Math Questions

A machine that manufactures automobile parts produces defective parts 12% of the time. If 9 parts produced by this machine are randomly selected, what is the probability that fewer than 2 of the parts are defective? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

The function h(x)= (x+2)³ can be expressed in the form f(g(x)), where f(x)= x³, and g(x) is defined below: g(x)=____

A company's marginal cost function is MC(x) = 1/8x + 1 and its fixed costs are 100. Find the cost function. (Remember to use absolute values where appropriate.)

Use a half angle formula or formula for reducing powers to fill in the blanks in the identity below: (cos(3x))² = _____ + ____ cos(_____ x)

What is the area of a regular hexagon inscribed in a circle of radius 9 meters? 35.074 square meters 175.370 square meters 192.589 square meters 210.444 square meters

There are two machines that produce aluminum cans. The newer machine can produce 5400 cans in 180 minutes. It takes the older machine 270 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5400 cans? ________minutes

Which expression below can be obtained from 10sin²x by using a power reducing formula? Select the correct answer below: 5 - 10cos (5x) 5-5cos (2x) 10-5cos (2x) 5-10cos (x) 5-5cos (x)

A college reported the following based on their graduation data. 60% of freshman had attended public schools. 60% of freshman who had attended public schools graduated within 5 years. 80% of other freshman graduated within 5 years. What percent of freshman graduated within 5 years? A. 68% B. 66% C. 47% D. 69%

Suppose it was determined that the water footprint for a typical American is 2,483 m³/year. a. A family of three would like to reduce their water footprint so that it is 75% of the typical American's water footprint. Which calculation shows how they can estimate their target water footprint for one day? There may be more than one correct answer. ÷ 365 0 (3) 3 x 2,500 × 3 2,500 × 3 × 4 03 x 2,500 x 0.75 ÷ 365 2,500 (365 × 0.75) × 3 2, 500 x 3 x 0.75 3x (2, 500 x 0.75) ÷ 365 4 3 2, 500 x 3÷ 0.75 ÷ 365

Solve for the roots in simplest form by completing the square: x² + 16x - 61 = 0

An accounting firm has ordered 60 new computers at a cost of $1657 each. The machines will not be delivered for 5 months. What amount could the firm deposit today in an account paying 3.33% simple interest to have enough money to pay for the machines in 5 months? The present value PV of a future amount of FV dollars at a simple interest rate r for t years is given by which formula? A. PV=FV(1 + rt) B. PV= FV c. PV=rt(1 + FV) FV 1 + rt D. PV= The firm should deposit $ (Round to the nearest cent as needed.)

The radius, r, in centimeters, of a melting snowball is given by r = 60 — 2.5t, where t is the time in hours. The snowball is spherical with volume V = πr³ cm³. Find a formula for V = f(t), the volume of the snowball as a function of time. V = f(t) = (Be sure to include units!) help (formulas) with help (units)

Refer to the functions r, p, and q. Find the function r(x) = 5x Part: 0/2 Part 1 of 2 Part: 1 / 2 Part 2 of 2 p(x)=x² + 8x The domain of 5x 2-x 5 X • (²) (x) (x) in interval notation is q q (x) = √2-x 0/0 (x) and write the domain in interval notation. 8 -8 (0,0)

Find the real solutions, if any, of the following equation. Use the quadratic formula. 2x(x+2) = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your answer. The solution set is -1+√√2,-1-√√2 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to se B. The solution is not a real number.

Let (X) be a sequence of independent exponentialy distributed random variables with means respectively (a) Does (X) converge in distribution? (6) Does (X) converge almost surely?

Write the complex number in trigonometric form r( cos0+ i sin 0), with 0 in the interval [0°,360°). -1-i -1-i=(cos + i sinº)

According to a Chinese legend from the Han dynasty (206 B.C.E.-220 C.E.), General Han Xin flew a kite over the palace of his enemy to determine the distance between his troops and the palace. If the general let out 800 meters of string and the kite was flying at a 35° angle of elevation, how far away was the palace from General Han Xin's position?

What is the slope of the line tangent to the graph of f(x) = 2x²e- at x = -2? Express your answer in simplest form with no negative exponents.

What effect did population and cultural shifts within New Mexican territory have? A. It allowed New Mexico more representation in the Senate. B. It helped New Mexico finally achieve statehood. C. It forced southern states to continue to refuse statehood. D. It lessened conflict between settlers and indigenous peoples.

For the following list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes (if any). 133, 135, 147, 131, 147, 136 (a) The mean is (Round to the nearest tenth as needed.)

A line passes through the point (-3,-9) and has a slope of 9. Write an equation in point-slope form for this line.

The infield of a youth softball field is a square that measures 55 feet on each side. The pitching circle is 16 feet in diameter. A general rule of thumb is that a person can take up 2.5 ft² of space. What is the area of the circle? How many people can fit in the pitching circle?

The average forward speed for neotropical butterflies can be modeled by the function, V(m)= 5.2 √m where V(m) represents the average forward body speed in meters per second and m represents the body mass of the butterfly in grams. According to this model, what would be the body mass of a butterfly that has an average forward speed of 10 meters per second? Round to one decimal place. {your final answer only number with one decimal place}

Find the formula, in standard form y = ar²+bx+c, for a quadratic that has roots at x = -9 and x = 5, and has leading coefficient of 1.

The half-life of the radioactive element unobtanium-59 is 10 seconds. If 176 grams of unobtanium-59 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds? The amount left after 10 seconds is grams. The amount left after 20 seconds is grams. The amount left after 30 seconds is grams. The amount left after 40 seconds is grams. The amount left after 50 seconds is grams. (Round to one decimal place.) .....

The factored answer (x-7)(x + 4) is the same as (x + 4)(x − 7). O True O False

A popular brand of pen is available in 7 colors and 2 writing tips. How many different choices of pens do you have with this brand? There are different choices of pens with this brand.

The Best Buy parking lot is a rectangle that measures 385 feet long and 180 feet wide. Each parking space is a rectangle that measures 20 feet long and 9 feet wide. On black Friday, the parking lot is full. How many cars are parked in the parking lot at Best Buy on black Friday? Hint: Calculate the area of the parking lot and the parking space to help find the answer.

Use the formula for simple interest, I=Pxrxt, to find the missing quantity. P=$5,500; r = 7%; t = 6 years A. 1 $2,510 B. 1=$2,310 C. 1 $231,000 D. 1 $23,100

Determine if each of the following functions is a growth exponential or a decay exponential. a.y=4-2.2x b. y=3e-7x c. y = 20.1x d.y=0.32x

Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score for the given score on this dental anxiety scale. Z4 = (Type an integer or a decimal.) .

What is one potential problem with this simulation? In order to run this simulation you would need to plot the data in a sampling distribution to see where the average shoe size was located. This is not an appropriate situation in which to run a simulation. The best thing to do is to collect all of the data from the school. The only shoe sizes that are represented are sizes 5-8. There are many males that have shoe sizes between 8 and 10. This is not a correct representation of the population. This simulation is run correctly. They are randomly generating 50 numbers to represent the shoe sizes of males in the school.

Interpret the slope in context for each situation. a. The average height of children ages 8 to 13 can be modeled by the equation y = 35 + 2x, where x is the age in years and y is the average height in inches. b. Researchers found that the weight of an infant less than 12 months old can be predicted using the equation y = 9.9 + 1.1x, where y is the weight in pounds and x is the age in months. www.ncbi.nlm.nih.gov/pubmed/18021105 www.ncbi.nlm.nih.gov/pubmed/18021105 c. The equation of the line that estimates the number of airports, y, a state has given its population in millions, x, is y = 6.1016+ 1.35x.

The population of a city was 132 thousand in 1992. The exponential growth rate was 1.7% per year. a) Find the exponential growth function in terms of t, where t is the number of years since 1992. P(t)= 132000 e 0.017t b) Predict the population in 2010, to the nearest thousand. (Round to the nearest thousand as needed.)

USE THE NORMAL CURVE TABLE TO DETERMINE THE PERCENT OF DATA SPECIFIED. A) BETWEEN z = -1.34 AND z = 2.24 B) GREATER THAN z = -1.90 C) TO THE RIGHT OF 1.78 D) TO THE LEFT OF 1.62 E) BETWEEN z = -1.53 AND z = -1.82

The number of federal income tax returns filed electronically since 1995 is estimated by y = 5.6524x + 8.731, where y is the number of returns (in millions) and x is the number of years since 1995. Which of the following statements interprets the equation for this situation? 1) The number of federal income tax returns filed electronically has decreased at an average rate of about 8.731 million returns per year since 1995. 2) The number of federal income tax returns filed electronically has increased at an average rate of 5.6524 million returns per year since 1995. 3) The number of federal income tax returns filed electronically has decreased at an average rate of 5.6524 million returns per year since 1995. 4) The number of federal income tax returns filed electronically has increased at an average rate of about 8.731 million returns per year since 1995.

Consider the system of equation: x+4y=13 3x+2y=19 (a) Multiply both sides of the second equation by-2. What equation results? (c) Now that you know the value of x, how can you find the value of y? Find it. (b) Add the equation from (a) to the first equation. What happens? What can you now solve for? (d) What could you have multiplied both sides of the first equation by to eliminate the x instead of the y?

Point E with coordinates (5, 7) is translated along a glide reflection to its image of E (4,3). Which best describes the glide reflection? (x,y) → (x-1, y - 4) followed by reflection across the x-axis (x,y) → (x-2, y - 3) followed by reflection across y = x (x,y) → (x-1, y - 4) followed by reflection across y = -x (x,y) → (x-2, y-3) followed by reflection across y = -x

A poll is given, showing 55% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 5 of them favor the new building project?

Line A passes through the points (0, 11) and (-5, 1). Line B passes through the points (0, 10) and (1, 12). Which of the following statements is true about the system of equations represented by line A and line B? A. The system of equations has exactly one real solution. B. The system of equations has an infinite number of real solutions. C. The system of equations has exactly two real solutions. D. The system of equations has no real solutions.

Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax+By = C. m = -7, (-6, - 3) The equation of the line in the form Ax+By = C is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Rewrite the following polynomial in standard form. -x+7-10x²

Simplify: (7-i)-(-6-8i)+(-2+6i) 19 +5i 11 + 15% 11 + 13i 15+i

For each of the following, find the formula for an exponential function that passes through the two points given. a. (0,8) and (3, 216) f(x) = b. (0,6860) and (3,20) g(x) =

A statistician uses Chebyshev's Theorem to estimate that at least 65 % of a population lies between the values 1 and 17. Use this information to find the values of the population mean, μ, and the population standard deviation o. a) μ b) o =

A person invests $1625 into a retirement account, with an interest rate of 0.9% compounded quarterly. Find the retirement account balance after two years. 1) The balance will be $1654.48 after two years. 2) The balance will be 1941.60 after two years. 3) The balance will be $1664.41 after two years. 4) The balance will be $3279.34 after two years.

1. Negative ions form when atoms valence electrons. 2. In the formation of an ionic compound, a metal atom is most likely to valence electrons. 3. lonic compounds form because charges attract.

Consider the following absolute value inequality. |5x + 2| < 44

A manufacturer producing a new product, estimates the annual sales to be 9,200 units. Each year, 8% of the units that have been sold will become inoperative. So, 9,200 units will be in use after 1 year, [9,200+ 0.92(9,200)] units will be in use after 2 years, and so on. How many units will be in use after n years?

Scores on a standardized test are normally distributed, perfectly symmetric and mound shaped, with a mean of 100 and a standard deviation of 20. If these scores are converted to standard normal z scores, which of the following statements will be correct? The mean of the standardized z-scores will equal 100. Both the mean and median score will equal 0. The mean of the standardized z-scores will equal 5. The mean will equal 0, but the median cannot be determined.