Math Questions

Find the area of a regular octagon circumscribed about a circle with radius of 6 inches. Hint: Draw a diagram. Round the final answer to the nearest hundredth.

University of Tennessee Volunteers women's basketball team. She has injured her ankle, and it is doubtful that she will be able to play in an upcoming game/If Candace can play the coach estimates that the Volunteers will score 78 points. If she is unable to play, the coach estimates that the team will Score 62 points. The team doctor estimates there is a 50% chance Candace will play. Determine the number of points the team can expect to score.

Suppose y = sin²x + 2sinx. Find dy/dx. Answer:

The population of Suffolk County in Massachusetts decreased from 663,906 in 1990 to 641,695 in 1999. b. Use your equation to predict the population of Suffolk County in 2020.

You conduct a statistical test of hypotheses and find that your data are statistically significant at a = 0.05. In other words, your P-value is equal to or smaller than 0.05. Does it imply that your data are also statistically significant at α = = 0.01? a. Yes b. No c. Cannot be determined

Evaluate (if possible) the six trigonometric functions of the real number t. (If an answer is undefined, enter UNDEFINED.) t = 7π/4

Camila invested $9,100 in an account paying an interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?

A friend lends you $175 for a week, which you agree to repay with 4.8% one-time interest. How much will you have to repay, including the amount you borrowed? Round your answer to two decimal places if necessary. $

Evaluate (if possible) the sine, cosine, and tangent at the real number t. (If an answer is undefined, enter UNDEFINED.) t=-11π/6

a. How many teams of six can be chosen out of 54 people? i. What type of problem? ii. Solve b. Out of 54 people how many ways are there to nominate a President and Vice President for the group i. What type of problem? ii.Solve

According to statistics, a person will devote 34 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 22. Over the lifetime, how many years will the person spend on each of these activities?

After a 70% reduction, you purchase a new clothes dryer on sale for $150. What was the original price of the clothes dryer? The original price was $

Compute the critical value Za/2 that corresponds to a 85% level of confidence. Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (Round to two decimal places as needed.)

Stephen opens a savings account with an initial deposit of $300. Every month, Stephen will deposit an additional $250 into the account from his paycheck. Which function below shows the total amount of his deposits for x number of months? y=12x+550 y=x(300+250) y = 250x + 300 y = 300x + 250

A support wire for a telephone pole makes an angle of elevation of 65° with the ground. If the bottom of the wire is 18 ft from the pole, how tall is the pole? (Round your answer to the nearest thousandth)

Which function represents a parabola that is translated 2 units to the left and 6 units down from the function f(x) = x²? A f(x) = 7(x + 2)²-6 B f(x) = 8(x - 2)²-6 C f(x) = 4(x-2)(x-6) D f(x)=3(x+2)(x-6)

Solve the equation using the quadratic formula. x² +10x+21=0

Which of the following is a possible description for the function below? y=2x+15 The function represents the tax on a pizza order if the tax is 2% of every $15 pizza, x, that is ordered. The function represents the total cost of a pizza if the sales tax, x, is 2 times the cost of a $15 pizza. The function represents the cost of each additional topping on a pizza if the pizza is $15 plus 2% sales tax, X. The function represents the total price of a pizza which is $15 plus $2 for each additional topping, X.

Two secondary fuel tanks are needed, one within each wing. The space available in each wing is 4' 7" by 3' 2", by 10". How many total gallons of fuel could be added to the aircraft? 90.48 gal. 180.95 gal. 68.5 gal.

A student has an average (arithmetic mean) score of 88 for the first 3 tests in a class. What is the lowest score the student can earn on the fourth test to have an average score of at least 90 for the 4 tests?

A grocery store manager notices that this month her store sold a total of 849 gallons of ice cream, which represents a decrease of 17% from last month. How much ice cream did the store sell last month?

The half-life of the radioactive element unobtanium-53 is 10 seconds. If 32 grams of unobtanium-53 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds? The amount left after 10 seconds is The amount left after 20 seconds is The amount left after 30 seconds is The amount left after 40 seconds is The amount left after 50 seconds is

The selling price of a refrigerator, is $601.65. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?

Suppose that W = span{V₁, V2, V3} where each v; is in R³. Consider the following statements. (i) If x is in W then x = C₁V₁1 + C2V2 + C3V3 for some scalars C1, C2, C3. (ii) 3v₁ - 2v2 is in W. (iii) W is a subspace of R³. Which of the above statements are always true? (a) (i) only (b) (ii) only (c) (ii) and (iii) only (d) (i) and (ii) only (e) (i), (ii), and (iii)

A manufacturer of face masks found out that the marginal revenue function is r(q) = 0.059q + 47.79 while the marginal cost function is c(q) = 0.0118q² - 1.18g + 59 where is the quantity of masks in thousands. Find the area between these two curves and the y-axis. Round your answer to 2 decimal(s).

I can find common factors and multiples. D Jerrie practices the piano every three days, and practices the trumpet every four days. Jerrie practices both the piano and the trumpet on May ST. When is the next day Jerrie will practice both Instruments at the same time?

Consider the function f(x)=2x² - 6x² 90x+6 on the interval -4,9] Find the average or mean slope of the function on this interval By the Mean Value Theorem, we know there exists at least one e in the open interval (-4,9) such that f'(e) is equal to this mean slope Find all values of e that work and list them (separated by commas) in the box below. If there are no values of c that work, enter None List of numbers

Imagine you are building a staircase with cubes. To build a staircase with one step, one cube is needed. To build a staircase with two steps, three cubes are needed. To build a staircase with three steps, six cubes are needed. Continue this pattern and determine how many cubes are needed to build a staircase with 50 steps, 250 steps, and x steps.

A wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

Let u = (0, -2, 2) and v= (1,3,-1). Which of the following vectors are in span {u, v}? (i) (1,-1,2) (ii) (1, 1, 1) (iii) (5, 3, 7) (a) all of them (b) (ii) only (c) (iii) only (d) (i) and (iii) only (e) (ii) and (iii) only

Fireman Bob leans a 40 foot ladder against a building at an angle of elevation of 70°. How far is the base of the ladder from the building (round your answer to the nearest thousandth)? Distance from base of the building = ft

A pair of dice is rolled. What is the probability that the sum is 3, given that the sum is odd? Write a fraction in simplest form For example, 12/17

The element plutonium-239 is highly radioactive. Nuclear reactors can produce and also use this element. The heat that plutonium-239 emits has helped to power equipment on the moon. If the half-life of plutonium-239 is 24,360 years, what is the value of k for this element?

The results of a statewide exam for assessing the mathematics skills of realtors were normally distributed with a mean score of 72 and a standard deviation of 12. The realtors who scored in the top 10% are to receive a special certificate. What score does a realtor need in order to receive a certificate?

The sides of a triangle are 12 inches, 15 inches, and 8 inches. Does the triangle contain a right angle? No, the sides of 8 inches and 12 inches do not add up to 15 inches. No, the sides of 8 inches and 12 inches squared and added together does not equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches squared and added together equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches are less than 15 inches.

A bacterial culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour there were 400 bacteria. When will the population reach 1000?

The members of a youth football program are required to sell tickets to chicken dinners for the program's fundraiser. They can sell adult tickets for $10 and child tickets for $5. Each athlete must bring in at least $350 from the ticket sales. a. Write an expression to represent the total amount of money an athlete makes from ticket sales. Let x represent the number of adult tickets sold and let y represent the number of child tickets sold. b. Write an inequality in two variables to represent the amount an athlete must make. c. Graph the inequality from part (b). d. Use the graph to determine whether an athlete will bring in at least $350 if they sell 10 adult tickets and 30 child tickets. Explain your reasoning.

Dave bought a new car 8 years ago for $8400 to buy a new car comparably equipped new would cost $12,500. Assuming a steady rate of increase, what was the yearly rate of inflation in car prices over the 8-year period?

A wheelchair ramp is 24 ft long and connects with a building 4 ft above the ground. What is the angle of elevation of the ramp? Round your answer to the nearest WHOLE degree. Angle of elevation =

What factors must be taken into account in order to form a meaningful conclusion? Randomization Replication and treatments Controlling variables, randomization, and replication and treatments Controlling variables

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of Information does he need to determine the confidence interval? A. the critical value B. the standard deviation C. the number of favorable responses D. the standard error of the mean

Emma's Pet Shop sells aquariums in the shape of a right rectangular prism. Each aquarium measures 50 inches long, 20 inches wide, and 30 inches tall. The recommended density of each aquarium is no greater than 0.002 fish per cubic inch. Based on the recommendation, what is the greatest number of fish that should be in one aquarium? 15 fish 60 fish 600 fish 15,000,000 fish

Find the equation of the plane containing the point P(3, 0, -1) and the line (x, y, z) = (2, 1, 3) + t(3, -1, -2). (a) 2x 6y + 2z = 4 (d) 3x - 17y + 5z = 4 (b) x + 5y-z = 4 (c) x+6y-z = 4 (e) 16y - 4z = 4

Fill in the type of market that matches each feature mentioned below. Feature Firm sets market price depending on other firm's market price. Firms with zero ability to affect price. A product with no close substitutes.

A wire is tied from the top of a telephone pole to a stake in the ground. If the stake is 12 ft from the bottom of the pole and the wire makes a 78° angle with the ground, how long is the wire? Round your answer to the nearest tenth.

AIR PURIFICATION To test air purifiers, engineers ran a purifier in a smoke-filled 10-ft X 20-ft room. While con- ducting a test for a certain brand of air purifier, they determined that the amount of smoke in the room was decreasing at the rate of R(t) = 0.00032t4 -0.01872t³ + 0.39481² - 3.83t+ 17.63 (0 ≤t≤20) percent of the (original) amount of the smoke per minute, t min after the start of the test. How much smoke was left in the room 5 min after the start of the test? 10 min after the start of the test?

Convert the complex number -9 + Oi into polar form. Express the angle using degrees over the interval 0° ≤0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

A management consultant estimates that the number h of hours per day that employees will work and their daily pay of p dollars are related by the equation 90h5 + 18,000,000 = p³. Find dh/ dp at p = 300 and interpret your answer.

In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables? Choose the correct answer below. A. The correlation between variables must be significant. B. The correlation between variables must be a y-value of a point on the graph. C. The correlation between variables must be greater than zero. D. The correlation between variables must be an x-value of a point on the graph.

We wish to test the claim that u > 32 at a level of significance of a = 0.05. The sample statistics are n = 50, and x-bar = 32.3. Moreover, it is known that the population standard deviation is a = 12. Compute the test statistic, rounded to two decimal places. 2.31 3.11 1.77 0.98