Basic Math Questions and Answers

The radius of a cylindrical water tank is 5.5 ft, and its height is 8 ft. What is the volume of the tank? Use the value 3.14 for π , and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.

Jada is making lemonade for a get-together with her friends. She expects a total of 5 to 8 people to be there (including herself). She plans to prepare 2 cups of lemonade for each person. The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n represent the number of people at the get-together, c the number of cups of water, the number of scoops of lemonade powder. Select all the mathematical statements that represent the quantities and constraints in the situation. A. 5 <n<8 B.5≤n≤8 C. c = 2n D. l = c E. 10 <c< 16 F. 10 ≤ l ≤ 16

Of 23 employees at a local supermarket, 11 work as cashiers and 12 stock shelves. If 2 employees are selected at random to work overtime, determine the probability that both are cashiers. The probability is (Type an integer or a simplified fraction.)

A rowing team rowed 100 miles while going with the current in the same amount of time as it took to row 20 miles going against the current. The rate of the current was 6 miles per hour. Find the rate of the rowing team in still water. Rate of the team in still water:

Maria, Sam, and Jose are standing in a triangle for the kick off of a soccer game. The referee wants to drop the ball so that it is the same distance to each player. Where should the referee stand so that he places the soccer ball the same distance from each player. Assume the players will take a direct path. Treat the players as sides of a triangle. The place the soccer ball is dropped is at the players incenter. Treat the players as vertices of a triangle. The ball should be dropped at the players incenter.. Treat the players as vertices of a triangle. The place the soccer ball is dropped is at the players circumcenter. Treat the players as sides of a triangleThe place the soccer ball is dropped is at the players circumcenter

The one-to-one function fis defined below. f(x)=(x-9)³ Find f-¹(x), where f-¹ is the inverse of f.

Utilize the Slide and Divide method to rewrite the following quadratic equation in factored form: 6x² +7x+2 (2x-1)(3x+2) (2x+1)(3x+2) (2x-1)(3x-2) (2x+1)(3x-2)

A windshield wiper blade is 9 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 132°? 93.26 inches2 75.4 inches² 46.63 inches² 20.72 inches²

There are 3 neighboring orchards, A, B, and C. Orchard A has 60 fewer fruit trees than Orchard B. Orchard C has 3 times as many fruit trees as Orchard B. If the three orchards have 430 fruit trees altogether, how many fruit trees does Orchard C have?

Suppose that the functions p and q are defined as follows. p(x) = -x q (x) = -2x²+1 Find the following.

The total cost C (in dollars) to participate in a ski club is given by the literal equation C = 85x + 60, where x is the number of ski trips you take. a. Solve the equation for x.

If 76 people attend a concert and tickets for adults cost $3 while tickets for children cost and total receipts for the concert was $184, how many of each went to the concert? adults children

Golf Clubs R Us had a set of 10 golf clubs that were marked on sale for $850. This was a discount of 35 % off the original selling price. Step 1 of 4: What was the original selling price? Follow the problem-solving process and round your answer to the nearest cent, if necessary.

When hunting prey at night, Japanese sea catfish use their sense of smell, their hearing, as scientists have recently discovered, and their ability to detect vibrations. these fish can additionally notice slight chemical changes in the water that indicate the presence of sea worms.

Find the slope-intercept form of the line whose slope is 2 and that passes through the point (-7,11).

Directions: For the given inequality, determine if the provided numbers are solutions. Place a check mark in the box if it is a solution, and an "x" in the box if it is not. 1. x>9 2.x≤-4 9 -5 -8 -4 0 -4 1.2 -4.2 5/2 -5/4

(a) A color printer prints 5 pages in 3 minutes. How many minutes does it take per page? (b) It takes 33 pounds of seed to completely plant a 5-acre field. How many pounds of seed are needed per acre?

What is 92% of 50? What is 16% of 25? What is 20% of 20? What is 35% of 25? What is 30% of 100? What is 40% of 25?

Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) f(x) = 3x4 - 18x³+x-6 Concave upward: Concave downward:

To find the proportion of San Diegans subscribed to Disney+ in 2019, a researcher randomly selected 200 people from San Diego and found that 101 were subscribed. a) Check that the assumptions are met for a confidence interval for proportions.

A pebble is tossed into the air from the top of a cliff. The height of the pebble over time is modeled by the equation y = - 16x² + 32x + 80. What is the maximum height, in feet, reached by the pebble? How long did it take to reach the maximum height?

Ms. O'Malley's cousin lives 1,650 miles away. Ms. O'Malley won a gift card for 100 gallons of gas. If her car can travel 35 miles on each gallon, can she drive roundtrip to see her cousin on the free gas? Explain how you know.

In a class of 30 IB students, 20 study mathematics SL, 12 study physics and 8 study both of these subjects. Find the probability that a randomly selected student does not study both of these subjects.

Employees at an office were surveyed about what types of hot beverages they drank that day. It was found that 50% of them drank coffee and 25% drank tea. The survey showed that 10% of the employees drank both coffee and tea. For these employees, are the events "drank coffee" and "drank tea" mutually exclusive? Choose 1 answer: AYes B No Find the probability that a randomly selected person from this group drank coffee OR drank tea. P (coffee OR tea):=

Identify the property that justifies each step asked about in the answer area below. Line 1: (7x) (10y) Line 2: 7. (x 10) y Line 3: 7.(10 x) y Line 4: (7.10)(x - y) Line 5: 70xy Line 1 to Line 2: Line 2 to Line 3: Line 3 to Line 4:

What is the equation, in standard form, of a parabola that contains the following points? (-2,-16), (0, -4), (4, -28) a y = 2x² - 2x - 4 b y = 2x² - 2x + 4 c y = 4x² + 2x + 2 d y = -2x² + 2x - 4

Ron needs 17 gallons of gas to get to and from work every week. Last week gas cost $2.44 per gallon. This week it dropped to $2.32 per gallon. How much less money did Ron spend this week on gas for work?

Four employees of Papa Tony's Pizza are cleaning up at the end of a busy night. There is a list of 43 clean-up tasks that need to be completed. If each employee does the same number of tasks, how many tasks should each employee do? Solve. Explain how you interpreted the remainder.

A rock thrown vertically upward from the surface of the moon at a velocity of 20 m/sec reaches a height of s=20t-0.8t meters in t sec. a. Find the rock's velocity and acceleration at time t. b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft? a. Find the rock's velocity at time t. Find the rock's acceleration at time t. (Simplify your answer. Use integers or decimals for any numbers in the expression.) b. How long does it take the rock to reach its highest point? (Simplify your answer.)

The weekly pay that Crystal receives varies directly with the number of hours she works. If she works 37 hours she makes 463.61, How much money would she make if she works 29 hours?

A town's population of children increased from 376 to 421 during the past year. Which equation shows how to find the percent increase? A.p =(421-376)/376 B.p =(421-376)/421 C.p =376/(421-376) D.p =(376+421)/376

Solve for q in terms of r and s. r = -qs q=

What is the image of (1, -1) after a dilation by a scale factor of 4 centered at the origin?

A sinusoidal function has an amplitude of 3, a period of π, and a maximum > 3. Which of the following functions could represent this data? y = 3 sin 2x + 1 y = 4 sin(x - π) + 3 y = 3 sin 2x - 1 y = 4 sin 2(x - π) + 3 y = 3 sin 2(x - π) + 4

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b= 1,500p where p represents the number of packets and b represents the number of bytes of information. Type the answers in the boxes below. 1. How many packets would be needed to transmit 30,000 bytes of information? 2. How much information could be transmitted in 30,000 packets? 3. Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets, p and the number of bits, z.

Members of a lacrosse team raised $1814.75 to go to a tournament. They rented a bus for $1168.50 and budgeted $58.75 per player for meals. Which equation could be used to determine x, the number of players the team can bring to the tournament?

The test scores of 32 students are listed below. Find Q 3. 32 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99 79.5 24 80 79

The measure of an angle is 1°. Find the measure of the complement. The complement is

There are 3 neighboring orchards, K, L, and M. Orchard K has 4 times as many fruit trees as Orchard L. Orchard M has 60 fewer fruit trees than Orchard K. If Orchards K and L together have 430 fruit trees, how many fruit trees does Orchard M have?

Graph the function by using transformations of the graph of y=1/x² Plot all necessary asymptotes. For vertical asymptotes, make sure there are at least two points on each side. g(x)=(1/(x+4)²)-2

Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (Enter your answers as a comma- separated list. If an answer does not exist, enter DNE.) f(t) = 2t + 1/t Relative maximum value(s): Relative minimum value(s):

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?

Penelope needs to borrow $9000. She can borrow the money at 4.5% simple interest for 3 yr or she can borrow at 5% with interest compounded continuously for 3 yr. (a) How much total interest would Penelope pay at 4.5% simple interest? (b) How much total interest would Penelope pay at 5% interest compounded continuously? (c) Which option results in less total interest?

Ursula has a mortgage of $88,000 at 6 3/4% for 25 years. Find the total interest. $79,184.27 $86,924.00 $94,424.00 $109,514.42

Of 26 employees at a local supermarket, 15 work as cashiers and 11 stock shelves. If 4 employees are selected at random to work overtime, determine the probability that all 4 are cashiers.

A student has some $1 and $5 bills in his wallet. He has a total of 14 bills that are worth $50. How many of each type of bill does he have?

Use the formula S = P(1 + r)t to complete parts (a) and (b). a. Graph the function that gives the future value of $70,000 invested at 3%, compounded annually, for t years, 0≤ts 12. b. Find the future value of $70,000 invested for 10 years at 3% compounded annually.

Bear Valley already had 4 centimeters of snowcover when a snowstorm moved in. The storm is increasing the amount of snowcover by 2 centimeters per hour. Write an equation that shows the relationship between the number of hours it has been snowing, x, and the total snowcover in centimeters, y. y =

Find an equation of the line with the slope m = -7 that passes through the point (-2,-4). Write the equation in the form Ax+By = C. Choose the correct answer below. A. 7x+y=18 B. 18x+y=7 C. 18x+y= -7 D. 7x+y=-18

When Sarah left her house this morning, her cell phone was 80% charged and it then started to lose 8% charge for each hour thereafter. Write an equation for B, in terms of t, representing the charge remaining in Sarah's battery, as a percentage, t hours after Sarah left her house.