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Algebra

Find the time points when the height is 1 foot

When a ball is thrown, its height in feet h after t seconds is given by the equation h = vt - 16t^2. where v is the initial upwards velocity in feet per second. If v = 9 feet per second, find all values of t for which h = 1. Do not round immediate steps. Round your answer to 2 decimals. If there is more than one ans

Together and Alone Word Problems

Jack can shovel snow off the sidewalk in 3 hours. Joe can shovel snow off the same sidewalk in 2 hours. How long will it take them to shovel the sidewalk working together?

Word Problem: Relative Speed

A child in an airport is able to cover 270 meters in 3 minutes running at a speed down a moving sidewalk in the direction of the sidewalks motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 256 meters in 4 mintues. What is the child's running speed and the she spe

Average Gas Mileage

There are two cars. The sum of the average miles per gallon obtained by the two cards in a particular week is 60. The first car consumed 20 gallons during that week and the second car consumed 15 gallons, for a total of 1100 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two ca

The weekly demand model for a new toy is given by functions

Please assist by showing how to solution is obtained. 12. The weekly demand model for a new toy is given by: N = -5p + 80 The weekly supply model for the same toy is: N = 3p + 40 For the models p is the price of the toy and N is the number of toys sold or supplied. Find the price at which supply and dema

Demand Curve for Prices

4) (demand curve)The demand curve for a certain commodity is p=-.001q+32.5 a) At what price can 31,500 units of the commodity be sold at? b) What quanities are so large that many units of the commodity can't possibly be sold no matter how low the price... The hint they gave was to drop the price, make an inequality and solve f

Find the number of boys and girls involved in the group

A professor started a project with a group of students, 60% of whom were boys, due to some unavoidable reason, six girls couldn't show up, so the professor had to make some changes in the group. He admitted six boys. In doing so the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in

Quadratic equations and inequalities

Minimizing Cost. A company uses the formula C(x)=0.02x^2 - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

Simple Groups and Sylow p-Subgroups

(1) Prove that if |G|=1365, then G is not simple. (2) Assume that G is a nonabelian group of order 15. Prove that Z(G)=1. Use the fact that the group generated by "g" is less than or equal to C_G(g) for all "g" in G to show that there is at most one possible class equation for G.

Inflation and present value

Please develop a hypothetical scenario in a word document illustrating these concepts. Inflation: 1. If your salary today is $55,000 per year, what would you expect your salary to be in 20 years (rounded to the nearest thousand dollars) if you assume that inflation will continue at a constant rate of 6% over that time peri

Radical Equations Word Problems

1. The equation D=1.2√h gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet. a. Solve this equation for h. b. Long's Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long's Peak? Can you see Cheyenne

Solving Radical Equations and Word Problems

See the attachment. 1. Solve the equation for r. 2. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.) 3. Use the value of C you found in the previous question to determine how much the object would wei

The Period of a Pendulum

The period T (time in seconds for one complete cycle) of a simple pendulum is related to the length L (in feet) of the pendulum by the formula 8T^2=(3.14)^2L. If a child is on a swing with a 10 foot chain, then how long does it take to complete one cycle of the swing?

Integer Linear Programming and Optimal Solution

1. Consider the following integer linear programming problem. Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 <= 30 4x1 + 2x2 <= 28 x1 <= 8 x1, x2 >= 0 and integer The solution to the linear programming relaxation is: x1 = 5.714, x2= 2.571. What is the optimal solution to the integer linear programming problem? State the value

Demand and Revune Equations for the Sale of Tiles

A. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in

Writing Inequalities from Word Problems

Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2500? Write an inequality that illustrat

Demand Equations

Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in th

Linear Programming

Consider the following linear programming problem. MIN Z = 10x1 + 20x2 Subject to: x1 + x2 >= 12 2x1 + 5x2 >= 40 x1, x2 >= 0 What is minimum cost Z=?? Put your answer in the xxx.x (to one decimal place)

Prove that W is a Subspace of V

Let F be the field of real numbers and let V be the set of all sequences: (a_1, a_2, ..., a_n, ...), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F. Let W = {(a_1, a_2, ..., a_n, ...) belongs to V | lim n -> infinity a_n = 0}. Prove t