Basic Math Questions and Answers

Let a, b, c, d are an increasing A.P. with integer terms and d = a² + b² + c2², then Common difference of A. P. is 2 The value of a + 2b + 3c+4d is 10 The value of 4a + 3b+2c + d is zero Common difference of A.P. is 1

A particle is moving along a straight line such that the distance traveled (in feet) after t seconds is given by the function s(t) = 8t² + 40t. At t = 6 seconds, what is the velocity of the particle?

The water in a pool is evaporating at a rate of 3% per day. If the pool has 21,200 gallons in it today, how many gallons will it have in 10 days? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window) 2 Points

Karla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. If she plans to spend less than $150 for the dress, how many weeks will it take her to save enough money to buy any dress in her price range?

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 150 milligrams of Medication A with 45 milligrams of Medication B. However this week, the doctor said to only use 6 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

be worth more or less (including zero) depending on your answer. Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $8 per hour. She has $150 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 12 hours 18 hours 13 hours 12.5 hours

You and your classmates create 25 self-portraits to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the self-portraits, you need to sell each of the self- portraits for $1.00. When transporting the self-portraits to the auction, one of your parents accidentally drops three of the self-portraits in the street and they are run over by a school bus. What is the new minimum price you need to set for the remaining self-portraits in order to pay for the materials?

Kala paid $14.75 for a 2.12-pound bag of shrimp at one store. The following week, she paid $24.99 for a 3.77-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 2.12-pound bag: per pound Unit price for the 3.77-pound bag: per pound The better buy: The 2.12-pound bag The 3.77-pound bag Neither (They have the same unit price)

Find all zeros of f(x) = x³ + 2x² - 6x - 4. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

- Manuel bought 9 pounds of apples. He has eaten 3/4 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

Arianna invests $5500 in a new savings account which earns 5.6 % annual interest, compounded daily. What will be the value of her investment after 7 years? Round to the nearest cent.

A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at his precious damsel, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?

Find the average rate of change of f(x) = 2x² +5 over each of the following intervals. (a) From 4 to 6 (b) From 2 to 0 (c) From 0 to 3 (a) The average rate of change from 4 to 6 is. (b) The average rate of change from - 2 to 0 is (c) The average rate of change from 0 to 3 is

Explain what "80% confidence" means in a 80% confidence interval. What does "80% confidence" mean in a 80% confidence interval? OA. The confidence interval includes 80% of all possible values for the parameter. OB. The value of the parameter lies within 80% of a standard deviation of the estimate. OC. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 80%. The probability that it does not is 20%. OD. If 100 different confidence intervals are constructed, each based on a different sample of size n from the san population, then we expect 80 of the intervals to include the parameter and 20 to not include the parameter.

Situation: A 50 gram sample of a substance that's used to treat thyroid disorders has a k- value of 0.1113. N = Noe^-kt No initial mass (at time t = 0) N = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days Find the substance's half-life, in days. Round your answer to the nearest tenth. Enter the correct answer.

A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, S2, and $3, respectively. Fixed costs are $17,000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and $7, respectively. Next year, a total of 8000 units of all three products is to be produced and sold, and a total profit of $12,000 is to be realized. If total cost is to be $54,000, how many units of each of the products should be produced next year?

Enrico deposited $2000 in a savings account. Each month he will deposit an additional $25. Which kind of function best models the relationship between time and the total amount in the savings account? Choose 1 answer: Linear Exponential

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. Complete parts (a) through (g) below. (a) Construct a probability distribution for the random variable X, the winnings of each spin. x P(x) 35 -1 (Type integers or decimals rounded to four decimal places as needed.)

A machine is valued at $10,000. If the depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 4 years.

Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. f(x)=e8x

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) =