Math Questions

Find the distance between the points (9, 10) and (-1, 6).

Determine whether the given relation defines y as a function of x. x² + y² = 100 Is y a function of x? No Yes

Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) - 2 is true? A. As x decreases, y moves toward the vertical asymptote at x = -3. B.As x decreases, y moves toward the vertical asymptote at x = -1. C.As x increases, y moves toward negative infinity. D.As x decreases, y moves toward positive infinity.

5. Brianna works at the Steve Lindquist Aquatic Center during her summer vocation. She is paid $10 per hour for teaching swim lessons and $20 per hour for teaching water aerobics She can work a maximum of 35 hours per week, and would like to earn at least $400 this week. If x represents the number of hours teaching swim lessons and y represents the number of hours teaching water aerobics. a. Write a system of inequalities that could be used to represent the given conditions. b. Insert a picture of the graph. (Sketch the graph if you're writing on paper.) c. Pick 2 ordered pairs, explain what they represent in terms of the problem, and how much money she would earn that week.

Find the center and radius of the circle with the equation (x-3)² + (x+7)² = 121 Center: Radius: r

An equation of an ellipse is given. x2/25 + y²/16 = 1 25 16 (a) Find the vertices, foci, and eccentricity of the ellipse.

Graph the solution to the inequality on the number line. |v-8] <2

What would f(x) be if x = 6 f(x)=⅓ ∙ 6ᵡ 13323 15552 1743 12345

Use the properties of logarithms to write the expression as a single logarithm. Assume that all variables are defined in such a way that the variable expressions are positive. log9(x+5)+ log9(x+3) log9(x + 5) + log9(x+3)= ________

Find the first-order Fourier approximation to f(t)=t+5. That is, find the the best approximation to f(t) by functions in Span{1,cos(t),sin(t)}

Give the following number in Base 10. (11011)2= [?]10

Given the trigonometric function defined by f(x) = cos(4x): 1. What is the amplitude of the function? _______ 2. What is the period of the function? ______ 3. Sketch one period of the function.

Which of the following is false? Enter a, b, c, d, or e. a. Every whole number is a natural number. b. Some rational numbers are whole numbers. c. O is an integer. d. No irrational numbers are integers. e. ∛729 is not irrational.

The slope of a line that is parallel to 4x-y=8 is m = ________ The equation of the line (in slope-intercept form) parallel to 4x-y=8 that passes through the point (0, 2) is y= __________

7π/6 in degrees is _____________ degrees The exact form of tan (7π/6) is ___________

Solve for x: log6 (3x + 10) = 2 Write log6 (3x + 10) = 2 in exponential form. _________________ Find the value of x. x= ___________

Let f be the one-to-one function given below. f(x)=(5x-4)/(6x-3) (a) Find the inverse function of f (i.e., f-¹(x).) f-¹(x) = _____ (b) Compute f-¹(-1). f-¹(-1)=_____

Which of the following is NOT irrational? Enter a, b, c, d, or e. a. π b. √7 c. √49 d. 7.313113111311113... e. √7-√3

Let the trigonometric function f be defined as f(x)= -2sin(9x), The amplitude of f is _____ The period of f is ____ The y-intercept is ____

Let f(x) = (x² + 1)² and g(x) = What is the slope of the curve og'(4) = 8 o g'(4) = // og'(4) = - 8 og'(4) = -1/ 4 f'(x). g(x) = f (x) at the point(4, 1)?

Person A can paint the neighbors house 6 times as fast as person B The year A and B worked together, it took them one day. How long would it take each to paint the house? find the how many days person A would tale and find how many days person B would take. there are two answers.

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true? A) 30x = 2 B) 2x = 30 C)2x = 30 D) x + 30 = 2

The exponential function f(x)=ab^x contains the points (0, - 4) and (-2, -4/25). Write the conditions as exponential equations involving the variables a and b. The point (0, -4) gives the equation ________. The point (-2, -4/25) gives the equation ________. Find the values of a and b that satisfy these equations. a= _________. b= _________.

Cost of goods sold is reported as a(n) a. current liability. b. long-term asset. C. current asset. d. expense.

What is a measure of central tendency (also known as a measure of center)? A. A number that separates the lower P% of the data from the upper (1-P)% of the data. B. A value that can stand in for and fairly represent all the data values in a large set of numbers; a typical value C. A value that can summarizes the spread or dispersion of a set of data D. A value that represents the probability of generating a test statistic at least as extreme than than the one you already hav E. A value equal to a data value's standard deviations from the mean

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.) (a) 2π/3 (b) -9π/4

Which of the following sets of numbers could not represent the three sides of a right triangle? {36, 77,85} {24, 45, 51} {7, 24, 25} {65, 72,96}

Which of the pairs of events below is dependent? Select the correct answer below. drawing a 7 and then drawing another 7 with replacement from a standard deck of cards rolling a 1 and then rolling a 6 with a standard die rolling a 3 and then rolling a 4 with a standard die drawing a heart and then drawing a spade without replacement from a standard deck of cards

e^(2x+1)=48 Write the equation as an equation involving logarithms. _______________ Find the solution of the equation in terms of logarithms, or correct to four decimal places. x=______________

Let f(x) = x+2/x-4 and and g(x) = 10x-22/x²-5x+4 Simplify f(x) - g(x): ____________ The values of x that need to be excluded from the domain of the difference function are x = _______

Use the table of critical values of the Pearson correlation coefficient to determine whether the correlation coefficient is statistically significant at the specified level of significance for the given sample size. Write the critical value to the nearest thousandth. r = 0.599.a = 0.05, n = 12

A certain radioactive substance has a half-life of five days. How long will it take for an amount A to disintegrate until only one percent of A remains?

A simple graph G on n vertices (n ≥ 2) is drawn in the plane. Prove that if every edge crosses at most one another edge, then the number of edges in G does not exceed 4n-8.

What is the solution set for |s+4| = 6? s=-2 and s=2 s=-10 and s=2 s=-10 and s= 10 s= 2 and s=10

Determine whether the proportion is a true proportion. 7/21 = 8/24 Is the proportion a true proportion? A. No, because 7+248 +21. B. Yes, because 7.24 = 8.21. C. Yes, because 7 + 24 = 8+21. D. No, because 7.24 #8.21.

Which is the logarithmic form of the given equation? 10ˣ = 1000 ○ log 10 = x ○ log x = 10 ○ log 1000 = x ○ log x = 1000

If the terminal side of angle θ, in standard position, passes through the point (-3, 4), what is the value of sin θ ? (A) -5/4 (B) -3/4 (C) 4/5 (D) 4/3

The function g(2) is shown in the table below. x g(x) -2 -11 -1 -8 0 -5 1 -2 2 1 Which of the following tables represents the inverse function, g‾¹(x)?

A machine that manufactures automobile parts produces defective parts 12% of the time. If 9 parts produced by this machine are randomly selected, what is the probability that fewer than 2 of the parts are defective? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

The function h(x)= (x+2)³ can be expressed in the form f(g(x)), where f(x)= x³, and g(x) is defined below: g(x)=____

A company's marginal cost function is MC(x) = 1/8x + 1 and its fixed costs are 100. Find the cost function. (Remember to use absolute values where appropriate.)

Use a half angle formula or formula for reducing powers to fill in the blanks in the identity below: (cos(3x))² = _____ + ____ cos(_____ x)

What is the area of a regular hexagon inscribed in a circle of radius 9 meters? 35.074 square meters 175.370 square meters 192.589 square meters 210.444 square meters

There are two machines that produce aluminum cans. The newer machine can produce 5400 cans in 180 minutes. It takes the older machine 270 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5400 cans? ________minutes

Which expression below can be obtained from 10sin²x by using a power reducing formula? Select the correct answer below: 5 - 10cos (5x) 5-5cos (2x) 10-5cos (2x) 5-10cos (x) 5-5cos (x)

A college reported the following based on their graduation data. 60% of freshman had attended public schools. 60% of freshman who had attended public schools graduated within 5 years. 80% of other freshman graduated within 5 years. What percent of freshman graduated within 5 years? A. 68% B. 66% C. 47% D. 69%

Suppose it was determined that the water footprint for a typical American is 2,483 m³/year. a. A family of three would like to reduce their water footprint so that it is 75% of the typical American's water footprint. Which calculation shows how they can estimate their target water footprint for one day? There may be more than one correct answer. ÷ 365 0 (3) 3 x 2,500 × 3 2,500 × 3 × 4 03 x 2,500 x 0.75 ÷ 365 2,500 (365 × 0.75) × 3 2, 500 x 3 x 0.75 3x (2, 500 x 0.75) ÷ 365 4 3 2, 500 x 3÷ 0.75 ÷ 365

Solve for the roots in simplest form by completing the square: x² + 16x - 61 = 0

An accounting firm has ordered 60 new computers at a cost of $1657 each. The machines will not be delivered for 5 months. What amount could the firm deposit today in an account paying 3.33% simple interest to have enough money to pay for the machines in 5 months? The present value PV of a future amount of FV dollars at a simple interest rate r for t years is given by which formula? A. PV=FV(1 + rt) B. PV= FV c. PV=rt(1 + FV) FV 1 + rt D. PV= The firm should deposit $ (Round to the nearest cent as needed.)

The radius, r, in centimeters, of a melting snowball is given by r = 60 — 2.5t, where t is the time in hours. The snowball is spherical with volume V = πr³ cm³. Find a formula for V = f(t), the volume of the snowball as a function of time. V = f(t) = (Be sure to include units!) help (formulas) with help (units)