At the end of each week, an employer gives some vacation hours to a few randomly selected employees. There are 25 employees in her department—11 males and 14 females. The employer wants to know how many ways there are to give vacation hours to 6 of the employees. How many possible groups of 6 employees can the employer choose?

Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i

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Work Shown:

[tex]\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\[/tex]

Equating terms, we have this system

[tex]\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}[/tex]

Solve the second equation for b to get b = 5/a

Plug that into the first equation to solve for 'a'

[tex]24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\[/tex]

Setting each factor equal to zero would lead to...

We're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5

If a = 5, then,

b = 5/a = 5/5 = 1

So

[tex]\sqrt{24+10i} = a+bi = 5+1i = 5+i[/tex]

or in short,

[tex]\sqrt{24+10i} = 5+i[/tex]

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If a = -5, then b = 5/a = 5/(-5) = -1

So it's very possible that we could also say

[tex]\sqrt{24+10i} = -5-i\\\\[/tex]

If you wanted to combine the two we would use the plus/minus notation like so

[tex]\sqrt{24+10i} = \pm(5+i)\\\\[/tex]

This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.

[tex]1\frac{1}{2}[/tex] [tex]batches[/tex]

➛➛➛➛➛

[tex]\frac{1/2}{1} =\frac{3/4}{x}[/tex]

[tex]\frac{1}{2} =\frac{3}{4x}[/tex]

[tex]cross~multiply[/tex]

[tex]4x=2(3)[/tex]

[tex]\frac{4x}{4} =\frac{6}{4}[/tex]

[tex]x=\frac{3}{2} =1\frac{1}{2}[/tex]

Answer: 8 feet below sea level is higher

Step-by-step explanation:

Answer:

[tex]b^{2} \sqrt{30b}[/tex]

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

the answer should be 5.47 if im seeing right the 30 only the b's only the the product or something  

Step-by-step explanation:

hope this helps if so mark it brainliest and if you want join meeting

Answer:

The answer is D

......(don't mind this it's because it says that it needs to be 20 characters long) but the answer is D

Responder:

750 + 0,025X

Explicação passo a passo:

Dado que :

Rendimento Fixo = R $ 750

Ganho variável = 2,5% das vendas totais

Se vendas totais em um mês = x

O valor total ganho = custo fixo + variável

Custo variável = 2,5% * x = 0,025X

Custo total: 750 + 0,025X

Answer:

24 area

18.80983669  perimeter

Step-by-step explanation:

1  (6*3/2)*2(1*3/2)+(4*3)

2 trust me

Answer:

I'm not 100% sure but I think its A

Answer:

32 cartons

Step-by-step explanation:

Total sets needed

48 + 43 + 46 + 50 = 187

Cartons needed

187 / 6 = 31 1/6

need 32 cartons

Answer:

32 cartons

Step-by-step explanation:

add up all of the students = 187

divide by 6 = 187/6 = 31.16

round = 32 cartons

Answer: A would be your answer.

Step-by-step explanation: Internal conflict is when you have a problem with yourself and this means your not intercating with others.

Answer:

merhabalar !

HAVE A NİCE DAY

Answer:

150.8 m³

48π m³

Step-by-step explanation:

V = πr²h/3

V = π · 4² · 9/3

150.8 m³

Decimal form is 3.96811878

Step-by-step explanation:

1*-2=-2, -2*-2=4, -2*4=-8, -8*-32=256

Answer:

Step-by-step explanation:

n = 3

Answer: n= 3

Step-by-step explanation:

i hope this helped :))

Answer:

$35.44

Step-by-step explanation:

We can use a proportion to solve this problem

20 : 100 : x : 29.53

x = (29.53*20)/100 = $5.906 (value of the tip)

total cost = 29.53 + 5.906 = $35.436 = $35.44

Answer:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 divided by 10 = 5.5 around 5

Add all your numbers

Divide by the many numbers there are, go by the exact value or estimate if needed.

Answer:

i think 11y

Step-by-step explanation:

Answer:

sub duplicate ratio of

hope it helps

Answer:

The mass of Element X will reach 62 grams in 7.0 years.

Step-by-step explanation:

We can find the time of decay of Element X by using the exponential decay equation:

[tex] \frac{dm}{dt} = -\lambda t [/tex]

The solution of the above equation is:

[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex]     (1)

Where:  

t: is the time =?

λ: is the decay constant                                                                                        

[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams

[tex]m_{0}[/tex]: is the initial mass = 90 grams

First, we need to calculate λ

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]   (2)    

Where [tex]t_{1/2}[/tex] is the half-life = 13 years

By entering equation (2) into (1) and solving for "t" we have:

[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]    

[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]      

[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]  

Therefore, the mass of Element X will reach 62 grams in 7.0 years.

I hope it helps you!

Answer:

∆ADE ≈ ∆ DCF

I hope this helps

Answer:

x=110˚

Step-by-step explanation:

We need to first find the other degree inside the triangle

first add 45˚ and 65˚

which is 110˚

subtract 110˚ with 180˚

which is 70˚

So we find x since a straight line is 180˚

subtract 70 and 180

which is 110˚

Hoped I helped!

Answer:

110 degrees

Step-by-step explanation:

A triangle is 180 degrees. So if the missing angle is 70, and 70+x=180 then x=110

Answer:

300 watermelons

Step-by-step explanation:

3:2 ratio

3 is water melons and 2 is mangoes.

200 mangoes were purchased.

200/2=100

The unit rate is 100, so multiply 3 by 100, which is 300.

So Jack bought 300 watermelons, and 298 of which will be devoured by yours truly.

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hope it helps

Answer:

The number -20 is rational

Answer:

the answer is irrational!

Step-by-step explanation:

Hi there!

[tex]\large\boxed{x = -1}[/tex]

We can solve by multiplying each term to get a common denominator:

[tex]\frac{1}{x - 4} + \frac{x}{x - 2} = \frac{2}{x^2-6x+8}[/tex]

[tex]\frac{x -2}{(x - 4)(x - 2)} + \frac{x(x - 4)}{(x - 2)(x - 4)} = \frac{2}{x^2-6x+8}[/tex]

Since the denominators are all the same (x² - 6x + 8 factors to (x - 2)(x - 4)), we can ignore them temporarily and solve the numerator:

x - 2 + x(x - 4) = 2

Simplify:

x - 2 + x² - 4x = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1) = 0

x = -1, 4

For the values of x to be a solution, they cannot cause the denominator to be equal to 0, so:

(x - 2)(x - 4) = 0

x = 2, 4. These values result in a denominator of 0, which is undefined.

Thus, the only solution is x = -1.

Answer:

c

Step-by-step explanation:

Interquartile range or IQR is the range of the "box" in the graph. So we have 54 and 36 so we subtract 54-36.

So we get 18.

Answer:38400000000

Step-by-step explanation: I just do it like 2 numbers i just write it down like a line it is kind of hard you could do it an easier way but i like doing it like that :)

Answer:

AA

Step-by-step explanation:

AA

Answer:

15+ 8d

After d day,she has read 15 +8d pages

Answer:

4.5 cm

Step-by-step explanation:

KL = LM as triangle is isosceles

LM = KM as LF = FM = KN = NM, so the triangle is equilateral

EF ║ NM as LE⊥EF and LN⊥NM

EF is half the midsegment as ∠KLN ≅ ∠MLN, and LN is angle bisector of ∠KLM

Midsegment is half the side length, and all sides are 18 cm.

EF = 1/2(1/2*18) = 4.5 cm