7 x 10^1 = 70
7 x 10^2 = 700
7 x 10^3 = 7000
Response:
Yearly average cost = 400 + 180/x
Detailed explanation:
Utilizing the equation y=mx+b
The value of b represents the initial costs or the y intercept, reflecting the start-up expenses
m signifies the cost increase per each unit of x, which is 400 each year
Total costs = 400x + 180
To determine the yearly average cost, we must divide by x
Average yearly cost = (400x + 180)/x
= 400 + 180/x
To clarify, let's use abbreviations: J for Justin, E for Eva, and M for Emma. Then, J = E + 7.50 and M = J - 12. Along with that, J + E + M = 63. You can substitute M into the third equation using the second equation and arrive at: J + E + J - 12 = 63. Simplifying gives us: 2J + E = 75. Since J equals E + 7.50, substitute that into the equation to find: 2(E + 7.50) + E = 75. This leads to 2E + 15 + E = 75, simplifying to 3E + 15 = 75, hence 3E = 60 which implies E = 20; therefore, Eva has $20. Justin has $7.50 more than Eva, totaling $27.50. Emma has $12 less than Justin, coming to $15.50. Verify by ensuring their totals sum to 63, which they do.
The area of a square is calculated by squaring the side length (A = s²). Consequently, 30 = s². Taking the square root gives us s = √30. A calculator shows that √30 is approximately 5.48, or through estimation, we can see that √25 < √30 < √36, suggesting that √30 falls between 5 and 6.
$5,000.00 invested for a period of 6 years doubles to $10,000.00.
What is the interest rate?
You will need to apply logarithms:
<span>log(1 + rate) = {log(total) - log(Principal)} ÷ Years
</span>log(1 + rate) = <span>{log(10,000) - log(5,000)} ÷ 6
</span>log(1 + rate) = (4 - 3.6989700043) / 6
log(1 + rate) =
<span>
<span>
<span>
0.301029957 / 6
</span></span></span>log(1 + rate) =
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
Next, raise 10 to the power of
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
which results in
<span>
<span>
<span>
1.1224620317
</span>
</span>
</span>
This value represents 1 plus the interest rate, so the interest rate is
0.1224620317 or 12.24620317 percent.
This concludes Part ONE.
Now, onto Part TWO.
How many years does it take for $300 to increase to $9,600 at an annual rate of <span>12.24620317%?
You will use the following formula:
</span>(More logarithms involved).
Years = {log(total) - log(Principal)} ÷ log(1 + rate)
Years = {log(9,600) - log(300)} / log(<span>1.1224620317)
</span>Years = (3.982271233 - 2.4771212547) / 0.050171659518
<span><span><span>Years = 1.5051499783 /
</span>
</span>
</span>.050171659518
Years = 30
