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Ann [662]
3 years ago
14

You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how ma

ny years should go by until you are making $120,000? (Round to the closest year.)
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
8 0

Answer:

94 years

Step-by-step explanation:

We can approach the solution using the compound interest equation

A= P(1+r)^t

Given data

P= $40,000

A=  $120,000

r=  1.25%= 1.25/100= 0.0125

substituting and solving for t we have

120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t

dividing both sides by 40,000 we have

(1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47

dividing both sides by 0.005 we have

t= 0.47/0.005\\t= 94

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Step-by-step explanation:

3tasks=7/10 hours

1 task=7/(10×3)

1 task=7/30 hours

Hence a robot takes 7/30 hours to complete one task

7 0
2 years ago
What is the equation in point slope form of a line that passes through the points (5,-3)
Illusion [34]
I think it's option 2 / b
4 0
3 years ago
Find the product of (x − 5)^2.
Alex17521 [72]
(x - 5)^2 =
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8 0
2 years ago
Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti
Vikki [24]

Answer:

General Solution is y=x^{3}+cx^{2} and the particular solution is  y=x^{3}-\frac{1}{2}x^{2}

Step-by-step explanation:

x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}

This is a linear diffrential equation of type

\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)..................(i)

here p(x)=\frac{-2}{x}

q(x)=x^{2}

The solution of equation i is given by

y\times e^{\int p(x)dx}=\int  e^{\int p(x)dx}\times q(x)dx

we have e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}

Thus the solution becomes

\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+cy=x^{3}+cx^{2

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have 6=8+4c

Thus solving for c we get c = -1/2

Thus particular solution becomes

y=x^{3}-\frac{1}{2}x^{2}

5 0
3 years ago
A store manager determines that, on average, it takes Jemel 26.1 seconds to fold and put away 1 shirt. The manager uses a clock
Furkat [3]
<span>This problem is an example of ratio and proportion. A ratio is a comparison between two different things. You are given the time of about 26.1 seconds to fold 1 shirt. Also you are given 48 shirts. You are required to find the time in seconds to fold 48 shirts. The solution of this problem is,</span>  
<span>
26.1 seconds /1 shirt = time/ 48 shirts</span>
<span>time = (48 shirts) (26.1 seconds /1 shirt)</span>
<span>time<u> = 1,252.8 seconds</u></span>
<u>The time it takes to fold 48 shirts is 1,252.8 seconds.</u>
3 0
2 years ago
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