the (subjective) Distribution of x = weight gain probability distribution for the random variable X= "Jack's weight gain over the summer" a) What are the possible values of X ? How do you know? What does that tell you about Jack? b) Which is more likely "Jack gains weight" or "Jack loses weight" ? How do you know? c) Use the graph to make a sensible estimate of Jack's EXPECTED weight gain, E(X). Explain how you found this number.

For a standard normal distribution, find: P(z>2.27) Express the probability as a decimal rounded to 4 decimal places.

Solve for x in each of the following. a. 2/5 = x/18 b. 5/6 = -35/x

-79=7w+3(4w-1)

Hexagon EFGHIJ can be mapped to hexagon E' F' G' H' I' J' by a translation 7 units to the left followed by a reflection. Write the functions that describe the translation and reflection. Translation: (x, y) -> ( , ) Reflection: (x, y) -> ( , )

Find the measure of angle C.

f(x)=-2x+2 f(x)=-2x^2-7x f(x)=-1/3x^4+4x^2 f(x)=x^4+2x^3 f(x)=x^2-3x f(x)=2x^3-3x+1 f(x)=-1/3x^3+x^2-4/3 f(x)=1/5x^5-2x^3+9/5x

Does the point P=(7,37,1296) lie on the path r=<1+t, 2+t^2, t^4> ? No, it doesn't. Yes, it does. Does the point Q=(-1,7,16) lie on the path r=<1+t, 2+t^2, t^4> ? Yes, it does. No, it doesn't.

57.28 × 2.36 =

Refer to functions (q) and (r). Evaluate ((q circ r)(x)) and write the domain in interval notation. Write your answers as integers or simplified fractions [ q(x)=frac1x-4 quad r(x)=2 x+3 ] [ (q circ r)(x)= ]

Find the domain of the following rational function. H(x)=-5x^2/(x-2)(x+8) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of H(x) is x ? (Type an inequality in the form x ≠. Use integers or fractions for any numbers in the expression. Use a comma to separate answers B. The domain of H(x) is the set of all real numbers

Find the volume of a beverage can that has a height of 8.5 in. and a diameter of 3.6 in. Use 3.14 as an approximation for π. The volume of the can is (Type an integer or a decimal rounded to the nearest hundredth as needed.)

Plant 1 Plant 2 Plant 3 --------- Output ATC Output ATC Output ATC 10 10 10 15 10 20 20 9 20 10 20 15 30 8 30 7 30 10 40 9 40 10 40 8 50 10 50 14 50 9 What is the long-run average cost of producing 30 units of output? Multiple Choice 7 8 9 10

Video Graph the line that has a slope of -1/6 and includes the point (0,4). Click to select points on the graph.

Solve for x. x^2 + 9x + 18 = 0

An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. Number of TV commercials, x 4 5 13 14 18 Car sales, y (in hundreds) 2 4 9 6 7

Use the standard normal distribution to find P(-2.25<z<1.25). A. 0.4878 B. 0.8822 C. 0.0122 D. 0.8944

Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y=mx+b. (4,5) ; 5x+y=6 The equation of the line is y= (Simplify your answer. Use integers or fractions for any numbers in the expression.)

A binomial experiment has the given number of trials N and the given success probability P. N=8, P=0.5 Find the variance and standard deviation. Round the variance to two decimal places and standard deviation to at least three decimal places.

Consider the given function d(x)=2x^2-4x-7 (a) Write the function in vertex form f(x)=a(x-h)^2+k. (b) Identify the vertex. (c) Determine the x-intercept(s). (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form.

Cuatro vectores se encuentran en el plano xy. El módulo del vector A es de 20 unidades y forma un ángulo de 40° con el eje x. El vector B, tiene magnitud de 15 unidades y forma un ángulo de 30° respecto del eje y negativo. El vector C, tienen 10 unidades de módulo y un triángulo rectángulo de catetos 4 y 3 puede formarse bajo él, tal como se indica en la figura. Un vector D parte en el origen y termina en el punto (-6,-7). Obtener en ángulo entre el vector A y el vector C.

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. System A x-2 y=6 -x+2 y=6 - The system has no solution. - The system has a unique solution: (x, y)= - The system has infinitely many solutions. They must satisfy the following equation: y= System B x-5 y =-5 -x+5 y =5 - The system has no solution. - The system has a unique solution: (x, y)=(, ) - The system has infinitely many solutions. They must satisfy the following equation: y=

Find the value of x. A. 4√2/2, B. 4 C. 4√2 D. 4√3

A one-to-one function is given. Write an equation for the inverse function. g(x) = (3-x)/8 g^-1(x) =

Question 15 (1 point) A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. HW3 Midterm 13.3 59.811 21.9 87.539 9.7 53.728 5.4 39.174 20.9 89.729 18.5 78.985 15.4 73.274 25 93.25 9.7 52.257 6.4 43.984 20.2 79.762 21.8 84.258 23.1 92.911 23 87.82 11.4 45.034 14.9 71.869 18.4 76.704 15.1 60.431 15 65.15 16.8 77.208 Find the predicted midterm score when the homework 3 score is 19.5. Do not round until the end, then round answer to 2 decimal places.

Use the graph of the quadratic function f(x) = a(x-h)^2 + k to find the vertex, axis of symmetry, and the minimum or maximum value of the function.

Graph each equation of the system. Solve the system to find the points of intersection. x^2 + y^2 = 25 y = x^2 - 100

Question 1 (4 points) Evaluate the following limit: lim x -> -∞ (-1-3x+4x^2) / (-6+11x-3x^2) A) -1 B) 1/6 C) -4/3 D) -∞ E) 0

The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving. Use the data provided in the table to complete parts a) through d). Weight (hundreds of pounds) 29 31 36 35 29 29 Fuel efficiency (mpg) 22 22 20 22 24 21 a) Determine the correlation coefficient between the weight of a car and the fuel efficiency. The correlation coefficient between the weight of a car and the fuel efficiency is r=-0.539 b) Determine whether a correlation exists at α=0.01. Choose the correct answer below. A. A linear correlation exists. B. A linear correlation does not exist.

Find the quotient and simplify the result. (x-3)(x+4)/4x^9 ÷ (5x-15)/20x^10 (x-3)(x+4)/4x^9 ÷ (5x-15)/20x^10 =

36.8 ÷ [11.5 - (2.5 × 3)]^2

What function is graphed below? f(x)=-3 * e^x+2 f(x)=-2 e^x+3 f(x)=2 e^x-3 f(x)=3 e^x-3 f(x)=3 e^x-2 f(x)=-2 e^x+2

Factor completely. -2v^2+11v+21

Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinomial. [ z^2+14 z ] Type the missing term that completes the square. [ z^2+14 z+square ] (Simplify your answer. Type an integer or a fraction.)

Find the constant rate of change for the graph.

Analyze the polynomial function f(x)=x^3+0.2x^2-1.4183x-0.41111. Complete parts (a) through (h). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y=x for large values of x. (b) Graph the function using a graphing utility. Use the window [-3,3,1] by [-2,2,1]. Choose the correct graph below. (c) Use a graphing utility to approximate the x- and y-intercepts of the graph. The y-intercept is (Type an integer or decimal rounded to five decimal places as needed.)

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distribu mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score gr -1.57.

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.81. Sketch the region. Choose the correct graph below. A. B. C. D. The probability is . . (Round to four decimal places as needed.)

Use algebra to find the inverse of the function f(x)=sqrt[11]x The inverse function is f^-1(x)=

Fall 2024 Online College Algebra Section 5.7 Question 3, 5.7.7 HW Score: 9.09%, 1 of 11 points Use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ≤ 0 (a) The solution set for f(x) > 0 is (Type your answer in interval notation.) (b) The solution set for f(x) ≤ 0 is (Type your answer in interval notation.)

Find the critical values χL2 and χU2 for the given level of confidence and sample size. Round your answer to 2 decimal places. a) 90% confidence, n=20; χL2= χU2= b) 99% confidence, n=14; χL2= χU2= c) 95% confidence, n=25; χL2= χU2=

The correlation coefficient is always a number between -1 and 1.

Here are summary statistics for the weights of Pepsi in randomly selected cans: n=36, x̄=0.82409 lb, s=0.00567 lb. Use a confidence level of 95% to complete parts (a) through (d) below. a. Identify the critical value tα/2 used for finding the margin of error. tα/2=2.03 (Round to two decimal places as needed.) b. Find the margin of error. E=0.00192 lb (Round to five decimal places as needed.) c. Find the confidence interval estimate of μ. 0.82217 lb<μ<0.82601 lb (Round to five decimal places as needed.)

The radical expression √[7](x^6) can be rewritten in the rational exponent form x^(a/b) where, a= b=

Find the inverse of the function f(x)=-3x^2.

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. [x=y^2] Note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one. Answer x 0 1 64 100 y sqrt6 -1

Differentiate the function y=e^(0.8 t). dy/dt=

At a community college, a survey was taken to determine where students study on campus. Of the 250 students surveyed, 176 studied in the library. 138 studied in the cafeteria. 81 studied in both the library and the cafeteria. Complete parts a) through c). a) Of those students surveyed, how many studied only in the library? (Type a whole number.) b) Of those students surveyed, how many studied only in the cafeteria? (Type a whole number.) c) Of those students surveyed, how many did not study in either of these places? (Type a whole number.)

Simplify the following radical. [ sqrt-300 ]

Solve the given linear system of equations: 8x - 2y = 4 -12x + 3y = 12 Enter your answer in the form of an ordered pair (x, y). If the system contains no solutions, enter DNE. If the system contains infinite solutions, enter oo.

Find the x-intercept and y-intercept of the line. 4 x+6 y=-24

lcm(51,68) and gcd(51,68)

Which property is shown here? (3 p+6) 4=4(3 p+6) Commutative Property of Multiplication Associative Property of Multiplication Commutative Property of Addition Associative Property of Addition Distributive Property

Question 9 2 pts A laboratory randomly selected and tested 12 chicken eggs and found that the mean cholesterol was 246 mg with a standard deviation of 11.7 mg. Construct a 95% CI for the true mean cholesterol content of all such eggs. 237, 255 mg 238.6, 253.4 mg 238, 255 mg 239.9, 253.4 mg

Find the derivative of the function. y=-4 e^(2 x^2)

Use an algebraic approach to find the measure of the two angles described below. Begin by letting x represent the degree measure of the angle complement. What is the measure of the complement? What is the measure of the angle? The measure of the angle is 76 degrees greater than its complement.

Find an equation of the line that is tangent to the graph of f for the given value of x. f(x) = sqrt(3x+16); x=0

The distance a car travels, d(t), at a constant 33 mph is given by the function d(t)=33 t, where t is the time in hours. Find the distance traveled in 3 hours. The car traveled miles in 3 hours.

Solve the system of equations (x-7 y=-36) and (-2 x-2 y=8) by c [ beginaligned (x-7 y =-36) (-2 x-2 y =8) x-7 y =-36 -2 x-2 y =8 o x+circ y = endaligned ]

Josh has to carry 172 apples from a farm to the market. How many baskets will he need, given that each basket can hold 45 apples? baskets

U A B 2 13 5 10 17 21 23 26

The length of human pregnancies is approximately normal with mean μ=266 days and standard deviation σ=16 days. Complete parts (a) through ( f ) A. If 100 independent random samples of size n=25 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 258 days. B. If 100 independent random samples of size n=25 pregnancies were obtained from this population, we would expect 1 sample(s) to have a sample mean of 258 days or less. C. If 100 independent random samples of size n=25 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 258 days or more. (e) What might you conclude if a random sample of 25 pregnancies resulted in a mean gestation period of 258 days or less? This result would be unusual, so the sample likely came from a population whose mean gestation period is less than 266 days. (f) What is the probability a random sample of size 19 will have a mean gestation period within 12 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 12 days of the mean is (Round to four decimal places as needed.)

The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through ( f ). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2), (e) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 19 second grade students was 93.4 wpm. What might you conclude based on this result? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to four decimal places as needed.) A. A mean reading rate of 93.4 wpm is not unusual since the probability of obtaining a result of 93.4 wpm or more is This means that we would expect a mean reading rate of 93.4 or higher from a population whose mean reading rate is 91 in of every 100 random samples of size n=19 students. The new program is not abundantly more effective than the old program. B. A mean reading rate of 93.4 wpm is unusual since the probability of obtaining a result of 93.4 wpm or more is 1. This means that we would expect a mean reading rate of 93.4 or higher from a population whose mean reading rate is 91 in of every 100 random samples of size n=19 students. The new program is abundantly more effective than the old program.

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.2 p a. Find the probability that, in a year, there will be 5 hurricanes. b. In a 45 -year period, how many years are expected to have 5 hurricanes? c. How does the result from part (b) compare to a recent period of 45 years in which 5 years had 5 hurricanes? Poisson distribution work well here?

f. The probability of A or B can always be found by just adding together the probability of A and the probability True False g. To find an "and" probability, you will need to multiply together the probabilities of each individual event True False h. If you are dealt one card from a 52 -card deck, then the probability that you are dealt an ace is 1/52. True False P(B A) is the probability that event B occurs given that the sample space is restricted to the outcomes associated True False j. If you roll a 6 -sided die one time, then the probability that you roll a 2 or a 3 is 1/6 * 1/6=1/36. True False

Fill in the table using this function rule. f(x) = sqrt(9-x) Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -40 9 18 20

What happens to the standard error of M as sample size increases?

Simplify the expression without using a calculator. log(π) 1=

Crave Creamery is an ice cream shop chain that has locations all across the nation. Customers at Crave Creamery have the option of ordering 1,2 , or 3 scoops of ice cream in their cone. The mean number of scoops ordered is μ=1.30, with a standard deviation of σ=0.68. Suppose that we will take a random sample of n=10 ice cream cone orders and record the number of scoops for each. Let x̄ represent the sample mean of the number of scoops for the 10 ice cream cone orders. Consider the sampling distribution of the sample mean x̄. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find μx̄ (the mean of the sampling distribution of the sample mean). μx̄= (b) Find σx̄ (the standard deviation of the sampling distribution of the sample mean). σx̄=

The exponential function f(x)=49.47(1.024)^x describes the population of a certain country, y, in millions, in year x. a) Substitute 0 for x and, without using a calculator, find the country's population in year 0. b) Find the country's population in year 24 as predicted by this function. A. a) 1 million; b) 91.652 million B. a) 49.47 million; b) 89.504 million C. a) 1.024 million; b) 85.357 million D. a) 49.47 million; b) 87.406 million

Solve the exponential equation. 10^(-x) = 5^(2x) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal B. The solution is not a real number.

Suppose that 20% of the people in a large city have used a hospital emergency room in the past year. If a random sample of 150 people from the city is taken, approximate the probability that at least 27 used an emergency room in the past year. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Work out the volume of this solid (made up of a cuboid and a half cylinder). Give your answer to two decimal places. Include units (cm^3) in your answer.

Determine whether the table represents a discrete probability distribution. Explain why or why not. x P(x) -2 0.35 0 0.15 2 0.25 4 0.15 The table represent a discrete probability distribution because does does not

Sharon worked on a straight 12% commission. Her friend worked on a salary of 650 plus a 5% commission. In a particular month, they both sold 21,300 worth of merchandise. How much did her friend earn for the same month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.

Find the z-scores that correspond to the percentage of adult spiders that have carapace lengths between 17 mm and 18 mm The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between -1.79 and -1.16. (Round to two decimal places as needed) Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 22 mm. The percentage of adult spiders that have carapace lengths exceeding 22 mm is equal to the area under the standard normal curve that lies to the right of (Round to two decimal places as needed)

Find the solution of the following using the quadratic formula. x^2+2 x-5=0 x=-1 pm 2 i x=-1 pm sqrt6 x=1 pm sqrt6 x=-1 pm 2 sqrt6

Find both the opposite, or additive inverse, and the reciprocal, or the multiplicative inverse, of the following number. -11/15 Type the opposite of -11/15. (Type your answer as an integer or fraction.)

UNV-103 Topic 6 DO 1 Counting and Probability Computing permutations and combinations Evaluate 10P5 and 5C4 10P5 = 5C4 =

The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y=-1 Y=1 Y=2 ----------------------- X=-3 0.08 0.01 0.01 0.10 X=0 0.06 0.60 X=3 0.03 0.30 0.80 0.10 0.10 1.00

∫(7x^4 - 6x^2 + 6) dx

If a function f is evaluated at 4 , the value of the function is 9 . Write this situation using function notation. What is the function notation?

Complete the following table. Round each of your answers to 3 significant digits. food energy content when eaten ------------ cal kcal kJ a kiwi fruit 4.50 x 10^4 450. a corn muffin 145. three ounces of cooked sirloin steak 1.00 x 10^3

Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two digits followed by two letters. The letters J, K, and L and the digits 3 and 6 will not be used. So, there are 23 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format?

The diagram shows a triangle. What is the value of u? u= 0

r(x)=(x^2+6x-7)/(x^2+2x-3)

Graf ktorej z nasledujúcich funkcií má na intervale ⟨0,2 π⟩ najviac priesečníkov s osou x ? (A) f1: y=2+sin x (B) f2: y=2 sin x (C) f3: y=sin (x/2) (D) f4: y=sin 2x (E) f5: y=sin x

Divide and simplify to lowest terms. (d^3-a^3)/(d^2-a^2) ÷ (7d-7a)/(7d+7a) = □ (Simplify your answer.)

What type of number will result from 5/12 * sqrt(16) ? (1 point) Irrational because one factor is irrational Irrational because both factors are irrational Rational because one factor is a radical Rational because both factors are rational

A graph with observed values on its horizontal scale and frequencies on its vertical scale and that uses bars to indicate frequency is called a square

Fill in the blank. The standard deviation of the distribution of sample means is - The standard deviation of the distribution of sample means is μ σ. μ/√n σ/√n

Correct Suppose a random sample of 36 measurements is selected from a population with mean 67 and standard deviation 12 Step 2 of 2: Find the standard deviation of the sampling distribution of sample means using the given information. Round to two decimal place, if necessary.

Consider the function g given by g(x) = x-7 + 4. (a) For what x-value(s) is the function not differentiable? (b) Evaluate g'(0), g'(1), g'(8), and g'(10). (a) The function is not differentiable at x = .

The Y-axis is labeled Real Aggregate Expenditure (AE), and the X-axis is labeled Real GDP (Y). The 45° line starts at the origin and rises to the right at a 45° angle. The 45° line is labeled Y=AE. One aggregate expenditure line, labeled AE1, starts at a point on the Y-axis and rises to the right with a slope that is less steep than the 45° line. AE1 has three points on it, labeled from left to right A, B, and C. Point B is where AE1 intersects the 45° line. Point A is closer to the Y-axis than Point B, while Point C is farther from the Y-axis than Point B. According to the graph above, which point indicates that aggregate expenditure is greater than GDP? B Both A and C C A

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If the system has one solution, find the solution. -1.5 x + 0.5 y = -7 1.5 x - 0.5 y = 7

Graph the horizontal or vertical line. 9) x=-5

Solve. √[4](k-3)+1=0

Change the following mixed number to an improper fraction. Reduce if possible. 6 1/49

Employee Pay Forty-three percent of employers said that their employees are fairly paid, while only 20% of the employees agreed. If 50 employers and 200 employees were surveyed, find the 90% confidence level of the proportions for each group. Round your answers to at least three decimal places.

Find a basis for the column space and the rank of the matrix. [ 2 4 1 6 ]

Find an equation for the tangent line to the graph of f(x)=x^2+4 at (-5,29). y=□

questions involving intervals, separate multiple answers by typing UNION to enter the U syn e:్ens more than one answer for a specific question, separate each answer from the following or ofanswer exists at all, enter NO SOLUTION. (a.) Enter as one or more points. x-intercept(s): (b.) Enter as a point. y-intercept:

Find the slope of the line graphed below.

Question If X ~ U(4.5,18.5) is a continuous uniform random variable, what is P(X<11) ? Select the correct answer below: 1/28 3/28 13/28 9/14 19/28

Find a basis for the row space and the rank of the matrix. [ [-3 1 2 10 6 5 -7 5 8] ]

Solve: 35/(y+4)+5/(y+2)=6 y= If there is more than one solution, enter the solutions separated with commas. If there is no solution, enter DNE.

Explain how the graph of the function f(x)=1/(x-7)^2 can be obtained from the graph of y=1/x^2. Then graph f and give the domain and range.

Bob's Auto Parts were currently 15 new cars, 9 new trucks, and 3 used trucks. Bob spent 10 hours on each new car, 8 hours on each new truck, and 4 hours on each used truck. Do not round intermediate computations, and round your answer to the nearest hundredth. The total of the hours that Bob spends on trucks?

Graph the parabola. y=-(x+2)^2-5

Use your calculator to find the area shown in RED. The zero is not x=5 ! Round the zero to 4 decimals within your calculation. Total Area = [ ? ] Round your final answer to the nearest thousandth.

Add or subtract the following rational expressions, as indicated, and simplify your answer. (x+4)/(x-2)-(x-3)/(x+6)-4/(x^2+4x-12)

Solve. x - 28 > -15 If all real numbers are solutions, click on "All reals". If there is no solution, click on "No solution".

-5 u - 8 = -2 u - 1 + 4 u u = □

Identify the function's local extreme values in the given domain, and say where they occur. Graph the function over the given domain. Which of the extreme values, if any, are absolute? f(x)=sqrt(100-x^2), -10 ≤ x ≤ 10 a. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a local maximum value at one value of x. The maximum value is f(0)=10. (Type integers or simplified fractions.) B. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f()=, f()=, and f()=. (Type integers or simplified fractions.) C. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f()= and f()=. (Type integers or simplified fractions.) D. There are no local maxima. Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The function has a local minimum value at one value of x. The minimum value is f()=. (Type integers or simplified fractions.) B. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are f() and f()= . (Type integers or simplified fractions.) C. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are f()= and f()=. (Type integers or simplified fractions.) D. There are no local minima.

Consider the function f(x)=3x^2-6x-3. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range.

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 56-62 10 63-69 5 70-76 5 77-83 8 84-90 13

A probability experiment is conducted in which the sample space of the experiment is S=3,4,5,6,7,8,9,10,11,12,13,14, event F=3,4,5,6,7, and event G=7,8,9,10. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or G= (Use a comma to separate answers as needed.) B. F or G=

(a) The minimum sample size required to construct a 99% confidence interval is 107 soccer balls. (Round up to the nearest whole number.) (b) The 99% confidence interval for a sample size of 117 is ( . the confidence interval. it seem possible that the population mean could be less than 27.7 inches because values below 27.7 inches fall (Round to two decimal places as needed.)

Counting and Probability Introduction to permutations and combinations Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair (a) How many ways can this be done, if the order of the choices is relevant? (b) How many ways can this be done, if the order of the choices is not relevant?

Determine whether the expression is a polynomial. If it is, state how many terms and vari 4 x^2-2 x+4 The expression is Select the correct choice below and fill in any answer boxes in your choice. A. The polynomial has term(s) and variable(s). B. The expression is not a polynomial. Select the correct choice below and fill in any answer boxes in your choice. A. Its degree is . B. The expression is not a polynomial.

Find the derivative of the function. y=8 sqrt(x)+4 x^(1/7) dy/dx=

Solve the equation. Give the exact solution or solutions. log (3+x)-log (x-5)=log 5 Select one: a. -7 b. ∅ c. 3.5 d. 7

Solve the equation. log base x of 16 equals 2 Select one: a. 2 b. 4,-4 c. 2,-2 d. 4 Solve the equation. log base 3 of 1/27 equals x Select one: a. 3 b. -3 c. 1/81 d. 1/9

Divide. [ left(4 s^4+3 s^3-9 s^2-3 s+12right) divleft(s^2-2right) ] Choose the correct answer. A. 4 s^2+3 s+1, R 3 s B. 4 s^2+3 s-1 C. 4 s^2-3 s-1, R 10 D. 4 s^2+3 s-1, R 3 s+10

Simplify the radical: ∛72 A. 8∛36 B. 6∛2 C. 8∛9 D. 2∛9

Select the best answer for the question. 16. Rationalize the denominator. -13/sqrt(x) A. It's already rationalized. B. 169/x C. -13 sqrt(x)/x D. x sqrt(x)/-13

Solve: 4 x-10=3(x+10)+6 x=□ σ^6

Solve the equation. 7 + √(4)m = 9 A. m=6 B. m=-13 C. m=16 D. m=1 / 2

Use the Second Derivative Test to find the location of all local extrema in the interval (-6,5) for the function given below. f(x) = (2 x^3)/3 - x^2 - 12 x If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter ∅ in the appropriate box. Answer should be exact. The local maxima occur at x= ∅ The local minima occur at x= ∅

QUESTION 2 · 1 POINT A casino features a game in which a weighted coin is tossed several times. The table shows the probability of each payout amount. To the nearest dollar, what is expected payout of the game? Payout Amount Probability 200 0.126 3800 0.03 190000 0.0002

The data set represents wait times (in minutes) for various services at a state's Department of Motor Vehicles locations. Which wait time represents the 50th percentile? How would you interpret this? 27 4 8 4 3 26 18 21 1 3 3 5 5 6 10 1 22 23 10 6 7 2 1 6 6 2 4 14 15 16 4 19 3 19 26 5 3 4 7 6 10 9 10 20 18 3 20 10 Which wait time represents the 50th percentile? 6 minutes (Type a whole number.)

Evaluate the limit as x approaches infinity of (sqrt(9x^2+2x)-3x). 1 / 3 0 2 / 3 infinity

lim (x -> ∞) (4x^5 + 10x^3 + 9x^2 + 2x + 1) / (2x^5 - 3x^4 - 9x + 5)

Find the derivative of the function. r(t)=(3 t-5)^7/(9 t^2+5) r'(t)=

Solve the following equation. 1/(y-5)+1/20=-5/(4y-20) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution set is y y is a real number, y ≠ . (Type an integer or a fraction. Use a comma to separate answers as needed.) C. The solution set is ∅.

The sum of all the probabilities in a discrete probability distribution must be equal to 1

Simplify the exponential expression. Assume that the variable represents a nonzero real number. (5 x^(-5))(9 x^(4)) (5 x^(-5))(9 x^(4))= (Type exponential notation with positive exponents.)

Find the vertex and focus of the parabola: x^2+14x-8y+65=0 Vertex = ([?],[]) Focus = ([],[])

Graph the compound inequality on the number line. x ≥ -1 or x < -4

12. Standard Form of Quadratic Function Explain the advantage of writing a quadratic function in standard form.

Simplify. (7 u^2+3)-(2 u^2-6 u+4)

Given the triangle below, find the angle A and length of side x Note: picture is NOT drawn to scale, but you can assume an angle that appears acute is acute and angle that appears obtuse is obtuse. A= degrees x=

Assume that when human resource managers are randomly selected, 47% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that at least 3 of them say job applicants should follow up within two weeks. The probability is (Round to four decimal places as needed.)

Solve the system by substitution. -x-5y = -20 6x = y+27 Select the correct choice below and, if necessary, fill in the answer box to complete your A. There are a finite number of solutions. The solution set is . (Simplify your answer. Type an ordered pair.)

What are the key points on the graph of y=x^2-2x-120 ? Name the vertex, x-intercept(s); and y intercept. (1 point) x-intercepts: (-10,0)(12,0) y-intercept: (0,-120) vertex: (1,-121)

Exponents and signed fractions 0 / 3 Evaluate. Write your answer 4^2 / -5 = - (5 / 2)^3 =

Find all complex solutions of 7x^2 + 7x + 3 = 0. (If there is more than one solution, separate them with commas.)

Find θ, 0° ≤ θ<360°, cos θ=-sqrt(3)/2 and θ in QII

Are the two lines parallel, perpendicular, or neither? Choose one · 1 point

We have a deck of 8 cards numbered from 1 to 8. Some are grey and some are white. The cards numbered 3, 4, 5, 6, 7, and 8 are grey. The cards numbered 1 and 2 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X. (a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event 1 2 3 4 5 6 7 8 Probability ----- - - - - - - - - ------------ X O O O O O O P(X)= not X O O P(not X)= (b) Subtract. 1-P(not X)= (c) Select the answer that makes the sentence true. 1-P(not X) is the same as (Choose one)

Solve the rational inequality and graph the solution set on a real number line. (3x+2)/(5x-1) <= 1 Solve the inequality. What is the solution set? Select the correct choice below and, A. The solution set is (Simplify your answer, Type your answer in interval notation. Type an exact B. The solution set is the empty set.

sqrt(144xy)/(2sqrt(2))

Find the area of the region between the curves 4x + y^2 = 12 and x = y.

Determine whether the following statement is true or false: Statistics are the "only" symbols allowed to go inside a probability statement (note that =>, etc are mathematical operators and not considered symbols)

In the yeast experiment measuring CO2 production, your trendline for the tubes in the room temperature water bath gives the equation: y=0.57x+5.86, where time (in minutes) is plotted as the independent variable and distance moved (in mm) is plotted as the dependent variable. How far would the water have moved after 25 minutes? 15.5 mm 20.1 mm 28.8 mm 14.7 mm 5.86 mm

In a sample of 18 students at East High School the following number of days of absences were recorded for the previous semester: 4,3,1,0,4,2,3,0,1,2,3,0,4,1,1,5,1,1. Find the class width when using four classes for the frequency distribution.

(5x-35)/27 ÷ (8x-63)/18 = □

Write 922 in the base-five system. 922=□(five )

According to Masterfoods, the company that manufactures MMs, 12% of peanut MMs are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123] Compute the probability that a randomly selected peanut MM is not red. Compute the probability that a randomly selected peanut MM is brown or red. Compute the probability that three randomly selected peanut MMs are all yellow (assume they are drawn at the same time). If you randomly select three peanut MMs, compute that probability that none of them are blue. If you randomly select three peanut MMs, compute that probability that at least one of them is blue.

f(x)=[?] cos (□x)+□

Subtract. x/(5x-6) - (x+3)/(6x) Simplify your answer as much as possible.

QUESTION 5 Determine whether f(x) and g(x) are inverses of each other. f(x)=3/2 x+6 g(x)=2/3 x-4 There is not enough information to solve No, they are not inverses Yes, they are inverses

A tree is 120 feet ( ft ) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation. Ratios: 36 in/1 yd 1 ft/12 in = in ft yd mi in

Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a queen? Now suppose that a single card is drawn from a standard 52-card deck, but it is told that the card is a face card (jack, queen, or king). What is the probability that the card drawn is a queen? The probability that the card drawn from a standard 52-card deck is a queen is (Round to three decimal places as needed.) The probability that the card drawn from a standard 52-card deck is a queen, given that this card is a face card, is (Round to three decimal places as needed.)

Lesson 13 Measures of Relative Position Question 3 of 5, Step 1 of 5 The number of hours per week that the television is turned on is determined for each family in a sample. The mean of this data is 35 hours and the median is 29.5 hours. Find the approximate z-score for the median. Step 1 of 5: Based on the given information, determine if the following statement is true or false: The first quartile is less than the Median. Answer: True False

Evaluate each expression. Write your answers as reduced fractions. A) sqrt(1/36)= B) -sqrt(1/36)=

Simplify the rational expression. (2x^2 - 3x - 2) / (6x^3 + 3x^2 + 2x + 1)

Let f(x)=2x-6 and g(x)=8-x. Find the following. (a) (f+g)(x) (b) (f-g)(x) (c) (f⋅g)(x) (d) (f/g) (e) The domain of (f/g) (a) (f+g)(x)= (Simplify your answer.) (b) (f-g)(x)= (Simplify your answer.) (c) (f⋅g)(x)= (Simplify your answer.) (d) ((f/g))(x)= (Simplify your answer.) (e) The domain of (f/g) is . (Type your answer in interval notation.)

Classify 29 / 580,059 as true or false. Choose the correct answer below. A. True, because 29 580,000 and 29 / 59 B. False, because 29 580,000 and 29 59 C. True, because 29 / 580,000 and 29 59 D. True, because 29 / 580,000 and 29 / 59

2(1-x)+3=8

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