Basic Math Questions and Answers

You plan to bake "apple crisp" for a dinner party you are hosting. Your recipe serves four people. The recipe calls for teaspoon of cinnamon. How much cinnamon will you need if make the apple crisp large enough to serve ten people? Please use an algebraic approach to determine your solution. you 4

S Evaluate the integral 2 40 x² + 4 -dx. Your answer should be in the form k, where k is an integer. What is the value of k? Hint: k = (b) Now, lets evaluate the same integral using power series. First, find the power series for the function 40 f(x): ao || - x² + 4 S. S should be an infinite series. What are the first few terms of S ? a1 = a2 = darctan(x) dx a3 = a = 1 x² + 1 - . Then, integrate it from 0 to 2, and call it

A boy weighs a pounds. His younger sister weighs 53 pounds less than him. His father weighs four times as much as his sister. A simplified expression that represents the father's weight (in pounds) is

A financial advisor recommends that a client deposit $2700 into a fund that earns 7.5% annual interest compounded monthly. What will be the value of the investment after 9 years? Use the compound interest formula P = A(1 + i)", where A is the original value of an investment, i is the interest rate per compounding period, n is the total number of compounding periods, and P is the value of the investment after n periods. Round to the nearest cent.

A 40-year-old man in the U.S. has a 0.247% risk of dying during the next year. An insurance company charges $250 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar. Expected Value: $ for the year

Find and simplify each of the following for f(x) = 5x² − 7x + 6. (A) f(x + h) (B) f(x+h)-f(x) (C) f(x+h)-f(x) h (A) f(x + h) = (Do not factor.) (B) f(x+h)-f(x) = (Do not factor.) f(x+h)-f(x) h (C) a (Do not factor.)

This exercise uses the radioactive decay model. If 250 mg of a radioactive element decays to 230 mg in 48 hours, find the half-life of the element. (Round your answer to the nearest whole number.) hr

16. Adrienne answered all 21 multiple-choice questions correctly on her science test. If her teacher decided to let one of the questions count as a bonus, worth the same number of points as the other problems on the test, what was Adrienne's test score? Write your answer as a decimal and as a percent.

A plumber needs to cut pipe into short sections for a project. The plumber needs meter for each piece that is cut. Draw a picture to show how many nieces of pipe will be cut from a pipe that is 10 meters long.

Florence School's spring festival is coming up, and Ms. Gardner is in charge of ordering the seed kits again. She knows she ordered 5 cases of seed kits last year but can't remember how many kits come in a case. When she checks the records, Ms. Gardner finds that the school used 396 of the seed kits last year and had 54 left over after the festival. Which equation can Ms. Gardner use to find how many seed kits, s, come in each case? 5s 396 = 54 - 5(s 396) = 54 - 396(s 5) 54 - 396s 5 54

Jada has $200 to spend on flowers for a school celebration. She decides that the only flowers that she wants to buy are roses and carnations. Roses cost $1.45 each and carnations cost $0.65 each. Jada buys enough roses so that each of the 75 people attending the event can take home at least one rose. a. Write an inequality to represent the constraint that every person takes home at least one rose. b. Write an inequality to represent the cost constraint.

At noon, there are 700 juniors and 1,100 seniors at a college fair. After 12:00 p.m., 20 juniors arrive every 15 minutes and 45 seniors leave every 15 minutes. What is the ratio of juniors to seniors at 2:00 p.m. in fraction form? Provide your answer below:

Which of the statements are true? 6 x 326 (3+2) = 6 (3) +6 (2) 3x 87-3 (80 + 7) = 3 (80) +3 (7) 12 (48) 12 (40 + 8) = 1 (40) + 2 (8) O14 (75) 14 (70+5) = 14 (70) + 14 (5) 9 (56) 9 (50+60) = 9 (50) + 9 (60) #

Drag each tile to the correct box. Match the text structure to the appropriate author's purpose. description problem-solution cause-effect to describe important facts and details about the Declaration of Independence to recount why students can no longer carry backpacks and the impact it has on students to inform readers about the trouble with excessive screen time and possible ways to reduce it 10

42. The radius of the Ferris wheel's circular path is 40 ft. If a "ride" of 12 revolutions is made in 3 minutes, at what rate in feet per second is the passenger in a cart moving during the ride? Merideth Book/Shutterstock

5. MANUFACTURING It takes 3 hours to build an arm chair and 2 hours for a side chair. Finishing an arm chair requires 2 hours, while a side chair requires 1 hour. There are 18 hours available for building and 10 hours available for finishing. Set up and solve a system of equations to determine how many of each chair can be made.

A tennis player keeps track of the number of successful first serves he makes. During the first 8 service points of a game, only 2 of his first serves are playable, so his first serve percentage is 25%. How many more consecutive successful first serves must he have to raise his first serve percentage to 60%?

You roll a standard die. (Enter your answers as comma-separated lists.) (a) What are the possible outcomes? (b) What are the favorable outcomes for the event of rolling an odd number? (c) What are the favorable outcomes for the event of rolling a number less than 3?

Complete the square to form a true equation. x² x2 2 z(¯¯¯ + x) =¯¯¯¯ + x ² + z( + x) = + x² 2 (Type a simplified fraction.)

There are three $20 bills, six $10 bills, seven $5 bills, and four $1 bills in your wallet. You select one bill at random. What is the expected value for this experiment? $ Need Help? MY NOTES Read It AS

Molly Hamilton deposited $70,000 at Bank of America at 20% interest compounded quarterly. What is the effective rate (APY)? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest hundredth percent.)

7. Jennifer wants to borrow $20,000. Her bank offers a 7.1% interest rate. She can afford $500 a month for loan payments. What should be the length of her loan to the nearest tenth of a year?

Part 3: Hitting the baseball over the lights Meanwhile at the ballpark Juan was practicing his hitting while talking to the girls standing around watching. He started telling them how he hit the ball over the 50 foot light tower yesterday. The girls were unsure that he really did that. The formula for this hit is: h(x) = -16x² + 60x+4 where h is the height of the ball and xis the number of seconds the ball is in the air. A. How can Juan provide proof to the girls that he actually hit the ball over the tower? I B. How high did Juan actually hit the ball?

The function f(x) = (2)(1.0)+x(0.5)/2+x models the concentration of pineapple when 2 gallons of pineapple juice are added to x gallons of another juice. Find the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice. Give the answer as a percent but do not include the percent sign (%).

Travis borrowed $5,000 at an interest rate of 1.10% p.m. for 6 months. Calculate the maturity value of the loan at the end of the period. No written response required.

The following table shows the distribution of family size in a certain U.S. city Family Size 234567 What is the expected number of family members for a family in this city? 6.1 0.442 4.5 Probability 0.405 0.239 0.203 0.097 0.040 0.016 3.2

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 115 miles per hour. The westbound train travels at 95 miles per hour. How long will it take for the two trains to be 294 miles apart? Do not do any rounding. hours

Bank A is lending money at 5.35% interest compounded quarterly. The rate at Bank B is 5.4% compounded annually, and the rate at Bank C is 5.3% compounded monthly. Which bank will you pay the least interest? Choose the correct answer. Bank B Bank C Bank A .……..

(1 pt) The production rate rifor an oil well in barrels/day is modeled by r(t) = 190e-0.2 where fl is the number of years the well has been in production. Find the total oil production in the first 5 years of operation. Total production = barrels

A small lake is stocked with a certain species of fish. The fish population is modeled by the function 10 P = 1+ 4e-0.4t where P is the number of fish in thousands and t is measured in years since the lake was stocked. (a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 5000 fish? (Round your answer to two decimal places. yr

A couple just had a baby. How much should they invest now at 5.7% compounded daily in order to have $35,000 for the child's education 17 years from now? Compute the answer to the nearest dollar. (Assume a 365-day year.)

Groom Lawn Equipment pays Kim Jones a $1520 monthly salary plus a 15% commission on merchandise she sells each month. Assume Kim's sales were $83,100 for last month. Calculate the following amounts: 1. Amount of Commission: 2. Gross Pay: $1 ?

A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly. (a) Find the amount after 3 years? (Round your answer to the nearest cent.) (b) How long will it take for the investment to double? (Round your answer to two decimal places.)

Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. A) Yes, because the sum of any two side lengths is greater than the third side length. B) Yes, because the sum of all three side lengths is greater than 20. C) No, because the third side length is greater than the sum of the other two side lengths. D) No, because 4 + 8 is greater than 10.

1.7.PS-16 A company's stock began the day at $30.12 per share. That price drops by $1.59 each hour. a. What is the price per share after 4 hours? b. What will it be after 21 hours if this rate continues? c. Explain what the signs of the answers mean in this context. OA. The price per share after 4 hours is $23.51. OB. The price per share after 4 hours is $23.76. OC. The price per share after 4 hours is $3.77. OD. The price per share after 4 hours is $3.27.

Solve the system of equations by graphing: y = 2x8 Y=2-6 First graph each line, then place a dot indicating the solution to the system.

Match each exercise with the first step needed to perform the operation. Do not actually perform the operation. x+1 X-1 X X Choose the correct answer below. ***** OA. Multiply the numerators and multiply the denominators. B. Multiply the first rational expression by the reciprocal of the second rational expression. C. Subtract the numerators. Place the difference over a common denominator. D. Multiply the second rational expression by the reciprocal of the first rational expression.

Given sets X, Y, Z, and U, find the set Xn(X-Y) using the listing method. X={e, b, g, a) Y-{e, d, b) Z-{d, b, f, g, c) U-(a, b, c, d, e, f, g Xn(X-Y)={ (Use a comma to separate answers as needed.) www

The function V(r) = πr³ can be used to find the volume of air inside a basketball given its radius. What does V(r) represent? O the radius of the basketball when the volume is V the volume of the basketball when the radius is r the volume of the basketball when the radius is V O the radius of the basketball when the volume is r

Find the equation of the line perpendicular to the given line and passing through the given point. y=-4x+2; (-1,4) Enter the correct equation in the box.

Explain how a cardinal number formula can be derived for the case where three sets occur. Specifically, give a formula relating n(A UBUC) to n(A), n(B), n(C), n(An B), n(An C), n(B n C), and n(A n B nC). Illustrate with a Venn diagram. Extend the procedure for cardinality from three sets to two sets. Which of the following formulas does this give? A. n(AUBU C) = n(A) + n(B) + n(C) - n(An B)-n(An C)- n(B nC) B. n(AUB UC) = n(A) + n(B) + n(C) n(An B)-n(An C)- n(B nC) + n(An B nC) C. n(AUB UC) = n(A) + n(B) + n(C) - n(An B)- n(An C)- n(B nC) - n(AnBnC) D. n(A UBUC) = n(A) + n(B) + n(C)

Question 6 of 10 Which statement is an inference about The Odyssey? A. The Cyclops reflects negative cultural values of ancient Greece. B. Odysseus escapes the Cyclops through trickery. C. The Odyssey is an epic poem retold by generations. D. The Odyssey was composed by Homer around 750 BC. SUBMIT

A radioactive substance has a decay rate of 0.073 per minute. How many grams of a 120 gram sample will remain radioactive after 30 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.

A chemist is estimating the volume of a solution in a test tube. The actual volume of the solution is 27.2 ml. The chemist's estimate is 30 ml. Find the absolute error and the percent error of the chemist's estimate. If necessary, round your answers to the nearest tenth.

Match each equation on the left with its solution on the right. No answer on the right will be used twice. 3x + 2(x-4)= 4(x - 1) + x x = 2 4x + 2(x-4)= 8(x - 1) - 2x 3x + 2(x-4)= 4(x - 1) - x 4x + 2(x-4)= 4(x - 2) + x No solution All real numbers x=0

= (1 point) Solve for all solutions to the trigonometric equation 1 - sin² (0) - 3 cos² (0) = = -0.7 on the interval [0, 2π]. Find exact answers if possible, and enter your answer as a comma separated list.

13. DETAILS LARMPMT1 16.2.018. MY NOTES You roll a pair of six-sided number cubes, numbered 1 through 6. What is the probability of rolling two odd numbers? (Enter your probability as a fraction.) Need Help? Read It ASK YOUR TEACHER

0 Finish solving the triangle: A . ZA= 64° ZB= 55° LC= b degrees a = b= C= 7 C Enter your answer as a decimal value. • You must be accurate to at least 3 decimal places. . Note that for these problems, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

4) In the early spring, the trout at Big Blue Lake swim at a depth of 30 feet below sea level. When the lake warms up in the summer, the trout swim 20 feet deeper than that. At what position relative to sea level do the trout swim in the summer? Submit feet

Match the given exercise with the first step needed to perform the operation. Do not actually perform the operation. 2/a * 3/(a+6) Choose the correct answer below. ***.. OA. Multiply the first rational expression by the reciprocal of the second rational expression. B. Find the LCD. Write each expression as an equivalent expression with the LCD as the denominator. C. Subtract numerators. Place the difference over a common denominator. D. Multiply numerators and multiply denominators.