Basic Math Questions and Answers

The function y = -16x² + 36 represents the height y (in feet) of an apple a seconds after falling from a tree. Find and interpret the x- and y-intercepts. The x-intercept is x = This means the apple hits the ground after seconds. The y-intercept is y=. This means the apple fell from a height of feet.

Suppose there are two routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from Beaver Dam to Star Lake, and three routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Step 2: Choose a route from Step 3: Choose a route from Beaver Dam to Star Lake. There are 2__choices for step 1, 4__to Beaver Dam. (b) How many routes from North Point to Star Lake bypass Beaver Dam? choices for step 3. Thus, the answer is 32

Andrew Merrill, owns a mobile sandwich and pretzel stand. Andrew borrows $5,200 for 135 days at ,9% ordinary simple interest. What total will Andrew need to repay for both interest and principal? (Use a 360-day year.) $175.50 $5,300.50 $5,375.50 $5,373.10

Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.25% compounded quarterly. The annual percentage yield is %. (Do not round until the final answer. Then round to two decimal places as needed.)

A beverage company tested a new flavor of fruit drink on a random, representative sample of consumers. The company found that 47 percent of consumers surveyed liked the new flavor, with a margin of error of 6 percent. Which of the follow- ing is the most appropriate conclusion about how consumers in general will like the new flavor? A) More than half of consumers will dislike the new flavor. B) The researchers who conducted the sampling are between 41% and 53% certain that customers will like the new flavor. C.) It is likely that the percentage of consumers who like the new flavor will be between 44% and 50%. D.) It is likely that the percentage of consumers who like the new flavor will be between 41% and 53%

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? an 18250n - 750 an= 750n + 18250 an = 18250n + 750 an= -750n + 18250

In a piano recital, Toby has to perform one piece from each era of western classical music. There are eight pieces from the Baroque period, five pieces from the Classical period, and six pieces from the Romantic period to choose from. How many possible choices could Toby perform in his recital? 40 48 200 240

Using data starting with 1950 and projected to 2050, the number of women (in millions) in the workforce is given by the function P=0.79x+20.86, where x equals the number of years after 1950. (a) Find the value of P when x=65. Explain what this means. (b) What value of x represents 2030? Use the model to find the number of women in the workforce in 2030. (a) The value of P when x= 65 is million. (Type an integer or decimal rounded to two decimal places as needed.) What is the meaning of this value of P? A. The value of P represents the number of women who will join the work force between the years 1950 and 2015. B. The value of P represents the number of women in the workforce in the year 1965. C. The value of P represents the number of women who will join the work force between the years 1900 and 1965. D. The value of P represents the number of women in the workforce in the year 2015. (b) The value of x that represents 2030 is x = The number of women in the workforce in 2030 will be million. (Type an integer or decimal rounded to two decimal places as needed.)

Inverse variation can be applied in physics. The relationship between wavelength and frequency of light are closely related. The equation λv=c where λ is the wavelength, v is the frequency and c is the speed of light represents the relationship between wavelength and frequency of light. When written as an inverse variation equation, we can write λ=c/v or we can write v=c/λ In this formula, which variable represents the constant of variation k? Is it logical that this variable represents the constant of variation? Explain your answer.

You are going to survey a random sample of the 300 passengers on a flight from San Francisco to Tokyo. Name each sampling method described. a. Randomly generate 30 seat numbers and survey the passengers who sit there. b. Randomly select a seat position (right window, center, aisle, etc.) and survey all of the passengers sitting in those seats.

A youth organization collected nickels and dimes for a charity drive. By the end of the 1-day drive, the youth had collected $48.65. If there were three times as many dimes as nickels, how many of each type of coin was collected?

Which function translates each point on the graph of y = mx + b so that the slope of the segment from the original point to the translated point is 1/2 ? t(x)=1/2x+b t(x) = m(x-2) +b+1 h(z) = mx + b g(x) = m(x-2) +b-1

On a poultry farm eggs are packed in cartons. Each carton contains 12 boxes and each box contains 15 eggs of mixed size (small, medium and large). On the farm 1 out of 9 eggs is large and the packing machine selects the eggs randomly. Find the expected number of large eggs in a carton.

A 28-year-old man pays $223 for a one-year life insurance policy with coverage of $60,000. If the probability that he will live through the year is 0.9993, what is the expected value for the insurance policy? -$181.00 $59.958.00 $42.00 -$222.84

An investment grows at 24% compounded monthly. How many years will it take to do the following? (Round your answers to one decimal place.) (a) double (b) increase by 65%

There's one other alternative-one that takes both skill and courage: Forgoing any cradling action, grasp the cone more firmly between thumb and forefinger and extend the other fingers so that they are out of the way of the dripping from the bottom, then increase the waist-bend angle from twenty-five degrees to thirty-five degrees, and then eat the cone, allowing it to drip out of the bottom onto the ground in front of you! Experienced and thoughtful cone-eaters enjoy facing up to this kind of sudden challenge. What is the author's purpose for including this portion of "How to Eat an Ice- Cream Cone"? A. To entertain the audience with humor B. To appeal to the audience with emotion C. To inform the audience with facts D. To persuade the audience with language

The product of two numbers is to be minimized. The second number is eight more than twice the first. Call the first number "x." a) Write an equation for the product of the numbers with respect to the first number. (4 points) b) What is their minimum product? (2 points) c) What two numbers make this minimum product? (4 points)

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₁9, the 19-percentile. This is the temperature reading separating the bottom 19% from the top 81%. P19 = °C

You invest $2500 in an account at interest rate r, compounded continuously. Find the time required for the amount to double and triple. (Round your answers to two decimal places.) r = 0.0485 (a) double (b) triple

For the function f(x) = - 1/12x, construct and simplify the difference quotient f(x+h)-f(x)/ h The difference quotient for f(x) = - 1/12x is (Simplify your answer. Use integers or fractions for any numbers in the expression.)

A bicyclist rides 24 mi against a wind and returns 24 mi with the same wind. His average speed for the return trip traveling with the wind is 8 mph faster, than his speed going out against the wind. If x represents the bicyclist's speed going out against the wind, then the total time, t required for the round trip is given by t = 24/x +24/x+8 where t is measured in hours a) Find the time required for the round trip if the cyclist rides 12 mph against the wind b) Find the time required for the round trip if the cyclist rides 24 mph against the wind

The running lanes at the Emery Sears track at Bluffton College are 1 m wide. The inside radius of lane 1 is 33 m, and the inside radius of lane 2 is 34 m. How much longer is lane 2 than lane 1 around one turn? * (25 Points) 106.814 m 103.673 m 3.142 m 4.142 m

Jessica Cardenas has a sprinkler that has several varieties of coverage. The quarter-circle sprinkler head sprays water a distance of up to 20 feet from the head. What area will be covered by the spray of the quarter-circle sprinkler head to the nearest square foot? * (25 Points) 493 ft² 314 ft² 25 ft² 31 ft²

A 95 kg basketball player jumped in the air to secure a rebound. During the last step before jumping in the air, 1,792 N of ground reaction force was applied to the basketball player over a duration of 400 ms a.What is the average net vertical force during the jump? b.What is the impulse the basketball player experienced during the jump? c. What is the momentum the basketball player experienced during the jump? d. What is the basketball player's vertical velocity at the instant of takeoff? e. How high did the basketball player's center of mass rise during his jump?

The cost of renting a space for up to 400 people is a $700 flat fee. The cost of catering a dinner for x attendees is given by C(x) = 300+ 32x. Write an equation for the total cost, T(x), of putting on a prom if these are the only two expenses.

11 Mr. Davis and Ms. Lee saved the same amount of money. Mr. Davis spent $1,140 on a television and Ms. Lee spent $580 on a stand mixer. Ms. Lee then had 9 times as much money as Mr. Davis. How much money did Mr. Davis have at first?

For every three girls taking classes at a martial arts school, there are 4 boys who are taking classes. Suppose there are 236 boys taking classes at the school. Write a proportion that could be used to predict the number of girls taking classes at the school. Use x to represent the number of girls.

The cost of reserving a particular domain name is $21 up front plus $4.49 per month. Find the cost of reserving that domain name for the following:

a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x) = 2x² +3x, a = -2

For a given input value u, the function g outputs a value v to satisfy the following equation. -12u + 3 = 8v + 1 Write a formula for g(u) in terms of u. g(u) =

A mirror should be centered on a wall. The mirror is 36 inches wide and the wall is 18 feet wide. Which equation helps determine the distance x on each side of the mirror? A) X + 3 + x = 18 B) X = 18 + 3 C) X + 36 + x = 18 D) 3 + x + 3 = 18

27) A-Plus Advertising charges a fee of $27 plust $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-plus Advertising less than the cost at Print and More?

Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, the ends of these mats are right triangles. If the height of the mat is 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?

To rent a certain meeting room, a college charges a reservation fee of $14 and an additional fee of $4 per hour. The chemistry club wants to spend less than $50 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use / for the number of hours. Write your answer as an inequality solved for t.

Differentiate the function, and find the slope of the tangent line at the given value of the independent variable. f(x) = 5x + 4/x, x = -5 The derivative of the function f(x) = 5x + 4/x is The slope of the tangent line at x = -5 is

A company pays its sales people a base salary of $38,500 per annum plus a commission of 12% on all sales. Stephen, one of the company's salespeople, made sales worth $105,000 in his first year. a. Calculate the commission Stephen earned during the year. Round to the nearest cent b. Calculate the total salary Stephen earned during the year.

A store pays $39.27 for a quilt. The store marks up the price by 26%. What is the new price? Round your answer to the nearest cent: $

Identify the zeros and y-intercept for the following function graphed below. a. zeros: (0, -3), (0, 5); y-intercept: (90, 0) b. zeros: (-3, 0), (5, 0); y-intercept: (0, 90) c. zeros: (5, 0); y-intercept: (0, 90) d. zeros: (0, 90); y-intercept: (5, 0)

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 70 workers to build a 80 story building? It will take years

On the planet Golgafrincham there are two systems for measuring temperature. Using the Celia scale, water freezes at 0° C and boils at 50° C. Using the Furryhat scale, water freezes at 10° F and boils at 110° F. Both systems divide the temperatures in between into equal increments. Let x be the temperature in degrees Celia and y be the temperature in degrees Furryhat. a. Find a formula which converts temperatures measured in Celia into Furryhat. y(x) = b. Find a formula which does the inverse. c. What temperature is the same in both Celia and Furryhat?

A student has student loans of $96,000. He would like to pay it back in 10 years. (10 points) a) Calculate the monthly payments if his loan has a fixed APR of 8%. b) What is the total amount that the student paid for his college education (principal and interest)?

The average cost of a 4-year college education is projected to be $130,000 in 20 years. How much money should be invested now at 8% compounded quarterly to provide $130,000 in 20 years?

Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous f(x)= (2x-2) / (x2+2x-3) is discontinuous at x =

A student has student loans of $96,000. He would like to pay it back in 10 years. a) Calculate the monthly payments if his loan has a fixed APR of 8%.

For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. Result is Rational Result is irrrational reason (a) 2/11 + 17/19 (b) 16+√13 (c) 20 + 8/9 (d) √2+38

If y=ex is reflected about the x-axis, what is the formula for the resulting function? y = help (formulas)

Suppose that $10,000 is invested at an APR of 6% for 4 years. a) Determine the accumulated balance assuming that interest is compounded annually. b) Determine the accumulated balance assuming that interest is compounded monthly. c) Determine the accumulated balance assuming that interest is compounded continuously.

Patricia receives a gross pay of $1,850 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive. Round to two decimal places

Alexander, a sales representative at a jewelry store, receives a 1.50% commission for the first $12,000 in sales he makes, 3.50% for the next $25,000, and 6.50% thereafter. If he was paid $2,000.00 in commissions last month, calculate the amount of sales he made.

A school superintendent purchase a new car for $26,788. A. If the sales tax is 7.75%, find the amount of sales tax. The sales tax is B.The superintendent makes a $3000 down payment and the license fee is $145. Find the amount the superintendent must finance. The amount financed is C. Assuming the superintendent gets the loan for the amount in part B at an annual interest rate of 8.1% for 5 years, determine the superintendent's monthly car payment. The monthly payment is