Answer:
The principal investment required to get a total amount of $ 1,000,000.00 from compound interest at a rate of 6% per year compounded 12 times per year over 45 years is $ 67,659.17.
Step-by-step explanation:
Given
- Accrued Amount A = $1000000
- Interest rate r = 6% = 0.06
- Compounded monthly n = 12
To determine:
Using the formula
substituting A = 1000000, r = 0.06, t = 45, and n = 12
$
Therefore, the principal investment required to get a total amount of $ 1,000,000.00 from compound interest at a rate of 6% per year compounded 12 times per year over 45 years is $ 67,659.17.
Answer:
8
Step-by-step explanation:
Let's just call the number x for simplicity.
So, 7x is 8 less than x².
Putting this into an equation would look like this
x² - 8 = 7x
It looks like we'll have to factor this to solve. Before we do that we need to move the 7x to the left side so that everything is together.
x² - 7x -8 = 0
Now, we can proceed. To factor we first need to find the factors of -8.
The factors of -8 are
-2 ⋅ 4, -4 ⋅ 2, -1 ⋅ 8, 1 ⋅ -8.
We need to find the pair of factors that adds up to -7. The only ones that do are -1 and 8.
So now that we have these we can create a pair of binomials using them. This will give us the factored form of this equation.
( x + 1 ) ( x - 8 )
To find the solutions we will have to set them to 0 and solve each of these binomials individually.
x - 1 = 0
x = 1
So, one of the solutions is 1. It's not the one we want, since it's positive.
x - 8 = 0
x = 8
This is the one we want since it is positive.
Answer:
Monday: 5x + 14
Tuesday: Average is about 55.77 and Median is 56
Step-by-step explanation:
To combine like terms means to add or subtract the terms with similar variables. So I did as such to find the answer.
24 - 10 = 14 and 7x - 2x = 5x
The average is found by dividing the sum of all values in the list by the number of list options. The median is the value found in the middle of the list.
Answer:
Her initial position was:
-29ft
Where we use the minus sign because this is below the ocean's surface.
Now we also know that she keeps descending at a rate of -29ft per minute, then if she keeps descending for t minutes, her position will be:
P(x) = -29ft - 29ft/min*t
Now, we also know that she does not want to descend more than 81ft below the ocean's surface, then we have the inequality:
P(x) ≥ -81ft
-29ft - 29ft/min*t ≥ -81ft
Now let's isolate t in one side:
- 29ft/min*t ≥ -81ft + 29ft = -52 ft
- 29ft/min*t ≥-52 ft
t ≤ -52ft/(- 29ft/min) = 1.79 min
Then the maximum amount of time that she can keep descending is 1.79 minutes.
I believe it is B, because going down would be negative, and it is subtracting 6.
