Basic Math Questions and Answers

Consider the following functions. x+2 3 Step 1 of 2: Find the formula for (fog)(x) and simplify your answer. Then find the domain for (f. g)(x). Round your answer to two decimal places, if necessary. f(x) = √√x+2 and g(x) = Answer (f. g)(x) = Domain = Keypad Keyboard Shortcut-

Suppose you take out a loan for 160 days in the amount of $14,000 at 7% ordinary interest. After 30 days, you make a partial payment of $1,500. After another 60 days, you make a second partial payment of $4,000. What is the final amount (in $) due on the loan? (Round your answer to the nearest cent.)

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f(x) = 4x²-16x +3 The quadratic function has a value

Use De Morgan's Laws to write a statement that is equivalent to the following statement: "It is not true that North Dakota and East Dakota are both states." Either North Dakota is not a state, or East Dakota is not a state. North Dakota is not a state, and East Dakota is not a state. Either North Dakota is a state, or East Dakota is not a state. Either East Dakota is a state, or North Dakota is not a state. North Dakota is not a state, and East Dakota is a state.

Aisha's office had already recycled 6 kilograms this year before starting the new recycling plan, and the new plan will have the office recycling 1 kilogram of paper each week. How many weeks will it take Aisha's office to recycle a total of 50 kilograms of paper? weeks

Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then answer the question. Suppose a baseball is thrown at 89 miles per hour. The ball will travel 338 feet when hit by a bat swung at 47 miles per hour and will travel 474 feet when hit by a bat swung at 81 miles per hour. Let y be the number of feet traveled by the ball when hit by a bat swung at x miles per hour. How much farther will a ball travel for each mile-per-hour increase in the speed of the bat? A ball will travel (Type a whole number) feet farther for each mile-per-hour increase in the speed of the bat.

A man purchased a used car for $4000. He decided to sell the car for 30% above his purchase price. He could not sell the car so he reduced his asking price by 30%. If he sells the car at the reduced price, will he have a profit or a loss or will he break even? Select the correct choice below and fill in any answer box to complete your answer. OA. The man will have a loss of $ B. The man will have a profit of $ OC. The man will break even.

a) What is the tax on the Leeseburgs' dinner? b) If the Leeseburgs decide to tip 20% of the pre-tax bill, how much is the tip? c) What is the total cost of the dinner including the tax and tip? According to the Original Tipping Page, www.tipping.org, it is appropriate to tip waiters and waitresses 15%-20% of the pre-tax restaurant bill. The Leeseburgs' dinner costs $49.00 before tax, and the tax rate is 6%. a) The amount of tax paid is $ (Round to the nearest cent as needed.) Points: 0 of 1 ***** Save

Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan's speed is 6 miles per hour faster than Leo's speed. Find the speed of the two bikers. Provide your answer below: Ethan's speed=mph, Leo's speed= mph

Use the ordinary interest method to find the rate of interest that Valley Mountain Vineyards pays on a loan of $5,300 for 236 days, if the amount of interest is $355.67. (Round to nearest tenth percent.) O 4.5% O 6.7% O 10.2% O 12.9%

Find any relative extrema of the function. (Round your answers to three decimal places.) f(x) = arctan(x) − arctan(x – 9) relative maximum (x, y) = (4.5,154.942

Fake Twitter followers: Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 62 twitter audits, the mean percentage of fake followers was 14.4 with a standard deviation of 10.4. Part 1 of 2 Construct a 98% interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place. A 98% confidence interval for the mean percentage of fake Twitter followers is 11.245 << 17.555 Part: 1/2 Part 2 of 2 Based on the confidence interval, is it reasonable that the mean percentage of fake Twitter followers is less than 11? reasonable that the mean percentage of fake Twitter followers is less than 11, It Choose one) is is not X

Different levels: Bertha and Nico are going to construct confidence intervals from the same simple random sample. Bertha's confidence interval will have level 99%, and Nico's will have level 95%. Part 1 of 2 (a) Which confidence interval will have the larger margin of error? Or will they both be the same? Nico's Bertha's They will be about the same. Part: 1 / 2 Part 2 of 2 (b) which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so? Nico's Ś O Bertha's They are both equally likely to do so. X

Ivan has a tree in his backyard. The tree grows 25 centimeters each year. Since the tree started growing, Ivan has trimmed 16 centimeters off its height. The goal for the tree's height is given by 25x-16>234, where x is the number of years the tree grows. Complete the parts below. (a) Solve the given inequality and graph the solution on the number line below.

16. After their boat capsized in the middle of Lake Tippecanoe, Acute Alice and Obtuse Ollie swam in opposite directions toward shore. Alice swam twice as fast as Ollie and, after 3 minutes, they were 1,125 feet apart. Find out how far each one swam by doing each of the following. a) If Ollie swam at the rate of x feet per minute, at what rate did Alice swim? b) Draw a diagram to represent the problem. c) Use the information in your diagram to write an equation. d) Solve the equation for x. e) How far did each one swim?

At the end of an advertising campaign, weekly sales declined according to the equation y = 13,000(5-0.05x) dollars, where x is the number of weeks after the end of the campaign. a. Determine the sales at the end of the ad campaign. b. Determine the sales 4 weeks after the end of the campaign. c. Does this model indicate that sales will eventually reach $0? a. The sales at the end of the campaign are $ (Round to the nearest cent as needed.)

narchitect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique pickel fencing are to be used to enclose the arden, find the dimensions of the garden. hat is the length of the garden? he length of the garden is That is the width of the garden? he width of the garden is *****

Solve the following equations for x. Check your answers. a) 9x - x = -24 d) (x + 8) + x = 6 b) 2x - 11 = 7x e) 4(x - 1) = * = 11 c) 5(x - 3) = 25 f) 10(x + 2) = 2(x + 10

Solve the problem. 3) The function D(h) = 7e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 12 hours?

The function f(x) = 2x + 3 is one-to-one. X+2 (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f¯1. (a) f¹(x) = 3-2x X-2 (b) Find the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) OA. The domain is {x|x≤}. (Type integers or fractions. Use a comma to separate answers as needed.) B. The domain is {xlx # - 2} (Type integers or fractions. Use a comma to separate answers as needed.) OC. The domain is {x|x>}. (Type integers or fractions. Use a comma to separate answers as needed.) ..... OD. The domain is the set of all real numbers. Find the range of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

4. Marnie conducted a survey of the cats in four shelters and wrote the following observations: 4 of the 18 cats in Shelter 1 were black 13 of the 24 cats in Shelter 2 were black 12 of the 20 cats in Shelter 3 were black 18 of the 25 cats in Shelter 4 were black Based on the survey, which shelter had the greatest percentage of black cats? (5 points) Shelter 1 Shelter 2 Shelter 3 Shelter 4

1. Charlie worked for a stone setting company this past summer. He earned $50 just for coming to work and an additional $30 every hour for each hour he worked. The linear function E(t) = 50+ 30t represents Charlie's earnings E as a function of time worked t (in hours).

A person earns $15,500 one year and gets a 5% raise in salary. What is the new salary? The new salary is $

What's the standard equation of the circle with the general equation x² + y² + 4x − 2y-20 = 0? 1) (x + 2)² + (y − 1)² = 25 2) (x - 2)² + (y + 1)² = 25 3) (x + 2)2 + (y- 1)² = 5 4) (x + 1)² + (y-2)² = 5

A new self-tanning lotion for everyday use is to be sold. First, an experimental lotion mixture is made by mixing 800 ounces of everyday moisturizing lotion worth $0.30 an ounce with self-tanning lotion worth $3 per ounce. If the experimental lotion is to cost $1.20 per ounce, how many ounces of the self- tanning lotion should be in the mixture?

Jefferson Bank made a loan at 7% interest for 236 days. If the amount of interest was $252.39, use the ordinary interest method to find the amount of principal (in $) borrowed. (Round your answer to the nearest dollar.)

k(t) = 10t - 19 k(-7)=[ Evaluate functions

Based on the 50/30/20 rule, Julia has needs of $2,600 per month, wants of $1,560 per month, and saves $1,040 per month. Which of the following is her after-tax income? $5,250 $5,200 $5,000 $5,500

Find the slope of the line that passes through (-4, 1) and (0, -5). Write your answer in simplest form. Select "Undefined" if applicable. The slope is 00 Undefined

Sonia wants to have $11,000 in 10 years. Use Table 11-2 to calculate how much she should invest now (in $) at 6% interest, compounded semiannually in order to reach this goal. (Round your answer to the nearest cent.) $

What is 18% of $70,000? $ is 18% of $70,000. (Type an integer or a decimal.)

Select all the situations for which only zero or positive solutions make sense. A. Measuring temperature in degrees Celsius at an Arctic outpost each day in January. B. The height of a candle as it burns over an hour. C. The elevation above sea level of a hiker descending into a canyon. D. The number of students remaining in school after 6:00 p.m. E. A bank account balance over a year. F. The temperature in degrees Fahrenheit of an oven used on a hot summer day.

Simplify without a Calculator log2(1/512) =

The length of a cell phone is 1.2 inches and the width is 4.6 inches. The company making the cell phone wants to make a new version whose length will be 1.74 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?

Fabiana is going to construct a rectangular metal box with a volume of 150 in³. Her box will have a length of x inches, a width of 3 inches less than its length, and a height that is 1 inch more than its length. Which cubic equation would help Fabiana find the length of the box? x²+x²-123-0 x-2x²-3x+150-0 x²³²-21-²-3x=0 x²-2x²-3x-150-0

In order to start a small business, a student takes out a simple interest loan for $4000.00 for 3 months at a rate of 6.50%. a. How much interest must the student pay? b. Find the future value of the loan. a. The amount of interest is $

Consider the parent function: y = |x|. Which equation transforms the parent function 3 units to the left, 1 unit up, stretching it vertically by a factor of 2 and flipping it vertically? A.y=|-2x - 3|- 1 B.y=2|x - 3|-1 C.y=|2x + 3| + 1 D.y=-2|x + 3|+ 1

The approximate areas of Wisconsin and Washington, D.C. are listed below: Wisconsin: 1.7 x 105 square kilometers Washington, D.C.: 1.77 x 102 square kilometers How much larger is Wisconsin? Express your answer using scientific notation.

A recipe uses 5 cups of milk to make 20 servings. If the same amount of milk is used for each serving, how many servings can be made from two pints? 1 gallon=4 quarts 1 quart=2 pints 1 pint = 2 cups 1 cup = 8 fluid ounces Before you try that problem, answer the question below. How many cups will you need to find the number of servings for?

What is the converse of this statement? If a polygon is not a trapezoid, then it is not a quadrilateral. If a polygon is not a quadrilateral, then it is not a trapezoid. If a polygon is a trapezoid, then it is a quadrilateral. A rectangle is also a quadrilateral.

Please: (1) solve the provided equation, (2) verify your solution, and (3) conclude with a solution set. x/ (11/3) = -3/13

1An inlet pipe on a swimming pool can be used to fill the pool in 15 hours. The drain pipe can be used to empty the pool in 30 hours. If the pool is 1/2 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Set a linear equation for the following linear scenario to answer the questions: A new car costs $32,000, and the car's value depreciates linearly to $9,600 in three years. Explain the process to write a formula that expresses the car's value, V, in terms of its age, t, in years. What is the car's value in 5 years? At what point is the formula useless? Explain.

A local home store had a wheel-of-savings display for customers to spin as part of its end-of-summer sale. John spun the wheel, and it landed on a markdown series of 30% and 20%, applied to his final purchase. He bought a stainless steel, side- by-side refrigerator for $1,599.99. What is the price of the refrigerator after the series discounts were applied? Round your answer to the nearest cent. $895.99 $1,503.99 $480.00 $800.00

Josh buys an $8000 10-year bond that has a coupon rate of 4.5 %. If he keeps the bond to maturity, how much interest will he collect? $3600 $6300 $360 $3750

Brianna broke a cell sample into 12 batches, each weighing 8.7 x 10-5 grams. How much did the original sample weigh? Use scientific notation to express your answer.

Jamie recently drove to visit her parents who live 455 miles away. On her way there her average speed was 24 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 13 hours driving, find the two rates. Jamie's average speed to her parents' house: Jamie's average speed from her parents' house:

A client is instructed to drink 20 ounces of water within 1 hour. The client has only been able to drink 12 ounces. What portion of the water remains? (Express your answer as a fraction reduced to lowest terms)

Alice prepares a cheese sandwich for her supper. She stuffs an isosceles triangular cheese slice in it. Which of the following is the possible side measures of the cheese slice? a) 3 in, 5 in, 8 in b) 4 in, 4 in, 6 in c) 3 in, 3 in, 6 in Checklist: 1)Divide the first term of the numerator by the first term of the denominator, and put that in the answer. 2)Multiply the denominator by that answer, put that below the numerator. 3)Subtract to create a new polynomial. 4) Repeat, using the the new polynomial.

What is a counterexample of this statement? If a polygon is a trapezoid, then it is a quadrilateral. If a polygon is not a trapezoid, then it is not a quadrilateral. A rectangle is also a quadrilateral. If a polygon is not a quadrilateral, then it is not a trapezoid.