How many cm in 1 and a quarter metres?
1 answer:
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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%.
Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables <em>a, b</em>, and <em>c</em>, respectively.
Since a total of 14 cups of coffee was served:
A total of 204 ounces of coffee was served. Therefore:
A total of $16.70 was collected. Hence:
This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract <em>a</em> and <em>b</em> from both sides:
Substitute this into both the second and third equations:
And:
In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:
And for the Third:
We can solve this using substitution. From the second equation, isolate <em>a: </em>
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Substitute into the third:
Distribute and simplify:
Therefore:
Using the equation for <em>a: </em>
<em /><em />
<em />
And using the equation for <em>c: </em>
<em /><em />
<em />
Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.