True or False

Please help me out and explain it to me

a_sh-v [17]

Answer: C

Step-by-step explanation:

You can solve this by first multiplying both sides of the fraction by the conjugate of the denominator.

In this case, the conjugate is (8 - 2i).

So:

$\frac{3-5i}{8+2i} *\frac{8-2i}{8-2i}$

Simplify:

$\frac{24-46i+10i^2}{64 - 4i^2}$

Simplify again, knowing that i^2 = -1

$\frac{14 -46i}{68}$

Then, divide both numbers in the numerator by 68 to get your answer.

$\frac{7}{34} -\frac{23i}{34}$

8 0

3 years ago

Complete the set of ordered pairs for the relation.

neonofarm [45]

The set of ordered pairs is:

{(-2, 2), (-1, 0), (0, 2), (1, 4), (2, 6)}

<h3>How to complete the set of ordered pairs?</h3>

Here we have the relation:

y = 2*|x + 1|

And the domain is x ∈ { -2, -1, 0, 1, 2}

Evaluating in the values of the domain, we get:

if x = -2.

y = 2*|-2 + 1| = 2

Then we have the ordered pair (-2, 2)

if x = -1

y = 2*|-1 + 1| = 0

Then we have the ordered pair (-1, 0)

if x = 0

y = 2*|0 + 1| = 2

Then we have the ordered pair (0, 2)

if x = 1

y = 2*|1 + 1| = 4

Then we have the ordered pair (1, 4)

if x = 2

y = 2*|2 + 1| = 6

Then we have the ordered pair (2, 6)

The set of ordered pairs is:

{(-2, 2), (-1, 0), (0, 2), (1, 4), (2, 6)}

If you want to learn more about ordered pairs:

brainly.com/question/1528681

#SPJ1

6 0

1 year ago

Does anybody know the answer <br>

IgorLugansk [536]

Answer:C

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Malik buys and sells car parts. He bought two tires for $45.00 each and later sold them for $65.00 each. He bought three rims fo

Alona [7]

The answer is $213 because you subtract the price sold by the price he bought them for and then you add them together (see work)

6 0

2 years ago

Read 2 more answers

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9

Eva8 [605]

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that $\mu = 8.9, \sigma = 2.9$

Sample of 37:

This means that $n = 37, s = \frac{2.9}{\sqrt{37}}$

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -0.53$

$Z = -0.53$ has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -3.08$

$Z = -3.08$ has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

7 0

2 years ago