Answer:
Step-by-step explanation:
Hello,
We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :
For the second week
After 52 weeks
and we want to be equal to 2000 so we need to solve:
![1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...](https://tex.z-dn.net/?f=1000%5Ccdot%20%281%2B%5Cdfrac%7Br%7D%7B5200%7D%29%5E%7B52%7D%3D2000%5C%5C%5C%5C%5Ctext%7B%2A%2A%2A%20divide%20by%201000%20both%20sides%20%2A%2A%2A%7D%5C%5C%5C%5C%281%2B%5Cdfrac%7Br%7D%7B5200%7D%29%5E%7B52%7D%3D%5Cdfrac%7B2000%7D%7B1000%7D%3D2%5C%5C%5C%5C%5Ctext%7B%2A%2A%2A%20take%20the%20ln%20%2A%2A%7D%5C%5C%5C%5C52%5Ccdot%20ln%281%2B%5Cdfrac%7Br%7D%7B5200%7D%29%3Dln%282%29%5C%5C%5C%5C%5Ctext%7B%2A%2A%2A%20divide%20by%2052%20%2A%2A%2A%7D%5C%5C%5C%5Cln%281%2B%5Cdfrac%7Br%7D%7B5200%7D%29%3D%5Cdfrac%7Bln%282%29%7D%7B52%7D%5C%5C%5C%5C%5Ctext%7B%2A%2A%2A%20take%20the%20exp%20%2A%2A%2A%7D%5C%5C%5C%5C%5Cdisplaystyle%201%2B%5Cdfrac%7Br%7D%7B5200%7D%3Dexp%28%5Cdfrac%7Bln%282%29%7D%7B52%7D%29%3D2%5E%7B%28%5Cdfrac%7B1%7D%7B52%7D%29%7D%3D%5Csqrt%5B52%5D%7B2%7D%5C%5C%5C%5Cr%20%3D%205200%5Ccdot%20%28%5Csqrt%5B52%5D%7B2%7D-1%29%3D69.77875...)
Rounded to the nearest percent, the solution is 70%.
If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
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Answer:
7 hours
Step-by-step explanation:
They will be at the same place when Kara completes one lap and Steven completes 2 laps. It will take Kara 7 hours to complete one lap.
(105 km)/(15 km/h) = 7 h
Answer:
Step-by-step explanation:
Arithmetic sequence:
a = first term = 4
d = common difference = second term - first term
= 9 - 4
d = 5
= 4 + (n - 1) *5
= 4 + 5n - 5
= 5n -1
Check; n= 1 , first term = 5*1 - 1 = 5 - 1 = 4
n = 2, second term = 5*2 - 1 = 10 -1 = 9
n = 3, third term = 5*3 - 1 = 15 - 1 = 1
The next term, fifth term = 5*5 - 1
= 25 - 1
= 24
The cafeteria sold 41 corn chips and 80 potato chips.
Step-by-step explanation:
Let,
Corn chips = x
Potato chips = y
Price of corn chips = $0.80
Price of potato chips = $0.60
According to given statement;
x+y= 121 Eqn 1
0.80x+0.60y=80.80 Eqn 2
Multiplying Eqn 1 by 0.80
Subtracting Eqn 2 from Eqn 3
Dividing both sides by 0.20
Putting y=80 in Eqn 1
The cafeteria sold 41 corn chips and 80 potato chips.
Keywords: linear equation, subtraction
Learn more about linear equations at:
#LearnwithBrainly
Answer:
4.53
Step-by-step explanation:
Given the data :
4, 5, 10, 11, 15
The mean = 9
The standard deviation of a sample :
s = √[Σ(x - mean)²/(n-1)]
s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]
s = √(25+16+1+4+36)/4
s = √20.5
s = 4.527
s = 4.53
