Math Questions

Write the expression cotθ cosθ tanθ cscθ using a single trigonometric function. cos θ sin θ sec θ cot θ

Journal entries based on the bank reconciliation are required in the depositor's accounts for a. bank errors. b. NSF items. c. deposits in transit. d. outstanding checks.

Find the vertical, horizontal, and oblique asymptotes, if any, of the following rational function. G(x)=x4 - 1/6x² - 6x *** Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The funct has one vertical asymptote, ____ (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is __(Type equations. Use integers or fractions for any numbers in the equations.) C. The function has no vertical asymptote.

The position function of an object is given by s³ + t²s = 2t, where the position, s, is a function of time, t, for t ≥ If ds/dt=2-2st/3s^2+t^2 determine why the acceleration is not defined at t = 0. 2-2st = 0 for t = 0 and s = 0 2-2st=0 for t = 0 and s = 1 (3s² +1²)² = 0 for t = 0 and s = 0 (3s² + 2)2 = 0 for t = 0 and s = 1

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. For the sake of argument, assume that 51 percent of the actual voters in the state support the incumbent governor (p= .51). Calculate the probability of observing a sample proportion of voters .55 or higher supporting the incumbent governor. .0166 .0247 .0082 .9918

g"(x)= 2/x^2 The second derivative of the function g is given by x² Given x = 0.4 is a critical point of g, use the Second Derivative Test to determine relative extrema for g. (10 points) g has a point of inflection at x = 0.4. g has neither a relative minimum nor relative maximum at x = 0.4. g has a relative maximum at x = 0.4. g has a relative minimum at x = 0.4.

For the following problems, calculate the probability of each event for one roll of a die. Hint: Use the formula for theoretical probability. 12) a number greater than 6

Suppose that $8500 is placed in an account that pays 16% 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. $

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 257. What is the probability that the sample proportion will be at least 4 percent more than the population proportion?

Find the distance between the pair of points (-3,-4) and (1,-3). If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is __ units. (Simplify your answer. Type an exact answer, using radicals as needed.)

A store sells portable MP3 players for $100 each and, at this price, sells 120 MP3 players every month. The owner of the store wishes to increase his profit, and he estimates that, for every $2 increase in the price of MP3 players, one less MP3 player will be sold each month. If each MP3 player costs the store $70, at what price should the store sell the MP3 players to maximize profit?

Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by 1/6. Is Sophia correct? Explain.

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)?