Answer:
Step-by-step explanation:
Base = 8 * 8 = 64 square units
4 (8*6)/2 = 96 square units
64 + 96 = 160 square units
Step-by-step explanation:
to calculate circumference:

if the diameter is 16 then the radius would be 8.

to calculate the area of a circle:

Answer:
3. y = 1
4. y = 3, x = 12
Step-by-step explanation:
Like the question says, we'll be using substitution, so for the first one, we'll be substituting the value of x into the equation
x = 5
3x- 5y = 10
3 (5) - 5y = 10
15 - 5y = 10
5y = 15 - 10
5y = 5
y = 1
For the next one, it's a similar idea, except the value of x has the variable y in it, which is fine, as there is still only one value in the equation we'll be solving:
x = 4y
x + y = 5
4y + y = 5
5y = 15 (we needed to collect like terms to simplify)
y = 15/5
y = 3
we still have to find x, to this, we substitute the value of y into any of the equations:
x = 4y
x = 4 (3)
x = 12
Hope this helps,
Cate
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula

to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.

Do the same for the AROC from x = 3 to x = 4.

The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
Answer:
- <u>The rate of return is 8.15%</u>
- <u>This is a good investment</u>
<u></u>
Explanation:
For the first question, you need to find the rate that makes the present value of a stream of ten constant annual payments of $15,000 equal to the $100,000 investment.
The formula that returns the present value of a constant payment is called the annuity formula and is:
![Present\text{ }value=payment\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]](https://tex.z-dn.net/?f=Present%5Ctext%7B%20%7Dvalue%3Dpayment%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7Br%7D-%5Cdfrac%7B1%7D%7Br%281%2Br%29%5Et%7D%5Cbigg%5D)
In your problem you know:
- Present value: $100,000
- payment: $15,000
- r: ?
- t: 10
You cannot solve for r directly. You must guess a value and calculate the right side of the equation until to you find the rate that makes it equal to 100,000.
Try 5%:
![\$15,000\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{10}}\bigg]=\$115,826](https://tex.z-dn.net/?f=%5C%2415%2C000%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B0.05%7D-%5Cdfrac%7B1%7D%7B0.05%281%2B0.05%29%5E%7B10%7D%7D%5Cbigg%5D%3D%5C%24115%2C826)
Then, the rate of return is greater than 5%. After several trials you will find that the rate of return is 8.15%.
Since this rate is higher than 8%, which is what the company requires, this is a good investment.