Basic Math Questions and Answers

Brian's Great-Grandma Pat is turning 100 years old! The family throws her a party, and Brian helps her open a large stack of birthday cards. After opening 46 cards, they stop so Grandma Pat can blow out the birthday candles. Brian and Grandma Pat leave the remaining 55 cards for later. Use an equation to find the total number of birthday cards in the stack. birthday cards

Announcers present music, news, and sports, and may provide commentary or interview guests about these or other important topics. Some act as masters of ceremonies (emcees) or disc jockeys (DJs) at weddings, parties, or clubs. Many announcers work in radio and television studios. Some announcers are self-employed; others work part time. The median annual wage for announcers was $29,010 in May 2014. SOURCE: United States. Department of Labor. "Announcers." Occupational Outlook Handbook. 17 Dec. 2015. Web. 8 March 2016. A newscaster earns $33,100 and wants to invest 10% of his/her monthly salary to save for retirement in 23 years. If he/she invests this money at 5.1% compounded monthly, how much money will he/she have at retirement? a) How much will be saved each year? b) What will be the monthly deposit? c) What will be the amount in the account after 23 years?

A new bank customer with $3,000 wants to open an IRA (Individual Retirement Account) to earn money for retirement. The bank is offering a simple interest rate of 11%. How much interest will the customer earn in 20 years? In 30 years? What will be the account balance after 20 years? After 30 years? in interest. In 20 years, the account will earn $ In 20 years, the account balance will be $ In 30 years, the account will earn $ in interest. In 30 years, the account balance will be $

A clothing manufacturer makes denim and hooded fleece jackets. Each denim jacket requires 2 labor-hours for cutting the pieces, 2 labor-hours for sewing, and 1 labor-hour for finishing. Each hooded fleece jacket requires 1 labor-hour for cutting, 4 labor-hours for sewing, and 1 labor-hour for finishing. There are 32 labor-hours for cutting, 60 labor-hours for sewing, and 18 labor-hours for finishing available each day. The profit is $7 per denim jacket and $4 per hooded fleece jacket. Complete parts (a) through (e) below. (b) Let x be the number of denim jackets made each day. Let y be the number of hooded fleece jackets made each day. Refer to the chart, and give three inequalities that x and y must satisfy due to the available labor hours. Give the inequality arising from the available cutting hours. Give the inequality arising from the available sewing hours. Give the inequality arising from the available Finishing hours. (c) Give other requirements that x and y must satisfy. x ≥ y²

Consider a student loan of $25,000 at a fixed APR of 9% for 20 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.

An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. The total cost of the electrician's services can be determined using the equation C = 65+ 60t, where t is the number of hours the electrician spends at the house working. What is the slope of the equation and what is its interpretation in the context of the problem?

If f(x) = x² and g(x)=x²-3, how has f(x) been transformed to get g(x)? The graph of f(x) has been shifted up three places The graph of f(x) has been shifted right three places The graph of f(x) has been shifted down three places The graph of f(x) has been shifted left three places The graph of f(x) has been stretched by a factor of 3

Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011? Last week, she made $ in commission. In 2011, she made $ in commission.

You decide to quit using your credit card and want to pay off the balance of $3,400 in 4 years. Your interest rate is 16.2% compounded monthly. What will your monthly payments be? How much interest do you pay?

Anusha brings a $20 bill to the store. She purchases 4 pairs of socks for $2.25 each and a new belt for $7.50. How much change will Anusha receive when she pays for her clothes? $3.50 $7.50 $9.00 $16.50

The equation V = -2000t + 24,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $16,000, substitute 16,000 into the equation to find the age of the car. 4 years 5 years 6 years 3 years

On Sunday, a local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 9x + 2(2x - 5) = 7 - 4x Identity Conditional equation Inconsistent equation

The Stock Market Alexander is a stockbroker. He earns 12% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? Last week, he made $ in commission. In 2011, he made $ in commission.

Name any two points on a horizontal line that is 8 units above the x-axis.

A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 253 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 0.36? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.36. Round the answer to 4 decimal places.

Abutcher shop knows that it must buy a new machine in 5 years. The machine costs $15,000. In order to accumulate enough money for the machine, the shop owner decides to deposit a sum of money at the end of each 6 months in an account paying 6% compounded semiannually. How much should each payment be? The deposits form an because the deposits are made at the should be used. Each payment should be $ (Do not round until the final answer. Then round to the nearest cent as needed.) of each period. Therefore, the formula

At the beginning of the year, the odometer on an SUV read 37,839 miles. At the end of the year, it read 52,799 miles. If the car averaged 22 miles per gallon, how many gallons of gasoline did it use during the year? A) 14,960 gallons B) 680 gallons C) 329,120 gallons D) 68 gallons

Point Q' is the image of Q(4, -6) under a translation by 1 unit to the right. What are the coordinates of Q'?

Stuart Daniels estimates that he will need $22,000 to set up a small business in 9 years. (a) How much (in $) must Stuart invest now at 8% interest compounded quarterly to achieve his goal? (b) How much compound interest (in $) will he earn on the investment?

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?