If he earns 6% interest per year, then he will have had money in his investment account for three years.
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Answer:
x = 12
prism's length = 36 centimeters
Prisms width = 25 centimeters
Step-by-step explanation:
volume of a rectangular prism, V = length × width × height
volume = 10,800 cubic centimeters
prism's length = 3x
Prisms height = 12 centimeters
Prisms width = (2x + 1)
volume of a rectangular prism, V = length × width × height
10,800 = 3x * 2x + 1 * 12
10,800 = 6x² + 3x * 12
10,800 = 72x² + 36x
72x² + 36x - 10,800 = 0
2x² + x - 300 = 0
Using quadratic formula
x = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4*2*-300 / 2*2
= -1 ± √1 - (-2400) / 4
= -1 ± √1 + 2400 / 4
= -1 ± √2401 / 4
= -1 ± 49 / 4
x = (-1 + 49)/4 or (-1 - 49)/4
= 48/4 or -50/4
x = 12 or -12.5
x cannot be a negative value
Therefore, x = 12
prism's length = 3x
= 3(12)
= 36 centimeters
prism's length = 36 centimeters
Prisms width = (2x + 1)
= 2(12) + 1
= 24 + 1
= 25 centimeters
Prisms width = 25 centimeters
<h2>Answer</h2>
2
<h2>Explanation</h2>
First, we are going to use the law of fractional exponents: ![a^{\frac{1}{n} =\sqrt[n]{a}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%3D%5Csqrt%5Bn%5D%7Ba%7D)
We can infer form our expression that
and
, so let's replace the values:
![a^{\frac{1}{n} =\sqrt[n]{a}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%3D%5Csqrt%5Bn%5D%7Ba%7D)
![16^{\frac{1}{4} }=\sqrt[4]{16}](https://tex.z-dn.net/?f=16%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%3D%5Csqrt%5B4%5D%7B16%7D)
Notice that we can also decompose 16 into prime factors to get
, so we can rewrite our expression as follows:
![\sqrt[4]{16}=\sqrt[4]{2^4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B16%7D%3D%5Csqrt%5B4%5D%7B2%5E4%7D)
Finally, we can use the rule of radicals:
, so:
![\sqrt[4]{2^4}=2](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%5E4%7D%3D2)
Y= 80.55% approximately, 80.6% rounded up
Calculations:
The percent (percentage) of a given number p/q can be found, for the most part, without a calculator by a slight change in the notation:
y=the number 29/36 expressed as a percent becomes
y=[29(2.7777777778 approx.)]/[36(2.7777777778 approx.)]
y=0.8055 approx. (Express the decimal numeral as a percent)
y=0.8055(100)
y=
80.55% approx., which is 80.6% rounded up to the nearest tenth percent