Basic Math Questions and Answers

The average electric bill from Duke Energy is $147 with a standard deviation of $32. What is the probability that the bill will be less than $100? 93% -7% 17% 10%

Suppose it is estimated that 14% of American women are currently on a diet. A researcher would like to test this claim, so he sets up a simple random survey. He asks 200 women if they are on a diet and 39 said yes. Conduct a one-proportion z test to determine if the percent of women on diets is not 14%

The following equation: C 45x + 6900 gives the total cost, in dollars, to produce a units of a product at a factory. If the monthly operating budget of the factor is $40200, how many units can be produced there in that month? Answer: In that month,units can be produced for $40200.

Five players agree to divide a cake fairly using the last diminisher method. The players play in the following order: Anne first, Betty second, Cindy third, Doris fourth, and Ellen last. In round 1, Ellen is the only diminisher In round 2, Betty and Cindy are the only diminishers In round 3, there are no diminishers Which player gets her fair share at the end of:

Solve: 5 + x = 52/3 x = 12/3 x= 37/3 x=57/3

The probability that it will snow on the last day of January is 85%. If the probability remains the same for the first eight days of February, what is the probability that it will snow at least five of those days in February?

Find the value of the expression (b + 3) (b2-5b + 7) when b = -3. 150 100 0

A store owner has these assets: Cash, $4,760; Merchandise Inventory, $78,200; Equipment, $25,600; Supplies, $1,240. One bill of $15,070 and another bill of $7,213 are owed. How much is the owner's capital?

On a map, the distance between two cities is 2.4 inches. The two cities are actually 768 miles apart. On this same map, what would be the distance between two cities in miles that are 4.8 inches apart on the map? A. 1536 miles B. 1600 miles C. 1443 miles D. 1564 miles

Donna bought a candy bar for $1.50. She paid with nickels and dimes. She used 21 coins in all. How many nickels (n) and how many dimes (d) did she use? n+d=21 .05n+.10d=1.50

On a world globe, the distance between City A and City B, two cities that are actually 10,900 kilometers apart, is 12.7 inches. The actual distance between City C and City D is 1600 kilometers. How far apart are City C and City D on this globe? City C and City D are inches apart on this globe. (Type an integer or decimal rounded to the nearest tenth as needed.)

Find the value of the expression 2x³-5xy + 2y when x = 2 and y = 3. -8 48 52

Find the 5th term in the expansion of (x+3). 1265x 2835x³ 945x² 2835x² 20 pts

Jeanne has $12.50 in her bag. How much money does she need to buy a game that costs $72.60? $60.10 $84.10 $85.10

A machine fills soda bottles according to a normal distribution with a mean of 590 milliliters and a standard deviation of 5 milliliters. If the machine fills 500 soda bottles, how many would be expected to have between 580 and 600 milliliters of soda? 340 590 475 499

4.75x = 25. Solve for x. x=10/19 x = 25/6 x =100/19

The sales tax rate in Fort Worth, Texas, is 8.25%. Find the tax charged on a purchase of $26.39. The tax charged on the $26.39 purchase is $ (Simplify your answer. Type an integer or a decimal. Round to the nearest cent if needed.)

Larkin and Mazern are partners. Their investments are $50,000 and $30,000, respectively. They share income in proportion to their investments. The net income last year was $53,600. What amount did Larkin receive?

A cylinder-shaped container is used to store water. The container has a height of 6 feet and a diameter of 3 feet. About how much water is in the container when it is 3/4 full? A. 42 cubic feet B. 32 cubic feet C. 127 cubic feet D. 14 cubic feet

Simplify the expression: 6ac + 2a(b + c). 2 ac-8 ab 8 ac + 2 ab 2 ac+8 ab

An expression 19.95 + 0.05x is given and the value of x is given as 50. Find the value of the expression. 24.51 32.46 22.45

The expression 1.5 1.09 models the housing costs, in thousands of dollars, for summer term t years since Chinedu applied to his college. What does 1.09 represent in this expression? Choose 1 answer: Chinedu applied to his school 9 years ago. The summer housing costs were $1,090 the year that Chinedu applied to his college. The summer housing costs increase by 9% each year. Show Calculator

What is the factored form of m² - 6m + 8? (m-4)(m - 2) (m-4)(m + 4) (m-4)(m + 2)

Bob throws a ball straight up with an initial speed of 52 feet per second from a height of 7 feet. (a) Find parametric equations that describe the motion of the ball as a function of time. (b) How long is the ball in the air? (c) When is the ball at its maximum height? Determine the maximum height of the ball. (d) Simulate the motion of the ball by graphing the equations found in part (a). Assume Bob stands at horizontal position 0, and use g = 32 ft/sec/sec.

Find the numerical value of the expression if x = 5. 7x - 19/3x

Simplify: m²-9m/m-6+ 18/m-6 m-3 m²-9 m+ 18/m-6 m+3

The Afton Star charges $35 per column-inch for advertising. You want to place an ad that is 3 columns wide and 5 inches deep. Find the total cost for a 5-day advertising campaign. Thein investments are $50.000 and

Find the value of the expression (x²-4)/3 x when x = 5. 1.4 1.0 1.1

Which statement is true about the x-intercepts of the parent sine function? The sine function has x intercepts at - and since the unit circle has y values equal to 1 at those angles. The sine function has x intercepts at and since the unit circle has x values equal to 0 at those angles. The sine function has x intercepts at and since the unit circle has y values equal to 1 at those angles. The sine function has x intercepts at 0 and π since the unit circle has y values equal to 0 at those angles.

Find the value of the expression 6x^4 + 5x³+4x² + 6x - 5 when x = ½. 0 -10 10

Tom has a credit card with an APR of 24.95% and a current balance of $13,650.35. He wants to pay it off in 3 years. What will Tom's monthly payment be? (Remember a credit card is compounded monthly.) Round to the nearest dollar.

A 75-gallon tank initially holds 35 gallons of salt water containing 6 pounds of salt. Suppose salt water containing 5 pounds of salt per gallon is pumped into the top of the tank at the rate of 8 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 4 gallons per minute. Let S(t) represent the number of pounds of salt in the vat after t minutes. (A) Write the DE model for the time rate of change of salt in the vat. Also include the initial condition. dS/ dt= S(O)= (B) Solve the initial value problem to find the amount of salt in the vat as a function of time. S(t)= (C) How much salt is in the tank when the tank is full? pounds.

On a test of 78 items, Pedro got 93% correct. (There was partial credit on some items.) How many items did he get correct? incorrect? Pedro got___items correct. (Type a whole number or decimal rounded to two decimal places as needed.)

When the Dragons have lost their most recent game, fans buy 200 tickets. For each consecutive win the Dragons have, the number of tickets fans buy increases by a factor of 1.1. Which expression gives the number of tickets fans buy after 4 consecutive wins? Choose 1 answer: 200 1.1 1.1 1.1.1.1 200 (1.1+1.1+1.1+1.1) 200+1.1 1.1.1.1.1.1 200+1.1+1.1+1.1+1.1

A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour. Write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens. A(t) =

Use the compound interest formulas A = P(1 + r/n) ^nt and A= Pe^rt to solve. Find the accumulated value of an investment of $4000 at 12% compounded continuously for 8 years. $10,161.41 $10,397.09 $10,446.79 $10,435.24

Suppose a bank offers you a 10% interest rate on a 20-year mortgage to be paid back with monthly payments. Suppose the most you can afford to pay in monthly payments is $700. How much of a mortgage could you afford? $72,537.23 $75,732.25 $76,237.53 $76,375.32

The distance from Springfield to Franklin is 395 miles. To find the time it will take for a train to trave from Springfield to Franklin, use the expression d/s, where d represents distance and s represents speed. Find the time if the train travels at a speed of 79 miles per hour. 4 hours 5 hours 3 hours

To get full credit for the application problems, you must define a variable, write and solve an equation (or system of equations), and write a sentence answer. One pump can fill a tank in 45 minutes and another pump can fill the same tank in 30 minutes. How long would it take to fill the tank using both pumps? (5 points)

ΔABC is dilated by a scale factor of 2 to create ΔDEF, where ΔABC ΔDEF. Which of the following statements are true? 1 m∠A= m∠D II DE = AC III. The area of ΔDEF is 4 times as large as the area of ΔABC A I only B. I and II only C.II and III only D.I. II, and III

Suppose that a company's daily sales volume attributed to an advertising campaign is given by the following equation. S(t)=4/t+9 - 28/(t + 9)² (a) Find how long it will be before sales volume is maximized. t= (b) Find how long it will be before the rate of change of sales volume is minimized. That is, find the point of diminishing. returns. t=

A woman expects to have $10,000 in 4 years to buy a pair of earrings. She plans to create a sinking fund by depositing an amount every 6 months. If the fund earns 16% interest compounded semi-annually, find the semi-annual deposit and construct a sinking fund schedule.

Simplify the given expression: 9/x+9 - 9/ x-9 2x²/x²+81 -162/x^2-81 2x²+(-162)/x²+81

A small city had a population of 110000 in 2010. Concerned about rapid growth, the residents passed a growth control ordinance limiting population growth to 1.7% each year. If the population grows at this 1.7% annual rate, what will the population be in 2020? What is the maximum growth rate cap that will prevent the population from reaching 150000 in 2025?

An arrow is shot vertically upward from a platform 16 ft high at a rate of 191 ft/sec. When will the arrow hit the ground? Use the formula: h= -16r² + vot + ho (Round your answer to the nearest tenth.)

Isaiah reads articles about the insufficient savings of those in retirement and decides he needs to start saving now, even though he's in his 50s. He saves $500 per month for 15 years and earns 7% by investing in the stock market through an index fund. The value of his retirement account after 15 years will be $ How much of the toal did Isaiah contribute himself? $ How much mondy did Isaiah make through compounded returns in this investment account? $

3. Find the first three terms of the geometric sequence where the first term is 4 and the common ratio is 1/2 a₁ = 4, a₂ = 1, a3 =1/4 a₁ = 4 , a₂ = 9/2, a3 = 5 a₁ = 4 , a₂ = 8, a3 = 16 a₁ = 4 , a₂ = 2, a3 = 1

Let g(x) = ∫f(t) dt, where f is the function whose graph is shown. (a) Evaluate g(0), g(1), g(2), g(3), and g(6). g(0) = 0 g(1)=2 g(2) = 5 g(3) = 7 g(6) = 3 (b) On what interval is g increasing? (Enter your answer using interval notation.)

I arrive home to find that my 40 foot by 30 foot basement has 3 inches of water in it. a) If 1 cubic foot of water is about 7.48 gallons, how much water will I be pumping out of my basement? Express your answer rounded to the nearest tenth of a gallon. b) If I have a pump that can pump 450 gallons of water per hour, how long will it take to empty the basement? Express your answer rounded to the nearest tenth of an hour.

Examine this expression and answer the following questions: 4log8x + 3log8(2x-5)-7log8(x-3) (a) After you condense this into one logarithm, what would the exponent in the denominator be (in the bottom part of the fraction)? (b) After you condense this into one logarithm, what would the base of the logarithm be?