Step-by-step explanation:
by considering how many inches (") are in one foot (').
the answer is 12. there are 12 in in every ft.
so, now we can convert everything to the smallest scale (inches) and do the calculation based on inches :
(8×12 + 4) - (2×12 + 6) = 96 + 4 - 24 - 6 = 100 - 30 = 70"
and now to translate 70" back into ft and in :
70/12 = 5 with a remainder of 10
70" = 5' 10"
Answer:
11.2 units
Step-by-step explanation:
From (-7, -7) to (-2, 3) is 5 units horizontally and 10 units vertically. Thus we have a right triangle with sides 5 and 10 respectively. The length of the hypotenuse of this triangle is the distance between (-2, 3) & (-7, -7):
d = √(5² + 10²) = √(25 + 100) = √125 = √25√5, or 5√5.
This is approximately 11.2 units
Answer:
40/51
Step-by-step explanation:
Answer:
The initial amount of investment was $7,822
Step-by-step explanation:
The formula for compound interest, including principal sum is:
, where
- <em>A</em> is the future value of the investment/loan, including interest
- <em>P</em> is the principal investment amount
- <em>r</em> is the annual interest rate (decimal)
- <em>n</em> is the number of times that interest is compounded per unit t
- <em>t</em> is the time the money is invested or borrowed for
Let us use this rule to solve the question
∵ Sam invests a sum of money in a retirement account with a fixed
annual interest rate of 7% compounded quarterly
∴ <em>r </em>= 7% = 
= 0.07
∴ <em>n</em> = 4 ⇒ compounded quarterly
∵ After 13 years, the balance reaches $19,280.02
∴ <em>A</em> = 19,280.02
∴ <em>t </em>= 13
Substitute these values in the rule above to find <em>P</em>
∵ 
∴ 
→ Divide both sides by 
∴ 7,821.99888 = <em>P</em>
→ Round it to the nearest dollar
∴ 7,822 = <em>P</em>
∴ <em>P</em> = $7,822
∴ The initial amount of investment was $7,822.
<h3>
Answer: 1/25</h3>
======================================================
Work Shown:
A = event of landing on a number greater than 8
P(A) = 1/5
We have 1 number that is greater than 8 (which is the space "9") out of 5 total
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B = event of landing on a divisor of 81
B = event of landing on 9, since 9 is a divisor of 81 (no other numbers listed are a divisor of 81)
P(B) = 1/5 for identical reasoning as above
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P(A and B) = P(A)*P(B)
P(A and B) = (1/5)*(1/5)
P(A and B) = 1/25
