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Natalija [7]
3 years ago
8

What is the value of k in the equation? 20^k/ 20^4 = 20^9

Mathematics
2 answers:
GalinKa [24]3 years ago
6 0

Answer:

k = 13

Step-by-step explanation:

20^k / 20^4 = 20^9

20^ k = 20^9 * 20^4

this is a math rule

a^n * a^m = a^(n+m)

this is because the denominators of a are the same

in this question , the bases are 20

in the case of multiplication when the bases are the same , we add the powers

hence we add the powers

= 9 + 4

= 13

hence <u>k = 13</u>

Luden [163]3 years ago
4 0

Answer:

k = 13

Step-by-step explanation:

20 ^ k / 20^4 = 20^9

knowing the laws of exponents, diving two numbers of the same base with exponents is like subtracting the exponents, so

k^x / k^y

= k ^ (x - y)

apply that knowledge here

20 ^ k / 20 ^ 4 = 20 ^ 9

20 ^ ( k - 4 ) = 20 ^ 9

now the bases have no use here so ignore them, and just calculate the exponents

k - 4 = 9

solve using inverse operations

k - 4 = 9

+4       +4

k = 13

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How would I graph

Solution:
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8 0
3 years ago
An elevator containing five people can stop at any of seven floors. What is the probability that no two people exit at the same
elena-s [515]

Answer:

Approximately 0.15 (360 / 2401.) (Assume that the choices of the 5 passengers are independent. Also assume that the probability that a passenger chooses a particular floor is the same for all 7 floors.)

Step-by-step explanation:

If there is no requirement that no two passengers exit at the same floor, each of these 5 passenger could choose from any one of the 7 floors. There would be a total of 7 \times 7 \times 7 \times 7 \times 7 = 7^{5} unique ways for these 5\! passengers to exit the elevator.

Assume that no two passengers are allowed to exit at the same floor.

The first passenger could choose from any of the 7 floors.

However, the second passenger would not be able to choose the same floor as the first passenger. Thus, the second passenger would have to choose from only (7 - 1) = 6 floors.

Likewise, the third passenger would have to choose from only (7 - 2) = 5 floors.

Thus, under the requirement that no two passenger could exit at the same floor, there would be only (7 \times 6 \times 5 \times 4 \times 3) unique ways for these two passengers to exit the elevator.

By the assumption that the choices of the passengers are independent and uniform across the 7 floors. Each of these 7^{5} combinations would be equally likely.

Thus, the probability that the chosen combination satisfies the requirements (no two passengers exit at the same floor) would be:

\begin{aligned}\frac{(7 \times 6 \times 5 \times 4 \times 3)}{7^{5}} \approx 0.15\end{aligned}.

5 0
2 years ago
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krok68 [10]
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rusak2 [61]

Answer:

1. B     2. B

Step-by-step explanation:

1. The formula for circumference is C= pi times diameter

Radius is half of diameter, so you'd multiply 14 times 2 which gives you 28. Since it's asking for it in pi, it'll be 28 pi.

2. I think instead of circumference, it's asking for area because if it was asking for circumference the answer would have been 6.6 pi, but that answer isn't there. So if it's asking for area, the formula is A= pi(r²) They gave the diameter instead. Remember, the radius is half of the diameter, so in order to get the radius, you'd divide 6.6 by 2 and get 3.3. Then, multiply 3.3 with the number itself, and you'll get 10.89.

Hope this helps!

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3 years ago
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