Basic Math Questions and Answers

The volume of a cone is 113.04 mm2. What is the approximate volume of a sphere that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth. 113.04 mm³ 226.08 mm³ 904.32 mm³ 3,052 mm³

Identify the number of solutions the following equation has: 7-5(z-6) +4=3-2(z-5)-3z +28. No Solution Unique Solution Infinitely Many Solutions

Which of the following represents vector t = -8i + 6j in trigonometric form? t= 10 (cos 36.87°, sin 36.87°) t= 10 (cos 143.13°, sin 143.13%) t= 10 (sin 36.87°, cos 36.87°) t= 10 (sin 143.13°, cos 143.13%)

The path of the object thrown above the ground level is given by the function s(t) = 2t2 + 5t + 3. Rewrite it in factored form. (2t+3)(t-1) (2t+3)(t+1) (2t-3)(t+1)

Solve for x and write the solution set using set-builder notation: 1.5-0.25x ≤ 6 {x|x ≥-18} {x|x ≥-10} {x|x ≤ 8}

Function W gives the weight of a cat t weeks after it was born. The weight is measured in pounds. Use function notation to represent this statement: 10 weeks after the cat was born, it weighed 8 pounds. t=8, W=10 10(8) = W W(10)=8 W(8)=10

Dan traveled to his friend's house and back. The trip there took two hours and the trip back took three hours. What was Dan's average speed on the trip there if he averaged 20 mph on the return trip? 25 mph 50 mph 42 mph 43 mph 30 mph

Write an equation for a line perpendicular to y = 2x - 5 and passing through the point (2,2) y =

A bike shop rents bikes for $4 per hour, and helmets for $8 per day. Justin has less than $ 20 to rent a helmet and a bike for x hours. Which of following inequality represents this situation? 4x+8 = 20 4x+8<20 4x-8<20

If a couple has $50,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6% compounded continuously? Write your answer as an exact value.

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its width Find the length and width of the pool. I=30, w = 30 I=52, w = 25 I=25, w = 35

Simplify the following expressions completely. Assume all variables represent non-negative numbers. A)√16p26 B)√81m22 =

Which is the equation of a circle with diameter AB where A(5, 4) and B(-1,-4)? Select one: a. (x + 2)² + y² = 5 b. (x + 5)² + (y - 4)² = 100 c. (x-2)² + y² = 25 d. (x - 5)² + (y-4)² = 10

Mary has $18.50 to buy pizza. A cheese pizza costs $14. Each extra topping cost $0.75. How many extra toppings can she buy? 4 toppings 6 toppings 3 toppings

A website uses the formula above to calculate a seller's rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of the other variables?

Find the Z-scores that separate the middle 75% of the distribution from the area in the tails of the standard normal distribution The Z-scores are

Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate. Determine the equation of the horizontal asymptote that corresponds to the limit as n → ∞. Equation of horizontal asymptote: No horizontal asymptote corresponds to the limit as n→∞. Determine the equation of the horizontal asymptote that corresponds to the limit as n → -∞. Equation of horizontal asymptote: No horizontal asymptote corresponds to the limit as n→-8

How many real and imaginary solutions does the equation x² + x = 11 contain? 1 real solution; 1 imaginary solution No real solutions; 2 imaginary solutions 1 real solution; no imaginary solutions 2 real solutions; no imaginary solutions

A certain forest covers an area of 1800 km². Suppose that each year this area decreases by 3%. What will the area be after 13 years? Use the calculator provided and round your answer to the nearest square kilometer.

The payments of a lease are $290 a month for 48 months. Jessica paid a deposit of $300, a title fee of $70, and a license fee of $30. At the end of the lease she can buy the car for a residual value of $5,500. What is the total cost if she buys the car at the end of the lease? $19,820 $18,920

An airplane flies on a compass heading of 90.0 degrees at 480 mph. The wind affecting the plane is blowing from 294 degrees at 28mph. What is the true course and ground speed of the airplane? Round results to an appropriate number of significant digits.

A stereo salesperson earns a salary of $1,900 per month, plus a commission of 4% of sales. If the salesperson wants to maintain a monthly income of at least $2,200, what is the total cost of the stereos that the salesperson must sell in each month (write the solution set)? {xx<3500} (x:x≥ 7500) (x:x>4500)

What are the 3 types of logarithms we have studied so far? In writing your answer, please make sure to use the proper mathematical notation, and focus in particular on the bases of the logarithms. Please spend at least 3 sentences to complete your answer.

A community center is selling greeting cards which are in a box. Its goal is to sell $100 worth of cards. Each box sells for $3. Determine the number of boxes needed to be sold in order to achieve the goal. 30 boxes of cards 28 boxes of cards 34 boxes of cards

Find the length of the longest side of the rectangle whose dimensions are given by 2x and 5x -1, and has a perimeter of 26 feet. 6 ft 9 ft 4 ft

The width of the rectangular room is 3 less than its length. If the perimeter of the room is 26 feet, find the dimensions of the room. Length = 5 feet; width = 3 feet Length = 3 feet; width = 5 feet Length = 8 feet; width = 5 feet

The manager of a store that specializes in selling tea decides to experiment with a new bieno. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $3 per pound to get 800 pounds of the new blend. The selling price of the new blend is to be $4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required? The blend should have pounds of Earl Grey and pounds of Orange Pekoe.

A landscaping company estimates the price of a job in dollars, using the expression 60 - 12h, where is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 12 in the expression? The company charges $12 per hour for each landscaper, A minimum of 12 landscapers will work on each job. The price of every job increases by $12 every hour, Each landscaper works 12 hours a day

An expedition leader estimates that a group of hikers can carry less than or equal to 561 lb of food and equipment. The group must carry 336 lb of equipment and 25 lb of food for each climber. What is the greatest possible number of people in the expedition? Write in set builder form. {TERI < 5.36} {XEN < 6 (XEN P

Robert is baking a cake. The recipe calls for more than 7 cups of sugar. He has already added 2 cups. Let x represent the number of more cups to be added. Which one of the following inequality represents the above situation? x+7<2 X-2<7 x+2>7

The city wants to determine whether your neighbourhood park should have an enclosed off leash area. Which sampling technique would be best to use? a. Simple Random b. Convenience c. Multistage d. All the above

Solve for v. v²+5v-6=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

Carlos rents CDs for $4.5 per hour, and CD player for $6.5 per day. Austin has less than $30 to rent a CD and a CD player for x hours. Which of the following inequality represents this situation? 45x-65<30 4.5x+6.5 > 30 4.5x+6.5 < 30

At the state senate, 78% of senators voted to support a bill. Assuming every senator voted and was recorded, the 78% represents a parameter sample statistic mean

Cut a 10 ft long piece of wood into two pieces, so that one piece is 2 ft. longer than the other. Which of the following equations depicts the given situation? 2(x+1)= 10 x+2=10 X/2=10

Solving z²+14z - 9 = 0 by completing the square method produces an equation of th (z+h) ² = k. Find h and k h = k=

Which question is biased? a. Are you dissatisfied with the current mayor? b. Should the government increase property taxes? c. Should the minimum age requirement to get a driver's license be changed? d. Do you prefer watching movies at home or in a theatre?

To earn full credit for this question, you must show all your work. Find the quotient and remainder. (12r³ - 5x² + 9x - 4) ÷ (4x − 3) The quotient is The remainder is

Solve for x. x² +8x+15=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

A ship traveled at an average rate of 22 miles per hour going west. It then traveled at an average rate of 12 miles per hour heading north. If the ship traveled a total of 158 miles in 9 hours, how many miles were traveled heading north? (Do not include the units in your response.)

A ship traveled for 4 hours heading south and for 5 hours heading west. If the total distance traveled was 191 miles, and the ship traveled 4 miles per hour faster heading west, at what speed was the ship traveling west? (Do not include the units in your response.)

On a snow day, Kayden created two snowmen in his backyard. Snowman A was built to a height of 59 inches and Snowman B was built to a height of 34 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 7 inches per hour and Snowman B's height decreased by 2 inches per hour. Let A represent the height of Snowman A t hours after sunrise and let B represent the height of Snowman B t hours after sunrise. Write an equation for each situation, in terms of t, and determine the interval of time, t, when Snowman A is taller than Snowman B.

Which of the following mathematical statements shows "the quotient of a number and six is eight"? X-6=8 X/6=8 Xx6=8

An electrician charges $15 per hour and spends $30 a day on gasoline. At the end of the day, he is left with $105. Represent his earnings for one day using a mathematical statement if he works for "x" hours in a day. 15/+30=105 15x-30 = 105 15x = 105

Three times a number x increased by 8 is 14. Which one of the following equations represents the given statement? 3(x+8)= 14 3 x=8+14 3x+8 = 14

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1% level?

Two times a number x increased by 8 is 20. Which one of the following equations represents this statement? 2 x-8 = 20 2x+8=20 8x+2=20

Alex needs to make a repair. The part costs $430 and labor is 4 hours at $70 per hour. Sales tax is 8%. Sales tax is charged on the parts but not on the labor. What is the cost for the repair? $766.80 $744.40

Ella is going to drive a distance of 332 miles each way on a trip. She used 12 gallons of gas going there and 11 gallons returning. What was her gas mileage to the nearest mile for the entire trip? 29 miles per gallon 30 miles per gallon

Douglas needs to make a repair. The part costs $305 and labor is 2 hours at $70 per hour. Sales tax is 6%. Sales tax is charged on the parts but not on the labor. What is the cost for the repair? $471.70 $463.30