Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?

First, determine what information you need to answer this question,

How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.

How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.79.

How much does a reusable water bottle cost? About $10.

How long does a reusable water bottle last? Basically forever (or until you lose it).

How much does a water filter cost? How much water will they filter?

A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)

A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months

An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.

Which option is cheapest over one year (365 days)? Select an answer Water bottles faucet-mount filter filter pitcher under-sink filter  

The cheapest option saves her $ over a year?

Give your answer to the nearest cent. Pro-rate the costs of additional filters (so if you only use part of a filter, only count the corresponding fraction of the filter cost).

Write out the addition and multiplication tables for the ring Z₂[x]/(x^2 + x). Is Z₂[x]/(x^2 + x) a field?

The Sandersons are planning to refinance their home. The outstanding principal on their original loan is $120,000 and was to amortized in 240 equal monthly installments at an interest rate of 10%/year compounded monthly. The new loan they expect to secure is to be amortized over the same period at an interest rate of 7%/year compounded monthly. How much less can they expect to pay over the life of the loan in interest payments by refinancing the loan at this time? (Round your answer to the nearest cent.)
$

In the real vector space R ³, the vectors u1 =(1,0,0) and u2=(1,2,0) are known to lie in the span W of the vectors w1 =(3,4,2), w2=(0,1,1), w3=(2,1,1) and w4=(1,0,2). Find wi, wj ?{w1,w2,w3,w4} such that W = span({u1,u2,wk,wl}) where {1,2,3,4}= {i,j,k,l}.

Sales Tax: If the purchase price of a bottle of California wine is $24 and the sales tax is $1.50, what is the sales tax rate?

The sales tax rate is %.

A tire salesperson has a 14% commission rate. If he sells a set of radial tires for $800, what is his commission?

His commission is $.

If an appliance salesperson gets 7% commission on all the appliances she sells, what is the price of a refrigerator if her commission is $36.75?

The price of the refrigerator is $.

A realtor makes a commission of $2,000 on a $50,000 house he sells. What is his commission rate?

His commission rate is %.

The sales tax rate is 9.25% and the sales tax is $14.35, what is the purchase price? (Round to the nearest cent.)

The purchase price is $.

What is the total price? (Round to the nearest cent.)

The total price is $.

Determine whether S is a basis for R³.

S = {(4, 2, 5), (0, 2, 5), (0, 0, 5)}

S is a basis for R³.S is not a basis for R³.    

If S is a basis for R³, then write u = (8, 2, 15) as a linear combination of the vectors in S. (Use s₁, s₂, and s₃, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.)

u =

1. For the function f (x) = 2x² + 8 use the limit definition (four-step process) to find f′(x) . Students must show all steps (more or less four of them) to compute the derivative. Simply giving the derivative of the function will not receive much credit.

2. For the function f (x) = x² + 2x

a. Find f′(x) . Students may use derivative rules to find this derivative. Show all work and clearly label the answer below.

b. Find the slope of the tangent line at (1, f (1)) . For full credit show steps with proper notation. Show all work and clearly label the answer below.

c. Find the equation, y = mx + b , of the tangent line at (1, f (1)) . For full credit all steps required for the final answer. Show all work and clearly label the answer below. Clearly label answer below.

3. The profit (in dollars) from the sale of x infant car seats is given by:

P (x) = 45x − 0.025x² − 5000 where 0 ≤ x ≤ 2, 400

a. Find the average rate of change in profit if production goes from 800 car seats to 850 car seats. Show all work and clearly label the answer below.

b. Find P′(x) . Students may use derivative rules to find this derivative. Clearly label the answer below.

c. Find P′(800). Interpret the meaning of this result in a complete sentence with correct units.

4. Use derivative rules to find d/dt ( 5/t³ − 4 √ t ). Show all work and clearly label answer below.

5. A manufacturer will sell N (x) speed boats after spending $x thousand on advertising, as given by

N (x) = 1200 − 3,845/x where 5 ≤ x ≤ 30

a. Find N′(x) .  Students may use derivative rules to find this derivative. Show all work and clearly label the answer below.

b. Find N′(10) and N′(25) . Interpret the meaning of these results with correct units.

Activity 1: How far can a soccer player kick a soccer ball down field? Through the application of a linear function and a quadratic function and ignoring wind and air resistance one can describe the path of a soccer ball. These functions depend on two elements that are within the control of the player: velocity of the kick (v k ) and angle of the kick (?). A skilled high school soccer player can kick a soccer ball at speeds up to 50 to 60 mi/h, while a veteran professional soccer player can kick the soccer ball up to 80 mi/h. Vectors Gravity The vectors identified in the triangle describe the initial velocity of the soccer ball as the combination of a vertical and horizontal velocity. The constant g represents the acceleration of any object due to Earth’s gravitational pull. The value of g near Earth’s surface is about ?32 ft/s2 . v x = v k cos ? & v y = v k sin ?

1. Use the information above to calculate the horizontal and vertical velocities of a ball kicked at a 35° angle with an initial velocity of 60 mi/h. Convert the velocities to ft/s. (2 pts) Project 2 368 MTHH 039 2. The equations x(t) = v x t and y(t) = v y t + 0.5 gt2 describe the x- and y- coordinate of a soccer ball function of time. Use the second to calculate the time the ball will take to complete its parabolic path. (4 pts) 3. Use the first equation given in Question 2 to calculate how far the ball will travel horizontally from its original position. (2 pts)

Activity 2: How far can a soccer player kick a soccer ball down field? Through the application of a linear function and a quadratic function and ignoring wind and air resistance one can describe the path of a soccer ball. These functions depend on two elements that are within the control of the player: velocity of the kick (v k ) and angle of the kick (?). A skilled high school soccer player can kick a soccer ball at speeds up to 50 to 60 mi/h, while a veteran professional soccer player can kick the soccer ball up to 80 mi/h.

1. Use the technique developed in Activity 1 to calculate horizontal distance of the kick for angle in 15° increments from 15° to 90°? Make a spreadsheet for your calculations. Use the initial velocity of 60 mi/h. (8 pts)

I want to know the answer of the last question that I write bold and italic. Let me know the answer of this questions!!!

Mimi can run around a quarter-mile track in 150 seconds. Judy can run around the same track in 120 seconds. Suppose they start running in the same direction from the same place at the same time. How long will it take for Judy to “lap” (catch up to) Mimi three times? How far will each woman have run? Hint: Find each woman’s speed (distance/time).

Please show work and explain how you got this answer :)

John has been hired to design an exciting carnival ride. Tiff, the carnival owner, has decided to create the world's greatest Ferris wheel. Tiff isn't into math; she simply has a vision and has told John these constraints on her dream: (i) the wheel should rotate counterclockwise with an angular speed of a = 13 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 5 feet above the level ground. The wheel starts turning when Tiff is at the location P, which makes an angle θ with the horizontal, as pictured. It takes her 1.5 seconds to reach the top of the ride. (Impose coordinates with units in feet.)

(a) Impose a coordinate system with the origin at the center of the wheel. Find the coordinates T(t) = (x(t), y(t)) of Tiff at time t seconds after she starts the ride. (Round values to three decimal places as needed.) x(t) = y(t) =

(b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiff's coordinates the instant she becomes a human missile. (Round your answers to three decimal places.) (x(6), y(6)) =

(c) Find the equation of the tangential line along which Tiff travels the instant she becomes a human missile. ketch a picture indicating this line and her initial direction of motion along it when the seat detaches.

Marvin was standing on the roof of his house throwing water balloons onto people on the sidewalk below. (Do not try this at home.) When he let the balloon go the balloon was 45 cubits off of the ground. He learned through trial and error that in order to hit someone on the ground he had to have the balloon reach a maximum height of 55 cubits off of the ground 2 seconds after he threw it. Let h left parenthesis t right parenthesis be the height of the water balloon in cubits t seconds after it was thrown. Assume that height is a quadratic function of time. (Note: A cubit is a measurement of distance. Since we are not using feet or meters you cannot use standard physics formulas to solve this.) a) Find a formula for h left parenthesis t right parenthesis . b) Find the time when the balloon hits the ground. Answer this question using a complete sentence in terms of this problem.

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 3 cubic feet in volume and 137 pounds in weight, and earns $30 in revenue. Each crate of cargo II is 3 cubic feet in volume and 274 pounds in weight, and earns $45 in revenue. The plane has available at most 270 cubic feet and 14,248 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

Which units do you prefer to use when performing calculations, American units or metric units? Why? Describe some advantages and disadvantages to both unit systems.

Please keep it simple for Hyperbolic Geometry (the response I was given was great, but it was well beyond what we needed)

Illustrate with a picture showing that the following are simply not true in Hyperbolic Geometry

c). The angle sum of any triangle is 180

d). Rectangles exist

Find the perimeter of a regular 36 sided regular polygon inscribed in a circle with a radius of 14 units. Then find the size of one of the inscribed angles.