Basic Math Questions and Answers

Fill in the blanks with the correct vocabulary term from this unit. The ___. refers to the amount you can fit inside of a shape. For example, how much paint to cover a wall, or how much grass seed to plant to cover a backyard The___refers to the distance to go all the way around a shape. For example, how much fence you need around your front yard, or how many holiday lights you need to hang up around a window.

Suppose I'm thinking of two different positive numbers. Choose the correct translation of the following into symbolic algebra: "The product of the two numbers is equal to eleven more than the larger number." where x = the smaller number y = the larger number xy = y +11 xy=x+11 x/y + 11 = y xy + 11 = y x-y = 11 x+y=11

The world population in 2000 was approximately 6.08 billion. The yearly rate of increase was about 1.0126. a. Find the a and the b for this problem. a = b = b. Write the equation that models this situation. c. Find the world population in 2019. y = Population: d. Your friend wants to use x = 2030 to find the world population in 2030. Do you agree or disagree with her and explain why.

Select the correct answer from each drop-down menu. A couple took out a 5-year $30,000 loan to pay for for their wedding. After 5 years, the loan payments they had made to the bank amounted to $38,250. The interest rate on the loan, compounded continuously, is %. If they had taken an 8-year loan instead of a 5-year loan, they would have paid approximately $ more.

A car parts company wishes to find the defect rate of a certain part. Of 346 items tested, 12 are found to be defective. Use this data to construct the 98% confidence interval for the proportion of all such items that are defective. 0.0345 < p < 0.0349 0.0110 < p < 0.0584 0.0118 < p < 0.0576 0154 < p < 0.0540

A local office supply store charges $20 to set up business cards and $0.25 in materials per business card to print. Write an equation that could represent an expression for the average cost A(x) of printing a batch of x business cards. (Look at lesson 2-18 p 202 and lesson 2-20 pg 216. Remember that we can break up the function into two fractions.) What is the price per card when you order 100 business cards? What is the price per card when you order 1000 cards? What is the price approaching as you make more and more cards?

Determine the x-intercepts of the following equation. (-x+5)(x+2) = y

Show complete work on your worksheet! You many use the !, nCr and nPr functions on your calculator to CHECK your calculations, but you must show the formulas with appropriate values substituted in first. There are 15 members on a city council. On a recent agenda item, 8 of the council members voted in favor of a budget increase. How many possible groups of council members could have voted in favor? Permutation Combination n= T= There can be groups.

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3 archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier? Choose 1 answer: Yes; a legionary costs 1 denarius per day to support, and an archer costs 2 denarius per day to support. Yes; a legionary costs 2 denarius per day to support, and an archer costs 4/3 denarius per day to support. No; the system has many solutions. No: the system has no solution.

A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches, and the radius of the bottom is 5 inches. What is the volume of the container to the nearest cubic inch?

Choose the answer that describes the set of ordered pairs below. Be prepared to justify your answer. {(Ford, blue), (Nissan, red), (Toyota, silver), (Subaru, black), (Chevy, blue), (Volvo, red)} A function with domain of (Ford, Nissan, Toyota, Subaru, Chevy, Volvo} A relation with domain of {Ford, Nissan, Toyota, Subaru, Chevy, Volvo} A function with domain of (blue, red, silver, black} A relation with domain of {blue, red, silver, black}

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 8 small boxes has a total weight of 162 kilograms. A delivery of 5 large boxes and 2 small boxes has a total weight of 117 kilograms. How much does each type of box weigh? Weight of each large box: kilogram(s) Weight of each small box: kilogram(s)

The standard deviation of the mass of 50 mice in a normal population is 5 g. How many mice are within one standard deviation of the mean?

Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842 buttons. A collection of 6 shirts and 7 jackets contains 137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?

Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citizen tickets cost $4.00. She spent a total of $76. Which system of equations will determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased? a. a + s = 76 6a + 4s = 15 c. a+s=15 4a + 6s = 76 b. a + s = 15 6a + 4s = 76 d. a + s = 76 6a + 4s = 15

If the population of a country increases at a rate of 1.5% annually and its current population is 430,000, how many years will it take for the population to triple? A. 74 years B. 3 years C. 2 years D. 150 years

Given the equation solve for x and identify if it is an extraneous solution. x = 4, solution is extraneous x = 4, solution is not extraneous x = 5, solution is extraneous x = 5, solution is not extraneous

Using your knowledge of exponential and logarithmic functions and properties, what is the intensity of a fire alarm that has a sound level of 120 decibels? 10 * 10-12 watts/m² 1.0 x 100 watts/m² 12 watts/m² 1.10 x 102 watts/m²

Situation: There is a linear relationship between the total cost of a gym membership for the month and the number of fitness class taken that month. One month Mari took 10 classes and it cost her $75. Another month she took 8 classes and paid $60. Question: If the total cost of a gym membership for the month was $97.50, how many fitness classes did Mari take? Answer: Mari attended fitness classes.

Bentley invested $1700 in an account that pays 1.5% interest compounded annually. Assuming no deposits or withdrawals are made, write a recursive formula that represents the amount of money Bentley has in the account n years after his initial investment. ao= an =

Avocado Pickers are paid as shown below. What would be the gross earnings for a worker that picks 1,108 avocados? 1-500 Avocados $0.10 each 501 - 700 Avocados $0.14 each Over 700 Avocados $0.18 each

Given the equation 2√x-5=2, solve for x and identify if it is an extraneous solution. a. x = 6, solution is not extraneous b. x = 6, solution is extraneous c. x= 11, solution is not extraneous d. x= 11, solution is extraneous

Complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per year. (Round your answers to the nearest cent.) Rate r = 7.5% Time t = 15 years Principal P = $1500 n 1 4 12 365 Continuous compounding A

A population of fish in a pond is decreasing by 4% each year. The population starts with 250 fish. Which of the following functions represent the population of fish as a function of time? P (t) = 250(4)^t-1 P (t) = 250(1 + .04)^t P (t) = 250(.04)^t-1 P (t) = 250(1-.04)^t

Tomas sells cars and there is a linear relationship between the number of cars he sells each week and his weekly pay. One week Tomas sold 4 cars and he made $820 that week. Another week he sold 6 cars and made $980. Write an equation that models the linear relationship between the number of cars Tomas sells in a week and his pay for that week. DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter y = 2x + 1. DO ENTER: y=2x+1. Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) To write your equation, use the variables: p = total weekly pay ($) n = number of cars sold during the week The equation in slope-intercept form is

Select the correct answer. Consider the equation below (x - 2)³ - 6=3 √x + 4. Which statement explains why the solution to the equation is x= 4? A. The x-value of 4 is a x-intercept for both f(x)=(x - 2)³ - 6 and g(x)=3 √x + 4. B. The x-value of 4 produces the same y-value in both f(x)=(x - 2)³ - 6 and g(x) =3√x + 4. C. The x-value of 4 is undefined for both f(x) = (x - 2)³ - 6 and g(x)=3√x + 4. D. The x-value of 4 is defined on the graphs of both f(x) = (x - 2)³ — 6 and g(x) =3√x + 4.

Kaylee is looking to take out a mortgage for $260, 000 from a bank offering an annual interest rate of 5.7%, compounded monthly. Using the formula below, determine her monthly payment, to the nearest dollar, if the loan is taken over 10 years. M = Pr(1+r)"/(1+r)" - 1

Daniela measures her math book and records its width as 21.9 cm to the nearest tenth of a centimeter. The actual measurement of the book's width is 22.0 cm. What is the percent error of her measurement? Round your answer to the nearest tenth of a percent. A. 0.2% B. 0.5% C. 2.3% D. 4.5%

Tara works in a clothing store where she earns a base salary of $100 per day plus 12% of her daily sales. She sold $800 in clothing on Saturday and $1500 in clothing on Sunday. How much did she earn over the two days? A. $276 B. $376 C. $476 D. $576

Use the function equation to find the n-intercept of the linear function algebraically. C(n)=8n-1240 Write the ordered pair using parentheses like this: (x,y) with no spaces but with the appropriate numerical coordinates instead of x and y. If there is no 'x'-intercept type "N/A" in the blank. The n-intercept is

Katherine just started a running plan where she runs 8 miles the first week and then increases the number of miles she runs by 5% each week. If she keeps up this plan for 19 weeks, how many total miles would Katherine have run, to the nearest whole number?

The price per share of a professional sports team increased from $58 to $65 over the past year. What is the stock's percent increase during this time? Round your answer to the nearest percent. A 7% B. 9% C. 11% D. 12%

Answer the following questions about P(x)=x^3-4x²-3x+18: a. The polynomial P(x) has no remainder when divided by (x+2). List all of the roots of P(x). showing how you found the roots algebraically. b. Sketch a graph of the function f(x) =x+2/P(x) and explain or show algebraically how you found P(x) the asymptotes and holes, if any.

Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. 1. Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving. 2. Graph your equation using graphing technology. Mark the point on the graph that represents the amount after 3 weeks. 3. How many weeks does it take her to have $250 in her bank account? Mark this point on the graph.

A cylinder with a diameter of 16 yd and a height of 12 yd. 3467.84 yd³ 2412.74 yd³ 1781.32 yd³ 1321.15 yd³

"Maddox starts hiking from the main entrance to a trail. Penny starts her hike from the same entrance a little while later. The equations below represent the distance, d, in yards, that each person is from the entrance of the trail m minutes after Penny starts hiking from the entrance. Maddox: d = 40m + 200 Penny: d = 50m Which statement is true? Penny will be able to catch up to Maddox 20 minutes after Penny starts hiking on the trail. Penny will be able to catch up to Maddox when they are both 500 yards from the entrance to the trail. Penny will not be able to catch up to Maddox because Maddox started hiking 10 minutes earlier than Penny. Penny will not be able to catch up to Maddox because Maddox was 200 yards ahead of Penny when she started hiking.

Madison was given a large box of 42 chocolates for her birthday. If she eats exactly 5 chocolates each day, how many chocolates would Madison have remaining 5 days after her birthday?

Rhett decides to build a square room for his movie and music collection. If the area of the room is 4x² + 28x + 49 square feet, what is the length of one side of the room? (7x + 2) feet (2x + 7) feet (2x-7) feet (7x-2) feet

Flying against the wind, an airplane travels 2670 kilometers in 3 hours. Flying with the wind, the same plane travels 6150 kilometers in 5 hours. What is the rate of the plane in still air and what is the rate of the wind? Note that the ALEKS graphing calculator can be used to make computations easier.

Charmaine bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 more than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 6% per year. The total finance charges for one year were $398. How much did each computer cost before finance charges? Note that the ALEKS graphing calculator can be used to make computations easier.

Point S is on line segment RT. Given ST= 2x- 10, RS = 2x - 5, and RT = 3x + 1, determine the numerical length of RT.

Certain radioactive material decays in such a way that the mass remaining after t years is given by the function m(t) = 275e-0.045 where m(t) is measured in grams. (a) Find the mass at time t = 0. Your answer is (b) How much of the mass remains after 10 years? Your answer is

Find the circumference and area of a circle with a diameter of 22 inches. Leave your answers in terms of pl.

A wheel with three numbers on it--0, 1, and 2--is spun so that there is a 40% chance that the wheel lands on zero, a 10% chance the wheel lands on one, and a 50% chance the wheel lands on two. You get back the amount in dollars of the number that the wheel lands on. If it costs $1 to play, what is the expected value of the game? * -$1.10 -$0.10 $0.10 $0.20 $1.10

The equation of an ellipse is given below. x2/17+y²/35= 1 What are the foci of this ellipse? Choose 1 answer: A(√18,0) and (-√18,0) B (0, √35) and (0, -√/35) c (0, 18) and (0, -√18) D (√35,0) and (-√35,0)

A company makes electronic gadgets. One out of every 50 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $3 profit on the sale of any working gadget, but suffers a loss of $80 for every faulty gadget because they have to repair the unit. Can the company expect a profit in the long term? * Yes, they can expect a profit. No, they will lose money in the long term.

Select all of the symbols that would make the comparison true -7_-4 ≠ > ≤ = < ≥

You rent an apartment that costs $1500 per month during the first year, but the rent is set to go up 11.5% per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment.

Which property should be used next in this solution process? 3x +2+3= 7 (x - 1)-4 3x+5= 7 (x-1) - 4 A Commutative Property of Addition B. Identity Property of Multiplication C. Associative Property of Multiplication D. Distributive Property

A company manufactures computers. Function represents the number of components that a new employee can assemble per day. Function E represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours worked in one day. N(t) = 50t/t + 4 E(t) = 70t/t + 3 Which function describes the difference of the number of components assembled per day by the experienced and new employees?