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Greeley [361]
2 years ago
8

A sphere of radius 7 in. Is placed inside a rectangular prism with length 15 in., width 18 in., and height 20 in. What is the vo

lume of the prism not occupied by the sphere?
Mathematics
1 answer:
iragen [17]2 years ago
5 0

Answer:

3964 in³

Step-by-step explanation:

volume of sphere:  V = 4/3 πr³

v₁ = 4/3 x 3.14 x 7³ = 1436

volume of prism: v = Bh     B = 15 x 18 = 270    h = 20

v₂ = 270 x 20 = 5400

v₂ - v₁ = 5400 - 1436 = 3964 in³

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Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr
siniylev [52]

Answer:

(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t

$29619.13

Step-by-step explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then  

f(t) = 14375 (1 + \frac{5.3}{100})^{t} ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.  

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write  

g(t) = 570 × 12t = 6840t ........ (2)

Therefore, (f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t

b. So, for t = 2 years,  

(f + g)(t) = 14375 (1 + \frac{5.3}{100})^{2} + 6840 \times 2 = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)

7 0
2 years ago
The original cost of an item is $64, but you have to pay $78.08. What is the markup of the item (as a percent)?
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Answer:

Step-by-step explanation:

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starting on the positive x axis and moving 1/3 of the way around the circle in 3 m radius, ow far will it go?
nlexa [21]
You will move 1/3 of the circumference of the circle with a radius of 3m.

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d=2π m

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2 years ago
Ken and Hamid run around a track. It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap. Ken an
likoan [24]

The <em><u>correct answer</u></em> is:

Ken will have run 3 laps and Hamid will have run 4.

Explanation:

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

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This means every 240 seconds they will both be at the start line.

Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.

Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.

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2 years ago
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