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Aleks04 [339]
3 years ago
5

Verify the following i.[ -3/4]3 = -27/64 ii. [-2/3]6 = 64/ 729

Mathematics
1 answer:
Juliette [100K]3 years ago
4 0

Answer:

The relationships are correct and valid

Step-by-step explanation:

The correct question is as follows;

Verify the following

i.[ -3/4]^3 = -27/64

ii. [-2/3]^6 = 64/ 729

We have the solution as follows;

i) we have;

(-3/4)^3

That means ;

-3^3 = -3^3 = -27

4^3 = 64

so;

(-3/4)^3 = -27/64

ii) (-2/3)^6

(-2)^6 = 64

3^6 = 729

Thus;

(-2/3)^6 = 64/729

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In ΔSTU, the measure of ∠U=90°, the measure of ∠T=32°, and US = 5.8 feet. Find the length of ST to the nearest tenth of a foot.
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A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.

B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.

C. The expected value of X is 6.75, and the standard deviation of X is 2.17.

Step-by-step explanation:

The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.

With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

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P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.00024*0.00423=0.183\\\\\\

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P(x\geq10)=1-P(x

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E(x)=\mu=n\cdot p=25\cdot 0.25=6.25\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot 0.25\cdot 0.75}=\sqrt{4.69}\approx2.17

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