Math Questions

The graph of the probability density function of a normal random variable with parameters 3 and 9 is symmetric A. with respect to the straight line r = 3 B. with respect to the straight line y = -3 C. with respect to the straight line y = 3 D. with respect to the straight line x = -3

Probability problems that contain the words and or or are considered probability problems. Probability problems that contain the words and or or are considered __________probability problems. a)mutually exclusive b)dependent event c)independent event d)compound

One hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female Male Total College degree 24 26 50 No college degree 15 35 50 Total 39 61 100 If a person is selected at random from those surveyed, find the probability if each of the following events. 1. The person is female or has a college degree. Answer: ▢ 2. The person is female and has a college degree. Answer: ▢ 3. The person is female or does not have a college degree. Answer: ▢ 4. The person is female and does not have a college degree. Answer: ▢

If A = {x | x is an even integer), B = {x | x is an odd integer), C = {2, 3, 4, 5), and D = {7, 8, 9, 10), list the element(s) of the following set. A∩D=_____

Let N denote the set of all natural numbers. Define two binary relations on N as R₁ = {(x, y) ∈ N × N: 2x + y = 10} and R₂ = {(x, y) ∈ N × N: x + 2y = 10}. Then : (a) Both R₁ and R₂ are symmetric relations (b) Range of R₁ is {2, 4, 8} (c) Both R₁ and R₂ are transitive relations (d) Range of R₂ is {1,2,3,4}

Let the region R be the area enclosed by the function f(x) = 2x³ and g(x) = 3x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is a semi-circle with diameters extending through the region R, find the volume of the solid.

The water level of a certain body of water is changing at a rate of W(t)=(3/4)cos(4-t/2) inches per hour, where t represents hours since 12 a.m. A): Using correct units, explain the meaning of ∫w(t)dt in terms of the context of this problem. B): Write the integral that represents the number of inches that the water level changes from 7 p.m. to midnight C): Use your calculator to evaluate your integral from Part B. Explain the meaning of the answer in terms of the context. ) D): What is the average hourly number of inches that the water level changes for this lake in one day?

Suppose tan(a) = 5/8, where 0 ≤ a ≤ π/ 2. The least solution to tan(3x) = 5/8 in [0, 2π) is x = The greatest solution to tan(3x) = 5/8 in [0, 2π) is x =

Which conditions are needed to conduct a one-proportion z test? (Check all that apply) 1. The probability of each sample is within 1 standard deviation of the mean 2. The samples are approximately normally distributed 3. The population proportion is statistically significant. 4. Each sample is independent of the others. 5. The sample was collected randomly.

The table below shows the 10 most popular destinations for college students from Country X studying abroad for the 2008-2009 school year. If a student were selected at random from those who studied abroad in 2008-2009 at one of the destinations in the table, determine the empirical probability that the student studied in a) Country E. b) Country B. c) Country F.

Bryce got a job selling glow sticks at the local fairground. He is paid a fixed amount of $480 per week plus $0.82 per item sold. This is represented by the equation P= 0.82n + 480 where P is the amount he is paid for the week and n is the number of glow sticks he sold. a)How much will Bryce be paid if he sells 340 glow sticks? If Bryce sells 340 glow sticks, he will earn $_____for the week. b)How many glow sticks did Bryce sell if he earned $1,177.00? If Bryce has earned $1,177.00, he sold_______glow sticks.

Some checking accounts pay a small amount of interest on the money in the account. In this case, interest is money that is paid to the account holder by the financial institution issuing the checking account. The interest is a percentage of the amount of money in the account. The percentage is called the annual percentage rate. Heather has $1,000 to deposit in an account for 1 year. Compare the following two offers. (A) Bank of Avalon pays 0.7% with no annual fee. (B) Cypress Savings pays 1.3% but charges a $10 annual fee. Which is the better offer?

Use the distributive property to help simplify the numerical expression 8√8 - 8√18 into the form A√C, where A and C are integers.

Let Xn+1 =1.2Xn + 29 be a linear DDS. a) Calculate the equilibrium value for this DDS. b) Suppose the initial value is x₀ = 66. Find the explicit solution. c) Determine the stability of the equilibrium. Choose the correct answer. The equilibrium of this system is Select an answer because (A) the slope is negative. (B) the slope in absolute value is less than 1. (C) the slope in absolute value is greater than I. (D) the slope is positive.

If A = {x | x is an odd integer), B = {xl x is an even integer}, C = {2, 3, 4, 5), and D = {5, 6, 7, 8), list the element(s) of the following set. a)A∩D=_____

A container holds 2 yellow balls and 4 red balls. A ball will be drawn, its color noted, and replaced. A second ball will be drawn, and its color recorded. Do not reduce. a. Draw a two-stage tree diagram for this. Indicate the probability on each branch b. Find the probability of drawing 2 red balls:______________ c. Find the probability of drawing at least 1 red:________________

Solve the compound inequality. 0≤2x-5≤7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is_________ B). The solution set is Ø.

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) (x^2)/9 - (y)^2/25 =1

Do the points (0, -7), (-3,- 22) and (2,3) lie on the same line? Explain why or why not. (Hint: Find the slopes between the points). Do the three points lie on the same line? (A) Yes, because the slopes are not the same. (B) No, because the slopes are the same. (C) Yes, because the slopes are the same. (D) No, because the slopes are not the same.

Solve the compound inequality. x+8≥8 and x +4≤3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is ___. (Type your answer in interval notation. Simply your answer. Use integers or fractions for any numbers in the expression) B. The solution set is Ø.

You are interested in estimating the mean distance students travel to school. From past data, you estimate that the standard deviation of distances to be approximately 2 miles. What sample size would you need to in order to estimate the mean distance students travel to school, with a 98% confidence level, to within 0.8 miles of the actual distance? Sample Size: n ≥_______

Suppose a computer processor can perform about 3.3 billion operations per second. How many operations can it perform in 0.1 second? It can perform about ______ operations in 0.1 second. (Type a whole number.)

Find the indefinite integral. (Use C for the constant of integration.) ∫eˣ√(1-e²ˣ) dx

Write an equation of the line using function notation. Horizontal; through (0.-4) The equation of the line is f(x) = _____

For the point (1,3π/4) in polar coordinates, (a) plot the point, (b) give two other pairs of polar coordinates for the point, and (c) give the rectangular coordinates of the point. (a) Choose the graph that represents the point (1,3π/4).

Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super-Fit takes 12 minutes to cut and 15 minutes to sew and finish. Each pair of Super-Hug takes 12 minutes to cut and 40 minutes to sew and finish. The plant has enough workers to provide at most 12,599 minutes per day for cutting and at most 28,249 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $6.50 and the profit on each pair of Super-Hug is $8.50. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit.

Minimize P subject to the given constraints. P = 16x + 2y constraints x ≥ 0 y ≥ 0 x + 2y ≥ 8 2x + y ≥ 8 a. P =16 at (0, 8) b. P = 8 at (0, 2) c. P = -32 at (-2, 0) d. none of these

You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. Is the slope an increasing or decreasing rate of change? What does this mean in the context of this situation?

Determine whether the statement mekes sense or does not make sense, and explain your answer. I factored 48x² -196 completely and obtained (7x +14)(7x -14). Choose the correct answer below. (A) It makes sense. Because 49x²-196 is the difference of two squares so the factors are (7x +14)(7x -14). (B) It does not make sense. Because (7x +14)(7x -14) is not completely factored and the complete factors are (7x +14)(7x +14). (C) It does not make sense. Because (7x+ 14)(7x- 14) is not completely factored and the complete factors are (7x -14)(7x -14). (D) It makes sense. There is no common factor in (7x+ 14) and (7x - 14) so these are completely factored.

A 10 foot ladder is leaning against a wall with the base of the ladder 6 feet from the wall. If the bottom of the ladder is pushed towards the wall at a rate of 1 foot per second, what is the average rate that the height of the ladder is changing from t=1 second to t=1.5 seconds

At what interest rate must $4,800 be compounded annually to equal $8,109.499 after 9 yr?(Round to the nearest percent.) A. 8% B. 7% C. 5% D. 6%

Which one of these statements is NOT an example of a straw-man null hypotheses? (A) Families with cars have the same access to healthcare providers as families without cars. (B) Cats and dogs differ in their interest in human relationships. (C) Students who do their homework regularly get better grades or the same grades as students who do not. (D) There is no difference in the number of doctor visits per year for people who wash their hands more than three times a day compared to those who wash their hands three times or less a day.

The Family Fine Arts Center charges $22 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 436 people paid admission, the total receipts were $5788. How many who paid were senior citizens? (A) 227 senior citizens (B) 119 senior citizens (C) 209 senior citizens (D) 317 senior citizens

For the differential equation dy/dx=-( e^-x)-3x^2 A): Find a general solution. Show all your work. B): Verify the solution. Show all your work.

Graph the linear equation. f(x) = -(2/3)x Use the graphing tool to graph the equation.

Assume that a hat contains four bills: a $1, a $5, a $10, and a $20 bill. Two bills are to be selected at random with replacement. Find the probability that both bills are $1 if at least one selected is a $1 bill? The probability that both bills are $1 if at least one selected is a $1 bill is ______

Use the model A = Pe^rt or A = P( 1 + r/n )^nt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. If a couple has $200,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6% compounded continuously? Round up to the nearest year.

A nationwide chain of cooking schools gives all students a test at the end of training. The mean score is 89.7 with a standard deviation of 20.3. If 60 students are sampled, the mean of the sampling distribution is and the standard deviation of the sampling distribution is

An auditorium has 20 rows of seats. There are n = 24 seats in the first row, 25 seats in the second row, 26 seats in the third row, and so on (see figure). How many seats are there in all 20 rows? ______________ seats

Solve by the elimination method. 4x - y = 1 x + 3y = 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

An artist creates a right prism whose bases are regular decagons. He wants to paint the surface of the prism. One can of paint can cover 32 square feet. How many cans of paint must he buy if the height of the prism is 11 ft and the length of each side of the decagon is 2.4 ft? Make sure to round to the nearest whole can.

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 26.6 for a sample of size 628 and standard deviation 10.3. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Consider the series Σ1/n (a) Does the sequence {an} = 1/n converge or diverge? (b) Does this series converge or diverge? (c) How many terms are required for the sum to exceed 50? Show work used to find this value.

The price-earnings (PE) ratios of a sample of stocks have a mean value of 10.5 and a standard deviation of 1.1. Assume the PE ratios have a bell shaped distribution. According to the Empirical Rule, what percentage of PE ratios that fall between, A 9.4 and 11.6 B 8.3 and 12.7 C 7.2 and 13.8

300 people are lined up outside of Disneyland, and all enter by 8:15 am. By 8:30 am, 550 more people enter, and every 15 minutes afterwards, the number of people who enter increases by 250. All of these people are planning to stay for the Marvel parade at noon. a. Represent this problem as a sequence and write a formula for the nth term. b. How many people will enter the park between 11:45 and noon?

Solve the rational equation. If the equation has no solution, so state. 32/(x² - 25) + 8/(x + 5) = 4/(x - 5) (A) The solution set is { } (B) There are infinitely many solutions. (C) There is no solution.

Find the indicated conditional probability using the following two-way table: Grade Drive to school Take the bus Walk Sophomore 2 25 3 Junior 13 20 2 Senior 25 5 5 P( Walk to school | Senior) = [?] Round to the nearest hundredth.

The Malones' electric bills for January through June, 2006, were $95.37, $106.51, $87.73, $83.07, $76.57, and $68.28. For these bills, determine the (a) mean and (b) median a) The mean is $______. (Round to the nearest cent as needed.)

Suppose a game has payoff matrix [0 -4 2] [3 2 -4] [1 -1 0] Find the expected value of the game for the following strategies for players A and B. (a) A=[ 0.1 0.4 0.5]; B = [0.2] (b) A = [ 0.3 0.4 0.3 ]; B =[0.8] [0.4] [0.1] [0.4] [0.1] (a) The expected value is -0.26 .(Round to two decimal places as needed.) (b) The expected value is ▢ (Round to two decimal places as needed.)

Find a1 and d for the following arithmetic series. S12 = 300, a12 = 47 a1 = ____.