Basic Math Questions and Answers

Chris spent half of his money on a pair of headphones. Then he spent half of his remaining money on CDs. Finally, he spent his remaining $11.75 on a book. How much money did Chris have to begin with? Chris began with $

One pipe fills a storage pool in 20 hours. A second pipe fills the same pool in 10 hours. When a third pipe is added and all three are used to fill the pool, it takes only 5 hours. Find how long it takes the third pipe to do the job.

A person invests 9000 dollars in a bank. The bank pays 6.25% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 13600 dollars? A = P(1 + 7) n² nt

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of 11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge. Both Truck 1 and Truck 2 can pass under the bridge. Truck 1 can pass under the bridge, but Truck 2 cannot. Truck 2 can pass under the bridge, but Truck 1 cannot. Neither Truck 1 nor Truck 2 can pass under the bridge.

People are waiting in line for a theater premiere. Every 5th person in line will receive a free theater ticket. Every 6th person will receive a gift card for $40. Which person is the first to receive both prizes? Explain.

(b) that a music download was neither tropical nor regional Next, calculate the relative frequency that a download was neither tropical nor regional. We are given that, of the 400 total downloads, 200 were regional, 110 were pop-rock, 80 were tropical, and 10 were urban. The categories of music that are not tropical and not regional are pop-rock and urban. So, the frequency of music downloads that are neither tropical nor regional is equal to the frequency of music downloads that are pop-rock or urban. The frequency of music downloads that are pop-rock or urban is 110 + 10 = 120 So the frequency of music downloads that are neither tropical nor regional is

Paul, a janitor, must move a large shipment of books from the first floor to the fifth floor. The sign on the elevator reads "maximum weight 900 pounds." If each box of books weighs 80 pounds, find the maximum number of boxes that Paul should place in the elevator if he does not ride.

The population of a certain species of oak tree in a national forest declines each year by one-fourth. So, after each year, only three-fourths of the trees present at the beginning of the year remain. Which of the following describes the rate of decline in the population of the species of oak tree? OA. neither linear nor nonlinear SOB. both linear and nonlinear OC. nonlinear O D. linear

Use the formula R = log t In May 2008, an earthquake measuring 6.8 on the Richter scale struck near the east coast of Honshu, Japan. In March 2011, a quake measuring 9.0 struck that same region. How many times more intense was the 2011 quake than the one in 2008? (Round your answer to one decimal place.) times

A large wind turbine can power 598 homes. A company had 4 turbines and then built 5 more. homes can How mar many the company power with its wind turbines?

2. (12 points) An open top box is to be constructed from rectangular pieces of cardboard. The base will be a square cut from sturdy and more expensive material, one that costs $4.00 per square foot. The four walls will be cut from more affordable material that costs $1.00 per square foot. What are the dimensions of the least expensive box one can design that will enclose 54 cubic feet of volume? How expensive will this box be to construct?

Truck #1 can haul 480 tons of steel in 24 trips. Truck #2 can haul the same amount of steel in 48 trips. How many trips would it take if both trucks are used? O 10 Trips 20 Trips 1 pt O 36 Trips O 16 Trips

A ball is thrown from a height of 164 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after seconds is given by the following. h=164-12t - 16t² How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

1190 1+28.75e-0.357 represents the population (in thousands) 13. The logistic growth model P = of a bacterium in a culture tube after t hours. a) What was the initial amount of bacteria in the population? b) When will the population be equal to 500,000? c) What is the carrying capacity of the population?

Videogame data: We collected data on the top 50 best-selling video games. These are the variable descriptions: Metascore: Score out of 100, based on major critic reviews as provided by Metacritic.com Total Worldwide Sales: Total number copied sold worldwide since December 31, 2015. GameRankings: Score out of 100%, based on an average scores from websites and magazine reviews. We used Metascore ratings as an explanatory variable and GameRankings ratings as the response variable in a linear regression. The r2 value is 48%. With Total Worldwide Sales as the explanatory variable and GameRankings ratings as the response variable in a linear regression, the r2 value is 62%. Using the ² value, which is a better predictor of a videogames's GameRankings score: Metascore or Total Worldwide Sales? Metascore Total Worldwide Sales

Mr. Young built a greenhouse 42 feet wide, 110 feet long, 5 feet to the eaves, and 14 feet to the ridge cap. a. How many square feet of plastic does it take to enclose the greenhouse? b. What is the slope of the roof? c. What angle does the roof make with the horizontal?

The Bonney Lake High track coach has a group of eight runners from which to choose a 4-person relay team. How many different 4-person teams can be formed from this group of runners? 70 16 1,680 24

Factor Completely: 18n³ +6n² +63n+21 Type your answer using equation editor or upload a picture of your paper using insert image.

A truck travels north from a warehouse at an average speed of 35 MPH. A second truck travels south from a store at an average speed of 40 MPH? If the store is 150 mile from the warehouse, how many miles from the warehouse will the trucks meet? 80 miles 75 miles 60 miles 70 miles

A stone is dropped from the upper observation deck of a tower, 700 m above the ground. (Assume g = 9.8 m/s².) (a) Find the initial values of the velocity v (in m/s) and the distance s (in meters) of the stone above the ground. v(0) = s(0) = Find the velocity (in m/s) of the stone at time t. v(t) = s(t): = Find the distance (in meters) of the stone above ground at time t. (b) How long (in seconds) does it take the stone to reach the ground? (Round your answer to two decimal places.) (c) With what velocity (in m/s) does it strike the ground? (Round your answer to one decimal place.) (d) If the stone is thrown downward with a velocity of 9 m/s, how long (in seconds) does it take to reach the ground? (Round your answer to two decimal places.)

Eden bought 15 tickets to a soccer game. The group rate saved her $4.75 per ticket. She paid a total of $307.50 for the tickets What was the regular price of a ticket to the game? Enter your answer in the box.

Lin's family has completed 60% of a trip. They have traveled 30 miles. How long is the whole trip? A.50 miles B. 48 miles C. 30 miles D. 18 miles

Given the variable in the first column, use the phrase in the second column to translate to an expression, and then continue to the phrase in the third column to translate to another expression. A number Twice the number Five divided by twice the number

In how many ways can 3 books be choosen from a group of nine? Your answer is:

You are building a hexagonal patio with sides of 10 ft. (Note: For help, see Figure 12-9 on page 163.) You are flooring it with 4" of concrete. a. What is the perimeter of the patio? b. What is the measure of the interior angle? c. How many equilateral triangles are formed have their vertices at the center of the hexagon? d. What is the height of one of the equilateral triangles? (Note: For help, see section 2.2) e. What is the area of the hexagon? f. How many yard (cubic yards) of concrete are needed?

Which of the following statements are true? To solve 2-95= 55+4, you can subtract 5s from each side of the equation. The equation-20-10d=5(-2d-4) has one solution, d = 2. The solution of 6 (p+ 3) = 5(p-3) is all real numbers. The equation -5(5x+9)=-45- 25x is an identity. Linear equations do not always have one solution.

The amount of sales tax on a new car varies directly to the purchase price of the car. On a $25,000 car, sales tax is $1,750. What's the purchase price of a new car with $3,500 in sales tax?

What does it mean for two shapes to be "similar?" Corresponding angles and sides are proportional. Corresponding angles are proportional and corresponding sides are congruent. Corresponding angles and sides are congruent. Corresponding angles are congruent and corresponding sides are proportional.

Solve the equation. Determine whether the equation has one solution, no solution, or infinitely many solutions. 4c-20=-20+4c infinitely many solutions c=0; one solution c--4; one solution no solution

Solve the following equation. 8lx| = 128 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is the empty set. B.The solution set is (Use a comma to separate answers as needed. Type an integer or a simplified fraction.)

A Ferris wheel at an amusement park is modeled by (x-80)2 + (y-80)2 = 5,625, where the measurements are in feet. A slingshot attraction is modeled by y=-3x² + 72x-280. Which attraction reaches a greater height, and what does it represent in terms of the context? The slingshot reaches a greater height at 280 feet, which is the vertex of the parabola. The Ferris wheel reaches a greater height at 155 feet, which is the highest point on the circle. The slingshot reaches a greater height at 152 feet, which is the vertex of the parabola. The Ferris wheel reaches a greater height at 150 feet, which is the highest point on the circle.

A local pizza place has a special deal on Thursday: Buy a large one topping pizza for $12 and each order of cheesy bread is $2.50. This creates a linear equation that represents the cost of the purchase of multiple orders of cheesy bread. What would be the rate of change in this word problem? O A 2.5 OB. O 2.5 C. 4.8 O D 4.8

An employee earns $48,000 in the first year with a company. Every year, the annual salary increases by $4,500. How much is earned during eight years with the company? $388,500 $420,000 $510,000 $636,000

Greenpoint is hosting a city-wide arts festival at which vendors can pay to have a small booth or a large booth. The fee for a small booth is $30, whereas the fee for a large booth is $83. The city hopes to receive at least $1,500 in fees. A Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of small booths y = the number of large booths 30x + 83y > 1,500 30 + x + 83 + y ≥ 1,500 30 + x + 83 + y > 1,500 30x + 83y2 1,500

Samantha donated 9 T-shirts to charity and has 16 left. Which equation could be used to find x, the number of T-shirts Samantha had originally? OA. x-16=9 OB. X+16=-9 OC. x+9=16 O D. X-9=-16

Nathan, a registered nurse, is working on an admissions essay for a BSN program. Select the sentence from his draft that has a verb tense error. a.) I am very excited to see what the future holds for me. b.) I first started working at the hospital as a nurse more than 10 years ago c.) I think that my many years of experience in the nursing field will help me to be successful in this program. d.) I want to continue my nursing training and became a more advanced medical practitioner.

3. Model with Math Clare had t seashells. After she bought 8 more seashells, she had 24 seashells. Write and solve an equation to find the number of seashells Clare started with.

Lincoln, Nebraska lies directly north of Dallas, Texas. Lincoln is at a latitude of 40.5° N and Dallas is at a latitude of 32.5° N. Assuming the radius of the earth is 3,960 miles, how far apart are these cities?

Stacey purchased four concert tickets and paid more than $200. The amount she paid for each ticket was equal to the face value plus a $15 service charge. Select the inequality where x represents the possible face value of each ticket and the solution of that inequality. OA. 4(x+15) > 200 The face value of a ticket is at least $46.25. OB. 4x+15 > 200 O D. The face value of a ticket is at least $46.25. OC. 4(x+15) > 200 The face value of a ticket is at least $35.00. 4x+15 > 200 The face value of a ticket is at least $35.00.

3. After a dinner party, 1/5 of a casserole remained. The leftover casserole was shared equally among the three children in the family for their lunch the next day. How much of a casserole did each child get?

Brian paid a total of $46.44 for a jacket at a department store. The jacket was on sale for 20% off the regular price, and he used a coupon for an additional $5.00 off of the discounted price. Brian had to pay 8% sales tax on the cost of the jacket after any discounts and coupons. Select the equation where p represents the original price of the jacket and the solution of that equation. OA. 1.08(0.8(p-5)) = 46.44 The original price of the jacket was $58.75. OB. 1.08(0.8p - 5) = 46.44 The original price of the jacket was $58.75. OC. 1.08(0.8(p-5)) = 46.44 The original price of the jacket was $60.00. OD. 1.08(0.8p-5) = 46.44 The original price of the jacket was $60.00.

Which expression is not equal to 30? (9 x 10) (4+1) + 12 ÷ (2 x 60 ÷ 30) x (24 + 2) (12020) x (2+3) X 2+ (30-8 ÷ 4)

Suppose that $2500 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $4000 at 4.25%. It would take approximately years. (Round to the nearest tenth.)

A pilot can travel 400 miles with the wind in the same amount of time as 352 miles against the wind. Find the speed of the wind if the pilot's speed in still air is 235 miles per hour.

Which of the following is a polynomial function? Select all correct answers. Select all that apply: f(x) = 4.11x f(x) = 3.18x f(x) = 10.17x f(x) = -4x³ - 4x² + 5x+1 f(x) = -2x - 1

Which functions have graphs with a slant asymptote? Select all that apply. Select all that apply: f(x) = x+1 x² f(x) = 3x² 5x ☐ f(x) = 2/1/2 2x² ☐ f(x) = 2x²+1 43 □ f(x) = 3x³ x+1

The Lincoln Memorial has dimensions of 189.7 ft wide, 118.5 ft deep, and 99 ft tall. (The structure, not the statue of Lincoln.) Sam is making a model of this to use in a presentation in his American History class. If his model is 1 foot tall, what are the width and length dimensions? Image Source Lincoln Memorial, public domain Ow= 61.84 in, L = 158.48 in Ow= 1.92 ft, L = 1.20 ft Ow=18780.3 in, L= 11731.5 in Ow= .52 ft, L = .84 ft

What interest will be earned if $7000 is invested for 4 years at 11% compounded monthly? (Round your answer to the nearest cent.) $3864.39 X

Consider the graph of the function f(x) =x²-4/x²-12x+20 Find the x-value of the removable discontinuity of the function. Provide your answer below: The removable discontinuity occurs at x =

Let's "Texas Size" the "Rattlesnake" drink. The ratios are 32 parts Whiskey, 24 parts egg, 6 parts lemon, 2 parts sugar, and 1 part Absinthe. If I'm planning on making 65 gallons, how many gallons of Absinthe will I need? O2 gallons 32 gallons 1 gallon O 3 gallons