Answer:
see below
Step-by-step explanation:
principal = $5,000
interest rate = 2.3%
account A: compound monthly for 10 years
account B: compound continuously for 10 years
<u>account A</u><u>: compound monthly for 10 years</u>
A = P (1 + r/12)^ r*t
= $5,000 (1 + .023/12)^ 12(10)
= $6,291.6
<u>account B</u><u>: compound continuously for 10 years</u>
FVn = PV * e^r*t
= $5,000 * e ⁽⁰ ⁰²³ˣ¹⁰⁾
= $6,293
Gregory may chose account B. (but the difference is only $1.40)
Answer:
Twice as many people prefer summer over spring.
Step-by-step explanation:
i took test
Answer:
Derlay will mix one-sixth of a cup with 112 cups of hydrogen peroxide.
Step-by-step explanation:
We are given the following in the question:
48 teaspoons = 1 cup
A chemical reaction involves mixing 1 teaspoon of yeast with 14 cup of hydrogen peroxide.
Thus, the ratio of yeast to hydrogen peroxide in teaspoons
![\dfrac{\text{Yeast}}{\text{Hydrogen Peroxide}} = \dfrac{1}{14\times 48} = \dfrac{1}{672}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BYeast%7D%7D%7B%5Ctext%7BHydrogen%20Peroxide%7D%7D%20%3D%20%5Cdfrac%7B1%7D%7B14%5Ctimes%2048%7D%20%3D%20%5Cdfrac%7B1%7D%7B672%7D)
112 cups of hydrogen peroxide are used.
Thus, we can write:
![\dfrac{1}{672} = \dfrac{\text{Teaspoons of yeast}}{112\times 48}\\\\\text{Teaspoons of yeast} = \dfrac{112\times 48}{672}\\\\\text{Teaspoons of yeast} = 8\\\\\text{Cups of yeast} = \dfrac{8}{48} = \dfrac{1}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B672%7D%20%3D%20%5Cdfrac%7B%5Ctext%7BTeaspoons%20of%20yeast%7D%7D%7B112%5Ctimes%2048%7D%5C%5C%5C%5C%5Ctext%7BTeaspoons%20of%20yeast%7D%20%3D%20%5Cdfrac%7B112%5Ctimes%2048%7D%7B672%7D%5C%5C%5C%5C%5Ctext%7BTeaspoons%20of%20yeast%7D%20%3D%208%5C%5C%5C%5C%5Ctext%7BCups%20of%20yeast%7D%20%3D%20%5Cdfrac%7B8%7D%7B48%7D%20%3D%20%5Cdfrac%7B1%7D%7B6%7D)
Thus, Derlay will mix one-sixth of a cup with 112 cups of hydrogen peroxide.
Step-by-step explanation:
Since
varies directly as
we can write the relation as
![x = k\sqrt{y}](https://tex.z-dn.net/?f=x%20%3D%20k%5Csqrt%7By%7D)
where k is the constant of proportionality.
a) To solve for the k, we substitute the given values:
![5 = k\sqrt{13} = k(13)](https://tex.z-dn.net/?f=5%20%3D%20k%5Csqrt%7B13%7D%20%3D%20k%2813%29)
![\Rightarrow k = \dfrac{5}{13}](https://tex.z-dn.net/?f=%5CRightarrow%20k%20%3D%20%5Cdfrac%7B5%7D%7B13%7D)
b) The equation relation x and y can be written as
![x = \dfrac{5}{13}\sqrt{y}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B5%7D%7B13%7D%5Csqrt%7By%7D)
c) When y = 9,
![x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B5%7D%7B13%7D%5Csqrt%7B9%7D%20%3D%20%5Cdfrac%7B5%7D%7B13%7D%283%29%20%3D%20%5Cdfrac%7B15%7D%7B13%7D)
a + (n - 1)d
a is 46, the initial.
n is the nth term, or in this case 12
d is difference, which is 4
plug this info in....
46+ (12-1)4
=90