Math Homework Questions & Answers Archive

Question 10 A sample of size 95 will be drawn from a population with mean 25 and standard deviation 13. Find the probability that x̄ will be between 22 and 27. 0.0668 0.9210 0.0122 0.9080 Question 11 The average number of mosquitos in a stagnant pond is 100 per square meter with a standard deviation of 16. If 9 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 104.8 mosquitos per square meter. Assume that the variable is normally distributed. 0.3% 81.6% 18.4% 31.6%

If z is a standard normal variable, find the probability that z lies between -2.41 and 0. Round to four decimal places. A. 0.5080 B. 0.4920 C. 0.0948 D. 0.4910

Solve the following equation using a graphical method. 5(x-8)=7(x-4)+4 Graph the left side of the equation as y1 and the right side as y2 on the same viewing window. Choose the correct graph below. All graphs have viewing window [-15,15] by [-100,100] with Xscl=1 and Yscl=10. A. B. C. D.

Find all rational zeros of the polynomial. (Enter your answers a P(x)=3 x^5-20 x^4-16 x^3+54 x^2+61 x+14 x=-1,1,2,-1/3, 7x Write the polynomial in factored form. P(x)=(x+1)^2(3 x+1)(x-2)(x-7)

Simplify. 12^0

Use the remainder theorem and synthetic division to find f(k) for the given value of k. f(x)=-x^3-8x^2-17x-6 ; k=-4 f(-4)=

Let f(x)=4x+6-5e^x. Then the equation of the tangent line to the graph of f(x) at the point (0,1) is given by y=mx+b for m= b=

Find the slant asymptote of the graph of the rational function. Follow the seven-step strategy and use the slant asymptote to graph the rational function. f(x)=(x^2+6 x-7)/(x-7) A. The x-intercept(s) is/are 1,-7. (Type an integer or a simplified fraction. Use a comma to separate answers if needed.) B. There are no x-intercepts. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete the choice. A. The equation of the vertical asymptote is 7. (Type an equation.) B. There is no vertical asymptote.

The expected value of a discrete random variable represents the mean value of the outcomes.

If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. A. 31/334 B. 334/365 C. 31/365 D. 11/12

For f(x)=5x-3 and g(x)=2x^2-5, find the following functions. a. (f∘g)(x); b. (g∘f)(x); c. (f∘g)(2); d. (g∘f)(2) a. (f∘g)(x)=10x^2-28 (Simplify your answer.) b. (g∘f)(x)=50x^2-60x+13 (Simplify your answer.) c. (f∘g)(2)=12 (Simplify your answer.) d. (g∘f)(2)= (Simplify your answer.)

Find the slant asymptote of the graph of the rational function. Follow the seven-step strategy and use the slant asymptote to graph the rational function. f(x) = (x^2 - 25) / x A. The equation(s) of the horizontal asymptote(s) is/are □ (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote Plot points between and beyond the x-intercepts and the vertical asymptote. Evaluate the function at -7, -4, 4, 7, and 8. x -7 -4 4 7 8 f(x) = (x^2 - 25) / x □ □ □ □ □ (Simplify your answers.)

Write a formula that expresses the indicated variation. A varies jointly as j and n Choose the formula that best represents the statement. A. A=k j n B. A=k j/n C. A=k/(j n)

If A=[[-2 -8], [-6 6]], then A^(-1)=[[n ], [ ]]

Participation Activity #19 This is similar to Try It #5 in the OpenStax text. Sketch a graph of f(x)=log3(x)+2 alongside its parent function. Include the key points and asymptotes on the graph. State the domain, range, and asymptote.

Perform a first derivative test on the function f(x)=x^(2/3)(x-4) ;[-4,4]. a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).

For f(x)=x+4 and g(x)=3x+3, find the following functions. a. (f ∘ g)(x); b. (g ∘ f)(x); c. (f ∘ g)(1); d. (g ∘ f)(1) a. (f ∘ g)(x)= (Simplify your answer.)

Find (d y / d x) by differentiating implicitly. When applicable, express the result in terms of (x) and (y) (4(x^2+1)^5+(y^2+2)^2=27) (fracd yd x=square)

Analyze the equation. That is, find the center, vertices, and foci of the ellipse and graph it. 25 x^2+y^2=100 What are the coordinates of the center? (Type an ordered pair.)

A trail mix contains a mixture of nuts: pecans, walnuts, hazelnuts, and peanuts. If the probability of reaching into the trail mix and getting pecans is 0.09, what is the probability of not getting pecans? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest hundredth.

Write the quadratic function f(x)=x^2+14x-29 in the form f(x)=(x-h)^2+k f(x)=

Graph the rational function. f(x)=(2x^2-6x+3)/(3x-9) Start by drawing the asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.

Perform the following operation, if possible. [ [8 -5 -9 7 0 0] - [1 1 -6 -8 -1 -9] ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. [[8 -5 -9 7 0 0]]-[[1 1 -6 -8 -1 -9]]=[[ ]] (Type an integer or a fraction.) B. Matrices cannot be subtracted.

Convert the number from octal to binary form. 513eight

The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was approximately 1.71 times 10^13. If you wrote this number in standard notation, it would be the number 171 followed by how many zeros?

Simplify. 18(v+2)(3 v-7)/6(v+2)(3 v-7)

Divide. (x^2+2x-35) ÷ (x-5)

Use a Venn diagram. Let P(Z)=0.47, P(Y)=0.34, and P(Z ∪ Y)=0.63. Find each probability. (a) P(Z' ∩ Y') (b) P(Z' ∪ Y') (c) P(Z' ∪ Y) (d) P(Z ∩ Y') Complete the Venn diagram using the given probabilities. region I represents 0.29 region II represents 0.18 region III represents 0.16 region IV represents 0.37 (Type integers or decimals.) (a) P(Z' ∩ Y')=0.37 (Type an integer or a decimal.) (b) P(Z' ∪ Y')=0.82 (Type an integer or a decimal.) (c) P(Z' ∪ Y)=0.71 (Type an integer or a decimal.) (d) P(Z ∩ Y')=

Solve the inequality. 3 x^2 + 7 x + 2 ≤ 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is the interval . (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution is the list of x-values x= . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) C. There is no solution.

Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate ln(e^4/11)

Solve the inequality. Write the solution set in interval notation. x^2-x-6<0 Choose the correct solution below. A. (-∞,-2) ∪(3, ∞) B. -2,3 C. (-2,3) D. No solution

Graph the line. y=1/2 x-2

Follow the seven step strategy to graph the following rational function. f(x) = (x+2)/(x^2+x-12) A. The equation(s) of the vertical asymptote(s) is/are x=-4, x=3. (Type an equation. Use a comma to separate answers as needed.) B. There is no vertical asymptote. Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are . (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.

Graph the inequality, (y<-frac54 x+5).

What is the length of the hypotenuse? If necessary, round to the nearest tenth. c= centimeters

Use properties of logarithms to condense the logarithmic expression below. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expression [ 4 ln x-5 ln y ] (4 ln x-5 ln y=) (Simplify your answer.)

What is the length of the hypotenuse? If necessary, round to the nearest tenth. c= meters

Evaluate the expression without using a calculator. log4 4^3 log4 4^3=

Find the product and write it in lowest terms. 6/7 * 9/4

Divide. (x^2+2x-35) ÷ (x-5)

Melissa is a civil engineer working for the city of Indianapolis on a project to widen some of its downtown streets. One aspect that she has to consider is that, during the hot summer months, the noonday temperature of the asphalt on these streets can get extremely hot. For the project, she models these temperatures of the asphalt using a normal distribution with a mean of 108°F and a standard deviation of 16°F. Use this table or the ALEKS calculator to find the percentage of noonday temperatures of the asphalt between 104°F and 132°F according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

Simplify. 5/6 divided by 2

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 95 and 115. The probability that a randomly selected adult has an IQ between 95 and 115 is

1. Assumptions of Parametric Tests -Know how to examine normality graphically (histogram, stem-and-leaf plot, normality plots) -Know how to examine normality statistically (Kolmogorov-Smirnov, Shapiro-Wilk tests) -Know how to examine homoscedasticity statistically (Bartlett's test, Levene's test) -Know the various data transformations, and what types of data they may be best used for -Know how to determine if a value is an outlier -Know the different options for dealing with outliers in your data

Graph the quadratic function f(x)=(x+2)^2. Give the (a) vertex, (b) axis, (c) domain, and (d) range. (a) The vertex is (Type an ordered pair.)

Solve for x . [ sqrt3 x-1=7 ] What is the root? If there is no root, choose none. 16 2/3 16 12 none

Solve for x ln x = 4

Use the Venn diagram to represent the set (A ∪ B)′ in roster form. (A ∪ B)′ = (Use a comma to separate answers as needed.)

Solve for (x, y, z) and (w). (Enter your answers as a comma-separated list.) [ left[beginarraycc x+y y+z z+w w endarrayright]=left[beginarrayll 3 5 5 2 endarrayright] ] ((x, y, z, w)=)

Suppose f'(9)=5 and g'(9)=7. Find h'(9) where h(x)=3 f(x)+4 g(x)+6. h'(9)=

Encontre uma equação da reta tangente à curva no ponto dado. y=sqrt(1+x^3), em (2,3)

Solve for (y). [ sqrt2 y-5+4=8 ] What is the root? If there is no root, choose none. (10 frac12) (5 frac12) none (8 frac12)

Simplify. -3(x+4)+2x

Assessment, Composing and ing Functions Question 4 of 7 This test: 7 point(s) possible This question: 1 point(s) possible Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range of the polynomial function. f(x)=x^3-1.5x+3 The zeros of the function are (Round to the nearest thousandth. Use a comma to separate answers as needed.) What is the value of the relative maximum of this function? (Round to the nearest thousandth.) What is the value of the relative minimum of this function? (Round to the nearest thousandth.) What is the range of this function? A. B. C.

Suppose you get a 80 music gift card. Each 1.29 song has an additional sales tax charge of 6% in your state. How many songs can you buy with the gift card? You can buy Jsong(s) with the gift card. (Type a whole number.)

Solve for q. √3 q + 2 = √5

Consider the equation: x^2 - 16x + 55 = 0 A) First, use the "completing the square" process to write this equation in the form (x+D)^2 = E and enter your results below. x^2 -16 x +55 = 0 is equivalent to: (x-8)^2 0^8 = 9 >0^8 B) Solve your equation and enter your answers below as a list of numbers, separated with a comma where necessary. Answer(s):

Look at the diagram. Which equation can be used to solve for x ? 6x-6=180 6x-6=90 12x=90 12x=180 Solve for x. x=

Sue saves 16.50 each week out of her paycheck of 550. What percent of her paycheck does her savings represent? Sue saves % of her paycheck.

For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets 8,15,9,6,17 The number of subsets is .

A piece of wire of length 62 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square? (a) To minimize the combined area, the wire should be cut so that 27.274 are used for the circle and 34.726 are used for the square. (Type integers or decimals rounded to the nearest thousandth as needed.) (b) To maximize the combined area, the wire should be cut so that are used for the circle and are used for the square. (Type integers or decimals rounded to the nearest thousandth as needed.)

Determine if the graph can represent a polynomial function. If so, assume that the end behavior and all turning points are represented in the graph.

What values of x and y make triangle FGH congruent to triangle CDE? x= y=

Determine if the survey question is biased. If the question is biased, suggest a better wording. How much do you sleep per night during an average week? Is the question biased? A. Yes, because it influences the respondent into thinking that sleeping 8 hours per night is good for you. A better question would be "Do you think that sleeping 8 hours per night is good for you?" B. No, because it does not lead the respondent to any particular answer. C. No, because it influences the respondent into thinking that sleeping 8 hours per night is good for you. D. Yes, because it does not lead the respondent to any particular answer. A better question would be "Why is sleeping 8 hours per night good for you?"

Graph both equations and find their point(s) of intersection, if any. Enter as coordinates, separating your answers with commas. x^2 - 9y = -18 -2x + 3y = 3

Find the exact value. Do not use a calculator. cos(pi/6) sqrt(3) sqrt(2)/2 sqrt(3)/2 2 sqrt(3)/3

At a sale, a table is being sold for 73% of the regular price. The sale price is 219. What is the regular price?

A frequency distribution is shown below. Complete parts (a) through (d). The number of televisions per household in a small town Televisions 0 1 2 3 Households 22 446 720 1400 (a) Use the frequency distribution to construct a probability distribution. x P(x) 0 square 1 square 2 square 3 square (Round to the nearest thousandth as needed.)

Write the vector v in the form al+bj, given its magnitude v and the angle α it makes with the positive x-axis. [ v=7, quad alpha=60^circ ] [ mathrmv=square ] (Simplify your answer. Type an exact answer using radicals as needed. Type your answer in the form al + bj.)

Convert the angle to D° M′ S″ form. Round the answer to the nearest second. 265.43° 265° 25′ 43″ 265° 26′ 47″ 265° 47′ 43″ 265° 25′ 48″

Country A has an exponential growth rate of 3.8% per year. The population is currently 4,891,000, and the land area of Country A is 20,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?

According to a study, the average person can listen to 6 hours of sound per day at a sound level of 86 decibels without experiencing hearing loss. A decibel is a unit for measurement of sound intensity. For each increase of 8 decibels, the exposure time must be divided by three. For example, an average person can listen to 2 hours of sound per day at a sound level of 94 decibels without experiencing hearing loss. (One overexposure may result in temporary, but probably not permanent, hearing loss). Complete parts (a) through (c) below. a. Let T=f(d) be the number of hours of safe exposure time in one day to a sound at a level of d decibels above 86 decibels. Find an equation of f. f(d)= (Use integers or fractions for any numbers in the expression.)

for the variable in the equation: (7x+4)/3 = 9/2 x = -2 1/14 x = -11/14 x = -4 9/14 x = 1 5/14

What is the least possible degree of the polynomial graphed above?

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. Slope -6 ; y-intercept (0, 8/9) The equation is (Type your answer in slope-intercept form.)

Evaluate. (Be sure to check by differentiating!) ∫ x^12 e^(x^13) dx Determine a change of variables from x to u. Choose the correct option: A. u=e^x B. u=x^12 e^x C. u=x^12 D. u=x^13

Find the marked price and sales tax. Total price 362.79, Sales tax rate 6.9%, Marked price, Sales tax. (Round to the nearest cent.)

QUESTION 16 Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle θ. sec θ = sqrt(10) Find cot θ. 1/3 3 sqrt(10)/10 sqrt(10)/3 sqrt(10)/10

(a) 25% of what number is 17? (b) 45% of 80 is what?

A manufacturing machine has a 9% defect rate. If 9 items are chosen at random, what is the probability that at least one will have a defect?

Answer the question below by choosing the correct response. A house was originally sold for 150,000. After 10 years, it is now worth 210,000. Which of the following represents the ratio of the original cost to its current value? a. 5 to 7 b. 7 to 5 c. 2 to 5 d. 5 to 2 e. 3 to 7

Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum. The dean wanted to find out how challenging the math coursework was for students. The proportion of math majors that stated the curriculum was challenging was 0.92 , with a margin of error of 0.07 . Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.

Three graphs are given below. For each, choose its equation from the following. y=2 sec x y=sec (x+π/4) y=tan x y=cot (x-π/4) y=-2+csc x y=-cot x Equation: (Choose one) Equation: (Choose one) Equation: (Choose one)

Question 9 0/1 pt This question is not about solving the stated problem, but about understanding it. A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t)=-4.9 t^2+1400 t+470. a) From what height was the rocket launched? To answer this question, we'd find: The t coordinate of the vertex ✓ b) What is the maximum height the rocket reaches? To answer this question, we'd find: The h coordinate of the vertex ~ c) If the rocket will splash down in the ocean, when will it splash down? To answer this question, we'd find: The h coordinate of the vertex ✓

Use a graph to solve the given equation for -2 π ≤ x ≤ 2 π. 10 tan x = -10 x = (Type an integer or a simplified fraction in terms of π. Use a comma to separate answers as needed.

Question Andy and Christopher are measuring a liquid solution using graduated cylinders. Andy uses 3,500 milliliters of the liquid solution, and Christopher uses 2,580 milliliters of the liquid solution. What is the ratio of Christopher's measurements to Andy's measurements in milliliters? Write your answer as a simplified fraction.

65% of the people in Missouri pass the driver's test on the first attempt. A group of 7 people took the test. What is the probability that at most 3 in the group pass their driver's tests in their first attempt? Round your answer to three decimal places. Remember: 65% = 0.65. Select the correct answer below: 0.944 0.144 0.468 0.200

Pregunta 1 (1 punto) ¿Qué función depende de encontrar una sustitución que convierta una integral que no es posible evaluar directamente? Método de sustitución Integral indefinida Antiderivada Teorema fundamental del cálculo

Find the radius of convergence and the interval of convergence of the power series sum from n=1 to infinity of (x-2)^n / (n^2+1).

How many distinct permutations can be formed using the letters of the word "PREPARED"? There are distinct permutations. (Type a whole number.)

X follows a normal distribution with mean 3 and variance 25, the probability of X being larger than 10 is (A) 0.92 (B) 0.08 (C) 0.61 (D) 0.39

The following stem-and-leaf plot represents the times in minutes required for 26 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in Minutes Stem Leaves 2 1 1 4 4 5 5 6 3 2 2 3 3 5 5 6 6 4 1 2 4 8 5 0 1 2 3 3 6 7 Key: 2 1 = 21

Use properties of logarithms to expand the logarithmic expression as much as possible. Assume s and t are positive real numbers. log(sqrt[3](s/t))

A population consists of 14 observations. Fix the sample size as 4 , if order is not important, the total number of possible samples using simply random sampling method is (A) 24040 (B) 3632428800 (C) 1000 (D) 1001

Add the radical expressions. 5 sqrt(96)+3 sqrt(150)= sqrt()

Write the equation of the line in slope-intercept form.

With 95% confidence, you can say that the population variance is between 6722229 and 38616699. What is the confidence interval for the population standard deviation σ ? (2593, 6214 ) (Round to the nearest integer as needed.) Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to the nearest integer as needed.) A. With 95% confidence, you can say that the population standard deviation is between and .

Question 3 Calculate the mass in grams of 2.80 moles of Ca. 112 g 80.2 g 42.0 g 150 g

At the animal shelter where Miguel volunteers on the weekends, there were three Siamese cats, five tabby cats, eighteen mixed-breed dogs, and six iguanas in their cages. If a customer picks any of these animals at random, find the probability that the animal is either a mixed-breed dog or a Siamese cat. Express your answer as a reduced fraction.

Si cuando se lanza un dado 4 veces, P1 es la probabilidad de que los 4 resultados sean iguales y P2 la probabilidad de que los 4 resultados sean diferentes, entonces ¿cuál es el valor de P1+P2?

Using Triangle Congruence Theorems Quiz Consider the diagram.

Find the area of the figure.

ln(x^2+y^2-6x)=5x-6 (a) Find dy/dx in terms of x and y:

George studied 1 / 4 hour on Monday and 3 / 8 hour on Tuesday. How long did he study altogether on both days?

5 · (1/5)=1 (Choose one) 0+8=8 (Choose one) 7 ·(d+3)=7 · d+7 · 3 (Choose one) c · 6=6 · c (Choose one)

Solve the following problems. C) Given: triangle AKM inscribed in k(O, r=2), m angle A=33°, and O in AM Find: Perimeter of triangle AKM

Collect like terms. [ 7 u^9 v-3 u v^2+2 u^9 v-3 u v^2 ]

Multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents. (y)(6xy-2x+7)

The normal distribution curve, which models the distribution of data in a wide range of applications, is given by the function p(x) = 1 / sqrt(2 π) e^(-(σ-μ)^2 / 2 s^2) where π = 3.14159265... and σ and μ are constants called the standard deviation and the mean, respectively. In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with μ = 4.3 and σ = 1.1. The percentage of consumers who gave the toothpaste a score between a and b on the survey is given by ∫ from a to b p(v) dx. Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 7 or higher. (Use the range 6.5 to 10.5.) Round to the nearest integer.

Automobil se giba jednoliko ubrzano iz mirovanja i kad prijeđe 100 m, postigne brzinu 10 ms¹. Kolika će mu biti brzina nakon što prijeđe 400 m? a) 20 m s⁻¹ c) 40 m s⁻¹ b) 30 m s⁻¹ d) 80 m s¹

logp V = -y The equivalent equation is □

Consider the function in the graph to the right. The function has a maximum of at x= The function has a minimum of at x= The function is increasing on the interval(s): The function is decreasing on the interval(s): The domain of the function is: The range of the function is:

Find the roots of the equation (x^2+x+4)(x-3)^2=0 a. 3,3,-1/2+2 i,-1/2-2 i b. 3, 3, -1/2+sqrt(15)/2 i,-1/2-sqrt(15)/2 i C. 3,3, 1/2+sqrt(15)/2 i, 1/2-sqrt(15)/2 i d. 3,-1/2+sqrt(15)/2 i,-1/2-sqrt(15)/2 i

The probability that x̄ will be greater than 32 is 0.9953. Part: 1/2 Part 2 of 2 (b) Find the 65th percentile of x̄. Round the answer to at least two decimal places. The 65th percentile of x̄ is .

In a survey of 2272 adults, 750 say they believe in UFOs. Construct a 99% confidence interval for the population proportion of adults who believe in UFOs. A 99% confidence interval for the population proportion is (0.305, 0.356). (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. A. The endpoints of the given confidence interval shows that 99% of adults believe in UFOs. B. With 99% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval. C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. D. With 99% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Question 17 of 31 (1 point) I Question Attempt: 1 of Unlimited Use the function below to answer the following questions. n(x)=-e^x-5 (a) Use transformations of the graph of y=e^x to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote. Part: 0 / 4 Part 1 of 4 (a) Use transformations of the graph of y=e^x to graph the given function. n(x)=-e^x-5 The graph of n is the graph of the parent function y=e^x reflected across the (Choose one) -axis and shifted 5 units (Choose one).

Find the required measurements of the following trapezoids. a=8 cm b=16 cm h=10 cm Compute the area.

If the area of the rectangle is 35x^2 - 50x + 8 square inches, and its length is 7x + 1 inches, find its width.

Use the zero-factor property to solve the equation. 9 x^2 = 22 x - 8 The solutions set is . (Use a comma to separate answers. Type repeated roots only once.)

The equation y=20 * 3^? shows the number of infected people from an outbreak of whooping cough. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 1,000? a.) 3.56 weeks b.) 2.45 weeks c.) 2.88 weeks d.) 3.24 weeks

Find the local minimum of the function f(x), which is given in the graph below.

Find the exact value. Simplify your answer completely. Write any fractional answers as a single fraction in simplest form. Rationalize your denominator, if necessary. tan(arccos(1/5)-arcsin(3/5))=

Solve the equation. x(5x+9)=2

Graph the rational function. f(x) = (2x^2 - 6x) / (x^2 - 4x + 3) Start by drawing the asymptotes (if there are any). Then plot two points on each piece of the graph. Finally, click on the graph-a-function button. Be sure to plot a hollow dot wherever there is a "hole" in the graph.

UNIT 3 - CHALLENGE 3.1: Exponents 3-Negative Exponents LEARNING OBJECTIVE: Simplify an expression with negative exponents. Simplify the expression to a form In which x is raised to a single integer power. (x^6)^3 x^-3 / x^-4 a.) x^13 b.) x^11 c.) x^16 d.) x^19

Which of these relations is a function?

If n=16, x̄=32, and s=4, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. <μ<

In the figure, triangle EBA is congruent to triangle EDC. Because CPCTC, which relationships are true? Check all that apply. - AE is congruent to CE - angle BAE is congruent to angle DCE - angle CDE is similar to angle BAE - AB is congruent to BE - AC is congruent to BD

Assume x and y are functions of t. Evaluate dy/dt for the following. y^2 - 5x^3 = -26; dx/dt = -3, x=2, y=6

Determine if the following statement is true or false. The graphs of y=sec(x/2) and y=cos(x/2) are identical. Choose the correct choice below. A. False. The cosine graph has a range of (-∞,-1] ∪[1, ∞), and the secant graph has a range of [-1,1]. B. True. Both secant and cosine graph's have a range of (-∞,-1] ∪[1, ∞). C. False. The secant graph has a range of (-∞,-1] ∪[1, ∞), and the cosine graph has a range of [-1,1]. D. True. Both secant and cosine graphs have vertical asymptotes at interval multiples of π.

Find the antiderivative for each function when C equals 0. a. f(x) = e^(10x) b. g(x) = e^(-5x) c. h(x) = e^(x/12)

Assume that all grade point averages are to be standardized on a scale between 0 and 5. How many grade point averages must be obtained so that the sample mean is within 0.011 of the population mean? Assume that a 98% confidence level is desired. If using the range rule of thumb, σ can be estimated as (range/4)=(5-0)/4=1.25. Does the sample size seem practical? The required sample size is 69.886? (Round up to the nearest whole number as needed.) Does the sample size seem practical? A. Yes, because the required sample size is a fairly small number. B. No, because the required sample size is a fairly large number C. No, because the required sample size is a fairly small number D. Yes, because the required sample size is a fairly large number.

Consider the following function. u(x)=-3 ∛(x-3)+3 Step 2 of 2: Determine the domain and range of the original function. Express your answer in interval notation.

A researcher wanted to determine which method would help smokers quit smoking. He divided a group of 183 smokers into three groups: Group 1 is given a patch, Group 2 is given oral medication, and Group 3 has no intervention. The results of the study are in the below table. Test the researcher's claim using a significance level of α=0.05. Group 1 Group 2 Group 3 --------- Did Not Quit 52 54 51 Quit 13 9 4 "Source: Harris Poll a. Determine the null and alternative hypotheses. H0: The methods for helping people quit smoking are independent. Ha: The methods for helping people quit smoking are dependent. H0: The methods for helping people quit smoking are the same. Ha: The methods for helping people quit smoking follow a different distribution. b. Determine the test statistic. Round your answer to two decimal places. x^2= c. Determine the p-value. Round your answer to four decimal places. p-value= d. Make a decision. - Reject the null hypothesis. - Fail to reject the null hypothesis. e. Make a conclusion. - There is sufficient evidence to support the claim that the methods for helping people quit smoking are different. - There is not sufficient evidence to support the claim that the methods for helping people quit smoking are different.

Suppose H(x)=(3x-4)^7. Find two functions f and g such that (f∘g)(x)=H(x). Neither function can be the identity function. (There may be more than one correct answer.)

Write a formula for the function, (g(x)), described as follows: Use the function, (f(x)=x^3). Move the function to the right by 2 units and down by 3 units.

Help Acellus Learning Unit Exam - Reasoning and Proofs Find the next two terms in this sequence. 1,3,9,27,81,[ ? ],[ ]

Let A=0,1,2 and B=5,6,7. Let R be the relation from A to B such that (a, b) in R provided that a+b=6. Then all the pairs in R are (0,6),(1,5)(6,0),(5,1). True False

PARTICIPATION ACTIVITY #23 A coffee shop determines that the daily profit on scones obtained by charging s dollars per scone is P(s)=-20 s^2+140 s-30. The coffee shop currently charges 3.25 per scone. Find P'(3.25), the rate of change of profit when the price is 3.25. P'(3.25)= Number per scone.

Find the domain of the function. f(x)=6/(x+15)+7/(x-10) The domain of f(x) is (Type your answer in interval notation.)

Describe the sampling distribution of p̂. Assume the size of the population is 30,000. n=300, p=0.4 Choose the phrase that best describes the shape of the sampling distribution of p̂ below. A. Approximately normal because n ≤ 0.05 N and np(1-p)<10. B. Not normal because n ≤ 0.05 N and np(1-p) ≥ 10. C. Approximately normal because n ≤ 0.05 N and np(1-p) ≥ 10. D. Not normal because n ≤ 0.05 N and np(1-p)<10. Determine the mean of the sampling distribution of p̂. μp̂=0.4 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p̂. σp̂= (Round to three decimal places as needed.)

Solve using the quadratic formula. -5s^2+8s+5=0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. s= or s=

If sin(46°) = cos(θ) and 0° < θ < 90°, then θ = □ degrees

The price of a gallon of milk is increasing at a rate of 1% per year. If a gallon of milk costs 3 in 2014, how much will a gallon of milk cost in 2018?

The points at -6 and -1 shown on the number line below are the real solutions to the polynomial equation x^2+7x+6=0 and represent the boundary points for the polynomial inequality x^2+7x+6>0. The points at -6 and -1 divide the number line into which three intervals? Choose the correct answer below. A. (-∞,-6),(-6,-1), and (-1, ∞) B. (-∞, 1),(1,6), and (6, ∞) C. (-∞,-1),(-1,-6), and (-6, ∞) D. (-∞,-6],[-6,-1], and [-1, ∞)

Find the Equation of the Parallel Line Instructions: Find the equation of the line through point (-2,3) and parallel to y=x+1. Use a forward slash (i.e. "/") for fractions (e.g. 1 / 2 for 1/2 ). y=

The total number of data items is needed to find the Standard Deviation. Given the following data set, how many data items are there? 0,1,2,1,3,1,4,4,2,1,3,0

How many different five-letter passwords can be formed from the letters A, B, C, D, E, F, G, and H if no repetition of letters is allowed? five-letter words can be formed.

Graph this function. f(x)= x+5 if x<1 6x-12 if x ≥ 1

s(x)=-1+3x-1

Use the leading-term test to match the function (f(x)=x^5+frac13 x-2) with one of the given graphs Choose the correct graph below. A. B. C. D.

Suppose that the polynomial function (f) is defined as follows. [ f(x)=(x-8)(x-11)(x+12)^2(x+5)^3 ] List each zero of (f) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity two: Zero(s) of multiplicity three:

A 4500 square foot roll of plastic wrap costs 23.95. If 120 square feet is needed for a party game, what is the monetary value of that 120 square foot piece of plastic wrap? Round to the nearest cent.

Use the five sentences below to answer the question. Mark had told him about the foxes. John looked out of the window. Could it be a fox? However, nobody had seen one for months. He thought he saw a shape in the bushes. How many different five-sentence paragraphs can be formed if the paragraph begins with "He thought he saw a shape in the bushes" and ends with "John looked out of the window"?

Move the points to change the order of the lines in the proof to show that (1-cos^2(θ))(1+cot^2(θ))=1 is true starting with something known and so each line of the proof follows from the previous line. sin^2(θ)(1+cot^2(θ))=1 (sin^2(θ)+cos^2(θ)-cos^2(θ))(1+cot^2(θ))=1 sin^2(θ)+cos^2(θ)=1 sin^2(θ)(1+(cos^2(θ)/sin^2(θ)))=1 (1-cos^2(θ))(1+cot^2(θ))=1

Given the graph of the Logarithmic Function g(x)=log2 x : The graph of the function f(x)=7+log2(x) can be obtained from the graph of g(x) by shifting the graph of g(x) 7 units; Identify the Domain and Range of f(x) using Interval Notation. Domain of the function f(x) is Range of the function f(x) is

sin^2(x) sec^2(x) - sin^2(x)

Graph the line with slope 3/4 passing through the point (-4,-2).

This exercise refers to a standard deck of playing cards. Assume that 8 cards are randomly chosen from the deck. How many hands contain exactly two 8s and two 9s? hands

1. y=1/2x^2-3 2. y=-2x^2+3 3. y=-2x^2+4x

Simplify: - 3 sin^5 x-3 sin^3 x cos^2 x a) 0 sin x cos^2 x b) 0 · 3 sin^3 x c) 03 sin^3 x d) 03 cos^3 x

Find an equation for the graph. Type the equation of the given graph in the form y=A sin Bx or y=A cos Bx. (Type an equation. Use integers or fractions for any numbers in the equation. Simplify your answer.)

What is the relative maximum and minimum for (x-1)/(x-2)^2 ?

Exponential and Logarithmic Functions Choosing an exponential model and using it to make a prediction The data points show the amount of money y (in dollars) in an account after a time x (in years). Each figure has the same data points. However, each figure has a different curve fitting the data. The equation for each curve is also shown. Answer the questions that follow. (a) Which curve fits the data best?

Perform the indicated operation by removing the parentheses and combining like terms. [ (-3 x^2+9 x)+(-2 x^2+5 x+6) ]

The probability of a company having a section in the newspaper is 0.43, and the probability of a company having a website given that the company has a section in the newspaper is 0.84. What is the probability of a company having a website and a section in the newspaper? Round your answer to three decimal places.

A headline read, "More Than Half of Americans Say Federal Taxes Too High." The headline was based on a random sample of 1221 adult Americans in which 632 stated the amount of federal tax they have to pay is too high. Is this an accurate headline? Assume the α=0.05 level of significance. Identify the null and alternative hypotheses for this test. A. H0: p=0.50 B. H0: p<0.50 C. H0: p ≠ 0.50 H1: p ≠ 0.50 H1: p=0.50 H1: p=0.50 D. H0: p=0.50 E. H0: p=0.50 F. H0: p>0.50 H1: p>0.50 H1: p<0.50 H1: p=0.50

For the following quadratic function, tell whether the graph opens upward or downward and whether the graph is wider, narrower, or the same as (f(x)=x^2). (F(x)=4 x^2+7) The graph opens A. upward. B. downward.

Liquid leaked from a damaged tank at a rate of r(t) liters per hour. The rate decreased as time passed and values of the rate at five-hour time intervals are shown in the table. t(hr) r(t)(L / h) 0 9.5 5 8.7 10 7.9 15 7.3 20 6.6 25 6.1 Find lower and upper estimates for the total amount of liquid that leaked out. lower estimate = liters upper estimate = liters

Solve the compound inequality. Graph the solution set, and write the solution set in interval notation if possible. (a) z ≤ -3 and z > -5 (b) z ≤ -3 or z > -5

Solve the following equation. v^2 + 3v - 40 = 0

You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.38. You use a significance level of α=0.05. H0: p=0.38 H1: p<0.38 You obtain a sample of size n=725 in which there are 259 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is less than 0.38. There is not sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is less than 0.38. The sample data support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.38. There is not sufficient sample evidence to support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.38.

If the sides of a right triangle are 10 and 24, what is the length of the hypotenuse?

The population of Williamstown is 9 times 10^6 people. The population of Smithville 3 times 10^5 people. How many times larger is Williamstown than Smithville? 3 30 300 3000

Assume the carrying capacity of the Earth is 16 billion. Use the 1960 annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current world population of 7.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.1% per year? What is the base growth rate? 2.5846% (Round to four decimal places as needed.) What is the estimated current growth rate? 1.32% (Round to two decimal places as needed.) How does the estimated growth rate compare to the actual current growth rate? The predicted growth rate is the actual growth rate. - smaller than - the same as - larger than

Completely factor the trinomial, if possible. x^2-3x-10

A student compared organic food prices at Grocery 1 and Grocery 2. The same items were priced at each store. The first three items are shown in the accompanying Figure A. Choose the correct accompanying output ( B or C ) for the appropriate test, explaining why you chose that output. Then test the hypothesis that the population means are not equal using a significance level of 0.05. Assume that all necessary conditions for carrying out a hypothesis test hold. Figure A and Outputs (Figure A) Food Grocery 1 Grocery 2 Bananas/1 lb 0.89 0.89 Grape tomatoes/1 lb 4.39 4.09 Russet potato/5 lb 4.49 4.89 (Figure B) Paired T-Test and CI: Grocery N Mean StDev SE Mean Grocery 1 39 3.01 1.34 0.21 Grocery 2 39 3.13 1.38 0.22 Difference 39 -0.12 1.32 0.21 95% CI for difference: (-0.548, 0.308) T-Test of mean difference = 0 (vs ≠): T-Value = -0.57 P-value = 0.574 (Figure C) Two-sample T-Test and CI: Grocery 1, Grocery 2 N Mean StDev SE Mean Grocery 1 39 3.01 1.34 0.21 Grocery 2 39 3.13 1.38 0.22

Sean B=[0 5; -4 -5; 2 1] y C=[0 -5; 2 -5; 1 7]. Hallar -6B-5C.

Given: AC is the perpendicular bisector of BD Prove: angle 1 is congruent to angle 2

Solve by using the quadratic formula. 6x^2 - 8x = 64 4,-8/3 4,-9/2 14/3,-3 -5 ± i sqrt(479)/6

Math

New Questions