Basic Math Questions and Answers

The lengths (in inches) of fish caught by two groups of fishermen are shown. Group 1: 20, 14, 14, 17, 23, 21, 9, 18 Group 2: 13, 14, 24, 12, 20, 20, 26, 7 Find the range of the fish lengths for each group. Compare your results.

A shipping container in the shape of a rectangular prism must have a volume of 25,000 cubic feet. The client tells the manufacturer that, because of the contents, the length of the container must be 10 feet longer than twice the width w, and the height must be 5 feet greater than the width. Find the equation, in terms of w, that could be used to find the dimensions of the container in feet. Your answer should be in the form of a polynomial equals a constant.

Explain why the initial value of any function of the form f(x)= a(bx) is equal to a.

Use synthetic division to find the result when 2x4 - 8x³ + 10x² − 6x – 49 is divided by x + 2. Write your answer in the form g(x) + d(x), where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Solve the following rational inequality. 3/x+2 ≥ -1 x ≤ -5 or x>-2 x< -5 or x≥-2 x < -5 or x>-2 x≤-5 or x≥-2

The number of computers N (t) (in millions) infected by a computer virus can be approximated by N (t)=2.8 / 1+17e^-0.8t where t is the time in months after the virus was first detected. (a) Determine the number of computers initially infected when the virus was first detected. Round t

Consider the line with the equation: y = x + 1 Give the equation of the line parallel to Line 1 which passes through (-3, 2): Give the equation of the line perpendicular to Line 1 which passes through (-3,2)

Solve the following rational equation, and make sure to exclude any extraneous solutions. x/x-3 + 2x/ x+3 = 3

Divide using long division: 24x³ - 31x² - 71x - 25 / 8x + 3 where Q(x) + R(x) / D(x)' where Q(x) is the polynomial quotient, R(x) is the remainder, and D(x) is the given divisor

Solve the rational equation by graphing. Make sure to exclude any extraneous solutions. 2x+1/x = x/x-2 No solution. x≈-0.6, 3.6 x≈ 3.6 0-0.6

Express the following fraction in simplest form using only positive exponents. 3v8/2(v)²

One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20 ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three items. How many customers ordered their pizza with pepperoni or sausage (or both)? A) 35 B) 72 C) 13 D) 50

A bank features a savings account that has an annual percentage rate of 3.4% with Interest compounded quarterly. Ashley opens one of these brand new savings accounts and deposits $2,000 into the account. What is her account balance after 4 years, rounded to the nearest cent?

Use synthetic division to find the result when 2x4 - 10x² + 16x + 13 is divided by x - 3. 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 divison

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.