Basic Math Questions and Answers

Two angles are supplementary if the sum of their measures is 180°. Find two supplementary angles such that the larger angle is 148 more than 3 times the smaller angle. (Round to two decimal places if necessary.)

Use the histogram and the normal probability plot of the data to assess the normality of the finger length data. A. Both the histogram and the normal probability plot imply that the data is normal. B. The normal probability plot implies normality but the histogram implies the data is not normal. C. The histogram implies normality but the normal probability plot implies the data is not normal. D. Both the histogram and the normal probability plot imply that the data is not normal.

Simplify sec² (t) - 1 / sec² (t) to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation. Example: Enter sin² (t) as (sin(t))².

Which reasoning process is shown in the following example? We examine the email addresses of 100 people. No two individuals from this group of people have identical email addresses. We conclude that for all people, no two people have identical email addresses. A) deductive reasoning B) reasoning by counterexample C) theoretical reasoning D) inductive reasoning

Match the descriptions with the compound interest formulas. A(t) gives the balance in dollars in an account after t years. A(t) = a(1+ r/4)^4t A(4) = a(1 + r/k)^4k A(t) = a(1 + 0.04/k)^kt A(t) = 4(1 + r/k)^kt A(t) = a(1 + 1.04/k )^kt This account starts with 4 dollars. This is the balance in the account after 4 years. This account earns interest at a 4% nominal rate This account earns interest 4 times a year. None of these

A piece of sheet metal, w = 24 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 64 square inches, find the depth of the gutter. (Enter your answers as a comma-separated list.)

A shipping company is buying new trucks. The high-capacity trucks cost $50,000 and hold 340 cases of merchandise. The low-capacity trucks cost $30,000 and hold 200 cases of merchandise. The company has budgeted $1,140,000 for the new trucks and has a maximum of 30 people qualified to drive the trucks. Due to availability limitations, the company can purchase at most 15 high-capacity trucks. How many of each type of truck should the company purchase to maximize the number of cases shipped at one time? To maximize the number of cases of merchandise that can be shipped simultaneously, the company should purchase trucks. high-capacity trucks and low-capacity

A certain store has a fax machine available for use by its customers. The store charges $1.60 to send the first page and $0.45 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $7.00. 44 pages or fewer 16 pages or fewer 4 pages or fewer 13 pages or fewer

A dairy needs 270 gallons of milk containing 4 % butterfat. How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 270 gallons?

Think About the Process You deposit $3,900 into a bank account with a simple interest rate of 8%. How can you find the account balance after 6 years? Then find the account balance after 6 years. How do you find your account balance after 6 years? A. First use I = prt to find the simple interest earned after 6 years. Then add that to the rate. B. First use I = prt to find the simple interest earned after 6 years. Then subtract that from the principal. C. First use I = prt to find the simple interest earned after 6 years. Then add that to the principal. D. First use I = prt to find the simple interest earned after 6 years. Then add that to the time. After 6 years your account balance will be $ Resume later Submit Quiz

On the blueprint of a house, 55 millimeters represents 10 meters. The actual length of the living room is 8 meters. What is its length on the blueprint? millimeters

Dawn, Keith, and John are all working on a history project. Dawn spent 1.2 hours less than 6 times as many hours on the project as John did. Keith spent 0.8 hours more than 5 times as many hours on the project as John did. If Dawn and Keith spent the same amount of time working on the project, how many hours did John spend working on the project?

A company decided to fine its workers for parking violations on its property. The first offense carries a fine of $19, the second offense is $23, the third offense is $27, and so on. What is the fine for the eighth offense?

The variable X denotes a binomial random variable with parameters n and p. Indicate which area under the approximate normal curve would be determined to approximate the given binomial probability. P(X= 15) The area between the lower delimiting x-value, and the upper delimiting x-value, (Use integers or decimals for any numbers in the expressions. Do not round.) would be determined to approximate the binomial probability P(X = 15).

On a park map, the distance from a picnic table to the hiking trail is 6 centimeters. The map uses a scale of 2 cm = 150 meters. What is the actual distance from the picnic table to the hiking trail?

(a) The annual inflation rate is 3.8% per year. If a movie ticket costs $12.00 today, find a formula for y, the price of a movie ticket t years from today, assuming that movie tickets keep up with inflation. (b) According to your formula, how much will a movie ticket cost in 25 years?

A variable is normally distributed with mean 18 and standard deviation 3. a. Determine the quartiles of the variable. b. Obtain and interpret the 85th percentile. c. Find the value that 65% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025. Interpret the answer.

As Jupiter revolves around the sun, it travels at a rate of approximately 8 miles per second. Convert this rate to kilometers per second. At this rate, how many kilometers will Jupiter travel in 15 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate: Distance traveled in 15 seconds:

At the city museum, child admission is $6.20 and adult admission is $9.80. On Friday, twice as many adult tickets as child tickets were sold, for a total sales of $722.40. How many child tickets were sold that day?

Ms. Landry charges $40 an hour with a $5 flat fee for tutoring. Ms. Bowman charges $30 an hour with a flat fee of $10 to tutor. Which equation represents the situation when the cost is the same to be tutored by Ms. Landry and Ms. Bowman, where h is hours? A) 40h + 30h-5+10 B) 40h+30h-10-5 40h+5-30h +10 D) 40h+ 10-30h+5

Graph y = f(x) by hand by first plotting points to determine the shape of the graph. f(x) = -1

Solve the equation by hand, give an exact solution (the expression you arrived to without having to touch a calculator) "2x³-1= 3.5 Type the expression you found so Desmos computes an approximate solution: Check the solution works. 2( )³-1

At the end of a snow storm, Savannah saw there was a lot of snow on her front lawn.. The temperature increased and the snow began to melt at a steady rate. The depth of snow on Savannah's lawn, in inches, can be modeled by the equation S = -1.5t + 15, where t is the time, in hours, after the snow stopped falling. Wha is the slope of the equation and what is its interpretation in the context of the problem? The slope of the function is which reveals

You and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. What integer represents the total change in the time when you use 5 clues?

Solve the equation by factoring. x² = 3x+10 Rewrite the equation in factored form. = 0 (Factor completely.)

Arissa finds that the cost of a local college is $13,467 for students who live in the state. Which statements are true? Check all that apply. Rounding the cost to the nearest ten results in a value that is less than the exact cost of tuition. Rounding the cost to the nearest ten results in a value that is greater than the exact cost of tuition. Rounding the cost to the nearest hundred results in a value that is less than the exact cost of tuition. Rounding the cost to the nearest hundred results in a value that is greater than the exact cost of tuition. Rounding the cost to the nearest thousand results in a value that is less than the exact cost of tuition.

Public relations specialists create and maintain a favorable public image for the organization they represent. They design media releases to shape public perception of their organization and to increase awareness of its work and goals. The median annual wage for public relations specialists was $55,680 in May 2014. SOURCE: United States. Department of Labor. "Public Relations Specialist." Occupational Outlook Handbook. 17 Dec. 2015. Web. 8 March 2016. A public relations specialist earns $63,500 salary each year. He/she wants to spend no more than three times his/her salary on a house. What is the maximum price of a home that he/she can afford? If a 5% down payment is required, what is the amount financed? If he/she buys a home for the maximum he/she can afford, what is the monthly mortgage payment for a 20 year fixed interest loan at 3.1% compounded monthly?

There are 8000 students at Mountain High School, and 3/10 of these students are seniors. If 1/4 of the seniors are in favor of the school forming a debate team and 5/7 of the remaining students (not seniors) are also in favor of forming a debate team, how many students do not favor this idea?

A cyclist rides her bike at a speed of 2 meters per second. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 4 hours? Do not round your answers. Speed: Distance traveled in 4 hours:

Below, is the sample size, P is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation and the Cumulative Normal Distribution Table to find the probability. Round the answer to at least four decimal places. n=76, p=0.41 P(X>38) =

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?