Basic Math Questions and Answers

Greg deposited $4000 into an account with 4.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years? Do not round any intermediate computations, and round your answer to the nearest cent.

Write the equation of the line passing through (-2,-4) that is parallel to 3x + 5y = 11.

A projection made in January of 2005 determined that x years later, the average property tax on a three-bedroom home in a certain community will be T(x) = 48x 3/2 + 40x + 1300 dollars. Estimate the percentage change by which the property tax will increase during the first half of the year 2012.

Find the zeros of the following polynomial. f(x) = x³ + 12x4 +36x³ List the zeros separated by commas. For example, if you found that the zeros were x = 1, x = 2, enter 1, 2, 3. Provide your answer below:

A fence is to have 3 1/2 wide boards between two posts that are 94 1/4 apart so that the space between each board is the same. Calculate the number of boards and the spacing so that the spacing between the boards is as small as possible. Round your answer for the spacing to the nearest 16th of an inch.

A particle moves according to the law of motion s = t³ - 8t2 + 3t, t ≥ 0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1,2] (b) Find the velocity at time t. (c) What is the velocity after 3 seconds? (d) What is the acceleration after 7 seconds? (e) Fort > 0, when is the particle moving in the positive direction?

After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.

If a single pane of glass obliterates 2% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function below. p(n)= 100(0.98)n (a) What percent of light will pass through 20 panes? (b) What percent of light will pass through 30 panes? (c) Explain the meaning of the base 0.98 in this problem.

A gray crayon is made with 5 mL of black wax for every 6 mL of white wax. Which of the following wax mixtures will create the same shade of gray? Choose 2 answers: 10 mL of black wax mixed with 24 mL of white wax 15 mL of black wax mixed with 18 mL of white wax 35 mL of black wax mixed with 42 mL of white wax 20 mL of black wax mixed with 26 mL of white wax 45 mL of black wax mixed with 48 mL of white wax

Sketch the graph of a function f that satisfies all of the following properties. Indicate all asymptotes. (a) f(x) is defined for all real numbers except x = 1. (b) f(x) is discontinuous at x = -2 and x = 1, but is continuous for all other z. (c) f(x) is not differentiable at x = -2, x = 1, and x = 4 but it is differentiable for all other . (d) lim f(x) = 3, (e) lim f(x) = -2, (f) lim f(x) = -0.

A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. Find the length and the width The parking lot has a width of The parking lot has a length of yards. yards.

A lunar module weighs 12 tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 55 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth.

Henry made a shirt using 1/3 yards of red fabric and 3/4 yards of blue fabric. How many more yards of blue fabric did Henry use? Write your answer as a fraction in simplest form.

{(-9, 3), (5, -6), (3, -9), (-6, 5), ?} Which ordered pair can replace the missing value and create a function? (5,3) (9,3) (-6,-9) (-9,-6)

Graph the following quadratic function. f(x)=x²-9 Find the vertex of the function. The vertex is (Simplify your answer. Type an ordered pair.)

The local bakery requires that Josh must spend at least $7 to be able to pay using a credit card. Cookies cost $2.10 each. A bottle of water costs $1.10. If c represents the number of cookies Josh would need to buy to pay for one bottle of water and the A cookies using a credit card, which of the following inequalities best models the situation described above?

A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. a. How many miles has the car traveled if it has the following amounts of gas left in the tank? i. 15 gallons ii. 10 gallons iii. 2.5 gallons

Lottery Prizes A lottery offers one $800 prize, two $500 prizes, two $400 prizes, and five $200 prizes. One thousand tickets are sold at $7 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

Find the real solutions of the following equation. x4-17x² +16=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.

Multiple Choice Which is not a possible classification of the zeros of f(x) = x4 + 2x³-7x² - 7x + 3 according to Descartes' rule of signs? A. 2 positive real zeros, 2 negative real zeros, and 0 imaginary zeros B. 0 positive real zeros, 2 negative real zeros, and 2 imaginary zeros C. 0 positive real zeros, 0 negative real zeros, and 4 imaginary zeros D. 1 positive real zero, 1 negative real zero, and 2 imaginary zeros

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