C 87 the median :::::::::::::
Answer:
Bank B because the more often you compound interest, the more interest you earn.
Step-by-step explanation:
Bank A compounds the interest once a year.
Bank B compounds the interest twice a year.
Let's create an example of two investments of the same amount of money, the same interest rate, and the same time. The only difference will be the number of times the interest is compounded per year.
Compound interest formula:
![A = P(1 + \dfrac{r}{n})^{nt}](https://tex.z-dn.net/?f=%20A%20%3D%20P%281%20%2B%20%5Cdfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20)
where
A = future value
P = principal invested
r = interest rate
t = number of years
n = number of times interested is compounded in 1 year
Example:
P = $1000
r = 5%
t = 5 years
Bank A: n = 1
Bank B: n = 2
Bank A:
![A = $1000(1 + \dfrac{0.05}{1})^{1 \times 5} = $1276.28](https://tex.z-dn.net/?f=%20A%20%3D%20%241000%281%20%2B%20%5Cdfrac%7B0.05%7D%7B1%7D%29%5E%7B1%20%5Ctimes%205%7D%20%3D%20%241276.28)
Bank B:
![A = $1000(1 + \dfrac{0.05}{2})^{2 \times 5} = $1280.08](https://tex.z-dn.net/?f=%20A%20%3D%20%241000%281%20%2B%20%5Cdfrac%7B0.05%7D%7B2%7D%29%5E%7B2%20%5Ctimes%205%7D%20%3D%20%241280.08)
Bank A's investment is worth $1276.28 after 5 years, but Bank B's investment is worth $1280.08 after the same 5 years. Compounding twice per year instead of only once per year earns more interest.
Answer: (7x + 8)³ ↔ the cube of the sum of 7x and 8
7(x + 8)³ ↔ 7 times the cube of the sum of x and 8
7x³ + 8 ↔ 8 added to the product of 7 and x cubed
(7x)³ + 8 ↔ 8 added to the cube of 7x
Step-by-step explanation:
(7x + 8)³ ↔ the cube of the sum of 7x and 8: for this case you will find that the values are into the parenthesis, then for each value apply the same exponent because of that all the values into the parenthesis are elevated to the cube,
7(x + 8)³ ↔ 7 times the cube of the sum of x and 8: in this example the 7 is multiplying all the values into the parenthesis, then you can find six times the sum of x and 8 elevated to the cube, also keep in mind that exponent which is 3 only apply to the values which are into the parenthesis and this values are the x and 8
7x³ + 8 ↔ 8 added to the product of 7 and x cubed: for this equation, you will find that 7 is multiplying to the x elevated to the cube after that, the 8 is added to this product.
(7x)³ + 8 ↔ 8 added to the cube of 7x: this final we can see that the values into the parenthesis are elevated to cube, the values are 7 and x, after this equation the 8 is added to the product.
Answer:
P = 0.0909
Step-by-step explanation:
To know the number of ways or combinations in which we can select x elements from a group of n elements, we can use the following equation:
![nCx=\frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=nCx%3D%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
So, if you sat down at your computer and randomly loaded 4 of the 12 problems, there are 495 different possibilities and it is calculated as:
![12C4=\frac{12!}{4!(12-4)!}=495](https://tex.z-dn.net/?f=12C4%3D%5Cfrac%7B12%21%7D%7B4%21%2812-4%29%21%7D%3D495)
Then, from 495 different possibilities, there are 45 possibilities that both this problem and Richard Rusczyk's problem were among the four you loaded. This 45 possibilities are calculated as:
![(1C1)*(1C1)*(10C2)=(\frac{1!}{1!(1-1)!})*(\frac{1!}{1!(1-1)!})*(\frac{10!}{2!(10-2)!})=45](https://tex.z-dn.net/?f=%281C1%29%2A%281C1%29%2A%2810C2%29%3D%28%5Cfrac%7B1%21%7D%7B1%21%281-1%29%21%7D%29%2A%28%5Cfrac%7B1%21%7D%7B1%21%281-1%29%21%7D%29%2A%28%5Cfrac%7B10%21%7D%7B2%21%2810-2%29%21%7D%29%3D45)
Because you need to select: this problem and there is only one, the problem that Richard Rusczyk wrote and there is only one, and 2 problems from the other 10.
Finally, the probability that both this problem and Richard Rusczyk's problem were among the four you loaded is equal to:
![P=\frac{45}{495}=0.0909](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B45%7D%7B495%7D%3D0.0909)