Basic Math Questions and Answers

You roll two fair dice. If they land with a sum of 7, you get a $10. If they land with a sum of 6 or 8, you get $5. Everything else earns $0. Which of the following would be the highest value you could set the price and the player would still win? $10 $8 $5 $2

Without a calculator, determine whether the following quantities are positive or negative. 1.-51^-60 2. (−71)^8 3. (−67)^-7 4. (-71)⁰ 5.91^-1

Provide an appropriate response. Find the sample standard deviation. 22 29 21 24 27 28 25 36 1.6 4,2 4,8 2.8

Find the slope of the line that passes through (9, 9) and (1,4). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

A garden measures 24 feet by 21 feet, and the owner of the garden wishes to divide the garden into two parts by installing a fence from corner to corner. Find the cost of the total length of the fence if fence costs $2.00 per foot.

There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is that when added together, their ages total 106 years. Kirk is twice ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, and Matt is 6 years older than half the manager's age. What are all four of their ages? It may help to set up four let statements, one for each employee (including the manager).

Marcus needs to bike at least 80 miles this week for his training. If he has already biked 23 miles this week, then how many miles should he bike on each of the 5 remaining days this week?

Tamika finds some nickels and quarters in her change purse. How many coins does she have if she has 10 nickels and 11 quarters? How many coins does she have if she has a nickels and y quarters?

Suppose that $100,000 from a retirement account is invested in a large cap stock fund. After 25 yr, the value is $183,777.11. (a) Use the model A=Pez^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.

Victor and his sister have both been saving money to help pay for college. Victor deposited $750 at a local bank 3 years ago, earning a simple interest rate of 4% paid upon withdrawal. His sister deposited $800 at a local bank 3 years ago, earning a simple interest rate of 3% paid upon withdrawal. Compare the interest Victor earned after 3 years to how much interest his sister earned after 3 years?

Catherine earns a yearly salary of $75,000. Lola earns a yearly salary of $80,000. Catherine will receive a salary increase of $4,800 per year, and Lola will receive a salary increase of $3,900 per year. Which equation can be used to find n, the number of years it will take Catherine to earn the same salary as Lola? 75,000+ 4,800n = 80,000+ 3,900n 75,000n +4,800 = 80,000n + 3,900 75,000n + 4,800 = 80,000+ 3,900n 75,000n +4,800n = 80,000n + 3,900n

The equation c = 2.5t represents the cost, c, for t tickets to the school play. Does a value of 3.5 for t make sense in this situation? Explain your reasoning.

Use Hooke's Law to determine the work done by the variable force in the spring problem. Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

Two lines are cut by a transversal. If you want to show that the lines are parallel, which of the following angle pairs would you show to be congruent? I. Alternate interior II. Vertical III. Consecutive interior IV. Alternate exterior V. Corresponding A I, IV, and V only B I and IV only C I, II, and V only D I, III, and V only

What will a $150,000 house cost 10 years from now if the price appreciation for homes over that period averages 6% compounded annually? The future cost of the house will be $ (Do not round until the final answer. Then round to the nearest cent as needed.).

Use your calculator to find the value of y for the system of equations using matrices. 2x - 3y + 2z = 13 3x+y=z=2 3x - 4y - 3z = 1

A radio station claims that the amount of advertising per hour of broadcast time has an average of 12 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 15 minutes. Calculate the z-score for this amount of advertising time. z = 1.15 z = -2.50 Z=-1.15 z = 2.50

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $90 and you pay 70% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $30 and you pay 90% of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

An investment company pays 8% compounded semiannually. You want to have $17,000 in the future. (A) How much should you deposit now to have that amount 5 years from now? (Round to the nearest cent.) (B) How much should you deposit now to have that amount 10 years from now? (Round to the nearest cent.)

What is -9.2(8x-4) +0.7(2+6.3x) simplified? -69.19x-32.39 -69.19x + 38.2 72.2x + 41.21 75x-338.2

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = x, y = 0, X = 6 (a) the x-axis (b) the y-axis (c) the line x = 6 (d) the line x = = 9

A city's population in the year x = 1959 was y = 1,775,650. In 1953 the population was 1,774,750. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: The population is increasing at a rate of 150 people per year. The population is increasing at a rate of 50 people per year. The population is decreasing at a rate of 250 people per year. The population is decreasing at a rate of 150 people per year. The population is decreasing at a rate of 50 people per year. The population is increasing at a rate of 250 people per year.

Convert the measurement 2710 g= kg

Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the quadratic equation P = -1.94x²+76.35x+737. The variable x represents the number of years since 1990. According to the equation, how many prisoners were there in the year 2001 (x = 11) and 2006 (x = 16)? There were approximately thousand prisoners in 2001. (Simplify your answer. Round to two decimal places as needed.) There were approximately thousand prisoners in 2006. (Simplify your answer. Round to two decimal places as needed.) *****

Convert the measurement. 3 yd = inches

The projected worldwide spending for a certain type of service, in millions of dollars, for the years 2006-2011 can be estimated by the polynomial s= -35.4x² +924.6x +493, where x is the number of years after 2006. Find the projected worldwide spending for x=0, x=2, and x = 5. Use the polynomial to estimate the projected worldwide spending for this service, in millions of dollars, for the year 2006 (x = 0). $million (Type an integer or a decimal.)

Graph the following quadratic function. f(x) = 2x² + 4x + 5 Find the vertex of the function.

Leo invested $1900 in an account with annually compounded interest. After 3 years, he had $2275 in the account. What was the interest rate of the account? Round your answer to one decimal place. Do not write the percent sign. Provide your answer below:

Determine whether the ordered pair is a solution to the inequality. y≥(x-1)² (a) (-4, 31) (b) (3, 0) (c) (-3,-15) (a) Is the ordered pair (-4, 31) a solution to the inequality?

Darryl made a deposit into an account that earns 7% annual compound interest. After 36 months, the value of his account was $1,041.29. What was the approximate amount of Darryl's initial deposit?

Hunter makes shoelaces for the cleats to earn money for the football team. Each shoelace needs to measure 50 3/4 inches long. He needs to make 4 shoelaces. How many inches does he need to make the 4 shoelaces?

The position function of a particle is given by s = 2t³ - 15t²-81t, t> 0. where s is measured in meters and t in seconds. Find all values of t> 0 for which the particle is moving at a velocity of 3 m/s t=

A pumpkin is launched 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s (t)=-4.92t2 +19.6t+58.8, where s is in meters. When does the pumpkin strike the ground?

The ages of 10 grooms at their first marriage are listed below. Find the midquartile. 35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9 34.2 43.7 34.1 34.5

x+2y-2z = 10 -3x+4y+z=-5 -5x+y+3z=-21 Find the unique solution to this system of equations. Give your answer as a point.

Josie and Red are two dogs standing next to each other at the dog park. Josie starts running straight west and Red starts running straight east. After 22 seconds, the two dogs are 1,100 feet apart. Suppose Red runs 4 feet per second faster than Josie. How fast were each of the dogs running?

A gardener has 880 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. shorter side: What dimensions would guarantee that the garden has the greatest possible area? ft (feet) longer side:

Find the x-intercept(s) algebraically. f(x)=2x²-9x+9 X= (Type an exact answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once. Use a comma to separate

Solve the system by elimination or by any convenient method. (If the system is dependent, enter DEPENDENT. If there is no solution, enter NO SOLUTION.) x + 2y = 3 3x+6y= 12 (x, y) =

If a car travels 37 miles per gallon of fuel (in other words, the car does 37 mpg), how many kilometers does it travel per liter of fuel? Use the conversion factors on page 55 (that is, use 1 mile 8/5 km and 1 gallon = 8 pints and 1 liter ≈ 2 pints). The car trav's about km on one liter of fuel

Suppose you wish to take out a loan for $15,000 at an annual interest rate of 5.25%, compounded monthly. If you want each payment to be as close as possible to $200.00, how long should the period of the loan be? Choose the correct answer below. 10 years 9 years 8 years 7 years

Tomas needs exactly 6 potatoes to make 12 potato pancakes. Which of the following statements are true? Tomas needs exactly 12 potatoes to make 24 potato pancakes. Tomas needs exactly 18 potatoes to make 36 potato pancakes. Tomas needs exactly 24 potatoes to make 44 potato pancakes. Tomas needs exactly 30 potatoes to make 60 potato pancakes. Tomas needs exactly 36 potatoes to make 78 potato pancakes.

Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?

In ΔCDE, M∠C = (x − 4)°, m∠D = (11x – 11)°, and m∠E = (x + 13)°. Find m∠C.

Find the LCM of the set of algebraic expressions. 20y², 12yz, 15z

The owner of Kensington Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 15 small arrangements and 15 large arrangements, which took her a total of 195 minutes. After lunch, she arranged 12 small arrangements and 7 large arrangements, which took 121 minutes. How long does it take to assemble each type?

The function g is defined as follows. g(x)=4x²+3 If the graph of g is translated vertically downward by 8 units, it becomes the graph of a function f. Find the expression for f(x). Note that the ALEKS graphing calculator may be helpful in checking your answer.

Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

Standard form: Expanded form: 9 * 1,000,000 + 8 * 1,000 + 7 * 100 + 6 * 10 Word form:

Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour? 0.8 of an inspection in 1 hour 4 inspections in 5 hours 1.25 inspections in 1 hour 5 inspections in 4 hours