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You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 6 or a number greater than 3 (b) Rolling a number less than 4 or an even number (c) Rolling a 2 or an odd number (a) P(6 or number >3) = (Round to three decimal places as needed.)
What is the approximate volume of the tank? a) 70 b) (1^1^30)
Simplify the following rational expression. [ fracx^2-13 x+40x^2-7 x+10 ] Give your answer as a reduced rational expression.
Write the number in scientific notation. 1,740,000 1,740,000=
Calculate [ (x^2-4 x+2)(3 x-5) ]
x+y ≤ 40 x ≥ 5 y ≥ 10 100x+200y ≤ 7,000
Find each product. (8x-1)(2x-5)
(a) Determine if the upper bound theorem identifies 2 as an upper bound for the real zeros of f(x). (b) Determine if the lower bound theorem identifies -7 as a lower bound for the real zeros of f(x). f(x)=x^5+5x^4+3x^3+51x^2-94x+38
Divide using synthetic division (3x^3-2x^2+5x-1)-(x-2)
The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist. A is 5 x 3, and B is 3 x 5. Find the size of the product AB. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The size of product AB is . B. The product AB does not exist.
QUESTION 12 · 1 POINT In the relation in the table below, write a value that will make the relation not represent a function. Input 4 7 5 ? Output 2 1 3 8
Solve the rational equation. Express numbers as integers or simplified fractions. p/(p-5) + 5/6 = 2/(p-5) The solution set is .
Find the slope-intercept form of the line that passes through (-6,10) and (2,-3) A. y=-16/5 x+17/5 B. y=16/5 x+17/5 C. y=13/8 x+1/4 D. y=-13/8 x+1/4
Write the equation of this line in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Write each polynomial as the square of a bisemial or as an expression opposite to the square of a binomial. (C) (9/16) a^4 + a^3 + (4/9) a^2
Find the indicated probability using the standard normal distribution. P(z<1.52) Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. P(z<1.52)= (Round to four decimal places as needed.)
Factor the trinomial completely. x^2+18x+13
Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly three boys in ten births. Round the answer to the nearest thousandth. A. 0.030 B. 0.117 C. 15.000 D. 0.300
Test: Test 2 - Chs 3 and 4 - Fall 2024 Question 17 of 37 This test: 94 point(s) possible This question: 3 point(s) possible Submit test Question list Question 9 Question 10 Question 11 Question 12 Question 13 Question 14 Question 15 Question 16 Match the accounting terminology to the definitions. Definition Term Requires companies to record revenue when it satisfies each performance obligation. Assumes that a business's activities can be sliced into small time segments and that financial statements can be prepared for specific periods. Guides accounting for expenses, ensures that all expenses are recorded when. they are incurred during the period, and matches those expenses against the revenues of the period. Matching principle Revenue recognition principle Time period concept
Which property of equality is shown below? If: 76=89 n Then: 76/24=89 n/24 Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality
(c) We are 90% confident that the interval from 0.52 to 0.64 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low. Is the interpretation reasonable? A. The interpretation is reasonable. B. The interpretation is flawed. The interpretation indicates that the level of confidence is varying. C. The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true. D. The interpretation is flawed. The interpretation provides no interval about the population proportion.
Find the equation of the tangent line at the given value of x on the curve. 2 y^3(x-5)+x sqrt(y)=10 ; x=5 y=
An employment information service claims the mean annual salary for senior level product engineers is 99,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At alpha=0.01, test the claim that the mean salary is 99,000. Complete parts (a) through (e) below. Assume the population is normally distributed. Annual Salaries 100,627 96,301 93,591 112,783 82,571 74,234 77,022 80,943 102,417 76,200 104,072 104,036 91,077 82,162 85,025 110,222 (c) Find the standardized test statistic, t. The standardized test statistic is t= (Round to two decimal places as needed.)
Write the expression as a single logarithm. Express powers as factors. log6 sqrt(x) - log6 x^5 log6 sqrt(x) - log6 x^5= (Type an exact answer. Use integers or fractions for any numbers in the expression.)
A marketing team is targeting people who might buy a hybrid car. In their city, with a population of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=121. Round all answers to 3 decimal places. Provide your answer below: p= μp= σp=
About what percent of x values lie between the first and third standard deviations (both sides)? (Enter an exact number as an integer, fraction, or decimal.)
In this trapezoid, how many degrees is angle "x" if B=70 degrees? A 20= B 70 degrees C 110 degrees D 290 degrees
Graph the solution of the system of linear inequalities. y ≥ -x + 4 y ≤ 2x + 6
Jorge weighs 198 pounds. What is his weight in kilograms? (1 kg=2.2 lbs) a. 120 kg b. 90 kg c. 100 kg d. 80 kg
Aşağıdaki sayı doğrusunda bazı pozitif tam sayıların kareköküne karşlık gelen noktalar gösterilmiştir. B u sayı doğrusu üzerinde bulunan a ve b tam sayıları arasındaki nokta sayısı >a, b< sembolü ile gösteriliyor. Örneğin; >1,2<=2 Buna göre >2024,2025< ifadesinin eşiti kaçtır? A) 1 B) 44 C) 4048 D) 4049 E) 4050
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 10% of UGPAs? (b) Between what two values does the middle 50% of the UGPAs lie? (a) The minimum UGPA that would still place a student in the top 10% of UGPAs is (Round to two decimal places as needed.)
Homework (Ch 04) Complete the following worksheet and then use it to calculate the coefficient of determination. The coefficient of determination (r^2) is The F-ratio is , which means that the assessor reject, at the 5% level of significance, the null hypothesis that there is relationship between the selling price and the area of the house. (Hint: The critical value of F0.05,1,13 is 4.67.) Which of the following is an approximate 95% prediction interval for the selling price of a house having an area (size) of 15 (hundred) square feet?
Identifying The Domain, Range and Horizontal Intercepts of a Quadratic Function For each of the following quadratic functions: 1. Determine the Domain of the Function 2. Determine the Range of the Function 3. Use the Intersect Feature and your graphing calculator to determine the Horizontal Intercepts, if any. Round your answers to one decimal places as needed [Hint: If two Horizontal Intercepts exist, enter them as (x1, y1),(x2, y2). If only one exists, enter (x1, y1). If none exist, enter DNE] Function Domain In Interval Notation Range In Interval Notation Horizontal Intercepts As a list of ordered pairs f(x)=2 x^2+4 x-9 (-infty, infty) [-11, infty) (1.3,0),(-3.3, 0) g(x)=x^2+8 x+21 (-infty, infty) [5, infty) DNE (x)=-x^2+8 (-infty, infty) (-infty, 8] (-2.8,0),(2.8, 0) p(t)=3 t^2-12 t (-infty, infty) [-12, infty) h(x)=2 x^2 (-infty, infty) [0, infty)
Determine whether the statement makes sense or does not make sense, and explain your reasoning. I can solve x/9=4/6 by using the cross-products principle or by multiplying both sides by 18, the least common denominator. Choose the correct answer below. A. The statement does not make sense. Multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. However, the value of the missing quantity in a proportion cannot be found by using the cross-products principle if only three of the numbers are known. B. The statement makes sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. C. The statement does not make sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. However, the terms on both sides of the equation would need to be multiplied by 6 * 4=24, and not 18, to eliminate the fractions in the equation. D. The statement makes sense. If two of the numbers in a proportion are known, the value of the missing quantities can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation.
The P -value for a hypothesis test is shown. Use the P -value to decide whether to reject H₀ when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10. P=0.0237 (a) Do you reject or fail to reject H₀ at the 0.01 level of significance? A. Fail to reject H₀ because the P -value, 0.0237, is greater than α=0.01. B. Fail to reject H₀ because the P-value, 0.0237, is less than α=0.01. C. Reject H₀ because the P-value, 0.0237, is greater than α=0.01. D. Reject H₀ because the P-value, 0.0237, is less than α=0.01. (b) Do you reject or fail to reject H₀ at the 0.05 level of significance? A. Reject H₀ because the P-value, 0.0237, is greater than α=0.05. B. Fail to reject H₀ because the P-value 0.0237, is less than α=0.05. C. Reject H₀ because the P-value 0.0237, is less than α=0.05. D. Fail to reject H₀ because the P-value, 0.0237, is greater than α=0.05.
Montel owns a machine shop. In reviewing the shop's utility bills for the past 12 months, he found that the highest bill of 2,800 occurred in August when the machines worked 1,400 machine hours. The lowest utility bill of 2,600 occurred in December when the machines worked 900 machine hours. Requirement 1. Use the high-low method to calculate the variable cost per machine hour and the total fixed utility cost. First, calculate the variable cost per machine hour. Select the formula labels, then enter the amounts and compute the variable cost per machine hour. (Use the high-low method. Round your answer to the nearest cent) Change in total costs / Change in volume of activity = Variable cost per machine hour
Find the volume of the rectangular prism. Write your answer in simplest form.
Find the standard deviation for the group of data items. 11,12,13,14,15 The standard deviation is (Round to two decimal places as needed.)
Write the expression as a sum and/or difference of logarithms. Express powers as factors. log5(25 x) log5(25 x) = (Type an exact answer in simplified form.)
Factor f(x) into linear factors given that k is a zero of f(x). f(x)=4x^3+7x^2-142x+35; k=5 f(x)=(x-5)(x-4)(x+7) (Factor completely.)
Minimize z=3x+5y 2y+7x ≥ 20 7y+2x ≥ 20 Subject to y+x ≥ 5 x ≥ 0 y ≥ 0 Minimum is at x= y=
Solve the nonlinear inequality. Express the solution using interval notation. 15/(x-1) - 16/x ≥ 1 Graph the solution set.
Solve the following equation. If needed, submit your answer as a fraction reduced to lowest terms. y^(2/3) - 25/64 = 0
Use the slope formula to determine the slope of the line containing the two points. Express numbers as integers or simplified fractions. Select "Undefined" if applicable. (-6,4) and (-6,2) The slope is Undefined.
If f(2)=4 and f'(2)=3/4, use the formula (f^(-1))'(x)=1/f'(f^(-1)(x)) to find (f^(-1))'(4). (f^(-1))'(4)=
Fake Twitter followers: Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 44 twitter audits, the mean percentage of fake followers was 13.8 with a standard deviation of 9.4. Part: 0 / 2 Part 1 of 2 Construct a 90% interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place. A 90% confidence interval for the mean percentage of fake Twitter followers is <μ< .
ALEKS - 2024 Fall - College Algebra U15) Graphs and Functions Evaluating a piecewise-defined function Suppose that the function (h) is defined, for all real numbers, as follows. [ h(x)=left beginarrayll frac13 x^2-5 text if x neq-2 -3 text if x=-2 endarrayright. ] Find (h(-4), h(-2)), and (h(3)). [ beginarrayl h(-4)=square h(-2)=square h(3)=square endarray ]
You take a survey of your classmates' birthday months. A student is chosen at random. Find the probability of each event. (Enter your probabilities as fractions.) Month Number of students Month Number of students --- --- --- --- January 0 July 4 February 3 August 2 March 5 September 0 April 2 October 3 May 5 November 4 June 1 December 6 (a) The student was born in July. (b) The student was born in March. (c) The student was born in one of the last 3 months of the year.
In Δ STU, TU=17, US=12, and ST=15. Which statement about the angles of Δ STU must be true?
At a sale this week, a suit is being sold for 377. This is a 35% discount from the original price. What is the original price?
Question 12 Simplify. Assume all variables are nonnegative. √(48 b^12 y^5 / b^5 y^15)=
A simple random sample of size n=81 is obtained from a population that is skewed right with μ=74 and σ=27. (a) Describe the sampling distribution of x̄. (b) What is P(x̄>78.2) ? (c) What is P(x ≤ 66.95) ? (d) What is P(69.5<x̄<79.25) ?
The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency? 38 31 30 33 36 39 19 17 23 5 38 24 19 27 1 10 13 36 0 38 Complete the table, starting with the lowest class limit. (Simplify your answers.)
Find the area under the standard normal curve to the right of z=1.31. Round your answer to four decimal places, if necessary.
Consumer Mathematics Finding the present value of an investment earning compound interest To help with his child's college fund, Jose needs to invest. Assuming an interest rate of 2.14% compounded monthly, how much would he have to invest to have 78,900 after 12 years? Do not round any intermediate computations, and round your final answer to the nearest dollar. If necessary, refer to the list of financial formulas.
How much is (3i+2j) · (7i-3j)?
Write the first five terms of the geometric sequence. an=-8 an-1 ; a1=-4 -8,-32,-256,-2048,-16,384 -4,-12,-20,-28,-36 32,-256,2048,-16,384,131,072 -4,32,-256,2048,-16,384
The expression [ fracleft(x^4 y^3right)^4left(x y^4right)^-3x^4 y^6 ] equals fracx^ey^d where the exponent e of x is , the exponent d of y is
Complete the following. (a) The graph of y=h(x) is shown. Draw the graph of y=2h(x-4).
The weekly salaries (in dollars) for 10 employees of a small business are given below (note that these are already ordered from least to greatest.) 730, 761, 767, 777, 778, 795, 831, 880, 903, 948 Suppose that the 730 salary changes to 770. Answer the following. (a) What happens to the median? - It decreases by - It increases by - It stays the same. (b) What happens to the mean? - It decreases by - It increases by - It stays the same.
Given k(x)=-5x+6 and m(x)=x^2, (a) Find (k ∘ m)(x). (b) Find (m ∘ k)(x). (c) Is (k ∘ m)(x)=(m ∘ k)(x) ?
(20 x^3-14 x^2-19 x+5) ÷ (5 x+4) (20 x^3-14 x^2-19 x+5) ÷ (5 x+4) = □
Write equations for the horizontal and vertical lines passing through the point (-8,-2). horizontal line: vertical line:
y=-1/2 x+5 -8 x-4 y=-24 Is (2,4) a solution to the system above? True False
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns eight less than a number
21945, Fall 2024 Rational Expressions and Dividing Question 19, 6.1.141 Determine whether the following statement is true or false. If the statement is false, make the necessary change. The domain of f(x) = 5/(x(x-6)+8(x-6)) is (-∞, 6) ∪ (6, ∞). Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The statement is false. The domain of f(x) is (Type your answer in interval notation.) B. The statement is true.
Refer to functions n, p. Evaluate the function and Write the domain in interval notation. n(x)=x-6 p(x)=x^2+5 x Part: 0 / 4 Part 1 of 4 (n circ p)(x)= (Choose one) nabla
A data set includes weights (in grams) of 36 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 36 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk. Use a 0.01 significance level. Identify the null and alternative hypotheses.
Find the maximum value of [ P=9 x+8 y ] subject to the following constraints: Now, find the coordinates of the corner points. x y 0 0 6 0 0 7 [?] 8 x+6 y leq 48 7 x+7 y leq 49 x geq 0 y geq 0
Round the following decimal to the given place value. 248.352 to the nearest whole number
Calculate an exact answer using a sum or difference formula. sin 165°
Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find S the indicated probability. P((A ∩ B)′) P((~A ∩ ~B)′)= (Type a decimal.)
Cho hai tập hợp (X) và (Y) : [ X=1 ; 6 ; 2 ; 3 ; 14 Y=2 ; 9 ; 13 ; 1 text Tìm X cup Y ] Hãy chọn 1 đáp án: (A) (3,6,9,13) (B) (1,2,3,6,9,13,14) (C) (1,2) (D) (3,6,14)
Find the logarithm. [ log (1,000)= ]
The heights of adult men in America are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.64 inches. The heights of adult women in America have a mean of 64.2 inches and a standard deviation of 2.57 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z= b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z= c) Who is relatively taller? - The 5 foot 11 inch American woman - The 6 foot 3 inch American man
If (g(x)=left(frac15right)^x), find (g(2.95)) (g(2.95)=)
098.13.MANK09 Average total cost is increasing whenever a. marginal cost is greater than average total cost. b. total cost is increasing. c. marginal cost is less than average total cost. d. marginal cost is increasing. O- Icon Key 098.13.MANK09
A couple plans to have three children. What is the probability that a) they have all boys? 1/8 b) they have at least one girl? 7/8
Smartphones: A poll agency reports that 27% of teenagers aged 12-17 own smartphones. A random sample of 85 teenagers is drawn. Round your answers to at least four decimal places as needed. Part 1 of 6 (a) Find the mean μp.
The is the system whereby water continuously moves from the atmosphere to the land, plants, oceans, and freshwater bodies and then back into the atmosphere.
6^-8 * 6^5
Fill in the blank so that the resulting statement is true. The sum of the measures of the angles of a polygon with n sides is
Simplify, be sure to show work to receive credit. Assume all variables represent positive values. Do not use a calculator or round to a decimal. Write the exact simplified form. (2+√28)/6
In a unit circle, the radian measure of the central angle is equal to the length of the Choose the correct answer below. A. diameter of the circle B. intercepted arc C. radius of the circle
Find the mean, median, and mode for the following distribution. 4,7,4,3,5,8,6,9,10 A. The mode(s) is/are . (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is no mode for these data.
Suppose that you have 7820 to invest. Which investment yields the greater return over 7 years: 9.35% compounded quarterly or 9.45% compounded semiannually? The accumulated value of the 9.35% investment is 14,934.18 The accumulated value of the 9.45% investment is . CONCLUSION: The investment at 9.35% compounded quarterly yields a greater return.
Find the area of the region that lies inside the first curve and outside the second curve. (23.) r=4 sin theta, r=2
The Laplace transform of a continuous function over the interval [0, ∞) is defined by F(s)=∫ from 0 to ∞ e^(-sx) f(x) dx. This definition is used to solve some important initial-value problems in differential equations. The domain of F is the set of all real numbers s such that the improper integral converges. Find the Laplace transform F of the following function: f(x)=6x
In the simulation, when we are building a sampling distribution, what does each dot represent in the graph?
Describe the long run behavior of f(r)=-4r^7+3r^6-2r^5-5 As r → -∞, f(r) → ? As r → ∞, f(r) →
∫(3x^4 + 2/x - 3/x^5 - 6 √x) dx
Suppose that f(x, y) = y sqrt(x^3 + 1) on the domain D = (x, y) 0 ≤ y ≤ x ≤ 3. Then the double integral of f(x, y) over D is ∫∫D f(x, y) dx dy= Round your answer to four decimal places.
The interest amount of the 9th payment is 18.00
Math and Physics Identifying solutions to a linear equation II For each value of w, determine whether it is a solution to 76=6-7w. w Is it a solution? Yes No --------- 6 0 ? -10 0 0 -4 0 0 3 0 0
Write the equation in standard form to find the center and radius of the circle. x^2 + y^2 + 6x + 14y + 37 = 0
In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the opposite was true for dolphins in the Southern Hemisphere (Stafne and Manger 2004). They watched eight sleeping dolphins and recorded the percentage of time that the dolphins swam clockwise. Assume that this is a random sample and that this variable has a normal distribution in the population. These data are as follows: 77.7,84.8,79.4,84.0,99.6,93.6,89.4,97.2 Click to download the data in your preferred format. CSV Excel JMP Mac-Text Minitab PC-Text R SPSS TI CrunchIt! What is the mean percentage of clockwise swimming for Southern Hemisphere dolphins? Round your answer with precision to one decimal place. mean percentage: %
Find the exact solutions of the equation over the given interval. 2 cos^2 theta + 6 = 15/2, 0 ≤ x < 2π
16a^2-24a+9
If cos A = 7/8 with A in QIV, find sin (A/2). sin (A/2) = -sqrt(3)/5 sin (A/2) = 1/5 sin (A/2) = sqrt(3)/5 sin (A/2) = -1/5 sin (A/2) = 1/4
Simplify the rational expression. Select "Cannot be simplified" if applicable. (a^2-64)/(a-8)=□ Cannot be simplified
According to the Transportation Security Administration (TSA) data, 9% of the passengers fly first-class. A random sample of size 44 was obtained. Let p̂ be the proportion of the sample that fly first-class. Explain why the Central Limit Theorem cannot be used.
Simplify. [ (-8 x^2 z^4)^2 ] Write your answer without parentheses.
Find the quotient and remainder using long division for (x^2+3x-33)/(x-5)
The width of a rectangular slab of concrete is 2 m less than the length. The area is 35 m^2. Part: 0 / 3 Part 1 of 3 (a) What are the dimensions of the rectangle? The length of the slab is m.
3. Find the AROC on the interval [h, h + 2] for g(x) = 5 π
Find the area of the region inside (r=5 sin theta) but outside (r=4).
How many different committees can be formed from 9 teachers and 46 students if the committee consists of 3 teachers and 3 students?
Solve the equation by the method of your choice. (3x+1)(x+2)=1 The solution set is . (Simplify your answer. Type an exact answer, using radicals and i in the expression. Use a comma to separate answers as needed.)
A store manager decides to clear out playground slides to make room for new inventory. Now a 100 playground slide will be on sale for only 96. What is the discount, as a percentage? Write your answer using a percent sign (%).
You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 41.9 fluid ounces a standard deviation of 7.6 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below. 33, 46, 31, 33, 39, 43, 29, 52, 36, 42, 37, 27, 36, 46, 38, 37, 37, 41, 44, 44, 36, 31, 25, 39, 52, 38, 43, 37, 45, 34 Find the mean of your sample. The mean is 38.4. (Round to one decimal place as needed.) Find the standard deviation of your sample. The standard deviation is 6.6. (Round to one decimal place as needed.) Compare the mean and standard deviation of your sample with those of the previous study. Discuss the differences.
Use the midpoint approximation to approximate the area under the curve of f(x) = x^2/2 + 2 on the interval [-4,2] using n=6 rectangles. Submit your answer using an exact value. For instance, if your answer is 10/3, then enter this fraction as your answer in the response box.
A. y^2 + 10y - 36 = (Factor completely.) B. The trinomial is prime.
Solve the quadratic equation. -5x^2 + 6x - 2 = 0
Thirty-nine percent of U.S. adults have very little confidence in newspapers. You randomly select nine U.S. adults. Find the probability that the number who have very little confidence in newspapers is (a) exactly six and (b) exactly two.
There is a very popular lottery in which a ticket is called a scratcher. In this lottery, 41% of the scratchers are winning ones. Suppose that we will take a random sample of 7 scratchers. Let p̂ represent the proportion of winning scratchers from the sample. Consider the sampling distribution of the sample proportion p̂. Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed. (a) Find μp (the mean of the sampling distribution of the sample proportion). μp̂= (b) Find σp̂ (the standard deviation of the sampling distribution of the sample proportion). σp̂=
Rewrite cos(x - π/6) in terms of sin(x) and cos(x).
For the figure shown, find m∠1 and m∠2.
Similarity Finding a missing side length given two similar triangles triangle ABC and triangle XYZ are similar. Find the missing side length. (The triangles are not drawn to scale.)
Divide. Reduce if necessary. 2/3 ÷ 1/3 a) 1 b) 3/3 c) 1/3 d) 2
A single die is rolled twice. Find the probability of rolling a 1 the first time and a 4 the second time.
Find the exact value of each expression, (a) sin^(-1)(-1/2) (b) cos^(-1)(-sqrt(3)/2) (c) tan^(-1)(-sqrt(3)/3)
Subtract 14.6924 - 3.956= a) 2.412 b) 10.7364 c) 23.3584 d) 10.044 Write 0.113 as a percentage.
A 16-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 5 feet from the base of the building. How high up the wall does the ladder reach? The ladder reaches up the wall. (Round to the nearest hundredth as needed.)
log4(√4) log4(√4)=
A probability distribution functions is best described as a function that relates probability to outcomes an even functions is a function between continuous and discrete variables an odd function A discrete variable
Question 10 There are 9 seats in the front row of a popular English class, and 12 eager students wishing to fill them. Knowing that not all of the students can find a seat in the front row, in how many ways can these seats be assigned? (Enter your answer in the box below, without using comma in the number. The program will insert comma in the number where needed when you submit your answer.
Evaluate or simplify the expression without using a calculator. 10^(log 6)
32% of likely U.S. voters think that the federal government should get more involved in fighting local crime. You randomly select six likely U.S. voters and ask them whether they think that the federal government should get more involved in fighting local crime. The random variable represents the number of likely U.S. voters who think that the federal government should get more involved in fighting local crime. Find the mean of the binomial distribution. μ=1.9 (Round to the nearest tenth as needed.) Find the variance of the binomial distribution. σ^2=1.3 (Round to the nearest tenth as needed.) Find the standard deviation of the binomial distribution. σ= (Round to the nearest tenth as needed.)
Question 16 Express the ratio 1/4: 1/7 in simplest form 1: 1 cannot be done 4: 7 7: 4
Evaluate the expression. If the answer is not an integer, round to four decimal places. 6! Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is not an integer, 6!= . (Round to four decimal places as needed.) B. The value is an integer, 6!= . (Type an integer.)
Graph the inequality on a number line. x > 2 Choose the graph of the inequality A. [Number line graph with open circle at 2 and arrow pointing right] B. [Number line graph with closed circle at 2 and arrow pointing right] C. [Number line graph with open circle at 2 and arrow pointing left] D. [Number line graph with closed circle at 2 and arrow pointing left]
Giving a test to a group of students, the grades and gender are summarized below A B C Total --------------- Male 15 16 7 38 Female 5 2 9 16 Total 20 18 16 54 Answer the following using fractions or decimals rounded to three places. a. Find the probability that the student received an A in the class. b. Find the probability that the student is a female. c. Find the probability that the student was a male and received an A in the class. d. Find the probability that the student received an A in the class, given they are female. e. Find the probability that the student is a female given they received an A in the class. f. Find the probability that the student is a female and received an A in the class. g. Find the probability that the student received an A given they are female.
Fill in the Blank 3 points The graphs of f and g are given below. Compute the derivatives. If an answer does not exist, type DNE. (d/dx) f(g(x))(x=0)= type your answer.. (d/dx) f(g(x))(x=6)= type your answer..
A population of values has a normal distribution with μ=77.1 and σ=19.9. a. Find the probability that a single randomly selected value is greater than 82. Round your answer to four decimal places. P(X>82)= b. Find the probability that a randomly selected sample of size n=161 has a mean greater than 82. Round your answer to four decimal places. P(M>82)=
Consider the following piecewise-defined function. f(x) = 2x^2 + 2x + 2 if x ≤ 1 1/3 x + 1 if x > 4 Evaluate this function at x=1. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined". f(1)=
Find the derivative of the following function. y=-5 x^2+7 cos x dy/dx=
Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(35<X<61) Which of the following normal curves corresponds to P(35<X<61) ? A. B. ○ C P(35<X<6=0.9256 (Round to four decimal places as needed.)
The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 20100. (a) Find a function that models the population t years after 2000 ( t=0 for 2000). Your answer is P(t)=
Find the domain of the function. f(x) = 7 / (x - 14)
Solve the equation on the interval (0 leq theta<2 pi). (cos (2 theta-fracpi2)=1)
Diane deposits 7000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 6 years?
(23+ 12.2) - 410.16
Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (-3,-4) is on the terminal side of 0 . Then find the exact values of the six trigonometric functions for θ. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin θ= □ (Simplify your answer. Type an integer or fraction) B. The function is undefined.
The table shows the total product schedule of a firm that uses 1 sewing machine to sew 1 -shirts for another company. The firm's costs are rent a space for 200, the sewing machine for 40 a day and pays its workers 36 a day. Labour (workers per day) Output (pairs of jeans per day) ------ 0 0 1 6 2 14 3 22 4 28 5 31 Output (pairs of jeans per day) Total Cost ( Per Day) ------ 0 240 6 276 14 312 22 348 28 384 31 420 What are the firms Total Fixed Costs? The marginal cost when the firm increases production from 28 to 31 pairs of jeans a day is The firm changes production between 31 to 22 pairs of jeans a day the marginal cost is
Differentiate. y=(3x-1)/(6x^2+1) (-18x^2+9x+4)/(6x^2+1)^2 (18x^3-36x^2+15x)/(6x^2+1)^2 (-18x^2+12x+3)/(6x^2+1)^2 (54x^2-12x+3)/(6x^2+1)^2
According to the central limit theorem, the sampling distribution of the sample means is approximately normal if Multiple Choice the underlying population is not normal. the sample size n ≥ 30 both the underlying population is not normal and the sample size n ≥ 30 are correct. the standard deviation of the population is large.
Find the exact value of the real number y if it exists. Do not use a calculator. y = cos^(-1)(1/2)
Calculate the standard score of the given Y-value: Y = 36.5, where μ = 45.5 and σ = 45 and indicate on the curve where z will be located. Round the standard score to two decimal places.
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(-c ≤ Z ≤ c)=0.9199 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Find the absolute maximum and absolute minimum values of f(x) = (x^2 - 16) / (x^2 + 16) on the interval [-5,5]. a) Absolute maximum b) Absolute minimum
Claim: Fewer than 11.7% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 14,941 homes 5.79% had landline phones without wireless phones. Complete parts (a) and (b). a. Express the original claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone.
New parents wish to save for their newborn's education and wish to have 41,000 at the end of 19 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 8.5% compounded annually? (Round your answers to two decimal places.) How much interest would they earn over the life of the account? Determine the value of the fund after 12 years. How much interest was earned during the 12th year?
What are the coordinates of W? Isosceles Trapezoid
Find the exact value of each of the remaining trigonometric functions of (theta). (cos theta=-frac56, quad 90^circ<theta<180^circ) (sin theta=fracsqrt116) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) (tan theta=)
Let f(x)=x^2-10x-5. a. Find the values of x for which the slope of the curve y=f(x) is 0. b. Find the values of x for which the slope of the curve y=f(x) is -2.
Describe the sampling distribution of p̂ Choose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because n ≤ 0.05 N and n p(1-p) ≥ 10 B. Approximately normal because n ≤ 0.05 N and np(1-p)<10. C. Not normal because n ≤ 005 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. μp=0.4 (Round to one decimal place as needed) Determine the standard deviation of the sampling distribution of p̂ σp= (Round to six decimal places as needed)
In a certain country, the true probability of a baby being a boy is 0.539. Among the next four randomly selected births in the country, what is the probability that at least one of them is a girl? The probability is (Round to three decimal places as needed.)
What was the production cost in the year 2020? Write a formula for Q as a function of t, if (a) the initial amount is 23 and Q is increasing by f(Q)=23(1.12)^6 (b) the initial amount is 31 and Q is decreasing by Q=31(.88) t
55+32-24=? Select the single best answer: A. 63 B. 43 C. 53 D. 93 E. 86
Solve the system of equations by elimination/addition. Give your solution as an ordered pair. -9x + 9y = 6 -6x + 6y = 4
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=x^3, y=sqrt(x) ; about the x-axis v=
Multiply and collect like terms: (n+1)(n-6).
Determine whether the following equation represents exponential growth, exponential decay, or neither. y=10(2.3)^(0.5 x) growth decay neither
Find the number c that satisfies the conclusion of the Mean Value Theorem f(x)=sqrt(x), [0,4] c=
Determine whether the following statement represent an exponential function or a linear function. The average annual population of a pack of wolves increases each year by 25 wolves. exponential linear
Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". x^2+3x-28
The numbers of successes and the sample sizes for independent simple random samples from two populations are provided for a right-tailed test. Use a 90% confidence interval. Complete parts (a) through (d). x1=23, n1=90, x2=22, n2=100, alpha=0.05 Click here to view a table of areas under the standard normal curve for negative values of z. Click here to view a table of areas under the standard normal curve for positive values of z. Which of the following is the correct conclusion for the hypothesis test? A. At the 5% significance level, reject H0; the data provide sufficient evidence to accept Ha. B. At the 5% significance level, do not reject H0; the data do not provide sufficient evidence to accept Ha. C. At the 5% significance level, do not reject H0; the data provide sufficient evidence to accept Ha. D. At the 5% significance level, reject H0; the data do not provide sufficient evidence to accept Ha. E. Using the two-proportions z-procedures is not appropriate.
Strontium-90 has a half-life of 28 days. Suppose a sample has an initial mass of 225 mg. a) Find an expression for the mass of the sample of Strontium-90 after t days. m(t)=225 * (1/2)^(t/28) b) Find the mass of the sample after 70 days. Round to three decimal places. c) How long does it take for the sample to contain only 3 mg of Strontium-90? Round to three decimal places.
Consider the following graph. Step 2 of 2: Determine the domain and range of the graph.
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The indicated IQ score is (Round to the nearest whole number as needed.)
Use z scores to compare the given values. The tallest living man at one time had a height of 255 cm. The shortest living man at that time had a height of 110.6 cm. Heights of men at that time had a mean of 174.08 cm and a standard deviation of 7.77 cm. Which of these two men had the height that was more extreme? Since the z score for the tallest man is z= find the z score for the shortest man is z=, the man had the height that was more extreme. (Round to two decimal places)
Determine the mean of the sampling distribution of p̂. w = 0?0 (Round to two decimal places as needed) Determine the standard deviation of the Sampling distribution of p̂ σ = (Round to three decimal places as needed) (b) What is the probability that in a random sample of 900 adults, more than 32% do not own a credit card? The probability is 0.0038 (Round to four decimal places as needed) Interpret this probability If 100 different random samples of 900 adults were obtained, one would expect to result in more than 32% not owning a credit card
A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 14 bottles of regular cola has a mean of 500.6 mL of soda with a standard deviation of 3.8 mL. A random sample of 16 bottles of diet cola has a mean of 502.9 mL of soda with a standard deviation of 4.7 mL. Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2. Compute the value of the test statistic. Round your answer to three decimal places.
Determine whether the given point is in the feasible set of this system of inequalities. 9x + 3y ≤ 82 x + y ≤ 17 2x + 6y ≤ 66 ;(6,7) x ≥ 0 y ≥ 0 Choose the correct answer below. No Yes
The function f(x) is continuous on (-∞, ∞). Use the given information to sketch the graph of f. - f(0)=12, f(6)=0, f(12)=-12 ; f′(0)=0, f′(12)=0 - f′(x)>0 on (-∞, 0) and (12, ∞) ; f′(x)<0 on (0,12) - f′′(6)=0 - f′′(x)>0 on (6, ∞) ; f′′(x)<0 on (-∞, 6) Choose the correct graph of f below. A. B. C. D.
to a third number on the third cylinder and so on until a three-number lock combination has been effected. Repetitions are allowed, and any of the numbers can be used at each step to form the combination. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try? (a) The number of different three-number lock combinations is 125000. (Type an integer or fraction. Simplify your answer.) (b) The probability that the correct lock combination is guessed on the first try is (Type an integer or fraction. Simplify your answer.)
3. a binomial distribution with 3 trials and a success probability of 0.5. what would be the probability of a success on every trial?
Solve the following triangle. B=45°, C=64°, b=39 inches A= (Simplify your answer.)
Use the figure to find B ∩ BD→ Which of the following is B ∩ BD° ? A. BD→° B. BD→ C. BD D. ∅
Use a sum or difference formula to find the exact value of the trigonometric function. sin(11π/12) sin(11π/12)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)