Math Questions

A small corporation must appoint four officers (a president, a chief executive officer, a chief operating officer, and a chief financial officer). It must also appoint a Strategic Planning Committee with four people on it. There are a total of 9 qualified candidates, and the chosen officers may also serve on the committee. (a) How many different ways can the four officers be appointed? (b) How many different ways can the committee of four be appointed? (c) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x²-8x-4 are added? (1 point) a. 2x²-4x+2 will be a polynomial b. 2x²-4x+2 may or may not be a polynomial c. 2x²-12x-10 will be a polynomial d. 2x²-12x-10 may or may not be a polynomial

Sal is running on a treadmill at the gym. He is going to run for 7 miles at a constant speed of 1 mile per 8 minutes. Graph the distance Sal will run as a function of time. y= 1/8 x+0

6 calculate how much you can borrow with a $800 per month payment at today's mortgage rates and determine if it would be enough money to purchase the home you selected in #4. Do this for BOTH loans. a. For a 30-year mortgage. State your findings in a complete sentence.

Find the end behavior of the following polynomial: f(x)=-7(x-11)^3(x+13)³(x+2)(x-3)5 As x → ∞, f(x)→→ -∞ As x→ -∞, f(x) → ∞ As x→∞, f(x)→∞ As x→ -∞, f(x) → ∞ As x→ -∞, f(x) → -∞ As x→→ -∞, f(x)→ -∞ As x→ ∞, f(x) → ∞ As x→ -∞, f(x) → -∞

A sample of 14 squirrels were found to have an average weight of 9.8 ounces with a sample standard deviation is 0.30. Use this data to find the 95% confidence interval of the true mean weight. (9.59, 10.01) (8.92, 10.68) (9.63, 9.97) (9.72, 9.88)

The expression is given in standard form. Rewrite it in factored form. If it cannot be rewritten in factored form, write "cannot be done." p² + 18p-40 a (p-20)(p+2) b (p+20)(p+2) c (p+20)(p-2) d (p-20)(p-2)

The original 24 m edge length x of a cube decreases at the rate of 5 m/min. a. When x = 5 m, at what rate does the cube's surface area change? b. When x = 5 m, at what rate does the cube's volume change? a. When x = 5 m, the surface area is changing at a rate of m²/min. (Type an integer or a decimal.)

A long year-end status report for work is 82 pages long. You need to print 19 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.99 each. Give your answer to the nearest cent, only for the paper you use (partial reams are OK)

Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 15 + 110x -16x² can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.)

You randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 39 (inclusively). What is the probability of selecting an 18 both times?

Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4? -5 with multiplicity 2 and 1/3 with multiplicity 4 5 with multiplicity 2 and 1/3 with multiplicity 4 -5 with multiplicity 2 and 0 with multiplicity 4 5 with multiplicity 2 and 0 with multiplicity 4

Brandon is analyzing the profits from two of his restaurant locations. The first location showed a profit of $3,000 in the first week of the year but has a showed a steady decrease in profits of 1.5% each week since then. His second location showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then. Which system of equations can Brandon use to determine the number of weeks, x, until the profits, y, from the two locations are the same? A. y = 3,000 (1.015)^x y = 1,500 (1.012)^x B. y = 3,000(0.985)^x y = 1,500(1.012)^x C. y = -3,000 (1.015)^x y = 1,500(1.012)^x D. y = -3,000(0.985)^x Y = 1,500/(1,012)^x

A tire company tested a particular model of super radial tire and found the tires to be normally distributed with respect to wear. The "average" (mean) tire wore out at 59,000 miles, and the standard deviation was 2500 miles. a. If 2000 tires are tested, about how many are likely to wear out before 54,000 miles? b. What if the company wanted to guarantee 55,000 miles? What percent of the tires are likely to wear out before 55,000 miles? In this case, you cannot get an "exact" answer. What could you do to increase the accuracy of your estimate?

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p? A) 0.88p B) p / 0.88 C) (0.8) (1.08) p D) p / (0.8) (1.08)

Complete this expression. Assume that any variables are not equal to zero. z⁰ = Simplify the following expression completely. (5w+2)⁰ = Simplify the following. 3⁰ = Simplify the following. 0⁴ =

Suppose you and your brother each invest $5000 in a bank account. Both banks offer 6.5% annual interest. However, your brother's account is compounded annually, while yours is compounded monthly. a. How much do each of you have in your accounts after 3 years? b. How much more is your account worth than your brother's after 100 years? Find the Absolute difference (one is this many dollars more than the other) and the relative difference (one is this percent more than the other). c. What is the r ='annual percentage yield' for the account that is compounded monthly?

A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 96% confidence? 672 1142 336 571

An insurance company will insure a $220,000 home for its total value for an annual premium of $510. The company spends $30 per year to service such a policy, and the probability of total loss for such a home in a given year is 0.001. Assuming that either total loss or no loss will occur, what is the company's expected annual gain (or profit) on each such policy? -$220 $260 $290 $210

Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right. Column A Column B 1. x²-8x-20 a. Prime 2. x²+8x-20 b. (x-2)(x+10) 3. x² - x-20 c. (x-10)(x + 2) 4. x²-9x-20 d. (x - 5)(x+4)

The parent cosine function is shifted 5 units left, then vertically stretched by a factor of 4 and shifted up 2 units. Which statement is true about the graph of the transformed function? A. The midline is y = 2. B. The midline is y = 4. C. The midline is y = 8. D. The midline is y = 5.

The monthly rent for a pizza parlor is $1,200. The average production cost per pizza is $6.75. The monthly expenses for the pizza parlor are given by the function E(x) = 1,200 +6.75x, where x is the number of pizzas sold. For x pizzas sold, the pizza parlor's revenue is given by the function R(x) = 12.5x The monthly profit of the pizza parlor is the difference between its revenue and its expenses. Which function represents the monthly profit, P(x) ? A. P(x) =5.75x + 1,200 B. P(x) = 1,200 + 19.25x C. P(x) = 6.25x - 1,200 D. P(x) = 5.75x - 1,200

Betty has a checking account and a non-interest-bearing savings account. Function Crepresents her checking account balance, where x is the number of months. Function S represents her saving account balance. C(x) = -|240x -140| + 1,400 S(x) = 450x + 100 Which function represents Betty's total account balance, T(x)? A. T(x) = -|240x - 140| + 450x + 1,500 B. T(x) = -|240x - 140| + 450x + 1,400 C. T(x) = |240x + 140| +450x + 1,500 D. T(x) = -|240x - 140| +450x + 1,300

The function h defined by h(t) + (49+4.9t) (10-t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. From what height is the object dropped? a 500 b 490 c 480 d 460

Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank). (4 points)

A piece of cardboard is being used to make a container that will have no lid. Four square cutouts of side length h will be cut from the corners of the cardboard. The container will have a square base of side s, height h, and a volume of 80 in³. Which is the correct order of steps for finding minimum surface area A of the container? s²h = 80 and A = s² + 4sh I. A'=2s - 320/s² II. 0=2s - 320/s² III. A = s² + 320/s² s = 5.429 in and h = 2.714 in I, III, II III, I, II III, II, I I, II, III

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road, (x² + 3) miles downhill, and (x-7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested? (2 points) a. 3x²-4 b. 3x² +10 c. x²+2x-4 d. x²+2x+10

Answer the following. (a) The total surface area of Asia is approximately 17,200,000 square miles. Write this number in scientific notation. (b) The signal from a certain satellite takes approximately 4.1 x 10^-2 seconds to reach Earth. Write this number in standard notation.

A company that manufactures and ships canned vegetables is designing boxes in the shape of square prisms to meet specific requirements. The vegetables are packed into cans that are 2.5 inches in diameter and 4 inches in height. Company regulations state that boxes must be filled with two layers of 16 cans each, and be completely closed with no overlapping material. What is the smallest amount of cardboard needed to meet the company's requirements. They will need at least inches of cardboard. square

To find the distance AB across a river, a distance BC= 357 meters is laid off on one side of the river. It is found that B=115°11' and C = 11°20'. Find AB. The distance AB across the river is (Do not round until the final answer. Then round to the nearest whole number as needed.)

Molly starts an IRA (Individual Retirement Account) at the age of 32 to save for retirement. She deposits $450 each month. The IRA has an average annual interest rate of 8% compounded monthly. How much money will she have saved when she retires at the age of 65? Round your answer to the nearest cent, if necessary. Answer

Find an and a5 for the following geometric sequence. a1= 162, r=-3

Consider the curve given parametrically by x=4-t², y = t³ - 3t. (a) List all of the points (x, y) where the tangent line is horizontal. (b) List all of the points (x, y) where the tangent line is vertical.

Find the present value of the ordinary annuity. Payments of $40,000 made semiannually for 12 years at 4.2% compounded semiannually A. $674,532.00 B. $741,616.00 C. $751,336.00 D. $748,056.18

A circle has the equation x² + y²-3x+6y + 9 = 0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is. (Type an ordered pair, using integers or fractions.) The radius of the circle is. (Type an integer or a fraction.) (b) Use the graphing tool to graph the circle. (c) What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for

The half-life of radium-223 is approximately 11.43 days. How much of an 8 gram sample of radium-223 would remain after 3 days? Round to three decimal places.

A spinner is divided into 15 identical sectors and labeled 1 through 15. How many spins are expected for a multiple of 4 to be spun 7 times? Select from the drop-down menu to correctly complete the sentence. The spinner is expected to have to spin approximately Choose... times for a multiple of 4 to be spun 7 times.

Where is the function defined by f(x)= In (x) increasing? Where is f(x) decreasing? Where is the tangent line horizontal? Where is f(x) increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The function is increasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing. Where is f(x) decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The function is decreasing on the interval(s). (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never decreasing. Where is the tangent line horizontal? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The tangent line of the function is horizontal at x = (Use a comma to separate answers as needed.)

Two number cubes are rolled for two separate events: Event A is the event that the sum of numbers on both cubes is less than 10. Event B is the event that the sum of numbers on both cubes is a multiple of 3. In terms of a reduced fraction, find the conditional probability of B given that A occurs first.

At the beginning of an experiment, a scientist has 304 grams of radioactive goo. After 180 minutes, her sample has decayed to 19 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 14 minutes? You may enter the exact value or round to 2 decimal places.

If the alternator-to-engine drive ratio is 2.35 to 1, what rpm will the alternator have when the engine is idling at 500 rpm? Hint: Use a direct proportion. The alternator will have rpm when the engine is idling at 500 rpm. (Type a whole number or a decimal.)

Perform the indicated operation. Note that the denominators are the same. Simplify the result, if possible. (x² 1 / x² - 4x - 5) - (34 -2x / x² - 4x - 5 ) -

A man buys a car for $39,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $600 for 60 months, how much must he put down? (Round your answer to the nearest cent.) $

A random sample of 16 light bulbs has a mean life of 650 hours and a standard deviation of 32 hours. Assume the population has a normal distribution. Construct a 90% confidence interval for the population mean. (Answer in 2 decimal places.)

Complete the sentence below. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis.

Sandi weighs 145 lb, but she has started a new diet plan that promises she will lose 3 lb per month every month until she reaches her goal weight. Write a linear equation that describes how much Sandi weighs, V, each month, and then use your equation to find out how many months it will take her to get to 115 lb. Use X to denote the number of months since Sandi started her new diet. The linear equation that describes how much Sandi weighs each month is =

Country A has an exponential growth rate of 3.6% per year. The population is currently 4,957,000, and the land area of Country A is 27,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land? This will happen in year(s). (Round to the nearest integer.)

The following diagram is a rough sketch of a storage shed. The owner needs to know the area of the roof so that he knows how many roof shingles to purchase. The angle between the two edges of the roof (the gable) is 110°. The roof panels could be described as the quadrilateral DHKC and DHGE. The front has a width of 12 ft and the width of the side is 28 feet. The triangle CDE is an isosceles triangle. QUESTION: Find the area of the two quadrilaterals that represent the roof AND explain how you were able to determine the area.

The following equations define x = = f(t) and y = g(t) implicitly as functions of t. x³ - 2²2² = -17, 5y³ + 3t² = 67, Find the slope of this curve at the point on the curve associated with t = 3. Slope = Σ

Use properties of logarithms to rewrite the given expression as the logarithm of a single quantity, then enter that single quantity in the answer box to complete the expression. 2 logb (x) + 2logb (y) logb( )