Basic Math Questions and Answers

Jessie recently drove to visit her parents who live 540 miles away. On her way there her average speed was 21 miles per hour faster than on her way home (she ran into some bad weather). If Jessie spent a total of 15 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.

In a neighborhood 8/20 of the homes have waterfront views of a lake. What percentage is equivalent to the portion of homes that have a waterfront view of the lake?

The depth of the water in a water tank changes every time someone in the Harrison family takes a bath or does laundry. A bath lowers the water level by 4 inches. Washing a load of laundry lowers the level by 2 inches. On Monday the Harrisons took 3 baths and washed 4 loads of laundry. By how much did the water level in the water tank change?

Fuel Consumption From 1995 to 2002, the total fuel consumption 7 (in billions of gallons) by cars in the United States and the U.S. population P (in millions) can be modeled by T = -0.003x³ -0.02x² + 1.3x + 68 and P = 3x + 267 where x is the number of years since 1995. Write a function for the average amount of fuel consumed by each person from 1995 to 2002.

A cellular network transmits its signals in a circular pattern. If the tower is considered the origin, (0,0), of the signal and a house, is located on the edge of the circle at (8, 17), how far does the tower transmit the signal in miles? 18.8 miles 8 miles 17 miles 15 miles

Violet was given a box of assorted chocolates for her birthday. Each night, Violet treated herself to some chocolates. Violet ate 4 chocolates each night and there were originally 24 chocolates in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday.

In ΔMNO, MO is extended through point O to point P, m∠MNO: - (3x + 11), m∠OMN = (2x +20)°, and m∠NOP = (8x - 5)°. What is the value of a?

Noah is helping to collect the entry fees at his school's sports game. Student entry costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego collected $281.25. Select all equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game. A. 281.25 -5.25a = 2.75s B. a = 53.57-2.75/5.25 s C. 281.25 -5.25s = a D. 281.25 +2.75a = s E. 281.25 +5.25s = a

Find the derivative of the trigonometric function. g(x) = 4 tan(6x) g'(x) =

Find the real solutions of the following equation. x4 - 41x² + 400 = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Use a comma to separate answers as needed.) B. There are no real solutions.

Suppose that you follow a population over time. When you plot your data on a semilog plot (using logs with base 10), a straight line with slope 0.18 results. Furthermore, assume that the population size at time 0 was 60. What function best describes the population size at time t? Population at time t is (Simplify as much as you can; there should be no logs in your answer.)

Victoria is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. It is known that the total charge to use a computer for 5 minutes would be $6 and that the additional rate per minute of use is $0.60. Write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe.

For problems 5-7, solve each triangle by finding the measure of all the unknown angles and sides. Use degrees for angle measurements and round all answers to the nearest whole number. 5. For ΔUVW, UV = 9 mm, WV = 4 mm, and m∠V=74°.

A tank is being filled with a liquid. L (t), given below, is the amount of liquid in liters in the tank after 1 minutes. L(t)=1.25t+61 Complete the following statements.

Find the area of the region in the first quadrant bounded by the line y=5x, the line x = 5, the curve y=5/x2 and the x-axis.

A plumbing company charges $50 for the first hour of a service call and $30 per hour for each hour or part of an hour that a job requires after the first hour. If the Smiths bill included $65 for supplies and the plumber worked 2 hours and 35 minutes, how much was their bill?

The U.S. Senate has 100 members. After a certain election, there were 18 more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate? Democrats Republicans

Select the values that make the inequality -2w ≤-22 true. Then write an equivalent inequality, in terms of w. (Numbers written in order from least to greatest going across.)

The 8th grade fundraiser gives away a prize for the student who guesses the number of bubble gum balls in a jar shaped like a cube. Al decides to count the number of bubble gum balls along the length of one side. If Al guessed 343, how many bubble gum balls did she count along one side of the container?

A line passes through point (4, 2) and has a slope of -3/2 Write an equation in Ax+By=C form for this line. Use integers for A, B, and C.

You are trying to decide whether to pay $120 for a season pass to an amusement park. If you buy the pass, you get an unlimited number of visits to the park and reduced parking for $8. If 10X you do not buy the pass, you pay $23 admission and $10 for parking each time you visit the park. After how many visits to the park will the cost of visiting with the season pass be less than the cost of visiting without the season pass? 1) Write a variable expression for the cost of making v visits to the park if you don't buy a season pass. 2) Write an inequality in terms of v showing that the cost of visiting the park with a season pass is less than the cost of visiting the park without a season pass. 3) Solve the inequality.

The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. Find the top 2% of the scores. a. Find the z-value for the top 2%. Write your answer in 2 decimals (Read Table Z). b. Find the IQ scores of the top 2%. Write your answer in 1 decimal.

Mark flew from Boston to Baltimore, then Baltimore to Orlando. The number of people on his first flight was five more than four times the number of people on his second flight. If there were 365 people altogether on the two flights, how many were on the flight from Baltimore to Orlando?

Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone? Use 3.14 for π.

Convert this rational number to its decimal form and round to the nearest thousandth. 1/7 =

A principal of $4400 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 7 years?

A rectangle is inscribed in a circle of radius 4 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area changing at the insta when the length is 6 inches?

Steve was offered $5,025 per year for a weekend lifeguarding job at a local pool. He wants to know how much his monthly income will be at this salary level. What is his rate of pay in dollars per month?

There are 32 people in your math class and the classroom size is 22 feet long and 31 feet wide. How many square feet does each person get? Round your answer to two decimal places. 15.11 square feet 21.31 square feet 0.047 square feet 1.45 square feet

A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?

The Ward family and the Martinez family each used their sprinkders last summer. The water output rate for the Ward family's sprinkler was 15 L per hour. The water output rate for the Martinez family's sprinkler was 35 L per hour. The families used their sprinkders for a combined total of 40 hours, resulting in a total water output of 900 L. How long was each sprinkler used? Note that the ALEKS graphing calculator can be used to make computations easier.

Sales at a local ice cream shop went up 20% in 5 years. If 18,000 ice cream cones were sold in the current year, find the number of ice cream cones sold 5 years ago. (Round to the nearest integer, if necessary) A. 14,400 ice cream cones B. 15,000 ice cream cones C. 360 ice cream cones D. 90,000 ice cream cones

A CB radio is rated at 7.5 watts, and actual measurements show that it delivers 5.4 watts to its antenna. What is its efficienc The efficiency is %. (Type a whole number or decimal rounded to two decimal places as needed.)

Maya and Sally were the two finalists in a singing competition. The person with the most votes from the audience was chosen as the winner. Sally received 25% of the total votes and lost by 62,500 votes. No person in the audience was allowed to vote more than once. The equation below represents this situation, where y is the total number of votes cast and x is the number of votes Maya received: x-62,500=0.25y If a total of 125,000 people voted, how many votes did Maya receive? Do hot enter comma for placeholder values.

The daily expenses for each of a transportation service company's trucks is given by the function dx) = 15 +0.5x, where d(x) is the daily expense per truck (in dollars) and x is the daily mileage.

In North Texas there was .65 inches of snowfall overnight. Write a simplified form that represents .65 inches of snowfall.

A physics class has 50 students. Of these, 17 students are physics majors and 16 students are female. Of the physics majors, five are female. Find the probability that a randomly selected student is female or a physics major.

A ceiling fan can rotate 150.5 times per minute. The fan rotated a total of 2,426.06 times. Which of the following is true? A. The fan rotated for 17.12 minutes. B. The fan rotated for 15.12 minutes. C. The fan rotated for 16.12 minutes. D. The fan rotated for 18.12 minutes.

Solve the equations 2x + 3y = 1 and x - y = -9.

5 x 863 = ?

.Maggie spent $4.05 on cheese and fruit at the farmer's market. She bought 1/8 pound of apples, 1/4 pound of pears, and 1.25 pounds of bananas. If fruit cost $0.80 per pound, how much did Maggie spend on cheese?

Where do the lines y = 3x + 4 and 2y = x - 4 cross?

Joan built a table to sell. She wanted to sell it for $48 but her dad said she should sell it for less. So she decided to mark down the price by 1/6. What was the final price she sold it for? Solve by showing two methods to receive full credit.

p(x) is the unit price at which all x units will be sold. Assume p(x) is in dollars. Use marginal revenue to estimate the revenue derived from the sale of the 21st unit. What is the actual revenue obtained from the sale of the 21st unit? p(x) = -x² - 15x + 3500

A 52-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 3 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 20 feet from the wall?

Based on a survey, assume that 44% of consumers are comfortable having drones deliver their purchases Suppose we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by two consumers not comfortable, as in this calculation (0.44)(0.44)(0.56)(0.56)=0.0607? Choose the correct answer below.

Intersection points Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. 29. r=2 cosθ and r= 1+ cosθ 30. r=1-sinθ and r= 1 + cosθ

A researcher is studying the relationship between sugar consumption and weight gain. Twelve volunteers were randomly assigned to one of two groups. The first group of five participants was put on a diet low in sugar and the second group of the remaining seven participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant. What type of study is this? A double-blind experiment. An observational study. A matched pairs experiment. An experiment, but not a double-blind experiment.

A college official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a simple random sample from each class and asks the members' opinions regarding student services. The type of sampling used is a convenience sample. stratified random sample. simple random sample.

C(x) is the total cost of producing x units of a particular commodity. Assume C(x) is in dollars. Use marginal cost to estimate the cost of producing the 21st unit. What is the actual cost of producing the 21st unit? C(x) = 1/2 x² +57 estimated cost = $20.50; actual cost = $19.50 estimated cost = $20.00; actual cost $20.50 estimated cost = $20.00; actual cost = $19.50 estimated cost = $20.50; actual cost = $20.00