Basic Math Questions and Answers

Combine like terms to simplify the expression below. -6y + 7y = 1y 32 + y - 2y² Now, re-write the equation with the variable with the highest exponent first.

Two cities have nearly the same north-south line of 101° W. The latitude of the first city is 23° N, and the latitude of the second city is 36° N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $77 for parts. The total was $302. Which equation could be used to determine x, the cost of labor per hour? r

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create an x → y table and a graph for the function for which x represents the number of days since Junior started saving money and y represents the total money he has saved.

A pennant is shaped like a right triangle with hypotenuse 10 feet. The length of one side of the pennant is 2 feet longer than the length of the other side. Find the length of the two sides (legs) of the pennant. Enter your answers as a comma separated list.

You have tablets with a strength of 2.37 mg, and you must give 0.16 g. How many tablets will you need? Less than 1 Exactly 1 More than 1

- A boat leaves port A and travels 40 knots for 2 hours on a bearing of N 62° W then travels at the same speed for 3 hours on a bearing of N 28° E to port B. Find the distance and bearing from port B to A.

The city of Raleigh has 11,900 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 353 said they'd vote for Brown, 219 said they'd vote for Feliz, and 28 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. This sample statistic suggests that we might expect of the 11,900 registered voters to vote for Brown. Round to the nearest whole number.

In 2012, the population of a city was 5.62 million. The exponential growth rate was 2.48% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time. of the number of years since 2012

Alexis de Tocqueville observed American society during the beginning of industrialization. Which of the following best characterizes his observations? a) Americans are insufficiently focused on their careers and miss opportunities to advance in the job market. b) Americans need to be more like people who live in the Old World and lighten their spirits. c) Americans regularly participate in government elections but cannot agree on which path is the best one to follow. d) Americans have become so obsessed with accumulation that they have no time left to enjoy life and participate in their free political system.

In a recent survey of college-educated adults, 102 indicated that they regularly work more than 45 hr a week. If this represents 34% of those surveyed, how many people were in the survey? There were people in the survey.

Your patient is to receive a dosage of 15 mg and you have only 1 tablet labeled 5 mg. How many more mg are needed?

A rope is 60 in in length and must be cut into two pieces. If one piece must be three times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary. The length of the smaller piece is in. The length of the larger piece is in.

Complete the proof of the statement, "If a figure is a rectangle, then it must me a parallelogram". Use the diagram provided to help you. Angles A and D are supplementary [Select] transversal AD, so lines DC and AB are parallel by the [Select] Similarly, angles A and B are [Select] same side interior angles formed by transversal AB which makes lines AD and BC also parallel. Finally, ABCD must be a parallelogram because we have just proven both pairs of opposite sides are [Select]

Find the angular speed w for the following. a wind turbine with blades turning at a rate of 15 revolutions per minute The angular speed for a wind turbine with blades turning at a rate of 15 revolutions per minute is minutes. radians. radians per minute.

(a) Find the domain of the following function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. x², if 0<x≤2 f(x)= x+2, if 2<x<5 7, if x ≥ 5

Permutation and combination: What are your chances of winning the Lucky Millions Lottery if you You pick 4 numbers from 1 to 40 without replacement and 1 number from 1 to 30. Answer format:

3 days after picking apples, a family had 100 apples left. After 6 days, 76 apples were left. Assuming a linear function, write an equation in the form a(t) = mt + b that shows the number of apples, a(t), left t days after picking them. Be sure to include "a(t) =" in your answer.

Error Analysis Cheryl's math teacher asks, "7 is 50% of what number?" Cheryl incorrectly says, "350." What is the correct answer? What error did Cheryl likely make? 7 is 50% of .... What error did Cheryl likely make? A. She wrote the percent equation as whole = percent part and did not divide by 100. B. She did not divide by 100. C. She wrote the percent equation as percent = whole + part.

A motorboat travels 180 miles in 6 hours going upstream. It travels 264 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Charlie bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one year were $306. How much did each computer cost before finance charges?

Use the figure to the right to find the value of PT. T is the midpoint of PQ. PT=3x+2 and TQ = 5x-8 PT=

The drama club is printing t-shirts for its members. The printing company charges a certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club. Part A: If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning. Part B: The equation 201.50 = f +6.50 (21) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation.

Use the Zero Product Property and factoring, when necessary, to solve for x. The Math Notes box for Lesson 1.1.4 may be useful, if you need help. Homework Help a. (x+13)(x-7)=0 b. (2x+3)(3x − 7) = 0 c. x(x − 3) = 0 d. x² −5x=0 e. x² - 2x - 35 = 0 f. 3x² +14x − 5 = 0

A box of cereal states that there are 99 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 3 cups of the cereal? The unit rate is calorie(s) per cup. (Simplify your answer. Type an integer, proper fraction, or mixed number)

Find the initial value a, growth/decay factor b, and growth/decay rate, for the following exponential function: Q(t) = 0.0044(2.34) (a) The initial value is a = (b) The growth factor is b = (Retain at least four decimal places.) (c) The growth rate is r = % help (numbers) (Ensure your answer is accurate to at least the nearest 0.01%) (Note that if r gives a decay rate you should have r < 0.)

Solve each application below using systems. To receive full credit, you must 1) define all variables used, set up a system of 2 equations and 2 variables, 3) solve the system, and 4) write your solution as part of a complete sentence using appropriate units of measure. A Christmas charity party sold tickets for $45 for adults and $25 for children. The total number of tickets sold was 320 and the total for the ticket sales was $13,000. How many adult and how many children's tickets were sold?

A local race for charity has taken place since 1993. Using the actual speeds of the winners from 1993 through 1998, mathematicians obtained the formula y-0.16x+5.5, in which x represents the number of years after 1993 and y represents the winning speed in miles per hour. In what year is the winning speed predicted to be 7.42 mph?

A rectangle's width is one-third its length, and its perimeter is 96 m. Find the dimensions of the rectangle. The length is m and the width is

Stating Parametric Solutions State the standard parametric solutions with parameter k, and for inverse trig values, round your answers to four decimal places. sin(t) = 0.896 if and only if t = (primary solutions) (secondary solutions) t = cos(t) 0.05 if and only if t = (primary solutions) (secondary solutions) t tan(t) t =(primary solutions) (secondary solutions)

A random sample of size n = 616 from a population whose parameter is p = 0.31. a. What is the mean of the distribution of sample proportions? Round the answer accurate to 2 decimal places. b. What is the standard deviation of the distribution of sample proportions? Round the answer accurate to 2 decimal places.

Valentina's parents are planning a trip to the Typhoon Towers resort. They plan to get a 6- day Fun Pass, which will give Valentina access to all the slides and pools at the resort during their stay. Her parents also plan to get her a $30 arcade pass. Altogether, Valentina's parents will spend $129 on passes. What is the daily cost of a Fun Pass?

Javon is in a 26% tax bracket for his federal income tax. If the amount of money that he paid for federal income tax was $19,240, what was his taxable income?

Consider the Quadratic function f(x) = x² - 4x - 21. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The area of an 19-cm-wide rectangle is 380 cm². What is its length? The length is cm.

Car Survey In a survey of 1,700 people who owned a certain type of car, 935 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car? % of the people surveyed were satisfied with the car. (Type a whole number.)

At the time of her grandson's birth, a grandmother deposits $15,000 in an account that pays 9% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? Click the icon to view some finance formulas. The value of the account will be $ (Round to the nearest dollar as needed.)

You have a choice between going to an in-state college where you would pay $6500 per year for tuition and an out-of-state college where the tuition is $9000 per year. The cost of living is much higher at the in-state college, where you can expect to pay $700 per month in rent, compared to $450 per month at the other college. Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $ college. the and the yearly expense of the out-of-state college is $ Thus, on an annual basis, the less expensive choice is

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 5% each year. In other words, if you have $1 this year, next year it will only buy you $0.95 worth of stuff. How much will $100 buy you in 25 years?

Select the correct answer from each drop-down menu. A square rotated about its center by 360° maps onto itself at _____ different lines of reflection. across _____ different angles of rotation. You can reflect a square onto itself

Find the linear speed v for the following. the tip of a propeller 1 m long, rotating 500 times per min (Hint: r=0.5 m) The linear speed v for the tip of a propeller 1 m long, rotating 500 times per min is min. m per min. m.

How much should you deposit at the end of each month into an investment account that pays 7% compounded monthly to have $5 million when you retire in 38 years? How much of the $5 million comes from interest? Click the icon to view some finance formulas. In order to have $5 million in 38 years, you should deposit $ each month. (Round up to the nearest dollar.)

Select the correct answer. A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation? A. 1 B. 2 C. 4 D. 8

Find all values of c that satisfy the mean value theorem for integrals on the following interval. R(v)=v²-v; [5,8] C= (Round to two decimal places as needed. Use a comma to separate answers as needed.)

A container ship left the Dania Pier and traveled north at an average speed of 20 mph. Sometime later an aircraft carrier left traveling in the same direction but at an average speed of 30 mph. After traveling for two hours the aircraft carrier caught up with the container ship. Find the number of hours the container ship traveled before the aircraft carrier caught up. 3 hours 6 hours 4 hours 5 hours 7 hours

A ball is launched into the air from the top of a building. Its initial velocity is 20 feet per second. The equation h - 16² +20 t + 50 can be used to model the height h of the ball in feet after t seconds. What is the height of the building the ball is being launched from? How long does it take for the ball to hit the ground?

Investors buy a studio apartment for $200,000. Of this amount, they have a down payment of $60,000. Their down payment is what percent of the purchase price? What percent of the purchase price would an $80,000 down payment be?

The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let v represent the number of asthma sufferers (in millions) worldwide t years after 1990. (a) Write N as a linear function of t. Use exact values in your formula, not decimal approximations. N(t) = (b) Write N as an exponential function of t. Use exact values in your formula, not decimal approximations. N(t) = (c) How many asthma sufferers are predicted worldwide in the year 2014 with the linear model? (d) How many asthma sufferers are predicted worldwide in the year 2014 with the exponential model?

Mr. Smith decides to feed his pet Doberman pinscher a combination of two dog foods. Each can of brand A contains 4 units of protein, 1 unit of carbohydrates, and 2 units of fat and costs 60 cents. Each can of brand B contains 1 unit of protein, 1 unit of carbohydrates, and 4 units of fat and costs 40 cents. Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates, and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost? Mr. Smith should give his dog can(s) of brand A and can(s) of brand B to provide the minimum requirements at the least cost.

Suppose that you borrow $2000.00 from a friend and promise to pay back $3170.00 in 3 years. What simple interest rate will you pay?