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stepladder [879]
3 years ago
12

fabiana decides to save the money she is earning from her after school job for college. she makes an initial contribution of 300

0$ and each month deposits an additional $500. After one month she will have contributed $3500.A. white an equation for the nth term of the sequence B. how much money will she have contribute after 24 month
Mathematics
1 answer:
Oxana [17]3 years ago
3 0

Answer:

A. Total Money Contributed after n months = \$ 3000 + \$ (500\times n)

B. Total Money Contributed after 24 months = \$ \ 15000

Step-by-step explanation:

Given:

Initial contribution = \$\ 3000

each month contribution =\$\ 500

After 1 month contributed = \$\ 3000 + \$\ 500 \times 1= \$ \ 3500

Solving for Part A

let n be the number of months

∴ Total Contribution after n months = Initial contribution + (each month contribution \times Number of months = \$\ 3000 + \$\ 500 \times n

Solving for Part A

Now n= 24 months

∴ Total Contribution after 24 months = \$\ 3000 + \$\ 500 \times 24 = \$\ 3000 + \$\ 12000= \$\ 15000

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The distance of it away from zero cannot be a negative distance, distance is always positive therefor the absolute value will always be positive.

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3 years ago
Tomatoes cost $0.70 per pound.<br> 2<br> 6<br> 8<br> Weight (lb)<br> Price ($)<br> 1.40 2.10
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Answer: 2, 3, 6, 8 (top) 1.40, 2.10 4.20, 5.60 (bottom)

Step-by-step explanation: If 1 pound = 0.70, then 2*0.70=1.40. 2.10 divided by 0.70=3. 0.70*6=4.20. 0.70*8=5.60.

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2 years ago
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A metal manufacturing company reduces the length of a 12.5-inch cylindrical rod, after which the rod measures 7.8 inches. How ma
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Answer:

4.7 inches

Step-by-step explanation:

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7 0
3 years ago
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Quentin pays $178 every 4 months for his guitar lessons. At this rate , how much will Quentin pay for 3 years of guitar lessons
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$1602 would be the amount paid for 3 years of lessons.
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3 years ago
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A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.
noname [10]

Answer:

Width = 4ft

Height = 4ft

Length = 8ft

Step-by-step explanation:

Given

Volume = 128ft^3

L = 2W

Base\ Cost = \$9/ft^2

Sides\ Cost = \$6/ft^2

Required

The dimension that minimizes the cost

The volume is:

Volume = LWH

This gives:

128 = LWH

Substitute L = 2W

128 = 2W * WH

128 = 2W^2H

Make H the subject

H = \frac{128}{2W^2}

H = \frac{64}{W^2}

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

A = LW + 2(WH + LH)

The cost is:

Cost = 9 * LW + 6 * 2(WH + LH)

Cost = 9 * LW + 12(WH + LH)

Cost = 9 * LW + 12H(W + L)

Substitute: H = \frac{64}{W^2} and L = 2W

Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)

Cost =18W^2 +  \frac{768}{W^2}*3W

Cost =18W^2 +  \frac{2304}{W}

To minimize the cost, we differentiate

C' =2*18W +  -1 * 2304W^{-2}

Then set to 0

2*18W +  -1 * 2304W^{-2} =0

36W - 2304W^{-2} =0

Rewrite as:

36W = 2304W^{-2}

Divide both sides by W

36 = 2304W^{-3}

Rewrite as:

36 = \frac{2304}{W^3}

Solve for W^3

W^3 = \frac{2304}{36}

W^3 = 64

Take cube roots

W = 4

Recall that:

L = 2W

L = 2 * 4

L = 8

H = \frac{64}{W^2}

H = \frac{64}{4^2}

H = \frac{64}{16}

H = 4

Hence, the dimension that minimizes the cost is:

Width = 4ft

Height = 4ft

Length = 8ft

8 0
3 years ago
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