Basic Math Questions and Answers

Find R and θ given the components Rx = 15.07 and Ry = 5.29. R=

Use synthetic division to find the result when 2x³-9x² - 16x-2 is divided by x + 1. Write your answer in the form q(x) + r(x)/d(x) where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Use the model Q(t)=Qoe-0.000121t for radiocarbon dating to answer the question. A sample from a mummified bull was taken from a certain place. The sample shows that 76% of the carbon-14 still remains. How old is the sample? Round to the nearest year.

A boiler room has the shape of a rectangular prism. The area of the floor of the room is 112 square feet. The length of the room is 2 feet more than twice the width. The height is 1 foot greater than the width. What is the volume of the room in cubic feet? Do not include units in your answer. Provide your answer below:

The cost of a four-year private college education (after financial aid) has been estimated to be $50,000.+ How large a trust fund, paying 4% compounded quarterly, must be established at a child's birth to ensure sufficient funds at age 18? (Round your answer to the nearest cent.)

The math department faculty at a large university wanted to know what portion of the student body believes students should be able to enroll in any math class without meeting a prerequisite. The statistics departmer offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected fro the students enrolled in statistics classes. A survey form was sent by email to these 500 students and 236 responded. What is the population of interest for this study? all students enrolled in a statistics class 500 students who received the email survey all students at the university 236 students who responded to the email survey

Provide an appropriate response. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles What is the probability a particular tire of this brand will last longer than 58,900 miles? 0.8413 0.1587 0.2266 0.7266

Given that the degree of the polynomial f(a) is 7, which of the following most accurately describes the number of a intercepts that f(a) has? Select the correct answer below: f(x) has at least 8 a-intercepts. f(x) has at least 6 a-intercepts. f(x) has at most 8 ar-intercepts. f(x) has at most 6 x-intercepts. f(x) has at most 7-intercepts f(x) has at least 7 ar-intercepts.

Given that the polynomial f(x) has degree 9, which of the following most accurately describes the number of turning points of f(x)? Select the correct answer below: The graph of f(x) has at most 10 turning points. The graph of f(x) has at most 9 turning points. The graph of f(x) has at most 8 turning points. The graph of f(x) has at least 8 turning points. The graph of f(x) has at least 10 turning points. The graph of f(x) has at least 9 turning points.

The sum of two nonnegative numbers is 20. Find the numbers a. if the product of one number and the square root of the other to be as large as possible. b. if one number plus the square root of the other is to be as large as possible.

Find all the zeros of f(x) = 2x³ + 30x² + 18x + 270

Tremayne is saving for his daughter's college education. If the savings account earns 4% Interest compounded monthly, and he wants to have $50,000 in 15 years, what must the principal be? Round your answer to the nearest dollar. Do not round until your final step.

A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant. Provide your answer below:

Which is an equation of the degree 3 polynomial function with real coefficients having zeros (roots) located at x = = 2 with multiplicity 1 and x = -6 with multiplicity 1? The function also has a y-intercept located at (0, -36). Select the correct answer below: y=(x-2)(x-3)(x+6) y= (x+2)(x+3)(x-6) y=(x-2)(x+3)(x+6) y=(x+2)(x-3)(x-6)

A shed in the shape of a rectangular prism has a volume of 910 cubic feet. The length of the dumpster is 7 feet less than twice the width w, and the height is 3 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the shed in feet. Your answer should be in the form of a polynomial equals a constant.

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.