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Whitepunk [10]
3 years ago
14

Which of the following is the conjugate of a complex number with 5 as the real part and −2 as the imaginary part?

Mathematics
1 answer:
ololo11 [35]3 years ago
7 0

Hello!

Given two real numbers "a" and "b", the complex number z is defined as:

The complex conjugate of "Z = a + bi" is "Z = a – bi"

Given the complex number Z = a - bi, "a" is called the real part and "b" the imaginary part.

Therefore:

Re(a) = 5

Im(b) = -2

z = a - bi

z = 5 - (-2)i

\boxed{\boxed{z = 5 + 2i}}\end{array}}\qquad\checkmark

Answer: 

a. 5 + 2i

__________________________

I Hope this helps, greetings ... DexteR! =)

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Ms Thomas drove at a constant rate for 45. She drove 39 miles during that time. If distance is determined by the equation d=rt w
Cerrena [4.2K]

Answer:

Ms. Thomas was driving at constant rate of 52 miles/hour.

Step-by-step explanation:

Given:

Total time to travel (t) = 45 minutes

Distance drove (d) = 39 miles

we need to find the constant rate in miles per hour at which she was driving.

Solution:

Now we know that;

We need to find constant rate at miles per hour;

But time is given in minutes.

So we will convert minutes into hour by dividing by 60 we get;

time t =\frac{45}{60}= 0.75\ hrs

Now we know that;

Distance is equal to rate times time.

framing in equation form we get;

distance d =rt

Or

rate r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr

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3 years ago
How do you find and use the greatest common factor of two whole numbers
Tasya [4]
For example you have the 52, and you have the 24, you look for a number that can go into both that is the largest possible for my example it would be 4 since no number greater can go into both, while 2 would be a option it would not be the greatest.

7 0
3 years ago
In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha
Afina-wow [57]

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

\pi = 0.21

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.  

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}

0.09\sqrt{n} = 1.96\sqrt{0.21*0.79}

\sqrt{n} = \frac{1.96\sqrt{0.21*0.79}}{0.09}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.21*0.79}}{0.09})^{2}

n = 78.68

Rounding up to the nearest whole number.

A sample size of 79 is needed.

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3 years ago
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Sub x=-5+2y
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What is the constant of variation, k,
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3 years ago
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