Basic Math Questions and Answers

Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours of testing. Each soccer game requires 3 labor-hours of assembly and 1 labor-hour of testing. Each day there are 57 labor-hours available for assembly and 35 labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily output? Infotron should produce hockey games and soccer games

Reasoning Tommy earned $14.80 in interest after 4 years on a principal of $100. His simple interest rate is 3.7%. Jane earned $136.80 in interest after 3 years on a principal of $1,200. Her simple interest rate is 3.8%. Which bank would you rather use, Tommy's or Jane's? Explain your reasoning. Which bank would you rather use? A. Jane's because her bank accepted a smaller principal. B. Jane's because her bank offers a better interest rate. C. Tommy's because his bank paid more interest. D. Tommy's because his investment took less time.

Translate the sentence into an inequality. Nine subtracted from the product of 2 and a number is at most 15. Use the variable y for the unknown number.

Noah is solving an equation and one of his moves is unacceptable. Here are themoves he made. 2(x+6)-4 = 8 + 6x original equation 2x + 12-4 = 8 + 6x apply the distributive property 2x+8 = 8 + 6x combine like terms 2x = 6x subtract 8 from both sides 2=6 divide each side by x Which answer best explains why the "divide each side by x step" is unacceptable? A. When you divide both sides of 2x = 6x by x you get 2x² = 6x² B. When you divide both sides of 2x = 6x by x it could lead us to think that there is no solution while in fact the solution is x = 0. C. When you divide both sides of 2x = 6x by x you get 2 = 6x. D. When you divide both sides of 2x = 6x by x it could lead us to think that there is no solution while in fact the solution is x = 3.

What is the fourth step in construction of perpendicular bisector of the line segment AB? Draw a line segment using the ruler. Label it AB. Draw a line from X to Y. The line XY is the perpendicular bisector of the line segment AB. Without changing the compass setting, place the pointed end of the compass on B. Draw arcs above and below the line segment to cut the first two arcs. Mark the points where these arcs meet. Call them X and Y. Place the pointed end of the compass on A and draw arcs above and below the line segment.

Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 83? A) 80 B) 79 C) 81 D) 78

A Food Marketing Institute found that 29% of households spend more than $125 a week on groceries. Assume the population proportion is 0.29 and a simple random sample of 343 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.31. Round the answer to 4 decimal places.

A computer company makes desktop and laptop computers at factories in three states - California, Texas, and New York. The California factory produces 40% of the company's computers, the Texas factory makes 25% and the remaining 35% are made in New York. Of the computers made in California, 75% are laptops. Of those made in Texas and New York, 70% and 50%, respectively, are laptops. Find the following probabilities: P(computer is a laptop) 90% 65% 19.5% 75%

The test scores of the students in four classes are summarized below. Answer the questions about them. Class A: The mean score is 115 and the range of scores is 34. Class B: The mean score is 122 and the range of scores is 33. Class C: The mean score is 119 and the range of scores is 28. Class D: The mean score is 120 and the range of scores is 36. (a) Based on the information above, which class's scores have the most variability? Class A Class B Class C Class D (b) Based on the information above, which class has the lowest scores on average? Class A Class B Class C Class D X S ?

Boubacar and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.75 and a drink for $3.50. How much would it cost if they bought 6 bags of popcorn and 4 drinks? How much would it cost if they bought p bags of popcorn and d drinks? Total cost, 6 bags of popcorn and 4 drinks: Total cost, p bags of popcorn and d drinks:

The function h is defined as h (x) = 2x²-4 Find h (x+6).

10. Lin says that a solution to the equation 2x - 6 = 7x must also be a solution to the equation 5x - 6 = 10x. Write a convincing explanation about why this is true.

You want to buy a $197,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 6%? c) What will your monthly payments be if the interest rate is 7%?

Indicate whether the equation has no solution or is true for all real numbers. If neither is the case, solve for the variable. 10x 2(3 + 5x) = -6 A) 3/5 B) {xlx is a real number} C) 5/3 D) Ø

You want to buy a $209,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 5.85% interest for the rest. a) What is the amount of the down payment? b) What will the amount of the mortgage? c) The bank charges 2.5 points on the loan. What is the amount charged for points?

You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 6% interest. a) How big of a loan can you afford? $ b) How much total money will you pay the loan company? c) How much of that money is interest? SA

Think About the Process A restaurant customer left $2.20 as a tip. The tax was 7% and the tip was 20% of the after tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill? Which information is not needed to solve this problem? OA. The customer left $2.20 as a tip. B. The customer left a 20% tip. C. The tax was 7%. OD. All of this information is needed to solve the problem. The total bill is $

Which of the following is not a function for all values of x? f(x) = x³ f(x) = (-x)^1/2 f(x) = (-x)^1/3 f(x) = |-x|^1/2 f(x) = |-x|^1/3

Translate the sentence into an inequality. The sum of a number times 8 and 29 is greater than 23. Use the variable x for the unknown number.

2. Determine the smallest angle of rotation for each regular polygon to be mapped onto itself? a. Equilateral Triangle b. Square c. Regular Pentagon d. Regular Hexagon e. Regular Octagon f. Regular Nonagon g. Regular Decagon h. Regular Dodecagon

Michael participates in several motocross races. He has won 8 more silver medals than gold medals. The number of bronze medals he has won is half that of the silver medals. If he has won 27 medals in total, how many of each type of medal has he won?

Camden accepted a new job at a company with a contract guaranteeing annual raises. Camden's salary after working for n years can be determined using the equation S = 2000n + 55000. What is the slope of the equation and what is its interpretation in the context of the problem? The slope of the function is which represents

Find the compound amount and the amount of interest earned by the deposit below. $8,000 at 6.56% compounded continuously for 4 years. What is the compound amount? $ (Do not round until the final answer. Then round to the nearest cent.) What is the interest earned? (Do not round until the final answer. Then round to the nearest cent.) ****

A computer user has downloaded 24 songs using an online file-sharing program and wants to create a CD-R with 12-songs to use in his portable CD player. If the order that the songs are placed on the CD-R is not. important to him, how many different CD-Rs could he make from the 24 songs available to him? There are possible CD-R's.

Consider a home mortgage of $150,000 at a fixed APR of 6% for 15 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

What is the slope of the line that passes through the points (2, 0) and (1, 0)? Write your answer in simplest form.

A jar contains 32 red marbles numbered 1 to 32 and 32 blue marbles numbered 1 to 32. A marble is drawn at random from the jar. Find the probability of the given event. (Round to 4 decimal places) a) The marble is red. P(red) = b) The marble is odd-numbered. P(odd) = c) The marble is red or odd-numbered. P(red or odd) = d) The marble is blue or even-numbered. P(blue or even) =

Suppose you deposited $400 in a savings account 2 years ago. The simple interest rate is 2.6%. The interest that you earned in those 2 years is $20.80. Which of the following is/are true? r= 2.6% t = 400 p=2 t=400 A. I= 20.80 B. r= 2.6% C.p=2 D. t= 400 Which of the following is/are true? Select all that apply.

An investment is worth $2966 in 1992. By 1996 it has grown to $4894. Let y be the value of the investment in the year x, where x = 0 represents 1992. Write a linear equation that models the value of the investment in the year x. y = 4x+2966 y=482x+ 2966 y = -482x + 2966 y = -482x + 6822

Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes will it take for the two containers to have the same amount of water?

Color blindness About 8% of males are color-blind. A researcher needs some color-blind subjects for an experiment and begins checking potential subjects. a) On average, how many men should the researcher expect to check to find one who is color- blind? b) What's the probability that she won't find anyone color-blind among the first 4 men she checks? c) What's the probability that the first color-blind man found will be the sixth person checked? d) What's the probability that she finds someone who is color-blind before checking the 10th man?

Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. 5(4x-4)=23 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is (x|x is a real number). C. The solution set is . (Type an integer or a simplified fraction.)

The population of a country reached 317 million in August 2013. Write that number in scientific notation. 317 million = (Use scientific notation. Use the multiplication symbol in the math palette as needed.)

Helen and Reid are walking to their classes at Cedarburg College. Helen comes from her dorm room, walking at a speed of 4 miles per hour down a straight path. Reid comes from the gymnasium on the other end of campus, moving up the same path at 3 miles per hour. If they start out 3 miles apart, how long will it be before they meet? If necessary, round your answer to the nearest minute.

If possible, use the Law of Syllogism to make a conclusion. If it is not possible to make a conclusion, tell why. If the sum of the digits in a number is 9, then the number is divisible by 9. If a number is divisible by 9, then it is divisible by 3.

Jason is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. The equation P = 100+ 0.03x represents Jason's total pay on a day on which he sells a dollars worth of computers. What is the y-intercept of the equation and what is its interpretation in the context of the problem? The y-intercept of the function is which represents

Graph one polynomial function g(x) such that all of the following hold: a. g(x) has a zero at x = -1 with multiplicity 2 b. g(x) has a zero at x = 2 with multiplicity 1 c g(x) has a zero at x = 3 with multiplicity 1 d. There are no other zeros except for the ones stated above.

There is a sales tax of $6 on an item that costs $80 before tax. The sales tax on a second item is $11.25. How much does the second item cost before tax? $

Suppose that the population of some state in 2010 was P = 35 million and its annual percentage rate of continuous growth is R = 1.06%. (a) Write the formula f(x) = P e^rx, where r is in decimal notation, that models the population in millions x years after 2010. (b) Estimate the population in 2022. ..... (a) f(x) = (Use integers or decimals for any numbers in the expression.) (b) The population in 2022 will be approximately

Through how many radians will the hour hand on a clock rotate in (a) 14 hr? In (b) 4 hr? (a) In 14 hr, the hour hand on the clock will rotate radians. 7x/3 (Type an exact answer in terms of . Type an integer or a simplified fraction.) (b) In 4 hr, the hour hand on the clock will rotate radians. (Type an exact answer in terms of . Type an integer or a simplified fraction.)

The length of a rectangular deck is 4 times its width. If the deck's perimeter is 20 feet, what is the deck's area?

Mr. Jackson borrowed money from his bank and on his life insurance to start a business. His interest rate on the bank loan was 10%, and his rate on the insurance loan was 16%. If the total amount borrowed was $100,000 and his total yearly interest payment was $12,100, how much did he borrow from the bank?

Suppose the expression a(b)" models the approximate number of customers who applied for a credit card every month since a bank opened, where a is the initial number of customers who applied, b is the rate of Increase in the number of people who applied every month, and n is the number of months since the bank opened. If the expression below models the number of applicants for a credit card, what is the correct interpretation of the second factor? 27 (1.2) A There were 1.2 times as many customers who applied after the 4th month compared to the initial number of customers. B There were 4.8 times as many customers who applied after the 4th month compared to the initial number of customers. C There were 2.07 times as many customers who applied after the 4th month compared to the Initial number of customers. D There were 6.75 times as many customers who applied after the 4th month compared to the initial number of customers.

Laura and Martin obtain a 20-year, $90,000 conventional mortgage at 10.0% on a house selling for $110,000. Their monthly mortgage payment, including principal and nterest, is $869.40. Determine the total amount they will pay for their house. b) How much of the cost will be interest? c) How much of the first payment on the mortgage is applied to the principal?

The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age, 220-a. Your exercise goal is to improve cardiovascular conditioning. Use the following formulas to answer parts (a) and (b). Lower limit of range Upper limit of range H=(220-a) (220-a) H= D a. What is the lower limit of the heart range, in beats per minute, for a 20-year-old with this exercise goal? beats per minute. The lower limit of the heart range is (Round to the nearest integer as needed.)

Colise has 2 vases of flowers that each hold 10 red and 5 yellow roses. Michelle has the same total number of roses but in 3 vases. Each vase has 6 red roses. How many yellow roses is in each of Michelle's vase?

V = πr²h is an equation to calculate the volume of a cylinder, V, where r represents the radius of the cylinder and h represents its height. Which equation allows us to easily find the height of the cylinder because it is solid for h? A. r²h = V/π B. h = V-πr² C. h=V/πr^2 D. πh = V/r^2

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at z = 5 and x=0, and a root of multiplicity 1 at x = -2 Find a possible formula for P(x).

The mean SAT verbal score is 419, with a standard deviation of 96. Use the Empirical Rule to determine what percent of the scores lie between 227 and 515. (Assume the data set has a bell-shaped distribution.) 81.5% 68% 34% 83.9%

When Cara drives to work, it takes her 30 minutes to drive 15 miles. On her days off, she likes to drive to her favorite donut shop. It takes Cara 6 minutes to drive to The Dreamy Donut Shop at the same rate. How many miles away is The Dreamy Donut Shop?