Basic Math Questions and Answers

The average tuition, fees, and room and board rates charged per year for full-time students at a certain college is approximated by the polynomial C= 5x2 +38x+2876 for the years 1984 to 2006. Let x represent the number of years since 1984. Use this model to predict what the costs will be for a student at this college in 2018 (x=34) and 2032 (x = 48). The costs at this college in 2018 will be $ (Simplify your answer. Do not include the $ symbol in your answer.) The costs at this college in 2032 will be $ (Simplify your answer. Do not include the $ symbol in your answer.)

An object moves along a coordinate line, its position at each time t≥ 0 is given by x(t) = (t² - 2 t) (t² + 2 t). Find the acceleration at time to = 3. a) -4 b) 100 c) 84 d) -84 e) 816

Find the zeros of the polynomial function and state the multiplicity of each. f(x) = − 5(x - 1)4(x + 5)²x³ The zero 1 has multiplicity is a zero of multiplicity 2. The remaining zero is It has multiplicity

Find the slope m and y-intercept b. (If an answer is undefined, enter UNDEFINED. If an answer does not exist, enter DNE.) y = 7

Suppose that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions, can be modeled by N=0.150x + 36.4 where x is the number of years after 2020. (a) Viewing N as a function of x, what is the slope m of the graph of this function? (b) Interpret the slope as a rate of change. The slope m represents the number of females in the U.S., under age 18, in millions, in year 2060. Every m years, the population of females in the U.S., under age 18, in millions, is predicted to increase by 1. The slope m represents the number of females in the U.S., under age 18, in millions, in year 2020. Every year, the population of females in the U.S., under age 18, in millions, is predicted to increase by m. (c) What does the model predict the population of females under 18 (in millions) will be in 2040?

A Food Marketing Institute found that 27% of households spend more than $125 a week on groceries. Assume the population proportion is 0.27 and a simple random sample of 391 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 0.26? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.26. Round the answer to 4 decimal places.

inches is rated at R-11 and 6 inches is rated at R-19. Assuming that this relationship is linear, The R-value of insulation is a measure of its ability to resist heat transfer. For fiberglass insulation, 3(1/2) write the equation that gives the R-value of fiberglass insulation R as a function of its thickness t (in inches). (Give an answer using exact values. Do not round.)

A fair coin is flipped 13 times. Find the probability that more than 5 of the flips turn up tails. 0.757636 0.709473 0.683847 0.573194 0.734094 0.657303

Leticia manages a company whose total weekly revenue is R(q) = 240q - 0.04q² dollars when q units are produced and sold. Currently, the company produces and sells 60 units a week. Using marginal analysis, Leticia estimates the additional revenue that will be generated by the production and sale of the 61st unit. What does she discover? Based on this result, should she recommend increasing the level of production?

For 1998 through 2005, the sales S (in billions of dollars) of sporting goods can be modeled by S = 0.007³ + 0.1t² + 1.4x + 70 where t is the number of years since 1998. In which year were sales about $78 billion?

A particle is moving along the parabola x² = 4 (y + 3). As the particle passes through the point (8, 13), the rate of change of its y-coordinate is 2 units per second. How fast, in units per second, is the x-coordinate changing at this instant?

Grocery Store Revenue For the 25 years that a grocery store has been open, its annual revenue R (in millions of dollars) can be modeled by R= 1/10,000 (-t4 + 12t³ - 77t² + 600t + 13, 650) where t is the number of years the store has been open. In what year(s) was the revenue $1.5 million?

Two cities are 1800 km apart and lie on the same north-south line. The latitude of the northernmost city is 84° N. What is the latitude of the other city? The radius of the Earth is approximately 6400 km.

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.