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Elis [28]
3 years ago
7

Janelle earns $950 a week.Carter earns $50,320 a year.Each works 52 weeks a year.What is the difference between the amounts Jane

lle and Carter earn in 30 years? Explain.
Mathematics
1 answer:
Dvinal [7]3 years ago
6 0
First, let's figure out how much money Carter earns in 1 year.  This is equal to 50,320*30 = 1,509,600, so Carter makes $1,509,600 in 30 years.

Next, we need to figure out how much money Janelle makes.  We can do this two ways.  We can figure out how many weeks are in 30 years, or we can figure out how much money Janelle makes in a year and then multiplying that name by 30.  I will solve this problem in the second way.

In order to figure out how much money Janelle makes in a year, we do 950*52 = 49,400.  Janelle makes 49,400 per year.  Now, we multiply this number by 30 to see how much she makes in 30 years.  49,400*30 = 1,482,000.  Janelle makes $1,482,000 in 30 years.

Now, we need to finish the problem.  We do this by subtracting the amount of money that Janelle makes from the amount of money that Carter makes.  This is: 1,509,600 - 1,482,000 = 27,600.  The difference between the amount that Janelle makes and Carter makes in 30 years is $27,600
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Answer:

A)1st term:45

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3rd term:49.6875

4th term:49.921875

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Step-by-step explanation:

We are given;

h₀ = Initial height of the ball = 30

r = Rebound fraction = 0.25

a) The arithmetic sequence of bouncing balls is given by the following;

Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)

The first term of the sequence is;

S₁ = h₀ + 2h₀r¹

S₁ = 30 + (2 × 30 × 0.25)

S₁ = 45

The second term of the sequence is;

S₂ = h₀ + 2h₀(r¹+r²)

S₂ = 30 + (2 × 30 × (0.25 + 0.25²)) = 48.75

The third term of the sequence is;

S₃ = h₀ + 2h₀(r¹ + r² + r³) = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³)) = 49.6875

S₄ = h₀ + 2h₀(r¹ + r² + r³ + r⁴)

S₄ = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³ + 0.25⁴)) = 49.921875

B) The general expression for the nth term of the sequence is;

Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)

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Step-by-step explanation:

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