Answer: a) 8.779 years
b) 8.664 years
<u>Step-by-step explanation:</u>
a)

- A: accumulated amount (balance)
- P: principal amount (original/initial investment)
- r: interest rate (convert to a decimal)
- n: number of times compounded per year
- t: number of years
Given: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown

b)


3. Three and four tenths. 3+0.4=3.4
4. Two and fifty-one hundredths. 2+0.51=2.51
5. 8/10
6. 0.05
7. 46/100
8. 0.6
9. 9/10
10. 0.35
1 and 2 are correct btw
Short Answer: 18 minutes
Remark
The answer to this problem is less than the smallest time of the two people working together. that fact lets out C and D (38 minutes and 75 minutes). Now you have to choose 15 minutes and 18 minutes. There's a method. No guessing needed.
Givens
Let the time for Sophie = S
Let the time for Simon = M
Let the job to completion = 1
S = 45 minutes
M = 30 minutes
Step One
Convert minutes to hours.
45 minutes = 45 / 60 = 3/4 hour = 0.75 hour
30 minutes = 30 / 60 = 1/2 hour = 0.50 hour
Step Two
Set up the Equation
The formula is a form of job / hour.
Let the time = t that they both have to work
job = 1 in these problems.
1/S + 1/M = 1/t
1/0.75 + 1/0.5 = 1/t
Solve
1 ÷ 0.75 = 1.33333
1 ÷ 0.5 = 2
1.3333 + 2 = 3.33333
3.3333 = 1 / t Multlply both sides by t
3.3333*t = 1
t = 1 / 3.333333333
t = 0.3 of an hour
1 hour = 60 minutes
0.3 hours = x Cross Multiply
x = 60 * 0.3
x = 18 minutes
Answer working together it took them 18 minutes <<<<<
Option B is correct.
Step-by-step explanation:
We need to solve: ![\sqrt[3]{x^2}\sqrt[4]{x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E2%7D%5Csqrt%5B4%5D%7Bx%5E3%7D)
We know that: ![\sqrt[n]{x}\sqrt[b]{x} =\sqrt[n*b]{x.x}= \sqrt[n*b]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%5Csqrt%5Bb%5D%7Bx%7D%20%3D%5Csqrt%5Bn%2Ab%5D%7Bx.x%7D%3D%20%5Csqrt%5Bn%2Ab%5D%7Bx%5E2%7D)
Applying the above rule:
![\sqrt[3]{x^2}\sqrt[4]{x^3}\\=\sqrt[3*4]{x^2.x^3}\\=\sqrt[12]{x^5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E2%7D%5Csqrt%5B4%5D%7Bx%5E3%7D%5C%5C%3D%5Csqrt%5B3%2A4%5D%7Bx%5E2.x%5E3%7D%5C%5C%3D%5Csqrt%5B12%5D%7Bx%5E5%7D)
So, Option B is correct.
Keywords: Solving with Exponents
Learn more about Solving with Exponents at:
#learnwithBrainly