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kipiarov [429]
3 years ago
5

What is the completely simplified equivalent of 2/(5+i)?

Mathematics
1 answer:
Bezzdna [24]3 years ago
4 0

namely, let's rationalize the denominator in the fraction, for which case we'll be using the <u>conjugate</u> of that denominator, so we'll multiply top and bottom by its <u>conjugate</u>.

so the denominator is 5 + i, simply enough, its conjugate is just 5 - i, recall that same/same = 1, thus (5-i)/(5-i) = 1, and any expression multiplied by 1 is just itself, so we're not really changing the fraction per se.

\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}

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A regular hexagon is shown.
zhuklara [117]

The central angle of the hexagon is equal to 60º.

Therefore, the trigonometric relationship for the radius is given by:

cos (30) = \frac{a}{c}

Where,

a: apothema of the hexagon

c: Hexagon radius.

Clearing the radio we have:

c = \frac{a}{cos (30)}

Substituting values:

c = \frac{12}{cos (30)}  c = 13.85

Rounding to the nearest whole number we have:

c = 14 in

Answer:

The measure of the radius, c, rounded to the nearest inch is:

C. 14 in.

7 0
3 years ago
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abercrombie &amp; Fitch is having a sale. The sign posted in the store says, "everything is marked down 65%." Scott buys a jacke
nikdorinn [45]

a) We have that the discount is 65 %

Scott buys a jacket for $150

First, we will calculate the discount

150\times\frac{65}{100}=97.5

then we need to subtract the quantity calculated above from the original price

150-97.5=52.5

After the markdown Scott paid $52.5

b.

In order to know the taxes first, we need to calculate the 5% of $52.5

52.5\times\frac{5}{100}=2.625

then we will sum the 5% plus the price after the markdown

52.5+2.625=55.125

The total cost of the jacket is $55.125

5 0
1 year ago
What is 0.8% of 50?<br> A. 0.04<br> B. 0.4<br> C. 4<br> D. 40
BaLLatris [955]

Answer:

It would be A!

Step-by-step explanation:

.08 times .50 would be 0.04. (It's a quick way to be able to solve problems similar to that! :)

7 0
3 years ago
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A business school has a goal that the average number of years of work experience of its MBA applicants is more than three years.
gizmo_the_mogwai [7]

Answer:

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

p_v =P(z>0.280)=0.390  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=3.1 represent the sample mean

\sigma=\sqrt{6} represent the sample standard deviation for the sample

n=47 sample size  

\mu_o =3 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3  

Alternative hypothesis:\mu > 3  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

P-value

Since is a one side test the p value would be:  

p_v =P(z>0.280)=0.390  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

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Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the​ same? Yoga
sergiy2304 [10]

Answer:

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You'd have to write equations for the price per month for each club.

Let  x  equal the number of months of membership, and  y  equal the total cost.

Club A's is  y = 24x + 21.50 and Club B's is  y = 17.25 x + 41.00 Because we know that the prices,  y , would be equal, we can set the two equations equal to each other.

24x + 21.50 =17.25 x+ 41.00

subtract 21.50 both sides

. We can now solve for  x  by isolating the variable.

24x=17.25x+19.5

divide 17.25x

1.39x=19.5

divide 1.39 both sides

x=14.02

After five months, the total cost would be the same.

4 0
3 years ago
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