Math Questions

For each arithmetic series described below, write the series and calculate its sum. If it is not possible, explain why not. a. You know that the first term is 18, the last term is 72, and the common difference is 4.5. What is the series? What is the sum? b. You know that the series has nine terms and the last term is 18. What is the series? What is the sum? c. You know that the third term of an 18-term series is 29 and the terms are increasing by 10. What is the series? What is the sum?

Adelaide wants to buy a new generator. The generator costs $2750. Adelaide decides to finance the generator for 36 months at an APR of 11.5%. Determine Adelaide's monthly payment. Round your answer to the nearest cent, if necessary.

A ball is thrown vertically upward from the top of a building 144 feet tall with an initial velocity of 128 feet per second. The distances (in feet) of the ball from the ground after t seconds is s = 144 +128t- 16t2. After how many seconds does the ball strike the ground? 8 sec 145 sec 9 sec 11 sec

Jose will run at most 32 miles this week. So far, he has run 18 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.

Suppose you want to purchase a house. Your take-home pay is $2630 per month, and you wish to stay within the recommended guidelines for mortgage amounts by only spending 1/4 of your take-home pay on a house payment. You have $15,300 saved for a down payment and you can get an APR from your bank of 3.7 %, compounded monthly. What is the total cost of a house you could afford with a 30-year mortgage? Round your answer to the nearest cent, if necessary.

Two search teams spot a stranded climber between them on a mountain. The first team is 0.6 miles from the second team, and both teams are at an altitude of 0.2 miles. The angle of elevation from the first team to the stranded climber is 16 °. The angle of elevation from the second team to the climber is 24°. What is the altitude of the climber? Round to the nearest hundredth of a mile. miles

If you leave a 100°C pot of tea at room temperature (25°C) and an identical pot in the refrigerator (5°C), with k=0.02, the tea in the refrigerator reaches a drinkable temperature (70°C) more than minutes before the tea at room temperature. True False

For q (x) = -4x2+4x-1 / x²+2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote(s). Separate multiple equations of asymptotes with commas as necessary. Select "None" if applicable. The graph has no horizontal asymptotes. The graph has at least one horizontal asymptote. Equation(s) of the horizontal asymptote(s): Crossover point(s):

Let f(x) =5x+2 / x - 5 1) The domain of f(x) in interval notation is 2) The y intercept is the point 3) The x intercept(s) is/are the point(s) 4) The vertical asymptote is 5) The horizontal asymptote is

Suppose that $15,000 is deposited for seven years at 5% APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent.

In the mathematical system of clock 12 arithmetic, under the operation of addition the set of elements is {1,12}. {12}. {1,2,3,4,5,6,7,8,9,10,11,12}. {0,1,2,3,4,5,6,7,8,9,10,11}.

The formula v = √2.6r models the maximum safe speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature r, in feet. A highway crew measures the radius of curvature at an exit ramp on a highway as 670 feet. What is the maximum safe speed? For this problem, round your answer DOWN to the nearest whole number. (Think: Why is this type of rounding appropriate for this scenario?) max safe speed=

The diameter of a standard basketball is 9.5 inches. If the basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four basketballs?

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 29-foot ramp, to the nearest tenth of a degree, if its final height is 7 feet. The ramp's angle of elevation is (Round the answer to the nearest tenth of a degree.)

Joshua is going to invest $680 and leave it in an account for 19 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Joshua to end up with $1,680?

Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $6.00 per month charge along with a charge of $0.05 per text. Plan B: No per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.

Use the simplex method to maximize the following: Maximize f = 7x1 + 9x2 subject to 4x1 +5x2 ≤ 15 5x1 + 4x2 ≤ 32 4x1+5x2 ≤ 30 x1 ≥ 0, x2 ≥ 0 If no solutions exist enter DNE in all answerboxes. x1 = x2 = f =

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value. At a boating and sports store, the cost of renting a personal watercraft is $47.70 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax. The equation is The cost of a half hour rental is $45 per half hour. (Type an equation using x as the variable.)

Jen collects toy sports cars. She has 784 red cars and 224 black cars. She wants to line up the cars in groups so that each group has the same number of cars and contains only red cars or only black cars. What is the largest number of cars that she can have in a group? The largest number of cars that Jen can have in a group is. (Simplify your answer. Type an integer.)

You are working with the following quadratic function: y = x² - 2x - 8 a) Write the quadratic in factored form: y= b) Complete the square to write the quadratic in vertex form: y = Identify the vertex of the parabola: Remember that the vertex is a point! Identify the y-intercept of the parabola: Remember that the y-intercept is a point! Identify the x-intercepts: and Remember that the x-intercepts represent points on the graph!

A publishing company sold 26,265,591 books last year. Round the number of books sold to the nearest ten million. A. 30,000,000 B. 26,000,000 C. 20,000,000 D. 26,270,000

The intelligence of the clones of Jango Fett are deteriorating at a rate that has a standard distribution. If the average I.Q of a clone is 90 with a standard diviation of 2.6, what percent of the clones are smarter than a clone with an I.Q of 85? (round to the nearest hundredth.) % are smarter than a clone with an I.Q of 85.

The power of Darth Vader using the force can lift a speeder 14m off the ground with a thought. The average Sith can lift a speeder 10 meters with a standard deviation of 1.2. This data fits a standard distribution. What is Vader's z-score? (Round to the nearest 10th.) Z= type your answer...

Give the associative property of addition and illustrate the property with an example. Choose the correct answer below. A. For any elements a and b, a+b=b+a. An example of this is 4+7=7+4. B. For any element a, a +(-a)= -a+a=0. An example of this is 2+(-2)=-2+2=0. C. For any element a, a +0=0+a=a. An example of this is 8+0=0+8=8. D. For any elements a, b, and c, (a+b)+c= a + (b+c). An example of this is (3+2)+6=3+(2+6).

A rectangular kitchen has an area of 160 square feet. The length is 12 feet more than the width. a. Write an equation that represents the area of the kitchen. b. Find the dimensions of the kitchen by completing the square.

Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20 year period. Recall that r is the monthly rate. Show your work and carefully evaluate the above formula for m.

There are 30 students in a high school senior class. In how many ways could the yearbook choose the winners of Most Athletic, Class Clown, and Best School Spirit?

The population is decreasing at a rate of 4 % per year. If the population is 28,000 today, what will the population be in 12 years? Round your answer to the nearest whole number, if necessary.

Consider the parabola given by the equation: f(x) = 4x² – 10x-4 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas:

A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 121 feet long and makes an angle of 62° with the ground. The other rope is 115 feet long. What is the distance between the points on the ground at which the two ropes are anchored (just give one of the answers rounded to the nearest whole number)?

Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?

The HMS Sasquatch leaves port on a bearing of N29°E and travels for 7 miles. It then changes course and follows a heading of S31°E for 4 miles. How far is it from port? Round your answer to the nearest hundredth of a mile. What is its bearing to port? Round your angle to the nearest degree. Distance = miles Bearing with angle rounded to the nearest degree is ?

Given the vector u equal to 5 (cos 255°, sin 255°) and vector v equal to 7 (cos 150°, sin 150°), find the sum u + v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0° ≤0 < 360°.

The Marvel Costume Design Workshop employs 65 people. Eight of the 30 men and 21 of the 35 women work in the business office. What is the probability that an employee picked at random is a woman or works in the business office? A. 64/65 B. 21/65 C. 43/65 D. 10/13 E. 51/65

Consider the curve: y = 1-csc(2 (x-π)) (a) State the period of this curve. (b) State the phase shift of this curve, and whether it is to the right or to the left. (c) Sketch a sequence of 5 small separate graphs carefully labeled over a single period starting with y = sin(x) for x ∈[0,2π], moving one change at a time through 3 intermediate curves, and ending with the curve above, as we have done in class.

Brenda cuts her grass every 10 days and trims her shrubs every 24 days. If Brenda cut her grass and trimmed her shrubs on June 1, how many days will it be before she cuts her grass and trims her shrubs on the same day again? It will be days before Brenda cuts her grass and trims her shrubs on the same day again.

This question is not about solving the stated problem, but about understanding it. A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t) = 4.9t² + 1300t + 170. a) From what height was the rocket launched? b) What is the maximum height the rocket reaches? c) If the rocket will splash down in the ocean, when will it splash down?

The sales in thousands of a new type of product are given by S(t)=180-50 e -0.3t, where t represents time in years. Find the rate of change of sales at the time when t=3. Round to the nearest tenth. A. 6.1 thousand per year B.-36.9 thousand per year C.-6.1 thousand per year D. 36.9 thousand per year

Juan is going to invest $1,700 and leave it in an account for 14 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Juan to end up with $3,700?

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 4x-x². What rainfall produces the maximum number of mosquitoes? A. 16 inches B. 0 inches C. 2 inches D. Maximum number of mosquitoes does not exist E. 4 inches

Suppose the supply and demand for a certain DVD are given by p=1/6 q2 and p = -1/6q2+44, respectively, where p is price and q is quantity. Find the equilibrium price. A. $26 B. The supply and demand curves do not intersect. C. $24 D. $21 E. $22

Alexa invested $54,000 in an account paying an interest rate of 4% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $106,200?

Find the probability of the given event. A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. A randomly drawn marble is not blue. A. 6 B. None of these C. 1/2 D. 3/2 E. 1/3

Find the mean of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary. 22, 29, 30, 35, 18, 30, 31, 24, 28, 25, 25

At the beginning of an experiment, a scientist has 180 grams of radioactive goo. After 255 minutes, her sample has decayed to 5.625 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t)= How many grams of goo will remain after 17 minutes?

If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 66- x/36. How many bolts must be sold to maximize revenue? A. 1,188 bolts B. 2,376 bolts C. 1,188 thousand bolts D. 2,376 thousand bolts

Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?

If g(x) = 1/3 x3 + 2 1/4x²-5x and h(x) = 1 2/3x3 -3/4x2-3x then g(x) + h(x) = A) 11/3x3+3x²-2x B) 1 1/3x3-3x²-8x C) 2׳ +1 1/2x²-8x D) 2x³ + 1 3/4x² - 2x

The height y (in feet) of a ball thrown by a child is y=-1/14 x² + 2x + 3 where is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? feet (b) What is the maximum height of the ball? feet (c) How far from the child does the ball strike the ground? feet

Bella is going to invest $94,000 and leave it in an account for 9 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Bella to end up with $156,000?