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g100num [7]
2 years ago
8

A grade has 81 girls and 72 boys. The grade is split into groups that have the same ratio of girls to boys as the whole grade.Ho

w many girls are in a group that has 16 boys?
Mathematics
1 answer:
coldgirl [10]2 years ago
6 0

Answer:

18 girls I think.

Step-by-step explanation:

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Solve the following equation:
Rama09 [41]

Complete the square.

z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0

\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4

Use de Moivre's theorem to compute the square roots of the right side.

w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)

\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2

Now, taking square roots on both sides, we have

z^2 + \dfrac12 = \pm w^{1/2}

z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2

Use de Moivre's theorem again to take square roots on both sides.

w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)

\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}

w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)

\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}

3 0
1 year ago
Eight children are divided into two teams each containing 4 children. how many different divisions are possible?
Alekssandra [29.7K]
So this is what's known as a combination. a combination is a group where the order does not matter. to solve a combination, you use this equation:
n! / (r! *(n-r)!) 
n is the total number of objects being sorted (8)
r is the group you need to sort them into (4)
(i know it's 2 groups of 4 but if you solve this for 1 group, the other group is automatically made of the remaining kids)
definition of !:
a number with a ! means 1*2*3...*that number (so that number multiplied by every number smaller than it all the way to one)

so we put 8 and 4 in this equation:
8! / (4! *(8-4)!) 
simplify:
8! / *(4! 4!) 
multiply out:
(8*7*6*5*4*3*2*1) / (4*3*2*1 * 4*3*2*1)
and put that in your calculator
you will get 70
your answer is 70
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3 years ago
A card is in the shape of a rectangle. The length of the card is 7 cm
bogdanovich [222]

lol ok so

7*something or you can make it into a variable x=35

7*x=35

/7     /7

x=5.

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2 years ago
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