Basic Math Questions and Answers

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

Saige invests $400 into an account with a 2.3% interest rate that is compounded semiannually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar.

As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second. Convert this rate to kilometers per second. At this rate, how many kilometers will Mercury travel in 20 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers. Rate: Distance traveled in 20 seconds: km km

Select the correct function. In a finance company, there are two competing groups that are both vying for title of top earners. The first group's profits, in dollars, can be demonstrated by the following function, where x is the total number of hours the group works on a project. f(x) = -7.5x2 + 3,000 - 10,000 The second group's profits can be demonstrated by the following function, where x is the total number of hours the group works on a project. g(x) = -8.5x2 + 3,060* - 15,000 If both groups spend the same number of hours on a project, select the function which accurately represents the combined profits from both groups. h(x) = h(x) = g(x) + f(x) -16x2 + 6,060 - 25,000 h(x) = g(x) = f(x) h(x) - x2 60x + 5,000 h(x) h(x) = g(x) + f(x) - h(x) -16x2 + 60x - 25,000 h(x) = g(x) = f(x) = -x2 + 60x - 5,000

Use synthetic division to find the result when 3x3 - 10x² + 15x - 1 is divided by x + 2. Write your answer in the form q(x) + Provide your answer below: r(x) d(x)" where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Approximate the following number using a calculator. 2)24 5 6.3 2.4 6.3 3(²)² = (Round to three decimal places as needed.) 5

Faith is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.75%. If Faith would like to end up with $87, 000 after 7 years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer. A = d ((1 + i)” - 1)/i) A = the future value of the account after n periods d = the amount invested at the end of each period i = the interest rate per period n = the number of periods

Use this table to find the monthly mortgage payments, when necessary. Roberto has a mortgage of $81,500 at 7 % for 20 years. Find the total interest. 7-1⁄2% 2 O $76,153.60 O $82,345.85 O $88,201.93 O $94,226.02

One pipe fills a storage pool in 12 hours. A second pipe fills the same pool in 6 hours. When a third pipe is added and all three are used to fill the pool, it takes only 3 hours. Find how long it takes the third pipe to do the job. The third pipe can fill the pool alone in hours. *****

If the side lengths of a cube are dilated from 9 yards to 42 yards, find the scale factor that relates the area of one face of the original cube to a face of the scaled cube. . Write your answer as a number only. • Round your answer to two decimal places if necessary.

What method of factoring should first be used? 7wx² +6w Greatest Common Factor Trinomial Factoring Difference of Perfect Squares Does Not Factor

The muzzle velocity for a certain cartridge is 1500 ft/s for the starting load of 40 grains of powder. What is the final load to achieve a muzzle velocity of 1642.8 ft's, if the increase in velocity is 42 ft/s for eachbadditional grain of powder? 3.4 grains 36.6 grains 43.4 grains 42 grains

The angle of elevation of the sun is 39° from the ground. A business building downtown is 76 m tall. How long is the shadow cast by the building? Round to one decimal place if necessary and do not include units in your answer.

The expression for ordering brushes for an art class is 4c-5, where c is the class limit. Evaluate the expression when the class limit is 21. When the class limit is 21, the expression evaluates to