Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,700 per month for twenty years. (Round your answers to the nearest cent.)

(a) How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity, which she sets up thirty years before her retirement? (The two annuities pay the same interest rate of 7.8% compounded monthly.) $

(b) How large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement? $

Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x5 = t and solve for x1, x2, x3, and x4 in terms of t.) x1 − x2 + 2x3 + 2x4 + 6x5 = 16 3x1 − 2x2 + 4x3 + 4x4 + 12x5 = 33 x2 − x3 − x4 − 3x5 = −9 2x1 − 2x2 + 4x3 + 5x4 + 15x5 = 34 2x1 − 2x2 + 4x3 + 4x4 + 13x5 = 34 (x1, x2, x3, x4, x5) =

After a weekend of lucrative gigs, a singer finds herself with an extra $ 1,500. She currently has $4350 of credit card debt, on which she is charged an annual yield of 24%. Putting $1,500 toward this would cut that debt to $1,850. Calculate the annual rate of return if she does this. Round, if necessary, to the nearest 0.1%.

  Solve

a.      x + y = 3, 2x – y = 1

b.      3x + 2y = 6, x = 3

c.      2x + y = 4, y = -2x + 1

d.      x – 3y = 6, 2x – y =1

Question # 5
a. Briefly explain how the Bernoulli equation is derived. Discuss its application in oil / gas productions, including its limitation. [4 marks]
b. The water level in a tank shown in Figure Q5b is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 4 atm gage. Assuming the system is at sea level, determine: [5 marks]
i. The maximum height to which the water stream could rise.
ii, If the water level in the tank was 15 m, would the maximum water rise at the nozzle increase? Justify with calculation. (4 marks]
iii. If the gauge pressure increases to 5 atm for 20 m water level, show the formula of finding water velocity at the nozzle exit. [4 marks] 4 atm 20 m Figure Q5b

Graph all vertical and horizontal asymptotes of the function.

f(x)=-4x+11/-2x+7

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 :)