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Number of ways for the committee to have 3 boys, 3 girls: \(\binom{6}{3} \cdot \binom{4}{3} = 20 \cdot 4 = 80.\)

Number of total ways: \(\binom{10}{6} = 210\)

So, the answer is \(\frac{8}{21}.\)

Let the coordinates of T be \((x,y)\). Then, \((x+5) = 2*8, (y+3) = 2*6\). So, we get that \(T=(11,9).\)

Let f(x) = (1/x) -3. Find the largest x that is not in the domain of g(x) = f(f(x)) 

x cannot equal 0

and

(1/x)-3 cannot equal 0 either

\(\frac{1}{x}-3\ne0\\ \frac{1}{x} \ne 3\\\ x\ne \frac{1}{3} \)

x can't be 0 or 1/3

1/3 is the biggest.

Check out my graph:

the green graph is g(x)

This is fun hahahah.

algebra
Define
\(a@b = ab - b^2\) and
\(a\#b = a + b - ab\).
What is \((6@2)/(6\#2)\)?

\(\begin{array}{|rcll|} \hline (6@2)/(6\#2) &=& \dfrac{6@2}{6\#2)} \\\\ (6@2)/(6\#2) &=& \dfrac{6*2-2^2}{6+2-6*2} \\\\ (6@2)/(6\#2) &=& \dfrac{12-4}{8-12} \\\\ (6@2)/(6\#2) &=& \dfrac{8}{-4} \\\\ \mathbf{(6@2)/(6\#2)} &=& \mathbf{-2} \\ \hline \end{array}\)

r = 1/2{sqrt[CD² + (2 * AB)²]}

The possible rational roots are 1 and 1/2, so there are 2 possible rational roots.

The largest x that is not in the domain of g(x) = f(f(x)) is x = 9.

Find the complex number z that satisfies
\((1 + i) z - 2 \overline{z} = -11 + 25i\).

\(\text{Set $z=a+bi$} \\ \text{Set $\overline{z}=a-bi$}\)

\(\begin{array}{|rcll|} \hline \mathbf{ (1 + i) z - 2 \overline{z} } &=& \mathbf{ -11 + 25i } \\ (1 + i)(a+bi) - 2(a-bi) &=& -11 + 25i \\ (1 + i)a+(1+i)bi - 2a+2bi &=& -11 + 25i \\ a + ia+bi+bi^2 - 2a+2bi &=& -11 + 25i \quad | \quad i^2 = -1 \\ a + ia+bi-b - 2a+2bi &=& -11 + 25i \\ -(a+b) +i(a+3b)&=& -11 + 25i \qquad \text{compare}\\ \hline -(a+b) &=& -11 \\ a+b &=& 11 \\ \mathbf{a} &=& \mathbf{11-b} \\ \hline (a+3b) &=& 25 \\ 11-b+3b &=& 25 \\ 2b &=& 14 \\ \mathbf{b} &=& \mathbf{7} \\ \hline \mathbf{a} &=& \mathbf{11-b} \\ a &=& 11-7 \\ \mathbf{a} &=& \mathbf{4} \\ \hline z &=& a+bi \\ \mathbf{z} &=& \mathbf{4+7i} \\ \hline \end{array}\)

I assume you mean how to turn a repeating fraction like 0.99 repeating into a fraction?

Inorder to turn a repeating decimal into a fracation:

x = 0.99

10x = 9.99 i only multipplied x by 10^1 because the pattern is one long. if the decimal was something like 1.27272727, and repeats every two, do 10^2

10x-x = 9.99-0.99 this cancles out the repeating part of the fraction

9x = 9

x = 1/1

This is also a proof to why 0.99 repeating = 1.

Assuming youre asking how to simplify a fraction (idk you never know ig), simply find all the prime factors of the numerator and denominator.

For 2/4 it is 2/2*2. Then factor it out. 2/2*2 = 1/2.

-4.5 < t <= 2.25

Im not sure what subsituting it into the third equation, but the answer to the first system of equation is 

(87/17, -92/17). Hopes this helps

Leg = sin45º * 14     or    cos45º * 14

😂😂😂 i thought this problem was cut off or something but ok.

I think it is just    26 C 13    =   26! / (  13! 13!)

The  side  of  the square  =  42/sqrt 2   inches

So.....the number of feet of trim  needed  =    4 * 42  / sqrt 2   ≈  118.8  inches = 118.8/12  =  9.9 ft

The sq ft  of   glass  needed =   4 * (1/2) 21^2  =  2 * 21^2   = 882 sq in   =  882/12^2  = 6.125 ft^2

Oh...really?

2x = 40    divide both sides of the equation by 2

x = 20

.25 x     =  .15 (12)

x=7.2 liters of .25 bleach required.....    the REST of the 12 liters  would be water (4.8   not 7.8)

Motivation  

I believe there is insufficent evidence to solve this problem; I think the diagonals must be perpendicular. 

Assuming they are, then the length of the other diagonal is \(\frac{840*2}{42} = 40\)

Then, the length of each side is going to be \(\sqrt{20^2+21^2}=29.\)

40 coins

nickles = n          value = 5 n

dimes = (40-n)    value = 10 (40 -n)        summed = 285

5n    + 10 (40-n) = 285      solve for   n          then    d = 40 -n

Pythagorean theorem

14^2 = L^2  + L^2

196 = 2 L^2

98 = L^2

L = sqrt 98     SImplify further if needed .....

Let the number of nickels be x, and the number of dimes be y. Then, we can set up two equations.

\(x+y=40, 0.05x+0.10y=2.85. \)

We can then multiply both sides of the second equation by 20 to get \(x+2y=57\) so \(y=17, x=23.\)

So, the answer is that there are 17 dimes, 23 nickels

The bottom's length is \(4 \cdot 2 = 8\) units and using the pythagorean theorem we get that the maximum length is \(\sqrt{6^2+8^2} = 10.\)