Math Questions

A certain medical test is known to detect 79% of the people who are afflicted with the disease Y. Type numbers in the boxes. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

In a poll, 900 adults in a region were asked about their online vs. in-store clothes shopping. One finding was that 24% of respondents never clothes-shop online. Find and interpret a 95% confidence interval for the proportion of all adults in the region who never clothes-shop online. [Round to three decimal places]

A bank manager wants to know the average amount of time customers of the bank have to wait in line. The average waiting time for a sample of 35 customers was 3.5 minutes. What is the population? a) all customers of the bank b) the 35 customers studied c) 3.5 minutes d) the average waiting time for all customers

The posters must be rectangular in shape, and they must have an area of 100 square inches with 2-inch margins on the right and left sides, and a 1-inch margin at the top and bottom. What dimensions should the poster have in order to have the largest printed area?

Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 133.3 mmHg, with a standard deviation of 5.1 mmHg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five. (a) According to Chebyshev's theorem, at least of the measurements lie between 123.1 mmHg and 143.5 mmHg. of the (b) According to Chebyshev's theorem, at least 56% of the measurements lie between mmHg and mmHg. (Round your answer to 1 decimal place.) ?

Fill in each box below with an integer or a reduced fraction. (a) log₂ 32 = 5 can be written in the form 2^A=B where A = and B = (b) log5 125 =3 can be written in the form 5^C=D where C= and D=

For $3.98 you can get a salad, main course, and dessert at the cafeteria. If you have a choice of 5 different salads, 7 different main courses, and 3 different desserts, then how many different meals can you get for $3.98? How many different meals can you get for $3.98?

Fill in the blank to correctly complete the sentence. For the polar equation r= 6 sin 40, if 0= 15°, then r = For the polar equation r=6 sin 40, if 0=15°, then r = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Angela worked on a straight 9 % commission. Her friend worked on a salary of $900 plus a 6 % commission. In a particular month, they both sold $25,800 worth of merchandise. Step 1 of 2: How much did Angela earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.

The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell- shaped distribution. This distribution has a mean of 50 and a standard deviation of 10. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 30 and 80? Do not enter the percent symbol. ans %

If $1200 is invested at 4.5% annual interest, compounded continuously, when is it worth $30,000? Round your answer to three decimal places. The investment is worth $30,000 in i 73.12

If y varies directly with x and y = 35 when x = 7, find y if x = 4. y = 5x Now solve for y if x = 4. y = [?]

Given the recurrence relation x₁ = 3, x₁ = 3X(n-1) What is the solution? Xn= 2^n for all negative integers n Xn= 3^n for all negative integers n Xn= 3^n for all positive integers n Xn= 2^n for all positive integers n

An investor bought stock for $20,000. Fourteen years later, the stock was sold for $40,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? The annual nominal rate of interest earned is%. (Round to two decimal places as needed.)

Use the ALEKS graphing calculator to find the x-intercept(s) and vertex for the quadratic function. f(x)=x²+5x+1 Round to the nearest hundredth if necessary. If there is more than one x-intercept, separate them with commas. If applicable, click on "None". x-intercept(s): vertex:

Solve the equation for solutions over the interval [0,2x) by first solving for the trigonometric function. 8 sin x + 20 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an exact answer, using x as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

Short-term classes: Does taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student's likelihood of passing the course? For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%. Which of the following are the appropriate null and alternative hypotheses for this research question? A. O Ho: P = 0.59; Ha: p = 0.59 B. O Ho: P = 0.59; Ha: p > 0.59 C. O Ho: p = 0.78; Ha: p = 0.78 D. O Ho: p = 0.78; Ha: p > 0.59

Find the coordinates for the vertex of the following quadratic function algebraically. Be prepared to show your algebraic work. P(x) = -9x + x2 Enter the exact coordinates separately in each blank. (Do not round values.) The vertex is (

Use the sinking fund formula to determine the payment needed to reach the accumulated amount. Round to the nearest cent. Quarterly payments with 5.8% interest compounded quarterly for 3 years, and will accumulate to $82,000. A. $2,285.22 B. $6,305.36 C. $1,657.43 D. $1,789.73

Sets D and H are defined as follows. D = {0, 2, 3, 4, 6} H={-1, 1, 3, 4, 6} Answer each part below. Write your answer in roster form or as Ø. (a) Find. the union of D and H. (b) Find the intersection of D and H.

Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression. paintings

a. Approximate the given quantity using Taylor polynomials with n=3. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. e^0.09 a. p3 (0.09) (Do not round until the final answer. Then round to seven decimal places as needed.)

Consider the trigonometric equation 2 sin(0) + 3 = 4, where the angle is measured in degrees. One set of solutions is θ= Another unique set of solutions is θ=

Use the pythagorean theorem to find the length of TI. (leg)2 + (leg) = (hypotemuse)" Enter the answer in simplified form. 245

Given the angle θ= -7π/6 To which quadrant does θ belong? (Write your answer as a numerical value.) Find the reference angle for θ IN RADIANS. Find the point where θ intersects the unit circle.

Consider the graphs of the equations below. y = 3x + 5 (y-7)= 2(x - 1) -12x + 3y = 15 -y = 6x - 5 Select the true statement. A. All four lines cross the y-axis at (0,5). B. All four lines have a positive x-intercept. C. All four lines have a negative x-intercept. D. All four lines cross the x-axis at (5,0).

A robot's body is made up of a rectangular prism with side lengths 48 inches by 24 inches by 36 inches. The head is made up of a cylinder with a height of 24 inches and a radius of 6 inches. What is the volume of the robots head and body in cubic feet? 250.08 ft3 25.57 ft3 51.15 ft3 37.68 ft3

Suppose that $2000 is invested at a rate of 4.7%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 8 years. Do not round any intermediate computations, and round your answer to the nearest cent.

David borrowed money from a credit union for 3 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $1890. How much money did he borrow? If necessary, refer to the list of financial formulas.

Find the monthly payment R needed to have a sinking fund accumulate the future value A. The yearly interest rate r and the time t in years are given below. Interest is compounded monthly. A=$7,000; r=7%; t = 1 R=$ (Round up to the nearest cent.)

Michelle is a sales representative for a publishing company. For the past 16 years, she has exceeded her annual sales goal, primarily by selling mathematics textbooks. Therefore, she will also exceed her annual sales goal this year.

Lauren's science class is taking a field trip to the nearest natural history museum. The museum is 62.5 miles from Lauren's school. The class plans to stop after 30 minutes, or 0.5 hours, to visit a local wildlife refuge. The bus driver plans to drive at an average speed of 50 miles per hour. How many hours will the second part of the trip take? Write your answer as a whole number or a decimal. hours

Considering only the values of ß for which sin ß tan ß sec ß cot ß is defined, which of the following expressions is equivalent to sin ß tan ß sec ß cot ß? Select the correct answer below: sec ß cot β tan β cot tan β tan ß csc ß sec ß

f(x) = 2x and g(x) = x + 3 Step 1 of 2: Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary. Answer (f + g)(x) = Domain=

Given that f(x) = x² + 2x and g(x) = x + 2, calculate (a) (fog)(-2)= (b) (gof)(-2)= Enter an integer or decimal number [more..]

-6z² +6z +140/ (z + 5)² (3z-5) Determine the correct partial fraction decomposition for the expression above. Provide your answer below:

Teresa wants to save $600 to buy a TV. She saves $17 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function. A (w)=600-17w Answer the following questions. (a) If Teresa still needs $277, how many weeks has she been saving? weeks (b) How much money does Teresa still need after 7 weeks?

The following exercise presents problems similar to exercises from the previous sections of this chapter. Use Newton's Method to approximate the solution. the point on the graph of f(x) = 8 - x² that is closest to the point (1, 0). (Round your answer to three decimal places.)

Fill in the blanks below in order to justify whether or not the mapping shown represents a function. The mapping diagram above a function since where there

A certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P(t) = (684)2^1/3, where t represents the number of years from the time of introduction. Step 1 of 2: What is the doubling-time for this population of fish?

Solve the following equation for B, where -π ≤ β < π. sec^2β-1/tan(-β) = -√3/3 Select the correct answer below: β = π/6 β = -π/6 β = -5π/6 and π/6 β = -π/6 and 5π/6

Let x represent the number of hours Trenton spends studying algebra, and let y represent the number of hours he spends studying history. For parts (a) - (e), write an inequality to represent the given statement. (a) Trenton has a total of at most 6 hr to study for both algebra and history combined. An inequality that represents this statement is

You have 80 yards of fencing to enclose a rectangular region. a) Write a function for the area of the rectangular region in terms of x. b) Find the dimensions of the rectangle that maximize the enclosed area. c) What is the maximum area?

A ball is thrown from a height of 160 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after t seconds is given by the following. h=160-12t-167² How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71. 0.1293 0.0228 0.4772 0.3707

Each year, Giselle plants and grows tomatoes in her backyard garden. Her plants typically produce a total of around 300 tomatoes during the season. However, each week approximately 4 tomatoes are not usable due to destruction by local wildlife. Write an equation to represent the average number of usable tomatoes, t, produced per week over the course of wweeks in the growing season. A. t = 300/w-4w B. t = 300/4w C. t= 300-4w/w D. t= 300+4w/w

Online photos: A poll surveyed 1802 internet users and found that 843, of them had posted a photo or video online. Can you conclude that less than half of internet users have posted photos or videos online? Use the a 0.05 level of significance and the critical value method. State the null and alternate hypotheses. Ho: H₁: The hypothesis test is

In the Bible, Joash was 7 years old when he became king; Uzziah was 16; Ahaz was 20; Manasseh was 12; Josiah was 8; and Jehoiachin was 18. What was the average age of these young men when they became kings of Judah? Write the remainder as a fraction. On the blank, write the answer in simplest form.

For f(x) = x² +4 and g(x)=√x-2, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. A. The domain of fog is {x}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of f o g is all real numbers. (b) (gof)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice.

Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not. D = Ga +3h³a