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3 years ago

4. The distance between a + 7i and -8 + 4i

Mathematics

1 answer:

Elis [28]3 years ago

4 0

Answer:

Step-by-step explanation:

$\text{The formula of a distance between two complex numbers}\\\\z_1=a+bi,\ z_2=c+di:\\\\d(z_1,\ z_2)=|z_2-z_1|\ \text{where}\ |z|=\sqrt{Re^2+Im^2}\\\\=============================$

$z_1=a+7i,\ z_2=-8+4i\\\\d(z_1,\ z_2)=|(-8+4i)-(a+7i)|=|-8+4i-a-7i|=|-8-a-3i|\\\\=\sqrt{(-8-a)^2+3^2}\\\\d(z_1,\ z_2)=\sqrt{130},\\\\\text{therefore}\ \sqrt{(-8-a)^2+3^2}=\sqrt{130}\Rightarrow(-8-a)^2+3^2=130\\\\\bigg(-(8+a)\bigg)^2+9=130\qquad\text{subtract 9 from both sides}\\\\(8+a)^2=121\iff8+a=\pm\sqrt{121}\\\\8+a=\pm11\qquad\text{subtract 8 from both sides}\\\\a=-19\ or\ a=3$

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In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches.

Vladimir79 [104]

Answer:

A. 16%

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 64, \sigma = 4$

Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?

This is 1 subtracted by the pvalue of Z when X = 68. So

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

$Z = \frac{68 - 64}{4}$

$Z = 1$

$Z = 1$ has a pvalue of 0.84.

1 - 0.84 = 0.16

So the correct answer is:

A. 16%

6 0

3 years ago

The test scores of five students for the first two test of the semester are shown in the table below.

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Take test score from Test 1 and add them all together and divide by the number of test

ex) 77+82+69+85+93=406

406/5= 81.2

Then repeat with Test 2

ex) 75+76+71+68+72=362

362/5= 72.4

Therefore the MAD of Test 1 > MAD of Test 2

8 0

2 years ago

Read 2 more answers

higher order thinking shailen is adding three numbers he gets a sum that is an even number between 10 and 20 show two addition e

nika2105 [10]

18: 15+2+1=18

18: 12+3+3=18

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3 years ago

Simplify

ivolga24 [154]

The correct answer is: [A]: " $\frac{8}{729}$ " .
_________________________________________________________
Explanation:
_________________________________________________________
We are asked to simplify:

  → $(\frac{2}{9})^3$

_________________________________________________________
Note the following property of exponents:
_________________________________________________________

$( \frac{a}{b})^n$   = $\frac{(a^n)}{(b^n)}$ ; { b $\neq$ 0 } .

_________________________________________________________
As such:

→ $( \frac{2}{9})^3$ ;

= $\frac{2^3}{9^3}$ = $\frac{(2*2*2)}{(9*9*9)}$ = $\frac{8}{729}$ .

_____________________________________________________________

The answer is: " $\frac{8}{729}$ " ;

→ which is: "Answer choice: [A]:  " $\frac{8}{729}$ " .
_____________________________________________________________
Hope this answer—and explanation—is of some help to you.
Please comment below or otherwise respond to me if you have any questions or if I can be of further assistance.
Best wishes!

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3 years ago

Read 2 more answers

Find a rational and irrational number between 9.5 and 9.7.

pshichka [43]

So we know that it must be between 9.5 9.7.. So it has to be 9.56763865854637984... (rounded 9.57) it is irrational because it has no pattern.

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3 years ago