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3 years ago

If z = 1 - square root 3i, what is z^3 Answers -8 8 -8i 8i

Mathematics

1 answer:

sukhopar [10]3 years ago

7 0

Answer:

$z = 1 - \sqrt{3} i \\ {z}^{3} = (1 - \sqrt{3} i) ^{3} \\ =(1 - \sqrt{3} i)(1 - \sqrt{3} i)(1 - \sqrt{3} i) \\ open \: brackets \\ = (1 - 2 \sqrt{3} i + ( { \sqrt{3} i})^{2} )(1 - \sqrt{3} i) \\ but \: {( \sqrt{3}i) }^{2} = - 3 \: since \: {i}^{2} \: is \: - 1 \: in \: complex \: numbers \\ = (1 - 2 \sqrt{3} i - 3)(1 - \sqrt{3} i) \\ = ( - 2 - 2 \sqrt{3} i)(1 - \sqrt{3} i) \\ = ( - 2 + 2 \sqrt{3} i - 2 \sqrt{3} i + 2( { \sqrt{3} i)}^{2} ) \\ = - 2 - 6 \\ = - 8$

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The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds

Bumek [7]

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

$\text{z-score} = \frac{x - \mu}{\sigma}$

where

$t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}$

So, the z-score of 720 seconds is given by:

$\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}$

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

$P(t \ \textgreater \ 720) 
\\ = P(z \ \textgreater \ 1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\ \boxed{P(t \ \textgreater \ 720) = 0.115}$

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

8 0

3 years ago

In the first event, the eighth graders are running a baton relay race with three other classmates. The teams top speed for each

chubhunter [2.5K]

Answer:

The best time is 56.81 seconds

Average leg time is 58.3825 seconds

Step-by-step explanation:

Here, we want to start by stating the team’s best time for the race

The team’s best time for the race is the smallest time spent on a lap

From the times given, the best time is 56.81 seconds

Now, we want to calculate the average time

We simply add up all these and divide by count

Mathematically, that will be;

(56.81 + 59.22 + 57.39 + 60.11)/4 = 58.3825 seconds

8 0

3 years ago

Find the missing angle. Show all your work. Pls, answer!

slega [8]

Steps:
(n-2) * 180 = sum of interior angles
(3-2) * 180 = 180

Bottom Triangle
25 + 51 + x = 180
x = 104

Top Triangle
104 + 34 + x = 180
x = 42

Answer:
42

7 0

2 years ago

A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 fem

Butoxors [25]

Answer: = ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

65.3 +/-1.645(5.2/√36)

65.3 +/-1.645(0.86667)

65.3+/- 1.4257

65.3+/- 1.4

= ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

4 0

3 years ago

The mean number of hours of part-time work per week for a sample of 526526 college students is 2828. If the margin of error for

sveta [45]

Answer:

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

Step-by-step explanation:

A confidence interval has the following format.

$\mu_{x} \pm M$

In which $\mu_{x}$ is the mean of the sample and M is the margin of error.

In this problem, we have that:

$\mu_{x} = 28, M = 2.2$

$\mu_{x} - M = 28 - 2.2 = 25.8$

$\mu_{x} + M = 28 + 2.2 = 30.2$

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

4 0

3 years ago