Math Questions

Find the indefinite integral. 18/1 + 81x² dx

Multiply and simplify completely: (x + 2)(x − 2)

7.40 Testing a random number generator. Statistical software has a "random number generator" that is supposed to produce numbers uniformly distributed between 0 and 1. If this is true, the numbers generated come from a population with = 0.5. A command to generate 100 random numbers gives outcomes with mean = 0.531 and s = 0.294. Because the sample is reasonably large, take the population standard deviation also to be o = 0.294. Do we have evidence that the mean of all numbers produced by this software is not 0.5?

Furnace repair bills are normally distributed with a mean of 269 dollars and a standard deviation of 20 dollars. If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 269 dollars and 271 dollars. 0.7881 0.2881 0.5517 0.2119

Find the derivative of the function. y = - 8x In (8x + 7) dy/dx

Give the measure of the supplement of the angle. (180-y)° The supplement of the angle (180-y)° is

Consider a population of size N = 9, 800 with a mean of μ = 161 and standard deviation of a = 17. Compute the following z-values for either the population distribution or the sampling distributions of with given sample size. Round solutions to two decimal places, if necessary. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 165. Suppose a random single observations is selected from the population. Calculate the z-value that corresponds to x = 157.

The power rule for logarithms states that The logarithm of a number with an exponent is the Points: 0 of 1 of the exponent and the logarithm of that number.

Find an equation of the tangent line to f(x) = ex + 7x at the point (0, 1). Write your final answer in the form y = mx + b.

Angle x lies in the first quadrant such that cosx = 3/5the second quadrant such that siny = 7/25. Determine an exact value for cos (x - y).

The two Soup cans are similar. The large can has a height of 4 in in the smaller can has a height of 3 inches. Find the area of the smaller can give in the larger can has an area of 108 in squared. Round your answer to the hundredths of an inch.

Misu Sheet, owner of the Bedspread Shop, knows his customers will pay no more than $135 for a comforter. Misu wants a 20% markup on cost instead of on selling price. What is Misu's cost? (Round your answer to the nearest cent.)

Find the slope of f(x) at x = -2. The graph of f(x) is shown below. Move the point on the curve to x = -2. Then plot two points on the tangent line. Finally, calculate the slope of f(x) at x = -2. Write your answer as a simplified fraction or rounded to 4 decimal places.

Find all zeros of f(x) = x³ - 9x² + 22x - 10. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Graph the set {x|x≤4) on the number line. Then, write the set using interval notation.

Suppose that $2000 is invested at a rate of 4%, compounded annually. Assuming that no withdrawals are made, find the total amount after 9 years. Do not round any intermediate computations, and round your answer to the nearest cent.

A man is disabled in an accident and wants to receive an insurance payment that will provide him with $2900 at the end of each month for 20 years. If the payment can be placed in an account that pays 9% compounded monthly, what size payment should he seek? He should seek a payment of $ (Simplify your answer. Round to the nearest cent as needed.)

Graph f(x)=-2 log3 (x) + 5 using transformations by first graphing the basic logarithmic function (parent function), then the progression of transformations (in the correct order). State the domain, range, and vertical asymptote and end behavior.

Determine the Angle Pair Types that are CONGRUENT when two parallel lines are cut by a transversal. (Select ALL that apply) * Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Same-Side Interior Angles Linear Pair Vertical Angles

A rectangle is drawn so the width is 31 inches longer than the height. If the rectangle's diagonal measurement is 41 inches, find the height. Give your answer rounded to 1 decimal place.

The patient is using 2 devices to measure his heart rate as he runs. After 15 minutes of running, one device displays 90 bpm. The other device displays 100 bpm after 15 minutes of running.

A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. 0.949 0.839 0.162 0.111

Phillippe wants to drink at least 72 ounces of water every day while at work. He works 6 hours a day. How many ounces of water must Phillippe drink each hour? Write and solve an inequality to answer the question

Select the correct answer from each drop-down menu. Consider this expression. 3/x-2 + x-2/x- 4x+4 The simplest form of the expression has in the numerator and in the denominator.

If C=t-5 and B = t² + 2, find an expression that equals 2C + 2B in standard form.

The formula for the future value Q of a simple interest investment is Q=M + Mrt, where M is the original investment, r is the annual interest rate, and t is the time in years. Solve this formula for t.

A 24-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces. What is the length of the first piece? What is the length of the second piece?

When an object is dropped from a 1520 ft tower, the height of the object in feet after t seconds is given by the function f(t) = -16² +1520. Find the height of the object after 5 seconds. The height of the object after 5 seconds is feet.

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95% salt. She wants to obtain 70 ounces of a mixture that is 90% salt. How many ounces of each solution should she use?

Which of the following fractions is the largest? a. 2/3 b. 1/2 c. 4/9 d. 3/7

A problem states: "There are 3 more baseballs than bats in a dugout. There are 15 bats and baseballs in the dugout in all. How many bats are there in the dugout?" Let b represent the number of bats. Which equation represents the situation? 2(b + 3) = 15 26 - 3 15 2b +3= 15 b+3= 15

A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is y = -0.0507x+2.9232. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is (Round to the nearest hundredth as needed.)

Write the first five terms of the sequence. f(0) = 3: f(n) = f(n-1). 2 f(0) = ƒ(1) = f(2)= f(3) = f(4) = 0.00

The probability that an event will not happen is P (E') The probability that the event will happen is (Type an integer or a simplified fraction.) Find the probability that the event will happen.

Use the Change of Base Formula to evaluate log3 48. Then convert log3 48 to a logarithm in base 5. Round to the nearest thousandth. 3.524; logs 290.385 3.524; logs 80 3.871; logs 290.385 1.681; log, 80

Rewrite the equation of this circle in standard form: x² + 14x + y² + 16y + 75 = 0

A piece of equipment has cost function C(x)= 50x² + 1000 and its revenue function is R(x) = 500x- x², where x is in thousands of items. What is the least number of items that must be sold in order to break even?

The mean height of American women in their twenties is about 63.8 inches, and standard deviation is about 3.1 inches. The mean height of men the same age is about 68.9, with standard deviation about 3.6 inches. Suppose that the correlation between the height of husbands and wives is about r = 0.56. Find the least-squares regression line of wife's height on the husband's height in young couples. slope = y-intercept = Write your answer in 2 decimals. Write your answer in whole number.

Enter your answer in the provided box. How many grams of potassium chlorate decompose to potassium chloride and 727 mL of O₂ at 128°C and 756 torr? 2 KCIO3(s) → 2 KCl(s) + 3 0₂ (g)

Tiffany received a box of chocolates in the shape of a T for her birthday. She knows the volume of the box is 100 cubic inches. The volume of the horizontal part of the T is 36 cubi inches. She knows the length of the vertical par of the T is 8 inches and that the width is 2 inches, but does not know the height. Help Tiffany determine the height of the vertical par of the T-shaped box of chocolates she received

A population numbers 10,000 organisms initially and decreases by 4.1% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = ab, where P=

Going against the current, a boat takes & hours to make a 120-mile trip. When the boat travels with the current on the return trip, it takes 5 hours What is the rate of the boat in still water? 33 mph 02 mph. 20

A farmer has a triangular field with sides that measure 40m (side AB), 35m (side BC), and 38m (side CA). What are the measures of the angles A, B, and C in this field Provide a complete solution including a diagram.

Let P(x, y) be the terminal point on the unit circle determined by t. Then sin(t) = ___, cos(t) = ___ , and tan(t) = ___.

Nicole took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.75 per mile. The total fare was $44.90, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.

Use the intercepts to graph the equation. x = -1 x-intercept: Enter as a coordinate: such as (a, b). If there is no x- intercept, enter DNE. y-intercept: intercept, enter DNE Enter as a coordinate: such as (a, b). If there is no y-

Let's say you devise a blackjack strategy where you win 42% of the time, tie 9% of the time, and lose 49% of the time. When you lose you lose $1, on a tie you gain $0, and on a win you gain $1 (assume you aren't allowed to split or double). What is the expected value of your winnings? Note: Do not round your answer.

The area of the parallelogram whose adjacent sides are given by the vectors a = 3i + j + 4k and b = i - j +k (A) √50 (B) √42 (C) √44 (D) None of these

A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices in the coordinate plane represents 1 ft. What is the approximate at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit area of the baseball diamond? Show your work.

A company is making a new label for one of their containers. The container is a cylinder that is 9 inches tall and 5 inches in diameter. What is the area of the label that needs to be printed to go around the new container? Use = 3.14. A. 176.625 In² B. 120.65 In² C. 182.6 In² D. 141.3 In²