Math Homework Questions & Answers Archive

y=log6(x)

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct a 90% confidence interval about μ if the sample size, n, is 27. (b) Construct a 90% confidence interval about μ if the sample size, n, is 13. (c) Construct a 70% confidence interval about μ if the sample size, n, is 27. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? A. No, the population needs to be normally distributed. B. No, the population does not need to be normally distributed. C. Yes, the population needs to be normally distributed. D. Yes, the population does not need to be normally distributed.

x = int(input()) y = int(input()) x = x % y y = y % x print(y) ¿Cuál es el resultado del siguiente fragmento si el usuario ingresa dos líneas que contienen 11 y 4 respectivamente?

``` if (a == -1) left = FROM; right = TO; else cin >> b; left = min(a, b); right = max(a, b); answer = rand() % (right - left + 1) + left; ```

R³ 의 벡터 u=(1,-3,2), v=(2,-1,1) 에 대하여 다음 물 (1) (1,7,-4) 를 u, v 의 일차결합으로 나타내어라. (2) (2,-5,4) 를 u, v 의 일차결합으로 나타내어라.

Question 3, 5.3.23 Change the following improper fraction to a mixed number or a whole number 221/27 = (Simplify your answer. Type a whole number, proper fraction, or mixed number

The following rectangular prism has a width of 7 m, a length of 13 m, and a volume of 455 m^3. What is the height, h?

Use the quadratic formula to find the complex solutions of the quadratic equation. Give your answer(s) in a bi form. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) x=

Praxis Core Academic Skills for I this material to answer the following questions. length of a rectangular tapestry is three times that of its height. Let denote the length and height of the tapestry in meters, respectively. Let A denote the area of the tapestry (in meters squared), and let P denote the length of its perimeter. 18. Which of the following equations represents the area A in terms of h ? A=3 h^2 A=h^2 / 3 A=h^3 A=3 h^3 A=3 h

Solve the following logarithmic equation. log2(x+3)=log28 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be 9 and the last digit must be even. How many different codes are available? (Note that 0 is considered an even number.) The number of different codes available is (Type a whole number.)

APPLICATION INJECTIVE - APPLICATION SURJECTIVE SOLUTION On considère l'application : f : ℝ → ℝ x ↦ √(1 + x²) 1) a) Vérifier que pour tout x ∈ ℝ : f'(x) = x / √(1 + x²) b) L'application f est-elle injective ? Justifier votre réponse. 2) a) Montrer que pour tout x ∈ ℝ : f(x) ≥ 1 b) L'application f est-elle surjective ? Justifier votre réponse.

Draw the boxplot for the given data.

基本問題 2 以下の方程式を解き x を数字 2 桁で求めよ。当てはまる数字が同じ場合は数字を 1 つ、異なる場合は数字を 2 つ答えよ。 [20] 1.4=2 e^x [21] 1=5.4/e^(2 x) [22] 2.8=7.6/(e^x+2.2) [23] 27=3 e^(2 x^2) [24] 4.3=0.3 e^(x+2)-2.1

Each year, Kerri adds to her book collection a number of new books. She has categorized each of her 13 new books as hardcover, paperback, fiction, or nonfiction. The information is displayed in the table below. Fiction (F) Nonfiction (N) Totals ------------ Hardcover (H) 2 4 6 Paperback (P) 1 6 7 Totals 3 10 13 If she randomly chooses one of these 13 books, find the probability that it will be NONFICTION given it is PAPERBACK. 6 7

[ int x^4/3 d x ]

Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the constant of integration.) [ int frac110(x+1)(x^2+9)^2 dx= ]

f(x)=sqrt(x+13)/(x+3)(x-2)

Solve for C 425 = c^2

Solve for x. A) 8 B) 9 C) -9 D) -8

Question Given (f(t)=t^2-t) and (h(x)=3 x+2), evaluate (h(f(2))) :

y'(sinh 3y - 2xy) = y^2

The annual salary for one particular occupation is normally distributed, with a mean of about 134,000 and a standard deviation of about 15,000. Random samples of 44 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution. The mean is μbarx= , and the standard deviation is σbarx= . (Round to the nearest integer as needed. Do not include the symbol in your answers.)

The table shows the educational attainment of the population of a country, ages 25 and over, expressed in millions. Find the probability that a randomly selected person, aged 25 or over, has completed four years of high school only or some college, but less than four years. Years of High School Years of College --- --- --- --- --- Mase Less than 4 4 only Some (less than 4) 4 Female 16 24 24 Total 12 32 19 43 28 56 The probability is .

Determine if the line given below is increasing, decreasing, or constant. f(x)=x-6 Select the correct answer below: The line is increasing. The line is decreasing. The line is constant.

An ecologist is conducting a research project on breeding pheasants in captivity. She first must construct suitable pens. She wants a rectangular area with two additional fences across its width, as shown in the sketch. Find the maximum area she can enclose with 936 m of fencing. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The length of the shorter side of the larger rectangular area is 117^7 m and the length of the longer side of the larger rectangular area is 234 m. B. The length of each side of the larger rectangular area is the same and measures m. The largest total area that can be enclosed is

Graph the solution set of the system of inequalities. 2x-3y ≤ 6 2x-2y > 4

Evaluate σ=sqrt(n p(1-p)) for n=1582, p=2/5. σ= (Simplify your answer. Type an integer or decimal rounded to one decimal place as needed.)

Find the percent of the total area under the standard normal curve between the following z-scores. z=-1.2 and z=-0.75 Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The percent of the total area between z=-1.2 and z=-0.75 is % (Round to the nearest integer.)

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f(x)=3x+8; g(x)=7x-5 (a) Find (f+g)(x). (f+g)(x)=10x+3 (Simplify your answer.) What is the domain of f+g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is x (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is x x is any real number . (b) Find (f-g)(x) (f-g)(x)= (Simplify your answer.) What is the domain of f-g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is x (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is x x is any real number

Test the hypothesis using the P -value approach. Be sure to verify the requirements of the test. H0: p=0.59 versus H1: p<0.59 n=150, x=81, α=0.01 Is n p0(1-p0) ≥ 10 ? No Yes

Let p=19-sqrt(x) and C(x)=215+4x, where x is the number of garden hoses that can be sold at a price of p per unit and C(x) is the total cost (in dollars) of producing x garden hoses. (A) Express the revenue function in terms of x. (B) Graph the cost function and the revenue function in the same viewing window for 0 ≤ x ≤ 361. Use approximation techniques to find the break-even points. (A) R(x)=

80% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 39 owned dogs are randomly selected, find the probability that a. Exactly 30 of them are spayed or neutered. b. At most 32 of them are spayed or neutered. c. At least 33 of them are spayed or neutered. d. Between 30 and 35 (including 30 and 35) of them are spayed or neutered.

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3 -4 and 1+4i are zeros; f(-1)=60 f(x)= (Type an expression using x as the variable. Simplify your answer.)

1. Identify each situation below as continuous or discrete a. Mrs. Hickson makes jars of pickles. She can produce 24 jars of pickles per day.

685 ÷ 42

Solve the following quadratic equation by factoring. x^2+12x=-32 The solution set is . (Simplify your answer. Use a comma to separate answers as needed.)

Fill in the missing values below one at a time to find the quotient when (8 x^3+22 x^2+11 x+15) is divided by (2 x+5). (8 x^3) (2 x) (8 x^3) +5

When testing the difference between means, is the data pooled or not pooled for the following data? Claim: μ₁=μ₂ ; α=0.05. Assume σ₁²=σ₂² Sample statistics: x̄₁=45.7, s₁=4.2, n₁=15 x̄₂=48.7, s₂=3.2, n₂=12 Pooled Not Pooled

The stem-and-leaf display represents scores achieved on a 100-point biology exam by the 32 members of the class. Identify the mean, median and mode for the data represented. 4 7 5 2 5 6 6 2 3 3 6 6 8 7 0 2 3 3 3 3 5 5 6 6 The mean for the data is (Round to the nearest tenth)

Consider the following. (If an answer does not exist, enter DNE.) F(x)=x sqrt(6-x) (a) Find the interval(s) of increase. (Enter your answer using interval Find the interval(s) of decrease. (Enter your answer using interval (b) Find the local minimum value(s). (Enter your answers as a comma- Find the local maximum value(s). (Enter your answers as a comma (c) Find the inflection point. (x, y)=( ) Find the interval(s) where the function is concave up. (Enter your answer using interval

Complete Section 3.5 Activity A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 500 yd of rope. What dimensions of the rectangle will maximize the area? (Note that one side of the rectangle is the shoreline.) Let x be the length of a side of the rectangle perpendicular to the shoreline. Write the objective function for the area in terms of x. A(x) = 500x - 2x^2 (Type an expression using x as the variable.) The length of the shorter side of the rectangular region is [ ] y The length of the longer side of the rectangular region is [ ] y

Question Use a Computer Algebra System (CAS) to calculate the area below f(x) = 4x / (x^4 - 1), above the x-axis, and between x=3 and x=4, as shown by the shaded area on the graph below. Round your answer to three decimal places, if necessary.

Solve the equation for exact solutions over the interval [0°, 360°). 2 sin 2 theta = -1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a decimal. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.

Identify the measure of angle α.

The figure below shows the graph of a rational function f. It has vertical asymptotes x=5 and x=-6, and horizontal asymptote y=-3. The graph has x-intercepts 1 and -3, and it passes through the point (3,2). The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f(x), and then write the equation. You can assume that f(x) is in simplest form. f(x)=a/(x-b) f(x)=a(x-b)/(x-c) f(x)=a/((x-b)(x-c)) f(x)=a(x-b)/((x-c)(x-d)) f(x)=a(x-b)(x-c)/((x-d)(x-e))

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION 5 log (x-5)=12 x=163.489 x

The price p, in dollars, of a specific car that is x years old is modeled by the function below. p(x)=22,275(0.88)^x (a) How much should a 2-year-old car cost? (b) How much should a 7-year-old car cost? (c) Explain the meaning of the base 0.88 in this problem. (a) A 2-year-old car should cost approximately I. (Round to the nearest whole number as needed.)

Question For the functions f(x)=2 x-2 and g(x)=6 x^2-3, find (g ∘ f)(x). Provide your answer below: (g ∘ f)(x)=

Inverse Functions Question 8, 6.2.49 Part 2 of 6 The function f(x)=x^2-2, x ≥ 0 is one-to-one. (a) Find the inverse of f and check the answer. (b) Find the domain and the range of f and f^(-1). (c) Graph f, f^(-1), and y=x on the same coordinate axes. (a) f^(-1)(x)=sqrt(x+2) (Simplify your answer. Use integers or fractions for any numbers in the expression.) (b) Find the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is x x ≤ B. The domain is x x ≠ C. The domain is x x ≥ D. The domain is the set of all real number

The following data represent the daily high temperatures (in degrees Fahrenheit) for the month of June in a town. Complete parts (a) through (c) below. (a) Construct frequency and relative frequency distributions. (Round to the nearest integer as needed)

Evaluate the integral. [ int t^5left(7+t^6right)^2 d t int t^5left(7+t^6right)^2 d t= ]

Question 20 Solve the absolute value equation: -2-x+4-1=-19 -5 and 13 -5 and 5 -6 and 6 No Solution Submit and End

Câu 5: Cho hàm số y=f(x) có bảng biến thiên x -∞ -1 1 +∞ y′ - 0 + 0 - y +∞ Chọn khẳng định đúng? A. Hàm số nghịch biến trên (-1 ;+∞). B. Hàm số nghịch biến trên (-1 ; 1). C. Hàm số đồng biến trên (-1 ; 1). D. Hàm số đồng biến trên (-∞ ;-1). Câu 6: Cho hàm số y=f(x) có báng biến thiên như sau: x -∞ 0 3 +∞ y′ - - 0 + y Tổng số tiệm cận đứng và tiệm cận ngang của đồ thị hàm số đã cho là: A. 3 . B. 2 . C. 1. D. 4 . Câu 7: Hàm số y=√(-x^2+2 x) đồng biến trên khoảng nào? A. (0 ; 1). B. (-∞ ; 0). C. (2 ;+∞). D. (1 ; 2). Câu 9: Cho hàm số y=f(x) liên tục trên tập xác định D=ℝ 0 và có bảng xét dấu đạo hàm như sau: x -∞ -1 0 2 +∞ f′(x) + 0 - - 0 + Hàm số đã cho nghịch biến trên khoảng nào dưới đây? A. (-1 ; 2) B. (-1 ; 0) C. (-∞ ;-1) D. (0 ;+∞) Câu 10: Tâm đối xứng của đồ thị hàm số y=(x^2-x+2)/(2 x-3) là điểm nào sau đây? A. I(3/2 ; 1). B. I (-3/2 ;-1). C. I (-3/2 ;-1/2). D. I(3/2 ; 1/2).

Can you find the antiderivative for the given problems. Try to do one of them, 1. ∫(5x^4 - 3/x^4 - 6/x^(1/3)) dx 2. ∫x dx / √(2x^2 + 1) 3. ∫(x+2)^4 * x dx

Solve the inequality. x/4 > x + 6

The following is a set of data from a sample of n=11 items. Complete parts (a) through (c). X 20 6 11 14 13 17 16 12 10 1 7 Y 40 12 22 28 26 34 32 24 20 2 14 a. Compute the sample covariance. (Round to three decimal places as needed.)

If the radius of circle O is 14 meters and it is dilated by a scale factor of 2.5, then what will be the circumference of circle O'? 44 m 220 m 345 m 10 m

Find the x-intercept(s) of the following rational function: f(x)=(x+4)/(x+9)

Use identities to find values of the sine and cosine functions of the function for the angle measure. 2 x, given tan x=-4 and cos x<0 cos 2 x= (Simplify your answer, including any radicals. Use integers or fractions for any numbers the expression.)

Solve this inequality. -3 x>18 x<-6 x>-6 x<6

Write the system of equations as an augmented matrix 6 n -8 n+u r=100 n+7 r n [ ]

Use the given function to complete parts (a) through (e) below. f(x)=x^4-1x^2 a) Use the Leading Coefficient Test to determine the graph's end behavior. A. The graph of f(x) falls left and falls right. B. The graph of f(x) rises left and rises right. C. The graph of f(x) rises left and falls right. D. The graph of f(x) falls left and rises right. b) Find the x-intercepts. x=

Solve the following system of equations with the substitution method: x-4y=21 3x-5y=35 Answer: (x, y)= Preview x : Preview y : Enter your answers as integers or as reduced fractions in the form A/B.

The number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. 1) Find the constant of proportionality, k, to 2 decimal places if 610 workers work 20 hours and can produce 79178 widgets. k= 2) How many widgets (to the nearest tenth) can be produced by 655 workers in 37 hours? Widgets =

Intended major of high school students: Science: 32% Humanities: 20% Social Science: 8% Business: 16% Other: 24%

Answer parts (a)-(e) for the function shown below. f(x)=x^3-4x^2-x+4 A. The graph falls to the left and to the right. B. The graph rises to the left and falls to the right. C. The graph falls to the left and rises to the right. D. The graph rises to the left and to the right. b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. What are the x-intercepts? x=1,4,-1 (Type an integer or a decimal. Use a comma to separate answers as needed.) At which x-intercept(s) does the graph cross the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=1,4,-1 (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no x-intercepts at which the graph crosses the x-axis. At which x-intercept(s) does the graph touch the x-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no x-intercepts at which the graph touches the x-axis and turns around. c. Find the y-intercept. The y-intercept is y=

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.1 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.01. Assume that the sample is a simple random sample selected from a normally distributed population. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ<1.1 minutes B. H0: σ ≥ 1 HA: σ< H0: σ= HA: σ< c. H0: σ=1.1 minutes HA: σ ≠ 1.1 minutes b. Compute the test statistic. x^2= (Round to two decimal places as needed.) Customer Waiting Times Customer Waiting Times (in minutes) 6.8 6.9 5.6 6.7 6.6 6.2 6.1 6.2 7.6 7.6 6.8 7.1 7.6 7.4 5.3 7.9 8.7 6.1 7.1 6.7 7.7 7.5 6.4 6.1 7.3 6.6 6.8 8.2 7.9 6.7 6.5 6.1 72 8.4 6.1 7.3 6.4 6.2 8.3 6.1 6.7 6.5 8.3 8.3 8.6 7.6 7.5 7.2 56 6.7 7.6 7.7 6.5 7.3 7.5 7.8 6.1 7.8 7.3 7.5

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=34.8. You would like to be 99% confident that your estimate is within 4 of the true population mean. How large of a sample size is required?

The figure to the right shows the results of a survey in which 996 adults from Country A, 1008 adults from Country B, 999 adults from Country C, 1005 adults from Country D, and 1006 adults from Country E were asked whether national identity is strongly tied to birthplace. National Identity and Birthplace People from different countries who believe national identity is strongly tied to birthplace Country A 36 % Country B 22 % Country C 27 % Country D 51 % Country E 14 % Construct a 95% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. The 95% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is . 1 ). (Round to three decimal places as needed.)

What sample size is needed to give a margin of error within ± 1.5% in estimating a population proportion with 95% confidence? Round your answer up to the nearest integer.

Completely factor the expression by grouping, if possible. 9ba - 5 - 4b^2 - 5b

The following table represents a grouped frequency distribution of the number of hours spent on the computer per week for 54 students. What is the class width? Hours Number of Students 3.0-6.4 4 6.5-9.9 16 10.0-13.4 13 13.5-16.9 14 17.0-20.4 7

A recent study by the American Automobile Dealers Association surveyed a random sample of 17 dealers. The data revealed a mean amount of profit per car sold was 190, with a standard deviation of 124. Develop a 99% confidence interval for the population mean of profit per car. Note: Round your answers to 2 decimal places. The confidence interval is between and

For the given expression, find the quotient and the remainder. Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend. 9x^5-9x^2+6x+9 divided by 3x^3-1 Quotient: Remainder:

Find the inverse function for f(x) : f(x) = (e^x - 3e^(-x))/2

Question #1 A hypothetical population consists of eight individual ages: 13,14,17,20,21,22,24, and 30 years. a. What is the probability that a person in this population is a teenager? b. What is the probability of selecting a participant who is at least 20 years old? c. What is the probability of selecting a participant that is 30 or older?

In most modern programming languages, a variable or constant that is declared in a module is in that module. a. global b. invisible c. in scope d. undefined

2024R MATH-1324-40005 11.4a Polynomial Functions Due Monday, Dec 2, 11:59pm CST CURRENT Objective Determine equation of a polynomial given key information Question Which is an equation with a degree of 4, zeros located at (4,0) and (3,0) and a y-intercept located at (0,96)? Select the correct answer below: y=(x+4)(x+3)(x+8)(x+1) y=(x+4)(x+3)(x-2)(x-1) y=(x-4)(x-3)(x+2)(x+4) y=(x-4)(x-3)(x+8)(x-1) y=(x-4)(x+3)(x+8)(x-1)

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. x^2-3x >= 0 Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.

Question 3, 8.1.13 HW Score: 15%, 1.8 of Part 4 of 4 Points: 0 of 1 Complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph. Click the icon to view the graph. The value of μₓ̄ is 300 (b) What is the value of σₓ̄? The value of σₓ̄ is 20. (c) If the sample size is n=9, what is likely true about the shape of the population? A. The shape of the population is skewed left. B. The shape of the population is approximately normal. C. The shape of the population is skewed right. D. The shape of the population cannot be determined. (d) If the sample size is n=9, what is the standard deviation of the population from which the sample was drawn? The standard deviation of the population from which the sample was drawn is

What is the value of z?

T V ≅ U W. Complete the proof that triangle T U W ≅ triangle U W W. - Statement - Reason - V W ⊥ T U - Given - angle T U W ≅ angle U T V - Given - T V ≅ U W - Given - angle U T V ≅ angle T V W - - angle U W V ≅ angle T U W - Alternate Interior Angles Theorem - angle T U W ≅ angle T V W - Transitive Property of Congruence - angle U W V ≅ angle T V W - Transitive Property of Congruence - V W ≅ V W - - triangle T V W ≅ triangle U W V - SAS

Solve the following inequality and write interval notation for the solution set. Then graph the solution set. x<1 Select the correct choice below and, if necessary, fill in the answer to your choice. A. The solution set is (Simplify your answers.) There is no solution. Choose the correct graph below.

Find the inverse of the following function. f(x) = (-3x + 5) / (7x + 4)

Make the following conversion. 3.2 m^2 to square centimeters

Solve the linear programming problem using the simplex method. Maximize P = 9x1 + 2x2 - x3 subject to x1 + x2 - x3 <= 2 2x1 + 4x2 + 3x3 <= 6 x1, x2, x3 >= 0 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is when x1= , x2= , and x3= . (Simplify your answers. Type integers or decimals rounded to the nearest tenth as needed.) B. There is no optimal solution.

Select either < or > to make the statement true. -16 ? -15

log5(1)

At a local company, the length of service for employees is a normal random variable, where the mean length of service is 9.9 years and the standard deviation is 4.1 years. Find the length of service (to the nearest one-tenth of a year) for an employee whose time in service has a 2 -score of 1.46 . A. 15.9 years B. 20.4 years C. 8.5 years D. 18.6 years E. 3.9 years

Question 13 of 13 1.25 / 5 Felde Buchet Co, a manufacturer of rain barrels, had the following data for 2024 Sales quantity 2500 barrels Unit selling price 40 per barrel Unit variable costs 24 per barrel Fixed costs 149,500 (a) What is the contribution margin ratio? (b) What is the break-even point in sales dollars?

Is the inverse of the following conditional true? If g ≥ 6, then g>6. yes no

What is the solution to this equation? 3(4x+6)=9x+12 A. x=-10 B. x=10 C. x=-2 D. x=2

S U bisects angle T V X and angle U S W. Complete the proof that S U is congruent to S W.

Subtract and simplify. (11+9 i)-(6+7 i) (11+9 i)-(6+7 i)= (Simplify your answer. Type your answer in the form a+bi.)

Writing an equation of a line given its slope and y-intercept Write an equation in slope-intercept form for the line with slope -3/4 and y-intercept -1.

Farming: A 4-H Club group is raising lambs to show at the County Fair. Each lamb eats 1/8 of a bale of alfalfa a day. If the alfalfa costs 12.50 per bale, how much will it cost to feed one lamb for 152 days? It'll cost to feed the lamb for 152 days.

The graph of the function has one relative extreme point. Plot this point and check the concavity there. Using only this information, sketch the graph. f(x)=-x^2-6x-9 The relative extreme point on the graph is (Type an ordered pair.)

Step 2: Factor the completed square Step 3: Use the Square Root Property Add -25 to both sides to get (x+4)^2=-25 Take the square root of both sides, remembering the square root property (there are two square roots to consider, the positive and the negative!) x+4=

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.9 inches and a standard deviation of 0.8 inches. X be the head breadth of a potential clientele. a. What is the distribution of X ? X N 0 ( , ) b. If a client is randomly chosen, find the probability that his head breadth is at least 6.3 inches. c. If a client is randomly chosen, find the probability that his head breadth is between 5.5 and 5.9 inches. d. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 3.9 % or largest 3.9 %. What is the minimum and maximum head breadths that will fit the clientele? Minimum and maximum = and inches.

logp(625) = 4

aを正の実数とする。確率変数Xのとる値xの範囲が0 ≤ x ≤ 3であり，その確率密度関数f(x)が f(x)= 2 a x (0 ≤ x ≤ 1) -a x+3 a (1 ≤ x ≤ 3) で定められるとする。 (1) 直線y=2 a xと直線y=-a x+3 aの交点の座標はソ a) であり、直線y=-a x+3 aとx軸の交点の座標は , 0) である。 (2) 直線y=2 a xと直線y=-a x+3 a, およびx軸で囲まれた図形の面積はチaである。また，f(x)は0 ≤ x ≤ 3で定義された確率密度関数であるか5, 千a=ツ - すなわちa=である。 (3) P(0.5 ≤ X ≤ 2)=テである。

Solve the equation. log2(x+5)-log2 x=5 Select the correct choice below and fill in any answer boxes present in your choice. A. x= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.

Solve the absolute value inequality. x-1 ≥ 7 Select the correct answer below and, if necessary, fill in the answer choice. A. The solution set in interval notation is (-∞, -6) ∪ (8, ∞). B. The solution set is 6.

Find the necessary confidence interval for a population mean μ for the following values. (Round your answers to two decimal places.) 0.95% confidence interval, n=81, x̄=2.93, s²=0.1017

Solve by completing the square. x^2 + (13/2) x = 13 The solution(s) is/are x=

Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 16 boxes. It is reasonable to assume that the population is approximately normal. 14.07, 13.98, 14.16, 14.17, 14.11, 14.03, 14.16, 13.98, 14.06, 14.05, 14.12, 14.13, 14.19, 14.17, 14.05, 14.04, Send data to Excel Part: 0 / 2 Part 1 of 2 (a) Construct a 95% confidence interval for the mean weight. Round the answers to at least three decimal places. A 95% confidence interval for the mean weight is <μ< .

Use the following function to answer parts a through c. f(x) = x^3 + 6x^2 - 28x - 33 a. List all rational zeros that are possible according to the Rational Zero Theorem. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) b. Use synthetic division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is (Simplify your answer.) c. Use the zero from part (b) to find all the zeros of the polynomial function. The zeros of the function are (Simplify your answer. Use a comma to separate answers as needed. Type an integer or decimal rounded to three decimal places as needed.)

X is the weight in pounds of a newborn elephant, and X̄ is the sample mean of the 50 baby elephants.

For women aged 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122 mm Hg.

Multiply. -3(6)

As part of an annual fundraiser to help raise money for cancer research, Heather joined a walkathon. The track she walked on was 1600 yd long. Heather walked 16.5 laps. Her sponsors agreed to donate an amount of money for each mile she walked. How many miles did she walk? First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation. Ratios: 1600 yd/1 lap 1 lap/1600 yd 5280 ft/1 mi 1 mi/5280 ft 3 ft/1 yd 1 yd/3 ft 16.5 laps/1 × □ × □=□ m × □=□ □ □ □ □

Rationalize the denominator and simplify if possible. (sqrt[3]4)/(sqrt[3]9 z^2)

For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = 1/(2x), x ≠ 0 (b) f(x) = x + 6 g(x) = 1/(2x), x ≠ 0 f(g(x)) = g(f(x)) = f and g are inverses of each other f and g are inverses of each other f and g are not inverses of each other f and g are not inverses of each other

Sets (B) and (C) are subsets of the universal set (U). These sets are defined as follows. [ U=1,3,4,5,6,7 B=3,4,6,7 C=1,4 ] Find the following sets. Write your answer in roster form or as (varnothing). (a) ((B cap C)^prime=) (square) (b) (B^prime cup C=) (square)

Write the following equation in logarithmic terms. Do not simplify your answer. 3^x = y

Write the equation of the ellipse (16 x^2+25 y^2+160 x-50 y+25=0) in standard form (frac(x-h)^2p^2+frac(y-k)^2q^2=1) Where: (h=) (k=) (p=) (q=)

The one-to-one functions g and h are defined as follows g=(-9,1),(1,-2),(2,9),(6,-7) h(x)=2x+13 Find the following. g^-1(1)= h^-1(x)= (h^-1 circ h)(-5)=

-4(x+5)+33 ≤ 4(3-x)

h(x)=ln(4x+17)-5

Use the spinner below. P(9 or 5)=1/6

Convert 8207 fl oz to gallons. □ gal

Complete parts (a) through (h) for the data below. x 3 4 5 7 8 y 4 6 7 12 14 (f) Compute the sum of the squared residuals for the line found in part (b). (Round to three decimal places as needed.) (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (Round to three decimal places as needed.) (h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). The line in part passes through the most points. The line in part has the sum of the squared residuals, thus being the best-fitting line.

Solve. m-10.1=2.5 The solution is m= (Simplify your answer.)

Find the area of the blue region above. (The figure is not drawn to scale and remember to use π ≈ 3.14 for all calculations involving π ). Area = □ m^2 Round answers to 2 decimal places as needed.

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. 9 ln (8 x)=18 Solve the equation. What is the exact solution? Select the correct choice below and, if necessary, fill in the answer to complete your choice. A. The solution set is e^2/8. (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.) B. There are infinitely many solutions. C. There is no solution. What is the decimal approximation to the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or decimal rounded to two decimal places as needed.) B. There are infinitely many solutions. C. There is no solution.

Solve. [ z+2.6=6 ]

The exposure index EI for a camera is a measurement of the amount of light that hits the image receptor. It is determined by the equation EI=log2(f^2/t), where f is the "f-stop" setting on the camera, and t is the exposure time in seconds. Suppose the f-stop setting is 8 and the desired exposure time is 2 seconds. What will the resulting exposure index be?

Manufacturing Tests An inspector must select 5 tests to perform in a certain order on a manufactured part. He has a choice of 6 tests. How many ways can he perform 5 different tests? Use a graphing calculator. The number of ways the inspector can perform 5 different tests out of 6 tests is.

Use a Tree Diagram to Perform a Multiple-Part Counting Task Example Find the number of three-letter combinations that can be written using only the letters A, B, and C, assuming that a. repeated letters are allowed

from a random sample of 15 customers at each branch. Complete parts (a) through (d) below C. Do not reject H0. There is insufficient evidence that the mean waiting time between the two branches differ. D. Reject H0. There is insufficient evidence that the mean waiting time between the two branches differ b. Determine the p-value in (a) and interpret its meaning p-value =0 (Round to three decimal places as needed) Interpret the p-value Choose the correct answer below A. It is the probability the two banks have different population mean waiting times c. In addition to equal variances, what other assumption is necessary in (a)? A. The sample sizes must be equal B. The samples are specifically chosen and not independently sampled C. Both sampled populations are approximately normal D. Both sampled populations are not approximately normal

Find the perimeter of the rectangle. Express the perimeter using the same unit of measure that appears on the given sides. The perimeter of the rectangle is □

Computing expected value in a game of chance Carmen is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Carmen rolls the number cube once. She wins 1 if a 1 is rolled, 2 if a 2 is rolled, 3 if a 3 is rolled, and 4 if a 4 is rolled. She loses 5 if a 5 or 6 is rolled. (a) Find the expected value of playing the game. dollars (b) What can Carmen expect in the long run, after playing the game many times? Carmen can expect to gain money. She can expect to win dollars per roll. Carmen can expect to lose money. She can expect to lose dollars per roll. Carmen can expect to break even (neither gain nor lose money).

Find the domain of the function. f(x)=1/(sqrt(x+14)) The domain of f(x) is (Type your answer in interval notation.)

Find the complement and the supplement of the given angle. It is possible for the supplement not to exist. If there is no complement or supplement, enter DNE 89° Complement: Supplement:

Find the quartic function that is the best fit for the data in the table below. Report the model with three significant digits in the coefficients. x: -2, -1, 0, 1, 2, 3, 4 y: 36, 3.75, 0, 3.75, 36, 159.75, 480 y= (Simplify your answer. Do not factor. Use integers or decimals for any numbers in the expression.)

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. Find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes.

(4-5 i)(1-i)-(3-i)(3+i) (4-5 i)(1-i)-(3-i)(3+i)= (Simplify your answer. Type your answer in the form a + bi.)

1 gram of fat gives you calories (energy). 5 1 9 4

Sketch the graph of the following function, and state its domain and range. f(x) = ln(x+7) List ordered pairs that satisfy the equation. x -6 -4 -2 f(x) = ln(x+7) 0 1.1 1.6 (Round to the nearest tenth as needed.)

Multiply the polynomials. 5ab(2ab+2a-6b)=

Solve the equation: 3^x=47 a. Give the exact answer. x=ln(47)/ln(3) b. Give the decimal approximation rounded to 4 dec . places. x=1

Solve the given system of equations by determinants. All numbers are approximate. 1.8y + 10.3 = -8.6x 3.4x + 4.6y + 12.5 = 0 x = , y = (Round to two decimal places as needed.)

Let's eat: A fast-food restaurant chain has 604 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 604 to test market a new menu. Round your answers to four decimal places. Population of City Region --- NE SE SW NW Under 50,000 - - - - 50,000-500,000 34 40 13 9 Over 500,000 56 88 70 33 (a) Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast? (b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000? (c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less?

Use synthetic division to divide (7x^2+6x-7) by (x-1). Quotient: Remainder:

Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 117 inches and standard deviation σ = 18 inches. Round the answers to four decimal places. (a) What proportion of trees are more than 120 inches tall?

A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) The card drawn is 5 P(5)= (b) The card drawn is the 5 of clubs. P(5 of clubs )=

Which of the following pairs of numbers satisfies the equation 2x+3y=8? A x=1, y=2 B x=2, y=1 C x=-1, y=2 D x -> 2, y=4

Subtract. (7b+2)/(8b)-(b+9)/(2b) Simplify your answer as much as possible.

Find the indicated value of the logarithmic function. log(1/10)

The table shows the number of video games sold worldwide for the five highest-selling video games in 2010. Assuming this trend continues and that the total sales of all other video games is negligible, if a person chooses to purchase one of these video games, determine the empirical probability that the person will purchase a) Game 2 b) Game 5 c) Game 1. Game Games Sold Game 1 18,480,000 Game 2 17,880,000 Game 3 11,900,000 Game 4 11,060,000 Game 5 8,470,000 Total 67,790,000 a) P(Game 2) = (Type an integer or a simplified fraction.)

Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error; and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for μ using the sample results x̄=87.0, s=7.2, and n=42 Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places. point estimate = margin of error = The 95% confidence interval is to .

Factor completely. 5 w^2 + 60 w + 100

A population of values has a normal distribution with μ=131.6 and σ=76.2. You intend to draw a random sample of size n=212. Find the probability that a sample of size n=212 is randomly selected with a mean greater than 124.8 . P(M>124.8)= Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z scores rounded to 3 decimal places are accepted.

Complete parts a-d below. (a) Simplify log8(w^13) + log8(w^5). (b) Solve log8(w^13) + log8(w^5) = 1. (c) Compare the process of simplifying an expression with solving an equation. (d) Explain how simplifying an expression can help when you are solving an equation. (a) log8(w^13) + log8(w^5) = log8(w^18) (b) w ≈ 1.1225 (Type an integer or decimal rounded to four decimal places as needed.) (c) Which of the following is the correct comparison of simplifying an expression and solving an equation? A. Simplifying an expression gives a value that satisfies a given formula, while solving an equation is a process by which complicated logarithmic expressions are reduced. B. Simplifying an expression is a process by which complicated logarithmic expressions are reduced, while solving an equation gives a value that satisfies a given formula. C. Solving an equation is a way to find a value that simplifies an expression to a single logarithm. D. There is no difference. (d) Which of the following explains how simplifying an expression can help when you are solving an equation? A. Simplifying an expression given in an equation will make it easier to put the equation in logarithmic form and solve algebraically. B. Simplifying the expression in a given equation makes it easier to use the properties of logarithms. C. Simplifying an expression does not help when solving an equation. D. Simplifying an expression will help solve an equation because when the expression is fully simplified it can be changed from logarithmic form to exponential form, and then solved algebraically.

If a spherical tank 4 m in diameter can be filled with a liquid for 700, find the cost to fill a tank 16 m in diameter. The cost to fill the 16 m tank is

Babies: According to a recent report, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ=5.1 pounds. Part 1 of 3 (a) Construct a 99.5% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one decimal place. A 99.5% confidence interval for the mean weight in pounds of all one-year-old baby boys in the United States is <μ<.

The matrix below is the final matrix form for a system of two linear equations in the variables (x1) and (x2). Write the solution of the system. [ left[beginarrayrrr 1 0 -9 0 1 6 endarrayright] ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The unique solution to the system is (x1=) and (x2=) B. There are infinitely many solutions. The solution is (x1=) and (x2=t) for any real number (t). (Type an expression using (t) as the variable.) C. There is no solution.

Find the surface area and the volume of the cylinder. Use 3.14 for π. Surface area = (Round to the nearest

Use inductive reasoning to find the next equation 2^2 - 1^2 = 3 3^2 - 1^2 = 8 5^2 - 2^2 = 21

Question 4 The matrix [0.1 0.2; 0.1 0.3] is an input-output matrix for a market where the total output is [10; 25]. Determine the internal production matrix. [6.5; 15.5] [4; 16.5] [6; 8.5] [3.5; 9.5] Question 5 The matrix [0.2 0.3; 0.1 0.1] is an input-output matrix for a market where the total output is [15; 10]. Determine the internal production matrix. [9; 7.5] [4; 5.5] [11; 4.5] [6; 2.5]

For the function f(x)=-1-x, find each of the following. (a) f(p) f(p)=

Given that f(x)=x^2-7 x and g(x)=x-3, calculate (a) (f ∘ g)(x)= □ (b) (g ∘ f)(x)= □ (c) (f ∘ f)(x)= □ (d) (g ∘ g)(x)= □

Area Under a Normal Curve (a) Estimate the probability that a randomly selected student will complete their final exam in less than 63 minutes. (b) The final exam is scheduled to allow 2 hours. Estimate the probability that a randomly selected student will need more than 2 hours to complete their exam. (c) In a section with 120 students, how many students do you expect will need more than 2 hours to complete their exams? students

Find the domain of the function. y = x / sqrt(x-6) A. [6, ∞) B. (-∞, ∞) C. All real numbers except 6 D. (6, ∞)

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief executive office (CEO) was at least 9 years. A survey of 69 companies reported in The Wall Street Journal found a sample mean tenure of 7.4 years for CEOs with a standard deviation of s=5.2 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.002. In other words, your claim is that the mean tenure for a CEO was less than 9 years. Your hypotheses are: H0: μ ≥ 9 H1: μ<9 What is the test statistic for this sample? test statistic = -2.5559 What is the p-value for this sample? p-value = 0.0053

Find the critical numbers of the function. f(x)=x^3+3 x^2-45 x x=

Dado el conjunto de datos 1,7,2,5, x, si x es su mediana, entonces su rango es: A) x-1 B) 5 C) 6 D) 7

Write the statement in symbols. 5 times the difference of a number and 4 is 8. Choose the correct answer below. A. 5(x-4)=8 B. 5 x-4= C. 5 x-8=4 D. 5=8(x-4)

=∫ from 2 to 3 sec θ / tan^2 θ

HW 10.1 Question 5, 10.1.21 Find the cube root. ∛(-1/729) Select the correct choice below and, if necessary, fill in the answer box within your choice A. ∛(-1/729)= B. The root is not a real number.

Graph this function: y=x-1-4

Select the correct choices that complete the sentence below. De Morgan's laws state that ¬(p ∧ q) is equivalent to and ¬(p ∨ q) is equivalent to

Find the product. (p+5)(p-5) (p+5)(p-5)= (Simplify your answer.)

Suppose the region on the left in the figure (with blue shading) has area is 21, and the region on the right (with green shading) has area 7. Using the graph of f(x) in the figure, find the following integrals. ∫ab f(x) dx= □ ∫bc f(x) dx= □ ∫ac f(x) dx= □ ∫ac f(x) dx= □

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Suppose a sample of 1291 tenth graders is drawn. Of the students sampled, 1098 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

Multiply as indicated. If possible, simplify any radical expressions that appear in the product. Assume that all variables represent positive real numbers. ∛x(∛(250 x^2) - ∛x)

The Student Government Association is making Mother's Day gift baskets to sell at a fund-raiser, If the SGA makes a larger quantity of baskets, it can purchase materials in bulk. The total cost (in hundreds of dollars) of making x gift baskets can be approximated by C(x) = (6x + 1) / (x + 60). Complete parts (a) through (c) below. (a) Find the marginal cost function and the marginal cost at x = 20 and x = 40.

Factor the polynomial. 10h^2 - 9h - 9

The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t). (-2/5, sqrt(21)/5) sin(t)= cos(t)= tan(t)=

Math

New Questions