Math Questions

What is the center of the shape formed by the equation (x-3)²/49 - (y+5)²/25 = 1? (0,0) (-3,5) (3,-5) (9,25) (-9, -25) (x-3)²

Julio must invest a total of $6300 in two accounts, one paying 10% simple annual interest and the other paying 7% annual interest. If he wants to earn $534.00 annual interest, how much should be invested at each rate?

The length of a path going diagonally across a rectangular field is 100 yards, the width of the rectangular field is 50 yards. What is the measure of the angle these two lines form? (Round your measure to the nearest whole degree).

Consider the function f(x) = 25x² - 64. a) Determine the zeros of the function: Writing values as simplified fractions if necessary. If there are multiple values, separate the solutions with a comma. If there are no values, input "DNE". b) Determine the x-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple x-intercepts, separate them with a comma. If there are no x-intercepts, input "DNE". c) Determine the y-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple y-intercepts, separate them with a comma. If there are no y-intercepts, input "DNE".

The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x - 1. It goes through the point (5, 96). Find a formula for P(x). P(x) =

A sample of size 7-50 is drawn from a normal population whose standard deviation is a-7.1. The sample mean is x=48.52. (a) Construct a 99.9% confidence interval for H. Round the answer to at least two decimal places. A 99.9% confidence interval for the mean is 0<μ< (b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain. The confidence Interval constructed in part (a) (Choose one) be valid since the sample size (Choose one) ▼ large.

The two points (-3, 6) and (6, 0) are plotted on the grid below. (a) Find an equation, in y=mx+b) form, for the line passing through these two points. Use of the grid is optional. b) Does the point (30, -16) lie on this line? Justify.

A car was valued at $40,000 in the year 1995. The value depreciated to $14,000 by the year 2007. A) What was the annual rate of change between 1995 and 2007? T= Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? T = C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012? value = $ Round to the nearest 50 dollars.

Given a function f (x) = 2x² + 3, what is the average rate of change of f on the interval [2, 2 + h]? 11 2h +8 2h² + 8h 2h² + 8h + 11

Find a 95% confidence interval for the mean of the length of fishes in a pond based on the sample below. The measurements are in inches. 5, 6, 6, 7, 9, 9, 10, 11, 11, 12, 12, 12, 13, 14, 19 (8.62, 12.18) (8.63, 12.17) (8.69, 12.11) 8.56, 12.20)

Consider the equation below. f(x) = 2x³ + 3x² = 120x (a) Find the interval(s) of increase and decrease. (b) Find the local minimum and maximum values of f. (c) Find the inflection point and the intervals on which fis concave up and concave down. (a) Find the interval(s) of increase and decrease. For f(x) = 2x³ + 3x2 - 120x, we have the following f'(x) = This factors into(__)(x+__)(x-4).

Write the following as the sum and/or difference of logarithms. Assume all variables are positive. log (10z/4)= __ The answer format in lowercase characters is: log(number) Spaces in the answer are optional.

Suppose a flu epidemic has broken out in all math 120 courses at your school. Assume a total of 12 people have the flu as of today and that each day the total number people who have the flu quadruples. Estimate numerically when the number of people will reach 3072. {your answer input will be number only)

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. How rapidly is the area enclosed by the ripple increasing when the radius is 1 feet?

Solve the following equation on the interval [0°, 360°). Round answers to the nearest tenth. If there is no solution, indicate "No Solution." -6csc²(x) - 19cot(x) = 4

Find all values of c that satisfy the mean value theorem for integrals on the following interval f(x)=√x+9 . [0.4]

A linear function is given. Complete parts (a)-(d). f(x)=1/5x-6 (a) Determine the slope and y-intercept of the function.

A cashier has a total of 48 bills in her cash drawer. There are only $20 bills and $5 bills in her drawer. The value of the bills is $465. How many $20 bills are in the drawer? 31 $20 bills 17 $20 bills 15 $20 bills 33 $20 bills

Select the correct answer from each drop-down menu. The barley plant has seven pairs of chromosomes. For a gamete, the number of genetic combinations that are possible through independent assortment is __. For a zygote produced by two barley parents, the number of possible genetic combinations is__

Evaluate the expression without using a calculator. 7!/3!(7-3)! The answer is __ (Type an integer or a simplified fraction.)

John wants to prepare a sandwich. He has 4 choices for the type of bread, 5 choices for the meat, and 3 choices for dressing. How many different sandwiches can John prepare? Show you work and answer in the text box given below.

A building 29.94 feet tall has a shadow that is 33.11 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree. The angle of elevation is degrees. (Round to the nearest hundredth as needed.)

For a given function f(x), the operation 1/2f(x) will A) shrink the graph horizontally by a factor of 1/2. B) stretch the graph horizontally by a factor of 2. C) shrink the graph vertically by a factor of 1/2. D) stretch the graph vertically by a factor of 2.

A right triangle has sides that measure 24 and 32, but the length of the hypotenuse is unknown. What is the perimeter measurement of this triangle? Round your answer to the nearest hundredth 85.23 96 89 94.79

A candy company claims that 25% of the candies in its bags are colored green. Steve buys 32 bags of 32 candies, randomly selects one candy from each, and counts the number of green candies. If there are 7, 8, or 9 green candies, Steve will conclude that the company's claim is correct. What is the probability of Steve agreeing with the company's claim? Use Excel to find the probability • Round your answer to three decimal places.

A gallon contains 231 cubic inches. A cylindrical barrel full of juice concentrate has a diameter of 3 feet and is 8 feet high. How many gallons of concentrate are in the barrel? Use π = 3.14. There are __ gallons of concentrate in the barrel. (Type an integer or a decimal. Round to two decimal places as needed.) .....

On the left-hand side, for the first term 9x³, we have the following. d/dx[9x³]=_ Now, note that the second term x2y is a product, so we must use the product rule. We therefore have the following. d/dx[x²y] = (x²)(y') + __

If y varies inversely with the square of x, and y = 12 when x = 3, find y when x = 0.5. y= (Simplify your answer. Type an integer or a decimal.) *****

Which of the following statements is true for the quadratic equation x² - 16x+64 = 0? The equation has no solutions. The equation has two solutions. It's impossible to determine how many solutions the equation has. The equation has one solution.

Kevin the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 8 clients who did Plan A and 3 who did Plan B. On Tuesday there were 2 clients who did Plan A and 5 who did Plan B. Kevin trained his Monday clients for a total of 15 hours and his Tuesday clients for a total of 8 hours. How long does each of the workout plans last? Length of each Plan A workout: _hour(s) Length of each Plan B workout: _hour(s)

(a) Use one of DeMorgan's Laws to choose a negation of the following statement. Abdul is in art class or he has a test today. Negation: (Choose one) (b) Use one of DeMorgan's Laws to choose a statement equivalent to the following. It is not the case that "squares have seven sides and trapezoids have nine angles". Equivalent: (Choose one) Squares don't have seven sides and trapezoids don't have nine angles. Trapezoids have nine angles or squares have seven sides. Trapezoids have nine angles and squares have seven sides. Squares don't have seven sides or trapezoids don't have nine angles.

Solve the following equations for x, showing each step on a separate line. Check your answers. a) 5x - 3x = 8 b) 5x - 3 = 8 c) 5x - 3 = 8x d) 2x - 11 = 4-x e) 2x - 11 = 4+* f) 2x + 11 = 4 + x g) 7x 6 = 18 + 3x h) 7x + 6 = 18 - 3x

Solve for x. |2x - 3| ≤2 What is the solution? Select the correct choice below and fill in any answer boxes within your choice. A. x≤__ or x ≥__ (Simplify your answers.) B. _≤x≤_ (Simplify your answers.)

An endangered species of fish has a population that is decreasing exponentially (A - Agekt). The population 9 years ago was 1500. Today, only 1000 of the fish are alive. Once the population drops below 100, the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.) 51 years from today 53 years from today 50 years from today 52 years from today

A mortgage is paid off in 30 years with a total of $124,000. It had a 2% interest rate that compounded monthly. What was the principal? Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your final answer. Provide your answer below:

Suppose there is a list of fifteen jokes about marriage and divorce. In how many ways can people select their five favorite jokes from this list? Five favorite jokes can be selected from a list of fifteen thoughts about marriage and divorce in different ways. (Type a whole number.)

Determine if the function given below is increasing, decreasing, or constant. f(x) = 0 Select the correct answer below: The line is increasing. The line is constant. The line is decreasing.

Select a possible formula for the polynomial f(x), given that f(x) has degree three, f(-1) = f(3) = f(5) = 0, and limz⇒∞f(x) = -∞. A. -(x + 1)(x - 3)(x - 5) B. -(x + 1)2(x - 3)(x - 5) C. (x + 1)(x+3)(x - 5) D. -(x + 1)(x + 5)(x+3) Is there more than one possible solution? A. No, because there is only one function that meets all of the requirements. B. Yes, because the leading coefficient could be any negative number. C. Yes, because there could be different multiplicities for the roots. D. No, because we know the three roots and it is a degree three polynomial.

"Princess Tower" in Dubai is considered the world's tallest residential building, towering to 101 floors! T(n) models the number of tenants living on floor n of the tower. What does the statement T(20) = T(c) mean? Choose 1 answer: (A).Floor 20 and floor c have the same number of tenants. (B)The number of tenants on floor 20 is equal to C. (C)The number of tenants on floor C is equal to 20.

Describe the long-run behavior of the following functions, and identify horizontal asymptotes. a) g(x)=3x²/x² - 1 As a goes to +∞, g(x) goes to As a goes to -∞, g(x) goes to Horizontal asymptote: y =

Quadrilateral ABCD has vertices A(-2, 1), B(4,4), C(5, 0), and D(-1, -2). Which side is the longest? CD DA AB BC

Subtract the polynomials: (-8x5 + 10x² - 10x) - (-7x5 - 8x² + 6)

Is the function below exponential? m(t) = (2.3t) ³ If so, write the function in the form m(t) = abt and enter the values you find for a and b in the indicated blanks below. If the function is not exponential, enter NONE in both blanks below. a b

At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients. Then an average is determined by giving a weight of 4 for promptness, 2 for record keeping, 3 for appearance, and 1 for bedside manner with patients. What is the average rating for a nurse with ratings of 5 for promptness, 4 for record keeping, 9 for appearance, and 2 for bedside manner? (Enter your answer to one decimal place.)

In an article on Flurry Blog, a gaming marketing gap for men between the ages of 30 and 40 is identified. You are researching a startup game targeted at the 35- year-old demographic. Your idea is to develop a strategy game that can be played by men from their late 20s through their late 30s. Based on the article's data, industry research shows that the average strategy player is 28 years old with a standard deviation of 4.8 years. You take a sample of 100 randomly selected gamers. If your target market is 29- to 35-year-olds, should you continue with your development strategy?

Find allercepts and y-intercepts of the graph of the function. f(x)=3x² +17x+20 If there is more than one answer, separate them with commas. Click on "None" if applicable.

A clothing business finds there is a linear relationship between the number of shirts, it can sell and the price, P, It cancharge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $78 each, and that 7 thousand shirts can be sold at a price of $62 each. Find the equation of the form P(n) = mn + b that gives the price P they can charge for n thousand shirts. Select the correct answer below: P(n) = 0n + 78 P(n) = -4n +95 P(n) = -4n +90 P(n) = On +62 P(n) = -6n +104 P(n) = -6n +96

Using the slope formula, find the slope of the line through the given points. (6,7) and (9,4) What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is B. The slope of the line is undefined. (Type an integer or a simplified fraction.)

Mario has a 500-page novel which he is required to read over summer break for his upcoming language arts class. a. If Mario reads 24 pages each day, write a function to represent the number of pages that Mario has left to read p after d days.

The notation fog, called the of the function f with g, is defined by (fog)(x) =