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2 years ago

HELP!!!!!!!! Select an expression that id equivalent to 4squareroot of 2x^2 • 4squareroot of 2x^3

Mathematics

1 answer:

earnstyle [38]2 years ago

8 0

Answer:

Step-by-step explanation:

$\sqrt[4]{2x^2} *\sqrt[4]{2x^3} =(2x^2)^{1/4}*(2x^3)^{1/4}\\= 2^{1/4}*(x^2)^{1/4} *2^{1/4} * (x^3)^{1/4}\\$

combine like terms

$= 2^{2/4} *x^{2/4}*x^{3/4}\\= 2^{2/4} * x^{5/4}$

these steps use exponent laws

a few key ones i used:

(x^y^z) = x^(y*z)

x^y * x^z = x^(y+z)

let me know if you have any questions!

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3 years ago

Find the probability of exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%. rou

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Answer:

<u> The probability of exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%, is:</u>

<u>31.3% (Rounding to the nearest tenth)</u>

Step-by-step explanation:

With the information provided, P = 0.5, n = 6 and k = 3, we can build the binomial distribution table, this way:

Binomial distribution (n=6, p=0.5)

f(x) F(x)

x Pr[X = x] Pr[X ≤ x]

0 0.0156 0.0156

1 0.0938 0.1094

2 0.2344 0.3438

3 0.3125 0.6563

4 0.2344 0.8906

5 0.0938 0.9844

6 0.0156 1.0000

Under the first column we have the probabilities of success of every value from 0 to 6, and under the second column we have the values for answering the question at least how much probability we have of any number of successes. Our question is exactly 3 successes in 6 trials and we see that value under the first column: 0.3125.

Therefore, the probability of exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%, is:

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Let's recall that the formula for calculating the probability of exact successes is:

P(k out of n) = (n!/k!(n-k)!) * (p∧k*(1-p)∧(n-k))

in our case p=0.5, n=6, k=3

(n!/k!(n-k)!) = 20 and (p∧k*(1-p)∧(n-k)) = 0.015625

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