Math Questions

From 1983 to 2003, the number B of federally insured banks could be approximated by B(t) = 322.6t+13787 where t is the year and t=0 corresponds to 1983. How many federally insured banks were there in 1988? Find the slope of the graph of B. Interpret this slope as a rate of change. Choose the correct answer below. The number of banks increased by 12174 banks per year The number of banks decreased by 322.6 banks per year The number of banks increased by 322.6 banks per year The number of banks decreased by 13787 banks per year The number of banks decreased by 12174 banks per year The number of banks increased by 13787 banks per year Find the y-intercept of the graph of B. The y-intercept is Interpret the y-intercept. Choose the correct answer below. The y-intercept is the maximum number of banks allowed in the country The y-intercept is the number of banks in 1983 The y-intercept is the minimum number of banks allowed in the country The y-intercept is the number of banks in 1988 The y-intercept is the number of banks in 2003

Police use the formula: v = √20L to estimate the speed of a car, v, in miles per hour, based on the length, L, in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 208 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit. Answer: The car was traveling at approximately miles per hour.

Find the volume of a hemisphere with a great circle circumference of 37.7 centimeters. r= V =

In a high school basketball team there are 12 students competing to start a game. If 5 students can be chosen to start a game, how many different starting lineups can be formed from this group of 12 students? 3,991,680 95,040 120 792

Use the first derivative test to determine the location of each local extremum and the value of the function at that extremum. f(x) = (7-5x)4/3 +7 A. Local minimum at (7/5,7) B. Local minimum at (0,7) C. Local maximum at (7/5,7) D. No local extrema

Anne and Nancy use a metal alloy that is 18. 141% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 25%, copper to form 85 ounces of the desired alloy? Round to the nearest whole number. A. 53 ounces B. 37 ounces C. 55 ounces D. 32 ounces

On the planet of Endor, the Ewoks are building a trebuchet to attack the Storm Troopers. The test their new weapon and decided it can launch 100 kgs of rocks 50 meters, with a margin of error of 7 meters. What is the range of the rocks they can throw?

Dylah is going to invest in an account paying an interest rate of 4.1% compounded continuously. How much would Dylan need to invest, to the nearest cent, for the value of the account to reach $19,000 in 7 years?

A driver filled the gas tank and noted that the odometer read 57,491.9. After the next filling, the odometer read 57,838.4. It took 17.5 gal to fill the tank. How many miles per gallon did the driver get? The driver got mpg. (Type a whole number or a decimal.)

In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery commission, you win. a) How many different numbers may be chosen? b) If you purchase one lottery ticket, what is your chance of winning? a) There are different numbers that can be chosen. (Type a whole number.) b) There is a chance of winning. 1 in 10,000 1 in 9999 1 in 6561 1 in 100 1 in 1000

Minimize the following objective function subject to the given constraints. Find the corner points and state the minimum. Minimize: z = 10x + 4y subject to 2x + y ≥ 8 x + 3y ≥ 9 x≥0, y≥0 A. Corner Points: (8, 0), (0, 9), (3, 2) Minimum: 38 B. Corner Points: (0, 3), (4, 0), (3, 2), (0, 0) Minimum: 0 C. Corner Points: (0, 8), (9, 0), (2, 3) Minimum: 32 D. Corner Points: (8, 0), (0, 9), (2, 3) Minimum: 32 E. Corner Points: (0, 8), (9, 0), (3, 2) Minimum: 32

Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 5 ? (mod 9) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The positive number replacement(s) (less than the modulus) for the question mark is(are) (Use a comma to separate answers as needed.) B. There are no positive number replacements (less than the modulus) for the question mark that make the statement true.

A publisher has fixed costs of $74,968 on a book for development, editing, and advertising. It costs the publisher $4 per copy at the printer. The publisher charges $30 per copy. Write the linear profit function that represents the profit, P(x), for the number of books sold. A. P(x)=-26x + 74,968 B. P(x) = 26x+74,968 C. P(x) = 34x+74,968 D. P(x) = 26x-74,968 E. P(x) = 34x-74,968

Find the functions which are parallel. I. 3x + 5y = 9 II. 3x + 8y = 12 III. 3x + 9 = -5y IV. 27x - 45y = 1 I and IV I and III II and III

Find the producer's surplus if the supply function of some item is given by S(x)=x²+2x+8. Assume that supply and demand are in equilibrium at x = 30. A. 12,700 B. 17,200 C. 18,900 D. 19,800

A family wants to purchase a house that costs $190,000. They plan to take out a $140,000 mortgage on the house and put $50,000 as a down payment. The bank informs them that with a 15-year mortgage their monthly payment would be $723.49 and with a 30-year mortgage their monthly payment would be $520.82. Determine the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage. How much would they save if they selected the 15-year mortgage?

Suppose that $1600 is invested at an interest rate of 2.5% per year, compounded continuously. After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest hundredth.

The rate of growth of profit (in millions) from an invention is approximated by P'(x)=xe OA. P(x) = -5e 1 OB. P(x) = -- ze OC. P(x) = -5e OD. P(x)=-e -+² -x² 1² +0.044 - 44,000 + 44,000 -0.044 where x represents time in years. The total profit in year 2 that the invention is in operation is $35,000. Find the total profit function P(x).

In deciding whether or not to set up a new manufacturing plant, analysts for a popcorn company have decided that a linear function is a reasonable estimation for the total cost C(x) in dollars to produce x bags of microwave popcorn. They estimate the cost to produce 10,000 bags as $5,340 and the cost to produce 15,000 bags as $7,710. Find the marginal cost of the bags of microwave popcorn to be produced in this plant. Round answer to the nearest cent. A. $4.74 B. $0.47 C. $0.24 D. $47.40 E. $2.11

A lumber yard has fixed costs of $6,478.7 a day and variable costs of $1 per board-foot produced. The company gets $2.7 per board-foot sold. How many board-feet must be produced daily to reach the break-even point? A. 1,751 board-feet B. 3,811 board-feet C. 2,540 board-feet D. 6,478 board-feet CXXXP

17. Basketball Team A scored 4 three-point baskets, 22 two-point baskets, and 7 one-point baskets in a game versus team B. Team B scored 8 three-point baskets, 18 two-point baskets and 12 one-point baskets in the game. Write a 2 x 3 matrix that organizes this data. Let team A be row I, team B be row 2, three-pointers be column I, two-pointers be column 2, and one-pointers be column 3.

12-35. For each of the following equations, list all of the solutions without using a calculator. Use the unit circle or a graph to check your answer. Then, predict the solution that your calculator will give, and use your calculator to check your prediction. a. 2cos(x) - 1 = 0 b. 4sin²(x) - 3 = 0 c. 2sin(x) = √3

Four congruent isosceles right triangles are added to the edges of a regular octagon to form a square, as shown. If the legs of each of the four triangles are 3 centimeters long, which measure is closest to the perimeter of the octagon? OA. 24.0 cm OB. 25.5 cm OC. 33.9 cm OD. 72.0 cm

Give an example to show that the commutative property does not hold for the set of integers under the operation of division. Select each of the following that shows that the commutative property does not hold for the set of integers under the operation of division. A. 4+2#2÷4 B. 9+(6+2) # (9÷6)÷(9÷2) C. (10÷5) ÷2# (5÷10) ÷2 D. (18÷6)÷3# 18÷(6÷3)

Use the discriminant to determine whether the quadratic equation has zero, one, or two distinct real solutions. x² + 6x + 1 = 0 The quadratic equation has choose one real solution(s).

The difference in frequency between the first and the fifth harmonic of a standing wave on a taut string is f5 - f1 = 50 Hz. The speed of the standing wave is fixed and is equal to 10 m/s. Determine the difference in wavelength between these modes. A5-A1=-0.64 m A5-A1 -1.60 m A5-A1 = 5m A5-A1 = -0.80 m A5-A1 = 0.20 m

Each voter in a county is given a number that uniquely identifies them. A computer is used to select 500 of these numbers at random. The 500 voters identified by the computer are interviewed for a study. Which type of sampling was used? systematic random cluster convenience

Which of the following functions are parallel? I. 2x+4y=9 II. 5x-3y = 10 III. x + 7y=5 IV. 2x+9=-4y O I and IV OI and III OII and IV

Find the reflection of the function y = x² over y-axis. The reflection along the y-axis is (-x)². The reflection along the y-axis is x³. The reflection along the y-axis is -x².

Evaluate the following expression without using a calculator. Simplify your answer as much as possible, and enter your answer as a fraction. (27/64)* -1/3

One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 7 or a diamond. Note that the ace is considered a low card. The probability that the card selected is less than 7 or a diamond is (Type an integer or a simplified fraction.)

The volume of a rectangular pyramid is 60 cubic feet. The width of the base is then scaled by a factor of 3, the length of the base is scaled by a factor of 2, and the height of the pyramid is scaled such that the resulting pyramid has the same volume as the original pyramid. Find the scale factor used for the height. Leave final answer in fraction form.

Identify the horizontally shifted function. y=sin(x) y = (x + 4)² y = 5* x3

Please show all the work that you go through in order to complete the problems. 1. As part of an exercise in an elementary school reading class, the students are given 6 cards that each contain a picture and part of a story. The students are asked to put the cards into an order that tells a coherent story. If a student didn't understand the assignment and had no idea what the intended order was, how many different possible ways could that student choose to place the cards down in order?

The area of a regular pentagon is 50 cm². What is the area of a regular pentagon with sides 6 times the length of the smaller pentagon?

One year Alex had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.29. Also, Sally had the lowest ERA of any female pitcher at the school with an ERA of 2.68. For the males, the mean ERA was 4.047 and the standard deviation was 0.993. For the females, the mean ERA was 4.397 and the standard deviation was 0.626. Find their respective z-scores. Which player had the better year relative to their peers, Alex or Sally? (Note: In general, the lower the ERA, the better the pitcher.)

Select all the correct answers. Which two excerpts are written in a third-person omniscient point of view? Long, long ago there lived an old man and his wife who supported themselves by cultivating a small plot of land. (Yei Theodora Ozaki, "The Story of the Old Man Who Made Withered Trees to Flower") Every morning I lay on the floor in the front parlour watching her door. The blind was pulled down to within an inch of the sash so that I could not be seen. (James Joyce, The Dubliners) You may believe me who adore them, who have long given myself to them without reserve. (Anatole France, "The Adventures of the Soul") "The lamp! Put out the flame and bring me the lamp!" Surprised and suspicious, for why should the stranger, out of all such a treasure want only an old lamp, Aladdin wondered. (Brothers Grimm, "The Adventures of Aladdin") He was a man of exuberant fancy, and, withal, of an authority so irresistible that, at his will, he turned his varied fancies into facts. (Frank R. Stockton, "The Lady, or the Tiger")

(a) What positively impacts your persistence, confidence, and/or enjoyment in any class? Why? (b) What can be improved to increase the positive impact of any STEM class to your persistence, confidence, and/or enjoyment of the class? How would one operationalize your idea(s)?

A doctor is studying the effects that the amount of junk food has on blood pressure. As each patient enters his office, he/she fills out a survey about junk food. The doctor then takes the blood pressure of each patient. Is this an experimental or observational study? Explain your reasoning.

Select the correct answer. What is the key feature of the third-person omniscient point of view? A. It is told from the point of view of a specific character in the story. B.It is used to express the thoughts and feelings of the central character. C.It is used when directly addressing the reader or giving instructions. D. It has an all-knowing narrator who is aware of all the characters' perspectives.

Find the slope of the line X+ 9 = 14. zero 14 undefined

For a certain website, your password must be 10 digits long. If the first 8 digits are any numbers and the last 2 digits are any lower case letters, how many passwords are possible? 67,600,000,000 5,200,000,000 67,600 4,160

A particle moves along a line with a velocity v(t) = -4t + 2, measured in meters per second. Find the total distance the particle travels from t = 0 seconds to t = 2 seconds. Enter an exact answer.

What are the transformations performed in the function y = |x +41-8? 8 units to the right and 4 units up. 4 units to the left and 8 units down. 4 units to the right and 8 units down.

If a system of two equations in two variables is solved graphically, a unique solution exists when: The lines are parallel Both equations yield the same line The lines intersect at two distinct points The lines intersect at one point

What is the name of the transformation of the function f(x) = - tan(x)? Reflection about the x-axis Reflection about the y-axis Horizontal shift

Suppose in order for a bill to pass in Congress, 50% of voters must be in favor of it. In a random sample of 200 voters, 98 said that they were in favor of a new bill. State the p-value assuming the alternative hypothesis is Ha #.50 (Round to the nearest hundredth)

Find the indicated probability. If P(A and B) = 0.5, P(A) = 0.7, and P(B) = 0.6, find P(A or B).

Chase invested $39,000 in an account paying an interest rate of 3.2% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $66,100?

Emma is going to invest in an account paying an interest rate of 2.6% compounded quarterly. How much would Emma need to invest, to the nearest cent, for the value of the account to reach $66,000 in 7 years?