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4 years ago

Add the two complex numbers 6 + 7i and 10 + 2i. Write your answer as a complex number in standard form, a + bi.

Mathematics

2 answers:

lina2011 [118]4 years ago

8 0

1. The complex number 6 + 7i has

real part 6;
imaginary part 7.

2. The complex number 10 + 2i has

real part 10;
imaginary part 2.

3. When we add two complex numbers, we add real parts and imaginary parts separately:

(6+7i)+(10+2i)=(6+10)+(7+2)i=16+9i.

Answer: 16+9i

Fynjy0 [20]4 years ago

8 0

<u>Answer:</u>

16 + 9i

<u>Step-by-step explanation:</u>

Every complex number has a real and an imaginary part.

We are given two complex numbers: $6+7i$ and $10+2i$ .

The complex number $6+7i$ has 6 as the real part and 7 as the imaginary one. While in $10+2i$ , 10 is the real part and 2 is the imaginary part.

We add real parts and imaginary parts separately in complex numbers:

$(6+7i)+(10+2i)$

$= (6+10) + i(7+2)$

$=16+9i$

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The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that $\mu = 273, \sigma = 100$

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 30, s = \frac{100}{\sqrt{30}}$

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}$

$Z = 0.88$

$Z = 0.88$ has a p-value of 0.8106

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 50, s = \frac{100}{\sqrt{50}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}$

$Z = 1.13$

$Z = 1.13$ has a p-value of 0.8708

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}$

$Z = -1.13$

$Z = -1.13$ has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 100, s = \frac{100}{\sqrt{100}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}$

$Z = -1.6$

$Z = -1.6$ has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0

3 years ago

Calcular s, si la figura es un prisma a=15m2, b=20m2

julia-pushkina [17]

Celculate the figures by using the numbers,with letters

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3 years ago

Please help me with the correct answers

Anna11 [10]

Answer:

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Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

Rod is paid $85 to install a screen door and $115 to install a wooden door. In one week he installed 18 doors and was paid a tot

Rainbow [258]

Answer:Rod installed 7 screen doors

Step-by-step explanation:

Step 1

Let the number of screen door = x

And the number of wooden doors = y

since he installed 18 doors , we have that

screen door + wooden doors = 18

x + y = 18------ equation 1

Also the cost to install a screen door -= $85

and to install a wooden door = $115

And he was therefore paid a total of $1850

Therefore

85x + 115 y = $1860------- equation 2

Step 2----- Solving

x + y = 18------ equation 1

85x + 115 y = $1860------- equation 2

Multiplying equation 1 BY 85

85x + 85y= 1530------- equation 3

85x + 115 y = $1860------- equation 4

subtracting from equation 1 from (2)

115y- 85y= 1860-1530

30y=330

y = 330/30 = 11

To find x

x+ y=18

x= 18-y

x= 18-11= 7

Rod installed 7 screen doors and 11 wooden doors.

8 0

3 years ago

Solve the equation. Check your solution.

Tasya [4]

Answer:

x = 5

Step-by-step explanation:

x^2/(x + 5) = 25/(x+5) Subtract the right side from both sides.

x^2/(x + 5) - 25/(x + 5) = 0

x^2 - 25

======= = 0

x + 5

(x + 5)(x - 5)

============= = 0

(x + 5)

Cancel x + 5 in the numerator and denominator.

x - 5 = 0

x = + 5

Does it check?

x^2/(x + 5) = 25/(x + 5)

x = 5

5^2/(10) = 25/10

25/10 = 25/10 Yes it checks.

7 0

3 years ago