Answer:
After 20 months
Step-by-step explanation:
This is a compound growth problem which has the formula:
![F=P(1+r)^t](https://tex.z-dn.net/?f=F%3DP%281%2Br%29%5Et)
Where
F is future value
P is present amount
r is the rate of growth
t is the time (in months)
Future amount is $65, what he needs at-least
P is the initial amount, that is $10
r is the rate of growth, which is 10% or 10/100 = 0.1
t is time in months, what we need to find
Substituting and solving we get:
![F=P(1+r)^t\\65=10(1+0.1)^t\\65=10(1.1)^t\\6.5=1.1^t\\ln(6.5)=ln(1.1^t)\\ln(6.5)=t*ln(1.1)\\t=\frac{ln(6.5)}{ln(1.1)}\\t=19.64](https://tex.z-dn.net/?f=F%3DP%281%2Br%29%5Et%5C%5C65%3D10%281%2B0.1%29%5Et%5C%5C65%3D10%281.1%29%5Et%5C%5C6.5%3D1.1%5Et%5C%5Cln%286.5%29%3Dln%281.1%5Et%29%5C%5Cln%286.5%29%3Dt%2Aln%281.1%29%5C%5Ct%3D%5Cfrac%7Bln%286.5%29%7D%7Bln%281.1%29%7D%5C%5Ct%3D19.64)
<u>He would need 19.64 months to save up at-least 65. So, that means, he would need 20 months</u>
Answer:
![y=C_1e^{-x}+C_2xe^{-x}+\frac{1}{5}e^{2x}.](https://tex.z-dn.net/?f=y%3DC_1e%5E%7B-x%7D%2BC_2xe%5E%7B-x%7D%2B%5Cfrac%7B1%7D%7B5%7De%5E%7B2x%7D.)
Step-by-step explanation:
all the details see in the attached picture.
Width of foil is
inches
<em><u>Solution:</u></em>
Given that area of the rectangle piece of foil is
square inches
Its length is
inches
To find: width of foil
<em><u>The area of rectangle is given as:</u></em>
To find the area of a rectangle, we multiply the length by the width
![\text{ area of rectangle}= length \times width](https://tex.z-dn.net/?f=%5Ctext%7B%20area%20of%20rectangle%7D%3D%20length%20%5Ctimes%20width)
<em><u>Substituting the given values in above formula,</u></em>
![11\frac{1}{4} = 4\frac{1}{2} \times width](https://tex.z-dn.net/?f=11%5Cfrac%7B1%7D%7B4%7D%20%3D%204%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20width)
Let us solve above expression to find width
![\frac{4 \times 11 + 1}{4} = \frac{2 \times 4 + 1}{2} \times width\\\\\frac{45}{4} = \frac{9}{2} \times width\\\\width = \frac{45}{4} \times \frac{2}{9}\\\\width = \frac{5}{2} = 2\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%5Ctimes%2011%20%2B%201%7D%7B4%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%204%20%2B%201%7D%7B2%7D%20%5Ctimes%20width%5C%5C%5C%5C%5Cfrac%7B45%7D%7B4%7D%20%3D%20%5Cfrac%7B9%7D%7B2%7D%20%5Ctimes%20width%5C%5C%5C%5Cwidth%20%3D%20%5Cfrac%7B45%7D%7B4%7D%20%5Ctimes%20%5Cfrac%7B2%7D%7B9%7D%5C%5C%5C%5Cwidth%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20%3D%202%5Cfrac%7B1%7D%7B2%7D)
Therefore width of foil is
inches
Answer:
6:5:2
Step-by-step explanation:
We need the amounts for v to be equal, so
u:v = 12:10 v is 10
v:w = 25:17 v is 25
Multiply the first ratio by 2.5 to get an equivalent amount for v
u:v = 30:25
so u:v:w = 30:25:10
They can all be divided by 5
6:5:2
Thank you for posting your question here at brainly. Feel free to ask more questions.
The best and most correct answer among the choices provided by the question is <span>C. x over 520 = 5 over 13</span>.<span>
</span><span>
Hope my answer would be a great help for you.</span>