Basic Math Questions and Answers

Of all the rectangles with a perimiter of 168 feet, find the dimensions of the one with the largest area. a) 42 ft. x 42 ft. b) 14 ft. x 70 ft. c) 21/2 ft. x 147/2 ft. d) not possible e) 21 ft. x 63 ft.

Find the mathematical model for the following statement. Remember to use k as the constant of proportionality. z varies jointly as the square of and the cube of y.

Suppose that $12,000 is invested in a bond fund and the account grows to $14,146.32 in 5 yr. (a) Use the model A=Pe to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. The average rate of return under continuous compounding is approximately

Write the following expression without negative exponents and without parentheses. 2x3

A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1320 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area. a)330 by 330 feet with the divider 330 feet long b)350 by 230 feet with the divider 230 feet long c) 325 by 225 feet with the divider 326 feet long d) 330 by 220 feet with the divider 220 feet long e) 340 by 230 feet with the divider 340 feet long

A 12 volt battery is connected to a series circuit in which the inductance is henry and the resistance is 10 ohms. Assuming that E is constant, i. Determine the current i if the initial current is zero. ii. Find the limiting value of the current as t → ∞.

Find the inverse of the following function. f(x) = 6x - 7/2x 2 Do not include "f-¹(x) =" in your answer. For example, if you found f-¹(x) = 2x + 1, you would enter 2x + 1.

Factor the trinomial completely. m³ +24m² + 144m

Which question is best answered by an experiment? Is successful completion of a college-level English class within two years of enrolling in college linked with earning a degree or certificate? Are students who participate in an accelerated pathway through college-level English more likely to pass a college-level English class? Is entering the remedial English sequence at three levels below transfer associated with lower success rates in subsequent general education classes? Does a flipped-classroom format increase student success rates in English?

At Elisa's Printing Company LLC there are two kinds of printing presses: Model A which can print 70 books per day and Model B which can print 55 books per day. The company owns 14 total printing presses and this allows them to print 905 books per day. How many of each type of press do they have?

In a study, the sample is chosen by dividing the population by Gender, and choosing 30 people of each gender What is the sampling method? Simple Random Systematic Stratified Cluster Convenience

If f(x) = -2ex, find f(-2). Round your answer to the nearest hundredth, and if necessary, include a leading 0 with any decimals less than 1. For example, 0.5 Instead of .5.

In a study, the sample is chosen by asking our 40 closest friends What is the sampling method? Simple Random Systematic Stratified Cluster Convenience

Use synthetic division to find the result when 4 - 8x³ + 12x² + 12x - 38 is divided by x + 4. Write your answer in the form q(x) + r(x) / d(x) where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

A triangle has interior angle measures of 2x + 10°, 2x-17°, and x-3°. What is the value of x? Write your answer as an integer or as a decimal rounded to the nearest tenth. Submit

Consider the function f(x) = x³ + 15x² + 74x + 120. If f(x) = 0 for x = -6, for what other values of x is the function equal to 0?

If $500 is borrowed with an interest of 21.0% compounded monthly, what is the total amount of money needed to pay it back in 1 year? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your final answer.

A factory building built for $400,000 depreciates continuously at 10% per annum. What is its value after 7 years? Select the correct answer below: 188,634 178,634 168,634 158,634 148,634 198,634

Suppose Charmaine places $8500 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years.

The container of orange juice held 5 cups of juice. If a serving of orange juice is of a cup of orange juice, to the nearest whole serving, how many servings were in the container? 5 servings 6 servings 15 servings 19 servings

Evaluate e-0.87 Round your answer to five decimal places, and do not include "e-0.87"In your answer. If necessary, include a leading 0 before the decimal point. For example, 0.5 instead of .5.

Convert the angle in degrees to radians. 75°

Advice columnist Ann Landers once asked her female readers whether they would be content with affectionate treatment by men, with no sex ever. Over 90,000 women wrote in. 72% answered "yes." Many of the letters described bad experiences with relationships with men. Which is the most accurate statement about the survey? This poll is biased because of voluntary response. This result is not believable, so the survey is biased. This result is surprising, but reasonable, because many women have had bad relationships with men. This sample is large (over 90,000), so the results are representative of the population of all women.

The amount y (in dollars) that you raise by selling x fundraiser tickets is represented by the equation y = 5x Graph the equation and interpret the slope.

Total piston displacement is given by the following formula P.D.=πD²LN, where P.D. is the piston displacement in cubic inches, D is the diameter of bore of cylinder, L is the length of stroke in inches, and N is the number of cylinders. Find the diameter if the following are true. (a) PD. = 405 cu in., L = 4.7 in. (b) P.D. = 399.4 cu in., N=7 L = 2 in., N = 6

Use synthetic division to find the result when 3x4-3x³ + 10x² + x − 32 is divided by x + 5. Write your answer in the form g(x) + r(x)/d(x) where g(x) is the quotient, r(x) is the remainder, and d(x) is the

The funtion C= 100+.30m represents the cost (in dollars) of renting a car after driving m miles. a) The slope is which in this situation means b) The y-intercept is which in this situation means c) The total cost to rent the car and drive it for 100 miles would be $ d) If someone paid a total of $149.50 for renting the car, they drove the car for miles. Blank 1: Blank 2: Blank 3: Blank 4: Blank 5: Blank 6:

Amanda has 5 office assistants. If A is the event that at least 4 of them are men and B is the event that at least 4 of them are women, are A and B mutually exclusive? Choose the correct answer below. Yes No

The area of a triangle, a, varies jointly with the length of the base, b, and the height, h. The value of a is 24 when b = 6 and h = 8. Find the equation that represents this relationship,

Divide -60x^3-40x² +54x+38 by 6x + 4.

Consider the graph of the function f(x) = x^3 - 6x^2 + 8x / x^2 - 2x - 8 Select all that apply: Which is a removable discontinuity for the graph? Select all that apply. x = -4 x = -2 x = 0 x = 2 x=4

Find the real and complex zeros of the function f(x) = x³ + 13x² +57x+85

Money that is collecting interest in a bank account doubles in value every 8 years. When the account was opened, it contained 8 dollars, or 2³ dollars. In 32 years, the account balance has doubled 4 times, increasing by a factor of 24. It now has a balance of 23-24. Expressed as a power, how much money, in dollars, is in the account now? A. 2^4 B. 4^7 C. 2^7 D. 2^12

Solve the following equation for x. Provide your answer below: x^-2/3 = 1/16 Assume x is positive. Give your answer as a simplified integer or improper fraction, if necessary.

A loan shark lends you $70 at 3% compound interest per week (this is a weekly, not an annual rate). (a) How much will you owe after 2 years? (Use 52 weeks per year.) (b) In "street" language, the profit on such a loan is known as the "vigorish" or the "vig." Find the shark's vig.

What are the rational zeros of the function ƒ(x) = x³ – 5x² - 33x - 27? List the values separated by commas. Do not include "x =" in your answer.

In 1999, Charlie received the family heirloom marble collection consisting of 1239 marbles. Charlie's great-grandfather had started the original marble collection in 1905. Each year, Charlie's great-grandfather had added the same number of marbles to his collection. When he passed them on to his son, he insisted that each future generation add the same number of marbles per year to the collection. When Charlie's father received the collection in 1966, there were 810 marbles. B-17 HW eTool (Desmos). Homework Help a. By the time Charlie inherited the collection, for how many years had it been in existence? b. How many marbles are added to the collection each year? c. Use the information you found in part (b) to figure out how many marbles were in the original collection when Charlie's great-grandfather started it. d. Generalize this situation by writing a function describing the growth of the marble collection for each year (n) since Charlie's great-grandfather started it. e. How old will the marble collection be when Charlie (or one of his children) has more than 2000 marbles? In what year will this occur?

Divide and simplify the following rational expression. x² - 9x + 18 / x^2 +5x – 24 / x-2 / x+8 Give your answer as a reduced rational expression.

Given that the polynomial f(x) has 6 turning points, which of the following most accurately describes the degree of f(x) Select the correct answer below: The degree of f(x) is at most 6. The degree of f(x) is at most 5. The degree of f(x) is at most 7. The degree of f(x) is at least 7. The degree of f(x) is at least 5. The degree of f(x) is at least 6.

You have 3 chicken houses with an average of 23,800 broilers per house. You have broilers in a house for 7 weeks and then the house is empty for two weeks. You have your operation in a cycle, starting one house at a time throughout the year. a) How often do you start a new group of broilers? b) How many groups are sold per year? c) How many broilers are sold per year if there is a 4.5% loss?

From December 2007 through March 2012, researchers at the University of Pittsburgh studied a new medication to treat osteoporosis in frail elderly women. The researchers administered a daily dose of the medication or a placebo by injection along with calcium and vitamin D supplements. Then the researchers measured the hip and spine bone density of each patient at 12 and 24 months. Results were published in the Journal of the American Medical Association (JAMA) in April 2015. This is an example of which type of study? observational study experiment

An automobile depreciates by 30% per year. How soon will it be worth only half its original value? [Hint: Depreciation is like interest but decimal place.)

While shopping for clothes, Tracy spent $71 less than 3 times what Curtis spent. Tracy spent $16. Write and solve an equation to find how much Curtis spent. Let x represent how much Curtis spent.

Andy walked two miles to the bus stop and then rode the bus for 10 miles. His total travel time was 45 minutes. The average rate that the bus travels is 35 miles per hour faster than the average rate, x, at which Andy walked. Find an expression for the total amount of time that Andy traveled 45 = 2/x + 10/x+35 3/4 = 2/x + 10/x+35 45 = 2/x+35 + 10/x 3/4 = 2/x+35 + 10/x

Solve the following rational inequality. (x+3)(x-4)/ (x-2)>0 -3 ≤x≤2 or x ≥ 4 x>4 -3 < x < 2 or a > 4 -3 < x < 2

A classroom of 29 students wants to save up to buy an elephant. They need at least $75,000. If each student saves up $20 per week, how many weeks until they can afford the elephant?

When creating a budget, it's important to make sure you spend less than you make. In other words, your income should be higher than your expenses. If your expenses exceed your income, you may need to find ways to reduce spending or find ways to increase your income. Part A Use this information to organize estimated household expenses by monthly amounts. • rent: $13,800 annually • utilities: $5,400 annually cell phone: $534 semiannually • internet: $204 semiannually • car loan: $2,274 semiannually • insurance: $720 quarterly groceries: $4,332 annually • gym membership: $288 annually entertainment: $420 annually

The mass of an adult North Pacific right whale is about 70,000 kg, or 7 x 104 kg. The mass of a male African elephant is about 7000 kg, or 7 x 10³ kg. The right whale is about how many times more massive than the African elephant? A. 63,000 times B. 1.1 times C. 1x 10-¹ times D. 1x 10¹ times

The top of a ladder is resting on a tree branch. If the ladder is 17 feet long and the base of the ladder is 8 feet from the tree, how high is the tree branch? Answer How to enter your answer (opens in new window) feet Keyb

Let's try another riddle: One brother says of his younger brother: "Two years ago, I was three times as old as my brother was. In three years' time, I will be twice as old as my brother." How old are they each now? Try writing two different equations to show how the brother's ages relate then graph the functions below.