Math Homework Questions & Answers Archive

Solve with simplifying your answer including any radical. Use integers or Fractions b=3 sin(60°)

Completing a few rows of an amortization table Hawraa To help buy her new condominium, Lucy is taking out a 247,000 mortgage loan for 30 years at 3.5% annual interest. Her monthly payment for this loan is 1109.14. Fill in all the blanks in the amortization schedule for the loan. Assume that each month is 1/12 of a year. Round your answers to the nearest cent. Payment number Interest payment Principal payment New loan balance ------------ 1 2 246,221.42 ... ... ... ... 150 509.21 599.93 173,985.19 151

A factory produces light bulbs with a defect rate of 10%. If a quality control inspector randomly selects 10 light bulbs, what is the probability that: a) Exactly 4 of the light bulbs are defective? b) Fewer than 6 of the light bulbs are defective?

Solve the higher order inequality and sketch the solution on a number line, then write your answer in interval notation. x^4 + 4x^3 - 21x^2 ≥ 0 *Factor, find the zeros, put them on the number, shade the appropriate regions and then write the solution in interval notation.

Consider the continuous probability density function defined by y=4 on -0.05 ≤ x ≤ 0.2. Compute the following probabilities. P(X<0.15)= P(X>0.15)= P(-0.05<X<0.1)=

-1 4/5 ÷ 2 2/5

10/(a-6) = 5/6

MTH 263 Homework Ch 2.7 - MIH 26 The cost (in dollars) of producing x units of a certain commodity is C(x)=5,000 (a) Find the average rate of change (in per unit) of C with respect to x when nearest cent.) (i) x=103 26 per unit (ii) x=101 32.1 per unit (b) Find the instantaneous rate of change (in per unit) of C with respect to x chapter.) 32.0 per unit

Unit 7 Lab Quiz Stephanie Sanders 11/05/24 9:41 PM This quiz: 40 point(s) Question 14 of 20 This question: 2 point(s) possible Submit quiz (Calculation shown below) How much money do you have to deposit today so that beginning 11 years from now you can withdraw 5,000 a year for the next 7 years (periods 11 through 17) plus an additional amount of 10,000 in the last year (period 17)? Assume an interest rate of 11 percent. The amount of money you have to deposit today is (Round to the nearest cent.) Time Remaining: 02:17:03 Next

Approximate the solutions to the following equation on the interval [0,2 π). Round your answer to four decimal places. sin θ=-0.57 Select the correct choice and fill in any answer boxes in your choice. A. θ ≈ (Type your answer in radians. Round to four decimal places as needed. Use a comma to separate answers as needed.) B. There is no solution.

CP'/CP

12 = 3 + 3x

The following table represents data for Randle's Candles. Labor Units (Employees) Total Product (Candles per Hour) Marginal Product of Labor Average Product of Labor ------------ 0 0 - - 1 18 18 18.0 2 42 24 21.0 3 78 36 26.0 4 112 34 28.0 5 140 28 28.0 6 161 21 26.8 7 173 12 24.7 8 173 0 21.6 9 165 -8 18.3 10 150 -15 15.0 1.) Using the multipoint curve drawing tool, draw a graph showing the total product (TP), marginal product of labor (MP), and average product of labor (AP). 2.) Using the point drawing tool, identify where increasing returns, diminishing returns, and negative returns set in on the total product curve. Plot 3 separate points.

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions log(2x+3)−log(x) log(2x+3)−log(x)= (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.)

(7) LCM of 21 and 28

6 √(32x) - 5 √(18x)

Find the quotient and remainder using long division for [ frac2 x^3-8 x^2+7 x-172 x^2+5 ] The quotient is The remainder is

Rewrite each equation as requested. (a) Rewrite as an exponential equation. ln x=2 (b) Rewrite as a logarithmic equation. e^y=4

¿Cuál es el promedio de 141 y 116 ?

Graph the function and determine whether the function is one-to-one using the horizontal line test f(x) = x+4 Is the function one-to-one? A. Yes, because there is at least one horizontal line that intersects the graph more than once. B. No, because no horizontal line intersects the graph more than once. C. Yes, because no horizontal line intersects the graph more than once. D. No, because there is at least one horizontal line that intersects the graph more than once.

Write as a decimal number. 19/25

In this exercise, denominators are additive inverses. Add or subtract as indicated. 6x/(6x-y) + y/(y-6x) = □ (Simplify your answer.)

Use algebraic techniques to rewrite g(x) = (-5x^(9/4) + 3x^(13/4) + 2) / (x^(1/4)) as a sum of three terms. Then find g'(x).

Find the quadratic function (y=ax^2+bx+c) whose graph passes through the given points. ((1,1),(-1,-9),(-3,5)) (y=)

The estimated regression line and the standard error are given. Defects per Countertop = 6.717822 - 1.004950 (Hours of Training) sc = 1.229787 Suppose a new employee has had 10 hours of training, What would be the 99% prediction interval for the number of defects per countertop? Round your answer to two decimal places.

As part of a statistics project, a teacher brings a bag of marbles containing 500 white marbles and 200 red marbles. She tells the students the bag contains 700 total marbles, and asks her students to determine how many red marbles are in the bag without counting them. A student randomly draws 100 marbles from the bag. Of the 100 marbles, 26 are red. The data collection method can best be described as Survey Clinical study Census Controlled study The target population consists of The 700 marbles in the bag The 26 red marbles drawn by the student The 200 red marbles in the bag The 100 marbles drawn by the student None of the above The sample consists of The 700 marbles in the bag The 26 red marbles drawn by the student The 200 red marbles in the bag The 100 marbles drawn by the student None of the above Based on the sample, the student would estimate that marbles in the bag were red.

Simplify the expression without using a calculator. ln(1/e^5)=

Question 12 of 20, Step 1 of 1 Four scenarios of statistical studies are given below. Decide which study uses a sample statistic. Answer A study prompted by the increase in the use of assisted reproductive technology looked at hospital records across the country. The report stated that an estimated 32% of births in the U.S. last year resulted in twins. The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time of 5:53, and an average run time of 4:14. In 2001, 78% of children diagnosed with cancer were in remission after five years, and this number is improving. Lakeside Family Dentistry reported that 9 of the 15 patients who came in for a regular cleaning one day had at least one cavity. Submit

Quadrilateral XGLD can be mapped onto quadrilateral IMEW by a rotation. If LD=22, find EW.

The table below gives values of a differentiable function (f(x)). x012345678910 ------------ f(x)-5-21-1-3-212467 Estimate the (x)-values of critical points of (f(x)) on the interval (0<x<10) and classify them below. (f(x)) has relative maximum(s) at (x=) (f(x)) has relative minimum(s) at (x=) (f(x)) has critical point(s) that are not extrema at (x=)

Find all real square roots of 4 .

Write the standard form of the equation and the general form of the equation of the circle with radius r and center (n, x). Then graph the circle r=2; (x)=(-2,0) The standard form of the equation of this circle is (x-2)^2+(y+2)^2

Simplify. [ left(frac4 y3 y^-2right)^3 ] Write your answer using only positive exponents.

Let G(x) = ∫ from e^(x^2) to e^(e^(z^2)) ln(t)/t dt. What is the domain of G?

11√10+10√11=

Which of the following values cannot be probabilities? 0, 5 / 3, 1.29, 3 / 5, 0.02, sqrt(2), -0.47, 1 Select all the values that cannot be probabilities. A. 1 B. 0.02 C. -0.47 D. 1.29 E. 0 F. 3/5 G. 5/3 H. sqrt(2)

Which of the following calculations is NOT derived from the confidence interval? Choose the correct answer below. A. The point estimate of μ, x̄ = (upper confidence limit + lower confidence limit) / 2 B. The population mean, μ = (upper confidence limit) + (lower confidence limit) C. Difference between the limits, 2E = (upper confidence limit) - (lower confidence limit) D. The margin of error, E = (upper confidence limit - lower confidence limit) / 2

Factor the following. [ y^2-x^3 y^2 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ( y^2-x^3 y^2 = ) B. The polynomial is prime.

3 log2 y - 1/3 log2 z + 7 log2 x

The function (f) is defined by (f(x)=frac2 x+6x+5). Find (f(5 y)). [ f(5 y)= ]

Use the given zero to find the remaining zeros of the function. f(x)=x^3-4x^2+25x-100; zero: -5i

For each kilogram of a person's weight, 2.5 milligrams of a drug is to be given. What dosage should be given to a child who weighs 93 pounds? Use milligrams is the proper dosage for a child that weighs 93 pounds. (Round to the nearest hundredth as needed.)

Simplify. [ (4 x^-3 y^4)^-5(4 x^-3 y^4)^5 ]

Write the equation in exponential form. log(1/1,000,000) = -6 The equation in exponential form is □.

Find the foci of the ellipse. x^2/5 + y^2/21 = 1 (0,16) and (0,-16) (16,0) and (-16,0) (0,4) and (0,-4) (4,0) and (-4,0)

[-6 -1 -4 -2] = [5 1 2 2] A

Determine if the expression -a^-5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.

Use a combination of rules for exponents to simplify the expression. Give your answer in exponential form, using only positive exponents. k (x^(-2) y/z^(4))^(-3) (Simplify your answer. Type exponential notation using positive exponents.)

Simplify. (c^2+7c-18)/(c^2-9) * (c^2-5c+6)/(c^2+12c+27)=

Solve: 2/(b-4) + 7/(b+4) = 16/(b^2-16) b=

We are going to calculate the standard deviation for the following set of sample data. 11,15,6,13,3 1) First, calculate the mean. x̄= 2) Fill in the table below. Fill in the differences of each data value from the mean, then the squared differences. 3) Calculate the standard deviation. x x-x̄ (x-x̄)^2 11 15 6 13 3 Total Standard deviation: s=√(∑(x-x̄)^2)/(n-1)= Round to two decimal places

Use your knowledge of x - and y-intercepts to choose the correct graph of the equation. 2x + 2y = 10

Would you use SSS or SAS to prove the triangles congruent? if there is not enough information to prove the triangles by SSS or SAS, write "not enough information".

Question 2 Does (P=left[beginarraycc-2 -4 3 6endarrayright]) diagonalize (A=left[beginarraycc-52 -36 72 50endarrayright]) ? True False

Determine the interval(s) for which the function shown below is increasing. Write your response in interval notation using the symbol U when necessary.

Ive the problem that involves probabilities with events that are not mutually exclusive. There are 37 chocolates in a box, all identically shaped. There are 16 filled with nuts, 11 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row. Answer as a reduced fraction.

Assume the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ=1.2 kg and a standard deviation of σ=4.9 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is 0.2401. (Round to four decimal places as needed.) b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is 0.6316. (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. B. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. C. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

Proving triangles congruent by SSS and SAS VVZ YZ ≅ XZ and VZ ≅ WZ. Complete the proof that triangle VYZ ≅ triangle WXZ. Statement Reason --- --- 1 YZ ≅ XZ Given 2 VZ ≅ WZ Given 3 angle VZY ≅ angle WZX 4 triangle WZ ≅ triangle WXZ

Suppose a shipment of 160 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality-control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is the probability that the shipment is rejected? The probability that the shipment is rejected is (Round to four decimal places as needed.)

All of the following describe perfectly competitive firms, except each produces a negligible share of industry output they produced standardized products they make no attempt to differentiate their products they face large barriers to entry

Unit 3 Review: Chapter 5 6 Section 5.1 1. Use the normal curve to estimate the mean and standard deviation.

Find the exact value (in radians). arccsc(√2)=

Write the expression in radical notation without negative exponents:

Sea g: R^2 → R de clase C^2(R^2) y f una función de clase C^2 sobre el abierto Ω=(x, y) ∈ R^2 / y ≠ 0 y f(x, y)=g(xy, x/y). Calcular ∂f/∂x y ∂f/∂y.

Use this data to sketch a smooth curve relating the two variables. Draw rectangles on the graph you drew to help you underestimate the total pollutants that escaped during the first month. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the first month. What overestimate did you obtain? tons Draw rectangles on this graph to help you underestimate the total pollutants that escaped during the whole time. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the whole time. What overestimate did you obtain? 76 tons

Solve the following equation. For an equation with a real solution, support your answers graphically. x^2 - 9x = x - 22

Evaluate the following expression. Write the exact answer in radians. Do not round. If the answer does not exist, write DNE, [ sin ^-1(-frac12) ]

Use the graphs of f and g shown below to evaluate the expression. (If an answer is undefined, enter UNDEFINED.) (f+g)(2)

Analyze the graph to address the following about the polynomial function it represents. a. Is the degree of the polynomial function even or odd? b. Is the leading coefficient positive or negative? c. What is the value of the constant term? d. Identify the real zeros, and state the multiplicity of each. e. Select from the list a possible function that could be represented by this graph.

A distribution of numbers has the following five-number summary: 20.2, 22.4, 30.0, 37.6, 39.8 True or False? These numbers can be used to calculate the standard deviation of the distribution. A. True B. False

sqrt(22) * sqrt(2) = □ (Type an exact answer, using radicals as needed.)

y=sin ∧ 2 x. y=-sin 2 x y=sin -2 x y=sin 2 x

If GF=71, calculate JG. JG=

Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation. f(x)=4 sin x+5 x-1, x0=1.4 Complete the table. (Do not round until the final answer. Then round to six decimal places as needed.) k xk k xk 1 6 2 7 3 8 4 9 5 10

Geometry Finding an angle measure for a triangle with an extended side Find the value of x. x=

6x=540

Sea (an=n cdot operatornamesen(1 / n)) La sucesión (leftanright) diverge Seleccione una: Verdadero Falso

A city decides to make a park by fencing off a section of riverfront property. Funds are allotted to provide 80 meters of fence. The area enclosed will be a rectangle, but only three sides will be enclosed by fence - the other side will be bound by the river. What is the maximum area that can be enclosed in this way? a) Make a rough sketch of the park b) Decide how you will represent the dimensions. c) Develop a polynomial function to describe the area to be enclosed. d) Solve the problem showing all algebra work and include a graph of the polynomial with axes labeled and calibrated and key points shown. Please remember to title your graph.

On a math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class? A. 15 B. 16 C. 21 D. 30 E. 48

Find the degree of the polynomial function. f(x)=-3 x+4 x^2 A. 4 B. -3 C. 1 D. 2

Assignment 9.3: Double-Angle, Half-Angle Formulas If sin x = 1/4, x in quadrant I, then find the exact answers for the following (without finding x): sin (2 x)= cos (2 x)= tan (2 x)=

-16 t^2 + 364 t

For f(x)=5/(x+7) and g(x)=8/x, find a. (f ∘ g)(x); b. the domain of f ∘ g a. (f ∘ g)(x)=5x/(7x+8) b. What is the domain of f ∘ g ? The domain is

What is the median of the following distribution? 26,26,28,29,31,33,35,36,37,38,40,42,43,46,48 A. 56 B. 37 C. 36 D. 33 E. 43

14/7a^3 = /14a^3b^2 14/7a^3 = square/14a^3b^2

Consider the following data: 7,10,12,2,9,14 Calculate the value of the sample standard deviation. Round your answer to one decimal place.

g(x)=(1/3)^x Find g(x) for each x-value in the table x g(x) -3 27 -2 9 -1 3 0 333/1000 1

The double-bar graph shows sales of super unleaded and supreme unleaded gasoline at a service station for each of 5 years. Super unleaded- Supreme unleaded- Find the increase in supreme unleaded gasoline sales from 2009 to 2011. more gallons were sold in 2011 than in 2009. (Type a whole number.)

The table shows projections of sales (in billions of dollars) of hepatitis C treatments for a certain region from 2012 to 2016. Complete parts (a) through (c). Year Sales ( billions) 2012 4.6 2013 4.9 2014 6.6 2015 7.9 2016 9.7 a. What is the quadratic function that best models these sales as a function of the number of years after 2010? Let x represent the number of years after 2010 and y represent the number of billions of dollars in sales of treatments. y=0.186 x^2-0.166 x+4.060 b. Graph the model and the data on the same axes, with x equal to the number of years after 2010. Choose the correct graph below. A. B. c. D.

Which of these are measures of central tendency that can be found for this list of heights recorded in the high-jump event at a track meet? Check all that apply. 4' 9'', 5' 3'', 5' 4'', 5' 7'', 5' 3'', 5' 99'', 6' 0'', 5' 4'', 6' 0'', 6' 1'', 5' 7'', 5' 5'', 4' 5'' A. Standard deviation B. Mode C. Mean D. Range E. Median

The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers? Record your answer in the boxes below. Be sure to use the correct place value.

Simplify. -√45-4 √20

Use synthetic division to find the quotient and the remainder. (x^5+x^3-1) ÷ (x-3) Q(x)= R(x)=

Factor any perfect square trinomials. 36 x^2 -12 x + 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 36 x^2 -12 x +1= B. The polynomial is prime.

Rationalize the denominator and simplify. sqrt(11)/sqrt(7) sqrt(11)/sqrt(7)=

Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x)=x^3-5 Is the function one-to-one? Yes No Select the correct choice below and fill in any answer boxes within your choice. A. The inverse function is f^(-1)(x)= B. There is no inverse function.

Multiply. (y+5u-6)(4y-3u+4) Simplify your answer.

Graph this function: y=-3x-15

Factor completely, or state that the polynomial is prime. 27 x^2+27 y^2 Select the correct choice below and fill in any answer boxes within your choice. A. 27 x^2+27 y^2= B. The polynomial is prime.

Expand. (y-5)(y+4)=

Subtract the rational expressions. Reduce the final answer. 47/(2h-8) - 4/(h-4)

Simplify: (2 x^6 y^0)(7 x^0)

17. Determine whether each set of two fractions is equivalent by calculating equivalent fractions with a common denominator. (a) 18/42 and 3/7 (b) 18/49 and 5/14 (c) 9/25 and 140/500 (d) 24/144 and 32/96

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color green. If 20 buyers are randomly selected, what is the probability that exactly a fifth of the buyers would prefer green? Round your answer to four decimal places.

The lengths of lumber a machine cuts are normally distributed with a mean of 101 inches and a standard deviation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 101.15 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 101.15 inches? (a) The probability is . (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.)

Find (d y) for (y=(4 x+5)^2) (d y=) (square) (Simplify your answer.)

For f(x)=1-x and g(x)=4x^2+x+3, find the following functions. a. (f∘g)(x); b. (g∘f)(x); c. (f∘g)(3); d. (g∘f)(3) a. (f∘g)(x)=

A dietitian in a hospital is to arrange a special diet using three foods, L, M, and N. Each ounce of food L contains 10 units of calcium, 5 units of iron, 10 units of vitamin A, and 20 units of cholesterol. Each ounce of food M contains 5 units of calcium, 5 units of iron, 15 units of vitamin A, and 20 units of cholesterol. Each ounce of food N contains 5 units of calcium, 5 units of iron, 10 units of vitamin A, and 18 units of cholesterol. Select the correct choice below and fill in any answer boxes present in your choice. If the minimum daily requirements are 160 units of calcium, 100 units of iron, and 240 units of vitamin A, how many ounces of each food should be used to meet the minimum requirements and at the same time minimize the cholesterol intake? A. The special diet should include x1= ounces of food L, x2= ounces of food M, and x3= ounces of food N. B. There is no way to minimize the cholesterol intake.

Find the slope of a line passing through the pair of points: (-3,4) and (2,-2)

Express the set -2x + 18 ≥ 4x + 12 using interval notation.

Which of the following pairs of angles are corresponding angles? angle 7 and angle 3 angle 1 and angle 3 Two of these angle 8 and angle 5

Find the expected value E(X) of the following data. Round your answer to one decimal place. x -6 -5 -4 -3 -2 P(X=x) 0.3 0.1 0.1 0.1 0.4

Let f(x)=15x+14 f^(-1)(x)=

A survey was given to 18 students. One question asked them to rate their college on a scale from 1-5, with 5 being the highest. The results, in miles, are shown in the following table. Use the results to find the first, second, and third quartiles for the data.

Sea ( ak=6 k^2 ) El valor de ( sumk=1^n ak ) para ( n=96 ) es: Respuesta:

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of the function's domain and range. f(x)=x^2+16x+8 (-8,-56) (Type an ordered pair.) What are the x-intercepts? (-8+2sqrt(14), 0),(-8-2sqrt(14), 0) What is the y-intercept? (Type an ordered pair.)

What is the x-intercept of the graph that is shown below?

Find Dot Product A [dot] B.

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. How much does each type of box weigh? Weight of each large box: kilogram(s) Weight of each small box: kilogram(s)

Find the area K of the triangle. K = □ square units (Round to two decimal places as needed.)

Refer to functions n and q. Evaluate (q * n)(x) and write the domain in interval notation. Write your answers as integers or simplified fractions. n(x) = x + 3, q(x) = 1 / (x + 8) Part 1 of 2 (q * n)(x) =

The radius of a circle is 16.4 m . Find the circumference to the nearest tenth.

In order to start a small business, a student takes out a simple interest loan for 3000 for 9 months at a rate of 9.25%. a. How much interest must the student pay? b. Find the future value of the loan.

Factor the quadratic trinomial 4x^2+12x+9. Show your work.

On the set of aves below, graph the equation 3y+2x=15. Explain why (-6,9) is a solution to the equation.

Statistic: What is the statistic in this study?

Is the following an exponential function? y=3^2

A person tosses a coin 16 times. In how many ways can he get 15 tails?

Explain the difference between the z-test for μ using rejection region(s) and the z-test for μ using a P-value. Choose the correct answer below. A. The z-test using rejection region(s) is used when the population is not normal. The z-test using a P-value is used when the population is normal. B. In the z-test using rejection region(s), the test statistic is compared with the level of significance α. The z-test using a P-value compares the P-value with the critical values. C. In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance α. D. The z-test using rejection region(s) is used when the population is normal. The z-test using a P-value is used when the population is not normal.

Use the formula for nPr to evaluate the following expression. 18P0 18P0 = □

Polynomial and Rational Functions Finding the maximum or minimum of a quadratic function Answer the questions below about the quadratic function. f(x)=-2x^2-12x-20 Does the function have a minimum or maximum value? Minimum Maximum Where does the minimum or maximum value occur? x= What is the function's minimum or maximum value?

(2x^2+x-21)/(x^2+2x) * (8x+16)/(x-3)

What is the measure of minor arc XZ, given that YX and YZ are tangent to circle O? A. 40° B. 180° C. 1900 D. 140°

IQ scores form a normal distribution with μ=100 and σ=15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses?

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (15/17, -8/17). Find the exact values of sin θ, sec θ, and cot θ. sin θ= sec θ= cot θ=

Factor. Assume that variables in exponents represent natural numbers. 56 y^4 - 117 x y^2 + 36 x^2 The complete factorization is (Factor completely. Simplify your answer.)

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile. The 87th percentile is (Round to two decimal places as needed.)

Factor the polynomial. bc-a-ba+c bc-a-ba+c=

Find the measure of angle X. Explain how you Know.

[A garden table and a bench cost 150 combined. The cost of the garden table is two times the cost of the bench. What is the cost of the bench? X ↺]

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 100. (b) The square footage in square feet of a house. (a) Is the number of people in a restaurant that has a capacity of 100 discrete or continuous? A. The random variable is continuous. The possible values are x=0,1,2, ..., 100 B. The random variable is continuous. The possible values are 0 ≤ x ≤ 100. C. The random variable is discrete. The possible values are 0 ≤ x ≤ 100. D. The random variable is discrete. The possible values are x=0,1,2, ..., 100

Write in scientific notation. 0.00000655 0.00000655 =

A survey found that 16 out of 200 grocery store shoppers will donate 5 when asked by the cashier. a. What's the approximate probability that a random grocery store shopper will donate 5 when asked by the cashier? Type your answer as a percentage. % b. If 1000 people are asked to donate 5 by a cashier in one day, approximately how much money will be donated during that day?

Question 16 of 44 If polygon A is a parallelogram, and polygon B is a rectangle, which of the following is true? A. Polygon A and B are parallelograms so neither can be circumscribed by a circle. B. Both polygon A and B are quadrilaterals, therefore a circle can circumscribe either one. C. Polygon A can be circumscribed by a circle because opposite sides must be supplementary. D. Polygon B represents the only parallelogram that a circle can circumscribe because opposite angles are supplementary.

Compute the volume of the given frustum. Present your answer as a decimal, rounded to three decimal places. (Picture is not to scale.) V=490.016 × m^3

Find the exact values of the six trigonometric functions of the real number (t). (sin (t)= , csc (t)= ,) (cos (t)= , sec (t)= ,) (tan (t)= , cot (t)=)

Evaluate. 2 cdot(4+1)^2

Factor the polynomial completely using the grouping method. 21x-4+18x^2 21x-4+18x^2=

(x^3+7xy+6y^2)-(2x^3+2xy+7y^2) (x^3+7xy+6y^2)-(2x^3+2xy+7y^2)=

If the heights of all adult females are normally distributed with a mean of 5.5 feet and a standard deviation of 1 foot, how tall is Jada if she is in the 82 nd percentile? Round your answer to one decimal place. Do not include units in your answer.

CALCULUS AB SECTION II, Part B Time-45 minutes Number of problems-3 No calculator is allowed for these problems. 4. Consider the curve given by x^2+4 y^2=7+3 x y. (a) Show that dy/dx=(3 y-2 x)/(8 y-3 x). (b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. (c) Find the value of d^2 y/dx^2 at the point P found in part (b). Does the curve have a local maximum, a local minimum, or neither at the point P? Justify your answer.

Aisha has 100 saved from her job. She wants to b represents her spending, where x is the number of 4x + 5y < 100 Which ordered pair (x, y) represents a combination (16,8) (15,8) (9,13) (6,15) (5,16)

the graph of the polynomial function to solve the inequality. 3x^3 + 14x^2 ≥ 28x + 24 f(x) = 3x^3 + 14x^2 - 28x - 24 The solution set is (-∞, -4] ∪ [-2/3, ∞). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Use graphical methods to solve this linear programming problem. Maximize z=6x+3y subject to: 5x-y ≤ 16 3x+y ≥ 14 x ≥ 3 y ≤ 8 What is the maximum value of z? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum value is . (Simplify your answer.) B. There is no maximum.

4) At the end of a runner's half marathon, they ended up 510 feet above sea level. What was their change in elevation if the start was -320 feet below sea level?

Convert log base 4 of 16 equals 2 to exponential form.

Pivot once as indicated in the given simplex x1 x2 x3 s1 s2 z tableau. Read the solution from the result. [1 8 2 1 0 0 56; 2 4 1 0 1 0 18; -1 -6 -2 0 0 1 0] Pivot around the highlighted entry. [x1 x2 x3 s1 s2 z; (blank) 0 (blank) 1 (blank) 0 (blank); 2 4 1 0 1 0 18; (blank) 0 (blank) 0 (blank) 1 (blank)] (Simplify your answers.)

Suppose H(x)=(4x+8)^2. 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.)

Find the equation of the line that contains the point (6, -2) and is perpendicular to the line y = -2x + 8. y = 2x - 14 y = x - 8 y = 1/2x - 5 y = -2x + 10

f(x)=3x-4 g(x)=7x+1

Correlation Coefficient, The Coefficient of Determination The following data represent the number of calories per serving and grams of sugar per serving for a random sample of high-fiber cereal. Calories, x: 250, 220, 170, 190, 210 Sugar, y: 18, 13, 17, 17, 12 Is there a linear relation between calories and sugar content? A. Since the absolute value of the correlation coefficient is greater than the critical value, there is not a linear relation between calories and sugar. B. Since the absolute value of the correlation coefficient is greater than the critical value, there is a linear relation between calories and sugar content. C. Since the absolute value of the correlation coefficient is less than the critical value, there is a linear relation between calories and sugar content. D. Since the absolute value of the correlation coefficient is less than the critical value, there is not a linear relation between calories and sugar content. (c) Suppose that we add another cereal, which has 50 calories and 3 grams of sugar per serving, to the data set. Redraw the scatter diagram of the correct plot below. - A B. C.

The following table shows students' test scores on the first two tests in an introductory calculus class. Calculus Test Scores First test, x: 64, 90, 87, 69, 62, 95, 82, 56, 47, 77, 54, 91 Second test, y: 65, 82, 84, 62, 52, 93, 77, 54, 55, 70, 59, 85 Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.

Compute the difference and simplify your answer. 1/5 - 6/9

For which of the following is it true that n(A)+n(B)=n(A ∪ B) ? a. A=a, b, c, B=c, d b. A=a, b, c, B=b, e c. A=a, b, c, B=∅ a. The statement n(A)+n(B)=n(A ∪ B) is . b. The statement n(A)+n(B)=n(A ∪ B) is c. The statement n(A)+n(B)=n(A ∪ B) is

Find f+g, f-g, fg and f/g. Determine the domain for each function. f(x)=2x^2+13x+20, g(x)=x+4 (f+g)(x)=2x^2+14x+24 (Simplify your answer.) What is the domain of f+g ? A. The domain of f+g is . (Type your answer in interval notation.) B. The domain of f+g is . (Use a comma to separate answers as needed.) C. The domain of f+g is ∅.

If (f(x)=4 cos ^2(x)), compute its differential (d f). (d f=) Approximate the change in (f) when (x) changes from (x=fracpi6) to (x=fracpi6+0.1). (Round your answer to three decimal places.) [ Delta f approx ]

Write the decimal number in words. 16.28 Which of the following represents 16.28 in words? A. sixteen and twenty-eight hundreds B. sixteen and twenty-eight tens C. sixteen and twenty-eight tenths D. sixteen and twenty-eight hundredths

Factor the following polynomial. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient. 2y^3 + 8y^4 + 6y^3

Provide values of s and t, that will make each equation true. a. x^2 * x^t = x^10 b. y^s = 1 c. (a^t)^s = a^12 d. (k^5 y^t)^2 = k^4 y

Let A=[[4, 3, -5], [8, 1, 5], [-9, -6, 9]] Let B=A^-1. What is the value of b23? If B does not exist, enter 99999 as your answer.

x-4y=4 -x+4y=4

∫ x ln x dx

What type of transformation is demonstrated in the following figure? A. dilation B. reflection C. rotation D. translation Please select the best answer from the choices provided A B

b) f(x)=(x^3-6x^2-3x+18)/(x^2-4x-12) Hole(s): x-intercept(s): y-intercept: VA(s): HA/Slant: Domain and Range:

cm) released A 25 42 B 50 21 C 75 10 D 100 1 Which of the following conclusions is best supported by the results of the experiment? Choose 1 answer: (A) Light intensity does not affect the rate of photosynthesis. (B) A decrease in light intensity increases the rate of photosynthesis. (C) An increase in light intensity increases the rate of photosynthesis. (D) An increase in light intensity decreases the rate of photosynthesis.

Given the graph of the parent function below, identify the name of the parent function and the domain range of the parent function Linear Function - Domain: (-∞, ∞) Range: (-∞, ∞) Cubic Function - Domain: (-∞, ∞) Range: (-∞, ∞) Cubic Function - Domain: [-∞, ∞] Range: [-∞, ∞] Linear Function - Domain: (-0, ∞) Range: (-∞, 0)

Math 131-Practice Midterm Exam 2 SOLUTIONS Fall 2024 1. Assume that S is a sample space and A and B are two events. If n(S)=85, n(A ∪ B)=53, n(B)=28, and n(¬A)=35, find the following. Leave any probabilities as unreduced fractions. Show any calculations you are performing, and circle your answer. (a) n(A) n(A)=n(S)-n(¬A)=85-35=50 (b) P(A) P(A)=n(A)/n(S)=50/85 (c) n(A ∩ B) n(A ∩ B)=n(A)+n(B)-n(A ∪ B) n(A ∩ B)=50+28-53=25 (d) P(A ∩ B) P(A ∩ B)=n(A ∩ B)/n(S)=25/85

A group of storage silos can hold enough cocoa beans to make 5.7 billion chocolate bars. Write 5.7 billion in standard notation. 5.7 billion = □

Is the pair of hypotheses H0: μ ≤ 50, HA: μ>50 valid? A. No, because the parameter being tested is not a population parameter. B. No, because the alternative hypothesis does not include all population values that are not included in the null hypothesis. C. No, because the null hypothesis does not contain an equality sign. D. No, because the null hypothesis and alternative hypothesis contain population values that overlap. E. Yes, because the null hypothesis contains an equality sign and the alternative hypothesis includes all population values not included in the null hypothesis.

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