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3 years ago

Convert to rectangular form.

Mathematics

1 answer:

Artist 52 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

= 6cos ( $\frac{5\pi }{6}$ ) + 6i sin ( $\frac{5\pi }{6}$ )

the related acute angle of $\frac{5\pi }{6}$ is $\frac{\pi }{6}$

= - 6 cos ( $\frac{\pi }{6}$ ) + 6i sin ( $\frac{\pi }{6}$ )

= - 6 × $\frac{\sqrt{3} }{2}$ + 6 i × $\frac{1}{2}$

= - 3 $\sqrt{3}$ + 3i → B

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An angle measures 6 times the measure of its supplemantary angle. Find the measure of both angles

galben [10]

Answer:

Step-by-step explanation:

The measures of two supplementary angles add to 180 degrees.

One angle measures x.

The supplement measures 6x.

The sum of the measures is 180 deg.

x + 6x = 180

7x = 180

x = 180/7

6x = 1080/7

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3 years ago

Solve each equation for the indicated variable <br><br> g = c + x solve for x

Elis [28]

Answer:

Step-by-step explanation:

g = c + x |<em>subtract c from both sides</em>

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3 years ago

Discrete R.V. Assume a student shows up for EGR 280 completely unprepared and the instructor gives a pop quiz. Assume there are

Tom [10]

Answer:

a) p=0.2

b) probability of passing is 0.01696

c) The expected value of correct questions is 1.2

Step-by-step explanation:

a) Since each question has 5 options, all of them equally likely, and only one correct answer, then the probability of having a correct answer is 1/5 = 0.2.

b) Let X be the number of correct answers. We will model this situation by considering X as a binomial random variable with a success probability of p=0.2 and having n=6 samples. We have the following for k=0,1,2,3,4,5,6

$P(X=k) = \binom{n}{k}p^{k}(1-p)^{n-k} = \binom{6}{k}0.2^{k}(0.8)^{6-k}$ .

Recall that $\binom{n}{k}= \frac{n!}{k!(n-k)!}$ In this case, the student passes if X is at least four correct questions, then

$P(X\geq 4) = P(X=4)+P(X=5)+P(X=6)=\binom{6}{4}0.2^{4}(0.8)^{6-4}+\binom{6}{5}0.2^{5}(0.8)^{6-5}+\binom{6}{6}0.2^{6}(0.8)^{6-6}= 0.01696$

c)The expected value of a binomial random variable with parameters n and p is $E[X] = np$ . IN our case, n=6 and p =0.2. Then the expected value of correct answers is $6\cdot 0.2 = 1.2$