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algol [13]
3 years ago
10

Your friend multiplied complex numbers and expressions as shown. Find the error in your friends work. Then factor the expression

correctly. Show work please.
(4-7i)(4+7i)=16+28i-28i+49i^2
=16-49
=-33
Mathematics
1 answer:
MaRussiya [10]3 years ago
6 0

Answer:

  = 16+49 = 65

Step-by-step explanation:

The error is at the end of the first line. (-7i)(7i) = -49i² ≠ +49i².

The correct work is ...

  (4-7i)(4+7i)=16+28i-28i-49i^2

  = 16+49

  = 65

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The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012)
Wittaler [7]

Answer:

Yes, there is a difference between the population mean for the math scores and the population mean for the writing scores.

Test Statistics =   \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1 .

Step-by-step explanation:

We are provided with the sample data showing the math and writing scores for a sample of twelve students who took the SAT ;

Let A = Math Scores ,B = Writing Scores  and D = difference between both

So, \mu_A = Population mean for the math scores

       \mu_B = Population mean for the writing scores

 Let \mu_D = Difference between the population mean for the math scores and the population mean for the writing scores.

            <em>  Null Hypothesis, </em>H_0<em> : </em>\mu_A = \mu_B<em>     or   </em>\mu_D<em> = 0 </em>

<em>      Alternate Hypothesis, </em>H_1<em> : </em>\mu_A \neq  \mu_B<em>      or   </em>\mu_D \neq<em> 0</em>

Hence, Test Statistics used here will be;

            \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1    where, Dbar = Bbar - Abar

                                                               s_D = \sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}}

                                                               n = 12

Student        Math scores (A)          Writing scores (B)         D = B - A

     1                      540                            474                                   -66

     2                      432                           380                                    -52  

     3                      528                           463                                    -65

     4                       574                          612                                      38

     5                       448                          420                                    -28

     6                       502                          526                                    24

     7                       480                           430                                     -50

     8                       499                           459                                   -40

     9                       610                            615                                       5

     10                      572                           541                                      -31

     11                       390                           335                                     -55

     12                      593                           613                                       20  

Now Dbar = Bbar - Abar = 489 - 514 = -25

 Bbar = \frac{\sum B_i}{n} = \frac{474+380+463+612+420+526+430+459+615+541+335+613}{12}  = 489

 Abar =  \frac{\sum A_i}{n} = \frac{540+432+528+574+448+502+480+499+610+572+390+593}{12} = 514

 ∑D_i^{2} = 22600     and  s_D = \sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}} = \sqrt{\frac{22600 - 12*(-25)^{2} }{12-1} } = 37.05

So, Test statistics =   \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1

                            = \frac{-25 - 0}{\frac{37.05}{\sqrt{12} } } follows t_1_1   = -2.34

<em>Now at 5% level of significance our t table is giving critical values of -2.201 and 2.201 for two tail test. Since our test statistics doesn't fall between these two values as it is less than -2.201 so we have sufficient evidence to reject null hypothesis as our test statistics fall in the rejection region .</em>

Therefore, we conclude that there is a difference between the population mean for the math scores and the population mean for the writing scores.

8 0
3 years ago
Explain how you would order from the least to the greatest three numbers that include a positive number, a negative number, and
jeyben [28]
Well, zero is between negative and positive numbers. Negative number are less than zero and positive numbers. Positive number are greater than negative number and zero. And, zero is greater than negative number but smaller than positive number.

Negative number < Zero < Positive number
7 0
3 years ago
What is the range of the function represented by the table of values below?
Viefleur [7K]
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Smallest y values is -9 and the highest y values is 9.
So the range is -9 \leq y \leq 9
4 0
3 years ago
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KatRina [158]

Answer:

30-100

28-100

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7-100

Step-by-step explanation:

It's hard to explain but I try

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and the whole it he whole amount of the part

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8 0
3 years ago
PLEASE SOMEONE HELP QUICK What is the effect on the graph of the function f(x) = x when f(x) is replaced with f(− 1/3x)?
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Answer:

B

Step-by-step explanation:

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7 0
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