Math Questions

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 32 cubic cm. Determine the dimensions of the box that will minimize the surface area, where x is the length of each side of the base and y is the height of the box.

Solve by completing the square. 3z² + 30z - 33 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. Z or z =

Suppose we assume Google Maps is accurate 99.7% of the time. We then track the next 1000 trips we take using Google Maps and record the accuracy. What will be the shape of the sampling distribution of the sample proportion? Not approximately Normal skewed left normal skewed right

A sporting event held at a high school had 135 attendees. The event earned a total of $930. Admission to the event was $10 for adults and $4 for students. How many adults (a) and how many students (s) attended? a + s = 135 10a + 4s $930

Solve the equation x + 5.5 = 24. 29.5 20.5 18.5

A plane flew for 4 hours heading south and for 6 hours heading east. If the total distance traveled was 3,370 miles, and the plane traveled 45 miles per hour faster heading south, at what speed was the plane traveling east? (Do not include the units in your response.)

A certain drug dosage calls for 9 mg per kg per day and is divided into two doses (1 every 12 hours). If a person weighs 237 pounds, how many milligrams of the drug should he receive every 12 hours? (Round your answer to the nearest whole milligram.)

The gas tank of a 2010 Ford Focus holds 13.5 gallons. How many pounds of carbon dioxide are produced by burning an entire tank of gas? Express your answer rounded to the nearest tenth of a pound. lb of CO₂

If you use your portable stereo 35 hours per week, and do not unplug it when it is not in use, how much carbon dioxide is produced from the vampire energy used by the portable stereo in one year ? help (energyvampires) Express your answer rounded to the nearest tenth of a pound of carbon dioxide. lb of CO₂

An Air Conditioner uses 1200 Watts of electricity and local emissions from electricity produce 1.37 pounds of CO2 per kWh. If you run the AC for 2 less hours, how many pounds of CO2 would you keep from entering the atmosphere? 0.822 1.644 3.288 1.752

Graph the following function. y=-1-5 cos 4x

On the day their son, Peter, was born, Madeline and Ben invested $1500 for his education at 6.7% interest, compounded quarterly. Today is Peter's birthday. He is 19 years old and wants to go to college. a) Circle the four important pieces of information in the question. b) Use a TMV Solver to determine the value of the investment today. Fill in the box on the right. c) How much interest did the investment earn? d) How much interest would the investment have earned in a savings account that paid 0.7% interest per year, compounded yearly? N 1% PV PMT FV P/Y C/Y PMT: END BEGIN

What are the domain and range of the cosine function? Domain: All Real Numbers Range: (-1,1) Domain: All Real Numbers Range: [-1,1] Domain: [-1,1] Range: All Real Numbers O Domain: All Real Numbers where ... -, 0, ... Range: [-1,1]

A grocer needs to mix raisins at $2.00 per pound with granola at $3.25 per pound to obtain 10 pounds of a mixture that costs $2.50 per pound. How many pounds of raisins and how many pounds of granola must be used? (5 points)

What critical value of z or z* should be used in an 85% confidence interval? 1.645 1.282 1.960 1.440

Scores on an exam are distributed normally with a mean of 72.3 and a standard deviation of 8.9. If 200 students take the exam, how many students would be expected to score higher that 72.3? 100 72.3 200 150

A class has 20 students. What is the probability that at least 5 students were born on a weekend? 82% 1.4% 45% 72% 20 pts

A researcher wants a 68 ounce saline solution with a concentration of 6%. She has concentrations of 3% and 15%. How much of each solution must she use to get the desired concentration? Select the correct answer below: 51 ounces of 3% solution and 17 ounces of 15% solution 49 ounces of 3% solution and 19 ounces of 15% solution 16 ounces of 3% solution and 52 ounces of 15% solution 52 ounces of 3% solution and 16 ounces of 15% solution 19 ounces of 3% solution and 49 ounces of 15% solution 17 ounces of 3% solution and 51 ounces of 15% solution

An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed? Select the correct answer below: Speed in still air: 270 mph; Speed of the wind: 30 mph. Speed in still air: 280 mph; Speed of the wind: 40 mph. Speed in still air: 290 mph; Speed of the wind: 50 mph. Speed in still air: 300 mph; Speed of the wind: 60 mph.

In a physiology class, a student mist dissect three different specimens. The student can select one of nine earthworms, one of four frogs, and one of seven fetal pigs. In how many ways can the student select the specimen?

Determine the solution to the system of equations below. 5x+6y=-44 -7x-7y= 49 Select the correct answer below: (2,-9) (8,-14) no solutions infinitely many solutions

Solve by completing the square. -3f² + 18f = -33 Write your answers as integers, proper or improper fractions in simplest form, or decimal rounded to the nearest hundredth. f = or f =

In 2010, the state of Nevada had two area codes. The first three are the area code and the next seven are the local telephone number. (Note that at this time, a local telephone number cannot begin with 0 or 1) How many telephone numbers could Nevada's phone system have accomodated?

The graph to the right is obtained from the graph of g(x)=√x by applying several transformations. Describe the transformations and give the equation of the graph. A. Translate g(x) unit(s) down. (Type a whole number.) B. Translate g(x) 2 unit(s) up. (Type a whole number.) C. No vertical translation is needed. Give the equation of the graph. (Type an equation.)

On Monday, Ms. Liu asked the students how many Harry Potter books they have read in the last month and recorded the information in a dot plot. On Tuesday a new student switched from Launch Ed to F2F and Ms. Liu added his information to the dot plot. Based on the dot plots above, select whether the value of each statistic for the number of books read, listed below, is greater for Monday's class, equal for both days, or greater for Tuesday's class. Median Standard Deviation Mean

Identify the relevant information given to you in the application problem below. Use that information to answer the questions that follow on Practical Domain and Practical Range. Round your answers to two decimal places as needed. A local window washing company charges $9.38 for each window plus a reservation fee of $11. They wash a maximum of 19 windows. Also, they have the policy that once a reservation is made, if you cancel, the reservation fee is non-refundable. Let C represent the total cost from the window washing company and x represent the number of windows washed Identify the practical domain of this function by filling in the blanks below. Practical Domain: Identify the practical range of this function by filling in the blanks below. Do not include the dollar sign in your answers. Practical Range:

A basketball team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $10, deluxe for $3, and regular for $2. The total number of tickets sold was 276, and the total amount of money from raffle tickets was $855. If 90 more regular tickets were sold than deluxe tickets, how many premium tickets were sold? Provide your answer below:

Does the ordered pair (-6, 6, 1) satisfy the following system of equations? -3x - 5y + 2z = -10 x + 2y - 5z = 1 x-3y - 4z = -28 Select the correct answer below: Yes No

In 1955, Life Magazine reported that the 25-year- old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?

Use the following scenario for questions 1-4. Suppose it is estimated that 14% of American women are currently on a diet. A researcher would like to test this claim, so he sets up a simple random survey. He asks 200 women if they are on a diet and 39 said yes. Conduct a one-proportion z test to determine if the percent of women on diets is not 14% Using a significance level of 5%, what conclusion can we make? Accept the alternative hypothesis not enough information Fail to reject the null hypothesis Reject the null hypothesis

Graph the given ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and foci in the figure. (x-1)²/4 + (y + 1)²/9 =1 The center of the ellipse is (1,-1). (Type an ordered pair.) The vertices are . (Type ordered pairs. Use a comma to separate answers as needed.)

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of x, to the nearest tenth of a percent. y = 600(0.71) x/8

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. A = 41°, B = 36°, c = 3.6 O Law of Sines O Law of Cosines Solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.) C= a= b=

Internet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z - u = 3(x - y) + 28 x + y = 44+ z + u and x - y + z- u = 52. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo Google

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given. Student A Step 1: Step 2: cos X sin x Step 5: 1 cos x sin x Step 4: cos²x Step 3: cosx+sin² cos x sin x cos x sinx COS X sinx 11: = cot x + tan x cotx + tan x X cot x + tan x sin² x cos x sin x sin x COS X 11 cotx + tan x Student B Step 6: cot x + tan x = cot x + tan x Step 1: secxcsc x = Step 2: secxcscx = cotx + tanx Step 4: secxcscx = Step 3: secxcsc x = cos x sin x Step 5: secxcsc x = sinx cos x cos²x cosxsin x cos²x+sin² x cos x sin x 1 cos x sinx sin² x cos xsin x (x)(sinx) Step 6: sec x csc X = sec x csc X Part A: Did either student verify the identity properly? Explain why or why not. (10 points) Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 poin

Solve by completing the square. h² + 4h = 29 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. h or h=

In Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct Pennsylvania license plate numbers can be formed?

Which property is used to simplify 4/5y + 3(2/5x + 7/5y) to 5y + 6/5x? Distributive property Associative property of multiplication Associative property of addition

3. Match the expression to it's completely factored form. 1. x²-1 2. 25x² - 49 3. 9x² + 6x +1 4. 9x² - 1 5. x² - 2x + 1 6. 25x² - 70x+49 a. (x-1)² b. (x + 1)(x-1) c. (3x + 1)² d. (5x+7)(5x-7) e. (5x - 7)2 f. (3x + 1)(3x - 1)

Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive integer coefficient. Polynomial of lowest degree with lowest possible integer coefficients and zeros of 3i and 5-3i.

Write the equation in standard form for the circle that has a diameter with endpoints (1, 0) and (-1,0). (0)

How many three digit numbers can be formed under each condition? a) The leading digit cannot be 0. b) The leading digit cannot be 0 and no repetition of digits is allowed. c) The leading digit cannot be 0 and the number must be a multiple of 5.

Aileen Uzin runs a retail store. Her net sales for the year were $162,000. The cost of the merchandise that she sold was $118,500. Her operating expenses were $28,920. Her net income was what percent of the net sales for the year?

State the p-value. 0.02 .195 2.14 0.04

The function f(t) = 290(0.95)t/24 represents the change in a quantity over t days. What does the constant 0.95 reveal about the rate of change of the quantity? The function is_____% exponentially at a rate of _____% every______

A population of values has an unknown distribution with µ= 202.4 and σ = 11.5. You intend to draw a random sample of size n=144. What is the mean of the distribution of sample means? (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? (Please report your answer accurate to 2 decimal places.)

One hundred rats were exposed to high levels of e-cigarette smoke and were then put through a simple maze. They could make a choice between going left and going right. An SRS of 100 rats was chosen to be part of the experiment.. Eighty of the 100 rats went right when running through the maze. All conditions for inference have been met, Construct a 90% confidence interval for the proportion of rats that run right when going through the maze the first time. (0.722, 0.878) (0.734, 0.736) (0.71, 0.89) (0.76, 0.84)

A hollow glass cone is filled with perfume and placed inside of a hollow cylindrical container with the same height and diameter as the cone. The cylinder will then be filled with packing material. If the cone occupies 60 cm³ of space, how many cubic centimeters of packing material will be needed? A, 60 B. 30 C. 120 D 180

Why type of symmetry does the cosine function have? Cosine is an odd function, meaning it has rotational symmetry about the origin. Cosine is an even function, meaning it has symmetry with respect to the y axis. Cosine is an odd function, meaning it has symmetry with respect to the y axis. Cosine is an even function, meaning it has rotational symmetry about the origin.

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim?