Basic Math Questions and Answers

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.

x²-81 x³+7x² 18x Where is the removable point of discontinuity? Give only the x-value. Consider the graph of the function f(x) =

A gym charges a $615 yearly fee for membership plus $50 for each hour of personal training. What is the average total cost per hour of training if a member works with a personal trainer for 30 hours in a year? Do not include the dollar sign ($) in your answer. Provide your answer below:

The proportion of students in a psychology experiment who could remember an eight-digit number correctly for t minutes was 0.9 0.3 In(t) (for t > 1). Find the proportion that remembered the number for 5 minutes. (Round your answer to one decimal place.) X % 0.4

Consider the function f(x) = 2x¹ − 4x³ + 20x − 100. - What is the remainder if f(x) is divided by (x +11)? Do not include the divisor in your answer. Provide your answer below:

Find the derivative of the function. h'(t) = h(t) = 30 -sinh(-6t)

Find all real and complex solutions to the equation 2³-32²-10x + 24 = 0 Express your answer as a list separated by commas, entering each zero as a separate number.

After walking mile from home, Han is of his way to school. What is the distance between his home and school? 1. Write multiplication and division equations to represent this situation. 2. Use the given diagram to help you answer the question. Mark up and label it as needed.

Select the correct answer. The image of polygon MNOP after a similarity transformation is polygon WXYZ. Each side of MNOP is 2 times as long as the corresponding side of WXYZ. What is the scale factor of the dilation in the similarity transformation? OA. 4 OB. 0.5 OC 2 OD. 0.25

What are the rational zeros of the function f(x) = x³ + 3x²-x-3? List the values separated by commas. Do not include "=" in your answer. Provide your answer below:

Give a third degree polynomial that has zeros of 13, 5i, and -5i, and has a value of -680 when = polynomial in standard form ax + bxn-¹ +... 3. Write the

The physician ordered Platinol (cisplatin) 100 mg/m² IV to infuse over 6 hours once every 4 weeks for a patient who has a BSA of 1.66 m². (a) How many mg of this antineoplastic drug should the patient receive? (b) If the dose of cisplatin were administered in 1,000 mL D5 1/2 NS, at how many mL/h would the IV run?

Given f(x) = 2x³ + 2x - 8 verify that f(x) is invertible and, if so, find the equation of the tangent line to f-¹(x) at the point where x = 12. Note that f(2)= 12. a) O f(x) is not invertible. b) Oy+2=- c) Oy - 2 = d) Oy - 12 = ) Oy - 12 = 1 1 26 26 (x - - 12) (x - 12) 1 26 1 26 (x + 2) (x 2)

The function g is defined as follows. g(x) = -5x² +5 If the graph of g is translated vertically downward by 3 units, it becomes the graph of a function f. Find the expression for f(x). Note that the ALEKS graphing calculator may be helpful in checking your answer.

If the cost, C, for manufacturing x units of a certain product is given by C=x² + 35x + 40, find the number of units manufactured at a cost of $10,240. There are units manufactured at a cost of $10,240.

Divide using long division: Write your answer in the form Q(x) + the given divisor. Provide your answer below: R(x) D(x)' 2x³ - 6x² +5 x-1 where Q(x) is the polynomial quotient, R(x) is the remainder, and D(x) is

Consider the graph of the function f(x) = 2³-x²–2x x²+x Which is a removable discontinuity for the graph? Select all that apply. Select all that apply: 0 x = x = -2 x = −1 x=0 x = 1 ☐ x=2

Add the following rational expressions and make sure to state the restrictions on the variable: 3/x^2-16 + x/x+4 (214)(x-4), 2-4, 4 2+1 214-4 (2-3)(2-1) (14)(x-4), -4, 4 241 = 14,2 -4,4

If the formula y = x³ is changed by adding one as shown in red below. f(x) = (x + 1)³ Which values would be most directly affected by the change? Select an answer < What effect would it have on the graph? D

Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm. Which of these is closest to the percent error for Diego's measurement? O 4.3% O 4.5% O 95.7% O 104.5%

Given that the polynomial f(x) has 3 intercepts, 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 3. The degree of f(x) is at least 4. The degree of f(x) is at most 4. The degree of f(x) is at most 2. The degree of f(x) is at least 2. O The degree of f(x) is at least 3.

Which function has a remainder of -70 when divided by (x - 9)? Select the correct answer below: O g(x) = x³ - 2x² − 93x + 200 - O g(x) = x³ x² − 93x+20 O g(x) = x³ - 2x² − 90x + 200 - O g(x) = x³ - 2x² − 3x + 20 O g(x) = x³ = x² − 3x + 200

Multiply the following rational expression and state the restrictions on the variable: 4n²+32n 3n-2 1 2n+16 O O 2n 3n 2, n = // 2n-1-2 3n 2, n = ²/ 47 3n-2, 7-8, 12/0 2n 3n 2,7-8, 3/1

Use logarithmic differentiation to find dy/dx. y = (9 + x)4/x dy dx =

The number of hours needed to complete a trip. . varles inversely with the driving speed. &. A trip can be completed in 5 hours at a speed of 60 miles per hour. Find the equation that represents this relationship.

2. Camille stopped at the grocery store to buy milk. While at the store, she spotted cans of soup on sale for $2.25 each. If the milk costs $3.50 and she can spend no more than $35, how many cans of soup can she buy. b) a) Define your variable Write and solve your equation. c) Answer in a complete sentence.

Find the annual growth rate of the quantity described below. A stock portfolio drops to one-tenth its former value over a 7-year perio Round your answer to two decimal places. The annual growth rate is i %.

(1 point) In a random sample of 90 voters, the proportion of voters in favor of a bond issue is 0.8. Let p = proportion of all voters who favor of the bond issue. (1) Test Ho: p ≤ 0.65 against H₁: p > 0.65. Use a = The test statistic is The critical value is The final conclustion is 0.05. ⒸA. We can reject the null hypothesis that p < 0.65 and accept that p > 0.65. B. There is not sufficient evidence to reject the null hypothesis that p < 0.65

Two cube-shaped containers are filled with beads. Container A has side lengths of 2 inches and contains 142 beads. Container B has side lengths of 3 inches and contains 544 beads. Which container has the greater density in beads per square inch? Both containers have the same density. Container A Container B Impossible to tell from this information

38 A tire has a total of 638.3 pounds of pressure in it. If the inside of the tire has a surface area of 32.61 square inches, what is the tire pressure in pounds per square inch? . Write your answer as a number only. No units. Round your answer to two decimal places if necessary.

Use synthetic division to find the result when 3x³ + 11x² - 10x - 10 is divided by x + 5. r(x) Write your answer in the form q(x) + where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor. d(x)' Provide your answer below:

When 8 is subtracted from the square of a number, the result is 7 times the number. Find the positive solution. 4 5 7 8 16

Find the real and complex zeros of the function f(x) = 3x³ - 4x² + 11x + 10. Express your answer as a list separated by commas. Do not use a plus minus sign () in your answer; instead, list the zeros separately. Do not include "x =" in your answer. Provide your answer below:

Consider the function f(x) = x5 + 10. If f-¹(x) is the inverse function of f(x), find f¯¹ (42). Provide your answer below: f-¹(42) =

Al and Sarah are raking the yard. Al can rake the entire yard in 5 hours while it takes Sarah 9 hours to rake the yard. How long will it take Al and Sarah to rake the yard together? Choose the equation that should be used to solve this problem and state the solution.

You want to buy a house for $275,000 at 3.5% interest. What would your payment be if you pay it off over 15 years? What would your payment be if you pay it off over 30 years? How much would you end up paying all together for each of those?