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3 years ago

F. Please answer this as soon as possible.

Mathematics

2 answers:

Liono4ka [1.6K]3 years ago

7 0

Answer:

-12

Step-by-step explanation:

Convert the mixed number to an improper fraction.

-2 $\frac{2}{3}$ = $-\frac{8}{3}$

To divide, just multiply by the reciprocal.

So -2 $\frac{2}{3}$ ÷ $\frac{2}{9}$ becomes $-\frac{8}{3}$ ÷

Now you can multiply straight across.

$-\frac{8}{3}$ × $\frac{9}{2}$ = $-\frac{72}{6}$

And simplify.

$-\frac{72}{6}$ = -12

Please mark as Brainliest! :)

iris [78.8K]3 years ago

5 0

$(-2\frac{2}{3})/\frac{2}{9}\\$ , convert -2&2/3 to improper fraction. Use this rule: a&b/c=ac+b/c.

$-\frac{2*3+2}{3} /\frac{2}{9}\\\\-\frac{8}{3} /\frac{2}{9} \\$

Use this rule: a÷b/c=a*c/b

$-\frac{8}{3}* \frac{9}{2}$

Use this rule: a/b*c/d=ac/bd

$-\frac{8*9}{3*2} \\\\-\frac{72}{3*2} \\\\-\frac{72}{6}=-12$

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! As well as a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

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A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

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and all we have to do is solve it for a, b and r.

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From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

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3 years ago

Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all possibl

serg [7]

Answer:

P(X=i) where i = 1,2,3,4,5,6,7,8,9,10 = 1/2, 5/18, 5/36, 5/84, 5/252, 1/252, 0, 0, 0, 0.

Step-by-step explanation:

X denotes the highest ranking achieved by the woman.

When X=1, the top ranked person is a female.

When X=2, the first person is a male and the second ranked person is a female.

Similarly, when X=3, the first two ranked persons are male and the third one is a female.

When X=4, the first three persons are male and the fourth one is a female.

When X=5, the first four persons are males and the fifth person is a female.

When X=6, the first five people are males and the sixth person is a female. The rest of the four people are also females since there are only five men in a sample space.

The probability for X=7, 8, 9, 10 is zero because there are only five men who can achieve the first five positions and the last highest rank that can be achieved by a woman is 6.

To compute the probabilities, we will use the formula:

<u>No. of ways a female can be ranked X/Total number of ways to rank 10 people</u>

Note that the total number of ways of ranking 10 different people is 10P10 or 10!

For X=1, the first position can be taken by any of the 5 women. The possible ways of the first person being a woman is 5C1. The rest of the 9 people can take any of the ranks. They can be ordered in 9P9 ways.

So, P(X=1) = (5C1)(9P9)/(10P10) = (5 x 362880)/(3628800) = 1/2

For X=2, the first rank must be taken by a male. The number of ways to arrange the first person as a male out of the 5 men can be calculated by 5P1. The second position must be taken by a female and rest of the 8 positions can be taken by any of the 8 people in 8P8 ways.

So, P(X=2) = (5P1)(5C1)(8P8)/(10P10) = (5 x 5 x 40320)/(3628800) = 5/18

For X=3, first two people must be men and the number of ways to arrange 2 out of 5 males at the first two positions is 5P2. The third position is a female. The rest of the 7 people can be ordered in 7P7 ways.

P(X=3) = (5P2)(5C1)(7P7)/(10P10) = (20 x 5 x 5040)/(3628800) = 5/36

P(X=4) = (5P3)(5C1)(6P6)/(10P10) = (60 x 5 x 720)/(3628800) = 5/84

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P(X=6) = (5P5)(5C1)(4P4)/(10P10) = (120 x 5 x 24)/(3628800) = 1/252

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3 years ago

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