Math Questions

Using the formula A = ½bh for the area of a triangle where b is the base and h is the height, find the area of a triangle whose base is 12 units and whose height is 24 units. Enter only the numeric value with no letters or =.

For the polynomial function f(x) = .5x³ + .25x2 + .125x+ .0625, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept. x = .5, cross x = .5, touch x = -.5, touch x = -.5, cross

For the polynomial function f(x) = -0.02x4+.36x2 - 1.62, find all local and global extrema. No local extrema exist. The only extrema point is (-1.62, 0). The only extrema point is (9, 0). The local and global extrema are: (-3, 0), (0, -1.62) and (3, 0).

The number of bacteria in a certain sample Increases according to the following function, where y0 is the initial number present, and y is the number present at time t (in hours). y=y0e^0.05671 How many hours does it take for the size of the sample to double? Do not round any Intermediate computations, and round your answer to the nearest tenth.

Anthony owns a small business selling bagels. He knows that in the last week 3 customers paid cash, 33 customers used a debit card, and 34 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form.

Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin? 2x+y=-3 ? 3x-2y = 2 A. Multiply 1 by 2 and multiply by 3 B. Multiply 2 by 2 C. Multiply 1 by 2 D. Multiply 2 by 2 and multiply 1 by -2

Which is the contrapositive of the statement below? If you do your homework, then you will be prepared for the test. If you are prepared for the test, then you did your homework. If you are not prepared for the test,then you did not do your homework. If you do not do your homework, then you will not be prepared for the test. If you do your homework, then you will be prepared for the test.

Cost to store: $65 Markup: 25% 40% Sale Price Sale Price: $48 Selling Price: $81.25

A group of biologists is surveying the mice population in a forest. The equation n = 75.3¹ gives the total number of mice, n, t years since the survey began. Explain what the numbers 75 and 3 mean in this situation.

Tom is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 12 feet and its width is 10 feet. Suppose each bag of fertilizer covers 30 square feet. How many bags will he need to cover the garden?

Use Cramer's rule and the calculator provided to find the value of x that satisfies the system of linear equations. -4x-4y+5z=-2 -4x+2y+ 5z = -5 5x-3y-2z=1 Note that the ALEKS graphing calculator can be used to make computations easier.

A bag contains eleven balls labeled 1 through 11. One ball will be randomly picked. What is the probability of picking an even number? Write your answer as a fraction in simplest form.

There are 400 students in the senior class at Oak Creek High School. All of these students took the SAT. The distribution of their SAT scores is approximately normal. The number of students who scored within 2 standard deviations of the mean is approximately 1. 75 2. 95 3. 300 4. 380

You just bought a new car and need to expand your driveway by pouring more concrete. If the dimensions of the addition are 11 ft. by 6.5 ft., how many square feet of concrete do you need to pour? Your answer should be a number only. Do not round.

When Xochitl runs the 400 meter dash, her finishing times are normally distributed with a mean of 84 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of her finishing times in the 400 meter race.

The point P (1/2,8) lies on the curve y=4/x. If Q is the point, (x,4/x), find the slope of the secant line PQ for the following values of x. If x = 0.6, the slope of PQ is: 40/3 and if x = 0.51, the slope of PQ is: -18 and if x = 0.4, the slope of PQ is: -20 and if x = 0.49, the slope of PQ is: -18 Based on the above results, guess the slope of the tangent line to the curve at P(0.5, 8): -16

In a right triangle the two legs have measurements of 12 inches and 15 inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. 12.96 inches 5.2 inches 19.21 inches 340.00 inches 28.54 inches

Suppose that the functions and g are defined as follows. ƒ(x)= 5/x+1 g(x)=6/x Find f/g. Then, give its domain using an interval or union of intervals. Simplify your answers.

You buy a tarp to cover the driveway when it snows. The dimensions of your driveway are 10 ft. by 15 ft. If the tarp covers your entire driveway, how many square feet are covered? Your answer should be a number only.

Juan is going to watch a movie in his collection. He has 7 action movies, 12 comedies, and 2 dramas. He will randomly select one movie. What is the probability that the movie he selects is not an action movie? Write your answer as a fraction in simplest form.

Use the Factor Theorem to determine whether x-2 is a factor of P(x) = -2x³ + 3x²-3x+10. Specifically, evaluate P at the proper value, and then determine whether x-2 is a factor.

Consider the following quadratic function. g(x)=2x²-16x+37 (a) Write the equation in the form g (x)= a (x-h)²+k. Then give the vertex of its graph. Writing in the form specified: g(x) = Vertex: (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the ver vertex. Then click on the graph-a-function button.

Find the difference quotient f(x+h)-f(x)/h, where h≠0, for the function below. f(x) = 3x² - 4

Differentiate the following function. f(x)=3+2x+3 ex

Complete the statement: If two polygons are similar, then their corresponding (1)__ are congruent and their corresponding__(2)____ are proportional. 1) Sides; 2) Areas 1) Angles; 2) Areas 1) Angles; 2) Sides 1) Sides; 2) Angles

Given that sinθ= 35/37 and cosθ <0, determine the values of the sine and cosine functions for 2θ sin2θ = (Type an integer or a simplified fraction.)

The Eiffel Tower, shown to the right, has a width of 328 feet and a height of 984 feet. Maria is designing a T- shirt for her trip to France and she wants to put a picture of the Eiffel tower on the front of the shirt. The maximum space she can use on the shirt is a rectangle with a width of .75 feet and a height of 1.5 feet. Maria uses a sclale factor of 1/k where k is an integer, to shrink the Eiffel Tower and fit it on the t-shirt. What is smallest possible value for k?

Let (-4,-3) be a point on the terminal side of θ. Find the exact values of cos θ, sec θ, and cot θ.

Let θ be an angle such that csc0= 7/4 and tanθ <0. Find the exact values of cotθ and cosθ.

A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?

Consider the following quadratic function. f(x)= 3x² +6x-1 (a) Write the equation in the form f(x)= a (x-h)²+ k. Then give the vertex of its graph. Writing in the form specified: f(x) = Vertex: (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

You have a circular mirror in your house that desperately needs cleaning. The diameter of the mirror is 3 feet. How many square feet of the mirror will need cleaning?

Kuro has a stack of 15 coins on a table with a volume of 8 cubic centimeters. He has stacked them perfectly straight creating a cylindrical shape. He accidentally bumps the table, causing the coins to shift to a leaning position; but are still stacked. What would be the best estimate of the volume of the stack once it has been bumped/shifted? The volume cannot be calculated 8 cubic centimeters 9 cubic centimeters 7 cubic centimeters

The average cost per DVD, in dollars, for a company to produce x DVDs on exercising is given by the formula A = 8x + 300/x, where A is the average cost per DVD and x is the number of DVDs produced. Complete parts a through c. a. Find the cost for producing 1 DVD. The average cost for producing 1 DVD is $ 308 (Simplify your answer.) b. Find the average cost per DVD for producing The average cost for producing 100 DVDs is $ 100 DVDs. (Simplify your answer.)

Using interval notation, identify the domain for the function: f(x)=2x+1/ x-4 (-∞,∞) (-∞,4)U(4,∞) (-∞,-4)U(4,∞) (-∞,2)U(2,∞)

Find the exact value of arctan (tan5π/6) Write your answer in radians in terms of π.

Given Z1 = 3+0i and 22 = -1- 2i, calculate the product z1z2 and express all three complex numbers in polar form, rounding all angles to the nearest degree in the interval 0° 0 < 360°. Express all moduli in simplest radical form.

If a right triangle has two legs which have measurements of 12 inches and 14 inches, the length of the hypotenuse is inches. Use the Pythagorean theorem to calculate the length of the hypotenuse. Round answer to the nearest one hundredth.

A circular spinner is divided into 4 regions and the regions are colored blue, red, yellow, and green. Each region occupies a fourth of the circle. Suppose you decide to play a "game" with your friend. If he spins and it lands on green, you will give him $5. If he spins and it lands on any other color, he has to give you $3. What is the mathematical expectation for this game? Should your friend play with you? Your friend should play because on average he will win $1 each time he plays. Your friend should NOT play because on average he will lose $4 each time he plays. Your friend should NOT play because on average he will lose $1 each time he plays. I have no idea. When did we ever learn this?

A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 119 pounds requires 136 milligrams of medicine. What is the weight of a patient who requires 200 milligrams of medicine?

A company makes steel rods shaped like cylinders. Each rod has a diameter of 6 centimeters and a height of 20 centimeters. If the company used 45,781.2 cm of steel, how many rods did it make? Use 3.14 for π, and do not round your answer.

Find the exact value of sin (sin(-π/6) Write your answer in radians in terms of π.

Find the difference quotient f(x+h)-f(x)/h where h≠0, for the function below. f(x)=5x²-6x-7 Simplify your answer as much as possible.

California's growth rate in 2013 was 0.9%. There were roughly 38 million people living in California that year. Assuming the growth rate is stable, which equation models the population P, in millions, t years after 2013?

A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee? 116 sq ft 58 sq ft 89 sq ft 58 sq ft

Find the difference quotient f(x+h)-f(x)/h f(x)=1/x+6 Simplify your answer as much as possible.

The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the team's goals scored per game? Choose the correct answer below. A. The team scored fewer goals per game than 75% of the teams in the league. B. The team scored fewer goals per game than 25% of the teams in the league. C. The team scored fewer goals per game than 50% of the teams in the league. D. The team scored fewer goals per game than 100% of the teams in the league.

In triangle ABC, AC = 6, AB = 7, and BC = 5. Which is true? The measure of ∠C is the least of the three angles. The measure of ∠B is the greatest of the three angles. The measure of ∠B is the least of the three angles. The measure of ∠C is the greatest of the three angles.

Use a calculator and evaluate A to the nearest cent. A=$15,000 e 0.04t for t=2, 7, and 10 Ift=2, A-$

Ms. Pullara and Ms. Chng are both looking at the top of the school in the distance in the same line of sight, although Ms. Chng is 100 m ahead of Ms. Pullara. Ms. Pullara observes the school at an angle of 18 with the ground. If the top of the tower is 400 m from Ms. Chng, what is Ms. Chng's angle of sight with the ground? First make a sketch and then solve the problem to the nearest degree. /5