8k=4/9 what is the answer

Mathematics

1 answer:

ki77a [65]3 years ago

5 0

8k = 4/9

Divide 8 to both sides, or multiply by its reciprocal 1/8:

k = 4/9 * 1/8

k = 4/72

k = 1/18

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(3⁵)²/3⁻² A. 3¹⁰ B. 3¹² C. <img src="https://tex.z-dn.net/?f=3%5E%7B9%7D" id="TexFormula1" title="3^{9}"

Novosadov [1.4K]

Answer:

B. 3¹²

Step-by-step explanation:

To solve this we need to apply the following laws of exponents:

1. $(a^n)^m=a^{n*m}$

2. $a^{-n}=\frac{1}{a^n}$

Let's apply the first law to the numerator of our fraction and the second law to the denominator. For the numerator, $(3^5)^2$ , $a=3$ , $n=5$ , and $m=2$ . For the denominator $3^{-2}$ , $a=3$ and $n=-2$

Replacing values

$\frac{(3^5)^2}{3^{-2}} =\frac{3^{5*2}}{\frac{1}{3^2} } =\frac{3^{10}}{\frac{1}{3^2} }$

Now, remember that to divide fractions we just need to invert the order of the second fraction and multiply:

$\frac{3^{10}}{\frac{1}{3^2} }=3^{10}*\frac{3^2}{1} =3^{10}*3^2$

Finally, we can use the law of exponents for multiplication to get our answer:

$a^n*a^m=a^{n+m}$

$3^{10}*3^2=3^{10+2}=3^{12}$

We can conclude that the correct answer is B. 3¹²

8 0

4 years ago

If N = , r = , and n = , and assuming that X has a hypergeometric probability distribution, compute the following. Write your an

artcher [175]

Answer:

(a) The value of P (X = 2) is 0.3571.

(b) The value of P (X ≤ 1) is 0.5952.

Step-by-step explanation:

A Hypergeometric distribution is used to describe the probability distribution of x successes in n random draws from a population of size N that contains exactly r items that are considered as success. In this distribution each draw results in either a success or a failure.

The probability mass function of Hypergeometric distribution is:

$P(X=x)=\frac{{r\choose x}{N-r\choose n-x}}{{N\choose n}}$