Basic Math Questions and Answers

Compute the discriminant of 8x² - 6x - 6 = 0. The discriminant is: How many real solutions does the equation, 8x2 - 6x - 6 = 0, have? No real solution One real solution Two real solutions None of the above

If P dollars is invested in an account that earns interest at 7% compounded annually, the amount available after t years is A = P(1 +0.07). How many years will it take for $1500 in this account to grow to $3000? It will take approximately years for $1500 in this account to grow to $3000. (Round to the nearest whole year.)

A plane is 115 mi north and 176 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.

The formula for the braking distance of a car is: d =V²/2g(f+ G) where: d is the braking distance (in feet) V is the initial velocity of the car (in feet per second) G is the roadway grade (written in decimal form) f is the coefficient of friction between the tires and the roadway g is the acceleration constant due to gravity (32.2 ft/sec²) a) If a car's speed was 47 miles per hour, what value would be used in this formula for V? Round to the tenths place. Recall 1 mile = 5280 feet. feet per second b) If a car was going 86 feet per second when the driver applied the brakes, on a road with grade G = 0.03 and a coefficient of friction of f = 0.8, what distance would it go before stopping? Round to the tenths place. feet

Find the interest rate to the nearest hundredth of a percent that will produce $2000, if $1500 is left at interest compounded quarterly for 4.5 yr. Use the formula A=P (1+r/n)tn The interest rate to the nearest hundredth of a percent is. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Suppose that you are grading a classmate's work on a compound interest problem, shown below. If there is a mistake, select the step where the mistake was made. If there is no mistake, select "No mistake." Problem: How long will it take for an investment of $3500 to double if it is invested at 2.5% annual interest compounded monthly? Round your answer to three decimal places. Step 1: 7000-3500 (1 + 0.25) 12 Step 2: 2 = (1 + 0.25) 12 12 Step 3: log(2) = log ((1+0,25)¹²) Step 4: log(2) Step 5: t = O Step 1 Step 2 Step 3 Step 4 Step 5 No mistake 12t log(1 + 025) 12 log(2) (12 log (1+0)) 2.801 years 12

In a class, having more number of girls than boys, students were given a task of collecting flowers. Each boy collected 5 flowers whereas each girl collected 3 flowers. If a total of 46 flowers were collected, which of the following could be the number of girls in the class?

Landon went to the store to buy a new TV. The sales clerk asked "How large is your current TV?". Landon replied "It is 37 inches wide and 21 inches tall". The sales clerk explained that TVs are sold by the measurement along the diagonal of the screen. Save Landon a trip home to remeasure What is the diagonal measurement for Landon's current TV, rounded to one decimal place?

Use the multiplication principle to solve. An auto manufacturer produces 8 models, each available in 9 different colors, with 6 different upholstery fabrics and 7 interior colors. How many varieties of car are available?

The height of a trapezoid is 15 feet and the two bases are 10 and 11 feet. Find the area of the trapezoid.

Use A=(5, 6, 7, 8, 9) and B={1, 3, 7, 8) to find the set A∩B. A∩B= (Use a comma to separate answers as needed.)

Find the distance between the points (-10, -9) and (-2,-2).

In response to rising concerns about identity theft, the number of models of paper shredders a company manufactures increased approximately steadily from 5 models in 1997 to 37 models in 2008. Find the average rate of change of the number of shredder models manufactured per year between 1997 and 2008. The average rate of change of the number of paper shredders manufactured per year between 1997 and 2008 was (Type an integer or decimal rounded to two decimal places as needed.)

Jerome is planning on tiling his bathroom floor with square tiles measuring 8 inches on each side. The bathroom measures 13 feet by 15 feet. a) What is the area of the floor, in square feet? b) Convert this area to square inches. c) How many 8 inch square tiles will Jerome need to cover the floor?

The value of a machine, V, at the end of t years is given by V = C(1-r)', where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was $2387 and r = 0.2. Round to the nearest cent.

A student has a credit card that is only used for school expenses. Their fall tuition was $1295, and the cost of books was $100. Both of these are put onto their credit card. a) Suppose these are the only two expenses on their credit card. When the bill arrives, they pay the minimum payment of $30. How much will be left on their credit card bill and therefore subject to interest? b) If the annual interest rate for their credit card is 17.99%, what is the periodic (monthly) interest rate, to 2 decimal places? c) How many dollars of interest will be added to their bill for the next month, to the nearest cent?

The hotness of chili peppers is usually measured in Scoville units. Using a log scale for Scoville units works well to compare the heat of peppers. a) A Jamaican Hot Pepper has hotness around 200,000 Scoville units. Plot this value on the log scale below. b) Another chili's hotness is shown on the number line below. What is, approximately, the hotness of the chili shown on the number line? Scoville units.

The population of foxes in a certain region over a 2-year period is estimated to be P₁(t) = 300 + 60 sin(πt/12) in month t, and the population of rabbits in the same region in month t is given by P₂(t) = 2000 + 300 cos((πt/12) Find the rate of change of the populations when t = 4. (Express a decrease in population as a negative rate of change. Round your answers to one decimal place.)

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 3xex, a=0

The formula for changing Celsius (C) temperature to Fahrenheit (F) temperature is F = 1.8C + 32. To the nearest degree, what is the Fahrenheit temperature when the Celsius temperature is -8? A -18 degrees B -17 degrees C 17 degrees D 18 degrees

Emilio buys a sofa for a total purchase price of $1,309.79. State taxes were 4.4%. What is the sales tax amount for his purchase? (Round your answer to the nearest cent.) $50.38 $55.20 $57.63 $62.37

Randy buys a lawn tractor costing $975.90. The store charges $35 for assembly and $30 for delivery. State taxes are 4% and local sales taxes are 3%. What is the total purchase price? (Round your answer to the nearest cent.) $1,082.54 $1,109.21 $1,113.76 $1,115.01

Aliza had a tax liability of $6,218 last year. She was entitled to tax credits of $748 and withholding amounted to $540 per month. Aliza owed other taxes of $606. Calculate the amount of the refund or the amount of taxes due (as the case may be). $344 refund $404 refund $1,010 refund $4,930 due

Find the distance between the points (2, 9) and (-10, 1). Hint: Use the Pythagorean theorem.

Aaron's dad has a pickup truck and his mom has an SUV. Last week, his dad traveled 84 miles in the pickup truck on 4 gallons of gas. His mom traveled 72 miles in the SUV on 3 gallons of gas. How many more miles per gallon did the SUV get than the truck?

Jeremy has a total of $25 in dimes and nickels. He has 4 more dimes than nickels. Which system of equations can be used to determine the number of dimes, d, and the number of nickels, n, that Jeremy has?

Water is passed through a pipe containing porous material to filter out pollutants. Each inch of pipe removes 50% of the pollutant entering. (a) True or false: The first inch of the pipe removes 50 % of the pollutants and the second inch removes the remaining 50 %. (b) What length of pipe is needed to remove all but 8% of the pollutants? Round your answer to three decimal places. inches of pipe removes all but 8% of the pollutants.

Isosceles trapezoid ABCD with AB || CD has m (<A) = m (<B) = 60°, small base CD = 12 cm and non-parallel side BC = 24 cm. Find the large base AB and the lengths of the diagonals AC and BD.

Bernie and LuLu are selling fruit for a local fundraiser. Customers can buy boxes of apples or boxes of oranges. Bernie sold 7 boxes of apples and 7 boxes of oranges for a total of $147. LuLu sold 7 boxes of apples and 10 boxes of oranges for a total of $183. Determine the cost of one box of apples and one box of oranges.

Solve the equation 0.05e^-0.344t = 0.15 using natural logs. NOTE: Enter the exact answer. t =

Yolanda owns some property that has an assessed value of $59,928. Find the tax due if the tax rate is 8.33% of the assessed value. (Round your answer to the nearest cent.) $4,794.24 $4,974.02 $4,992.00 $5,393.52

Amy and Derek are married and filing jointly. Their taxable income is $36,847. Use the Tax Table, Exhibit 18-3 from your text to find the tax liability. $4,040.64 $4,149.64 $4,231.14 $4,421.64

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours. 0.0008 0.0025 0.0036 0.0103

Terrance hopes to earn $600 in interest in 4.9 years time from $30,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

A single fair die is tossed. Find the probability of rolling a number greater than 4. What is the total number of possible outcomes? What is the number of outcomes greater than 4? What is the probability of rolling a number greater than 4? (Simplify your answer. Type an integer or simplified fraction.)

If sin (θ) = 15/25 and θ is in Quadrant II, then what is sin(θ/2) ? your answer completely and rationalize the denominator.

The atmospheric pressure, p, in pascals, on a weather balloon decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the number of kilometers, h, above sea level by the function p(h) = 760 (2.7)-0.145h. Use this function to perform the following, showing your work and rounding answers to the nearest hundredth. 1. Find the atmospheric pressure, in pascals, at a height of 3 kilometers. 2. Find the height, in kilometers, when the atmospheric pressure is 200 pascals.

15.Suppose that you invest $2,500 in an account that makes 3% annual interest compounded monthly. Use the formula A = P(1+r/n)^nt to answer the following questions. a) How much money will be in the account after 6 years? b) How much money will be in the account after 4 months? c) How long will it take for the account to reach a balance of $7,000?

Video Games How many different ways can 10 different video game cartridges be arranged on a shelf?

Suppose you bought speakers for a total purchase price of $598.36. If state taxes were 5.65%, what was the amount of the sales tax? (Round your answer to the nearest cent.) $29.92 $32.00 $33.81 $37.31

A sample of 20 elements produced a mean of 91.4 and a standard deviation of 11.16. Assuming that the population has a normal distribution, the 90% confidence interval for the population mean is:

2014 Top Albums (Based on U.S. sales) Of all of the U.S. album sales, album 1 accounted for 25% of sales, album 2 accounted for 25.2 % of sales, and album 3 accounted for 0.2% of sales. What is the probability that a randomly selected album was something other than these three albums? The probability that a randomly selected album was something other than these three albums is

In a random sample of 53 items produced by a machine, the quality control staff found 5 of them to be defective. Calculate the point estimate of the population proportion of defective items. Round to 4 decimal places.

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. What is the minimum amount of hours she will need to babysit in order for her to buy her calculator?

Current Attempt in Progress Evaluate e ln11 - In e7 without a calculator, or say if the expression is undefined. If the expression is undefined enter NA, otherwise enter the exact answer.

You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately o = 26.3 dollars. You would like to be 95% confident that your estimate is within 4 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Algebraically solve the following system of equations. There are two variables that can be readily eliminated, but your answers will be the same no matter which you eliminate first. 2x+5y-z = -35 x-3y + 4z = 31 -3x+2y+2z = -23

Compute the upper Riemann sum for the given function f(x) = 5-x² over the interval x = [0, 1] with respect to the partition P = [ 0,1/4,3/4,1]

Assume that random guesses are made for 8 multiple choice questions on a test with 5 choices for each question, so that there are n-8 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers. The probability of no correct answers is (Round to three decimal places as needed)

Factor completely. 2x² - 12x - 144 prime (not factorable) (2x − 12) (x + 12) 2 (x - 72) (x + 1) 2 (x - 12) (x + 6)