A rectangular ink pad has a perimeter of 30 centimeters and an area of 54 square centimeters. What are the dimensions of the ink
1 answer:
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Answer:
a) 35, b) 25, c) 60
Step-by-step explanation:
The number of girls is 10 more than the number of boys, so it's a good thing to choose a variable to represent the number of boys.
Number of boys: b
Number of girls: b + 10
Ratio of girls:boys is 7:5, so
"Cross multiply" to get
There are 25 boys. There are 10 more girls, so the number of girls is 35, and the total number of students is 60.
That's a packed classroom!
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.
For the annually rate we have that:
Where
= initial investment.
= annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
= initial investment.
= quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
![\sqrt[4]{1.07} =1+ i_{q}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D1%2B%20i_%7Bq%7D%20)
![i_{q} = \sqrt[4]{1.07} -1](https://tex.z-dn.net/?f=%20i_%7Bq%7D%20%3D%20%5Csqrt%5B4%5D%7B1.07%7D%20-1)
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.