Answer:
n - (-6) < 9
n < 3
Step-by-step explanation:
When setting up an inequality, using the key words from the problem will help. The word 'difference' would indicate subtraction and 'less than' would be the '<' inequality sign. Since the expression is 'the difference of a number and -6', we write:
n - (-6) < 9
Whenever we subtract a negative number, we change both signs to positive:
n + 6 < 9
Using inverse operations to solve: n + 6 - 6 < 9 - 6
n < 3
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.
Answer:
0.000174
3.5841 x 10^7
4.67 x 10^6
Step-by-step explanation:
1.74 x 10^-4 as an ordinary number
As an ordinary number, the decimal point will be moved 4 times to the left due to the negative power
Hence 1.74 x 10^-4 as an ordinary number
= 0.000174
358.41 x 10^5 in a standard form
In standard form, only one number will be before the decimal point, the number of times the decimal point is moved (to ensure that only the first digit is before the point) is added to the power of ten. Hence
358.41 x 10^5 in a standard form
= 3.5841 x 10^5+2
= 3.5841 x 10^7
4 670 000 in a standard form
As done above, only one digit will be before the decimal
4 670 000 in a standard form
= 4.67 x 10^6
