Answer:
<em> The distance from your eyes to the stage is 8.85 ft</em>
Step-by-step explanation:
Your distance to the stage is 6 feet
Your eyes are 6.5 feet tall
You need to find the distance of your eyes towards the stage.
This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.
<u>Observe the attached image.</u>
Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.
So, using the Pythagorean theorem we have:
Where
therefore:
Answer:
The expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Step-by-step explanation:
The formula to compute the future value is:
![FV=PV[1+\frac{r}{100}]^{n}](https://tex.z-dn.net/?f=FV%3DPV%5B1%2B%5Cfrac%7Br%7D%7B100%7D%5D%5E%7Bn%7D)
PV = Present value
r = interest rate
n = number of periods.
It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.
The expression to compute the amount in the investment account after 14 years is,
![FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14%7D%2B3000%5B1%2B%5Cfrac%7B10%7D%7B100%7D%5D%5E%7B14-6%7D%5C%5CFV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D)
The future value is:
![FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27](https://tex.z-dn.net/?f=FV%3D5000%5B1%2B0.10%5D%5E%7B14%7D%2B3000%5B1%2B0.10%5D%5E%7B8%7D%5C%5C%3D18987.50%2B6430.77%5C%5C%3D25418.27)
Thus, the expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].
Answer:
8. $35.10
9. $59.63
10. $13.43
11. $70
12. Take the percent you pay (100-the discount) as a decimal and multiply it by the regular price.
Step-by-step explanation:
For finding the price we pay during a sale, we focus on the percent we pay. If 22% off is the sale, then we spend 78% or 100-22-78. We use this percent byb multiplying the price with a decimal. We convert percents into decimals by dividing the percent number by 100. For example, 78% divided by 100 becomes 0.78.
8. Percent off is 22%. We pay 78%=0.78.
45(0.78)=$35.10
9. Percent off is 33%. We pay 67%=0.67.
89(0.67)=$59.63
10. Percent off is 44%. We pay 56%=0.56.
23.99(0.56)=$13.43
11. Percent off is 75%. We pay 25%=0.25.
279.99(0.25)=$70
12. See explanation above.
Answer:
About 21.457 years
Step-by-step explanation:
You can solve this by setting up a simple equation.
log base 1.04 2.32=x
years
Hope this helps!
