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3 years ago

What is the product of 4+3i and 4-3i

2 answers:

8 0

So we know that i=the square root of -1 so
we multiply and notice that is is in the format of the differnece of two perfect squares which is (x)^2-(y)^2=(x-y)(x+y) so
we notice that 4=x and 3i=y so

(4-3i)(4+3i)=(4)^2-(3i)^2

(3 times the square root of -3)^2=(9 times -1)=-9
4^2 is 16
16-(-9)=subtracting a negative=adding a positive so =16+9=25
the answer is 25

mash [69]3 years ago

7 0

Use the formula $(a+b)(a-b)=a^2-b^2$ .

$(4+3i)(4-3i)=4^2-(3i)^2=16-9i^2 \\ \\
i^2=-1 \\ \\
16-9i^2=16-9 \times (-1)=16+9=25 \\ \\
\boxed{(4+3i)(4-3i)=25}$

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What is the practice of gathering data and ensuring that it is uniform, accurate, consistent, and complete, including such entit

baherus [9]

Answer: Option 2 is the answer

Step-by-step explanation:

Master data management (MDM) is the practice of gathering data and ensuring that it is uniform, accurate, consistent, and complete, including such entities as customers, suppliers, products, sales, employees, and other critical entities that are commonly integrated across organizational systems.

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3 years ago

Suppose in the University of Manitoba, 40% of the students live in apartments. If 600 students are randomly selected, then the a

just olya [345]

Answer:

$P(200\leq X\leq 400)=P(\frac{200-240}{12}\leq \frac{X-\mu}{\sigma}\leq \frac{400-240}{12})=P(-3.33\leq Z \leq 13.33)$

$=P(Z$

So then the correct answer would be:

B) .9996

Step-by-step explanation:

The exact way to solve this problem is using the binomial distribution, assuming that our random variable of interest is "number of students living in apartments" represented by X and $X \sim Bin(n=600, p =0.4)$

And we want this probability:

$P(200 \leq X \leq 400) [tex]In order to find this probability we can use the foloowing excel code:"=BINOM.DIST(400,600,0.4,TRUE)-BINOM.DIST(199,600,0.4,TRUE)"And we got:[tex] P(200 \leq X \leq 400) =0.999675[tex]But for this case the problem says that we need to approximate, so then we can use the normal approximation to the normal distribution. We need to check the conditions in order to use the normal approximation.
[tex]np=600*0.4=240\geq 10$

$n(1-p)=600*(1-0.4)=360 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=600*0.4=240$

$\sigma=\sqrt{np(1-p)}=\sqrt{600*0.4(1-0.4)}=12$

And then $X \sim N (\mu = 240, \sigma= 12)$

And we are interested on the following probability:

$P(200\leq X\leq 400)=P(\frac{200-240}{12}\leq \frac{X-\mu}{\sigma}\leq \frac{400-240}{12})=P(-3.33\leq Z \leq 13.33)$

$=P(Z$

So then the correct answer would be:

B) .9996

6 0

3 years ago

PLS HELP<br> how many solutions does this system of equations below have?<br><br> y=8x+4<br> y=8x+3

serious [3.7K]

There are to be exact only 2 ways to answer this equation because of the way math was made.

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3 years ago

The area of a rectangle is 8w + 18 square feet. The length of the rectangle is 2 feet. Use factoring to write an expression to r

qwelly [4]

Answer:

4w + 9

Step-by-step explanation:

Area of rectangle = length x width (or base x height, depending on how you look at it).

It is given to you that:

Area = 8w + 18

Length = 2

Let: width = x

Plug in the corresponding terms with the corresponding words:

8w + 18 = 2x

Isolate the variable, x. Divide 2 from both sides of the equation:

(8w + 18)/2 = (2x)/2

x = (8w + 18)/2

w = (8w)/2 + (18)/2

w = 4w + 9

4w + 9 is the expression that represents the width of the rectangle.

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2 years ago

A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 50 models

polet [3.4K]

Answer:

The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: $Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}$ , where:

$x_2$ is the second point in the function

$x_1$ is the first point in the function

$f(x_2)$ is the function evaluated at the second point

$f(x_1)$ is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so $x_1=1$ and $x_2=10$ . Replacing values:

$Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}$

$Av=\frac{-100+200+50-[-1+20+50]}{9}$

$Av=\frac{150-[69]}{9}$

$Av=\frac{150-69}{9}$

$Av=\frac{81}{9}$

$Av=9$

Since $f(x)$ represents the number of pounds per acre and $x$ the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

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3 years ago