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3 years ago

Simplify the problems

Mathematics

1 answer:

antoniya [11.8K]3 years ago

6 0

For most of them you can use a fraction simplifier calculator but so far i have b) 21/2 c) 203/2

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Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court

Ksju [112]

Answer:

$(a)\dfrac{92}{117}$

$(b)\dfrac{8}{39}$

$(c)\dfrac{25}{117}$

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

$P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}$

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed) $=P(MW)+P(WM)$

$=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}$

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.
Two women are appointed

P(at least one woman is appointed) $=P(MW)+P(WM)+P(WW)$

$P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}$

In Part B, $P(MW)+P(WM)=\frac{8}{39}$

Therefore:

$P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}$

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Use a graphing calculator to find the value of f(x) when x= 3 for each function

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9. f(x)= 1/3x-2
f(3)= 1/3(3)-2
f(3)= 1-2
f(3)= -1

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Mike and Felix are collecting newspapers for a recycling project. Mike collected 14.66 pounds and Felix collected 11.5 pounds. T

densk [106]

14.66+11.5
=26.16 pounds

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4 years ago

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Convert r=53sinθ−cosθ to rectangular form.

Helga [31]

Answer:

$y = \frac{1}{3} x + \frac{5}{3}$

Step-by-step explanation:

r = 5/(3sinθ-cosθ)

multiply both sides by (3sinθ-cosθ):

r(3sinθ-cosθ) = 5

expand:

3rsinθ-rcosθ = 5

replace rsinθ with y and rcosθ with x:

3y-x = 5

add x to both sides:

3y = x + 5

divide both sides by 3:

y = 1/3x + 5/3

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there are 5 sodas, 3 grape sodas, 7 root beers, and 8 lemon lime sodas in a cooler. What is the probability of choosing a grape

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To calculate probability take the events / the outcome.

3 grape sodas / total drinks

You will need to add all the drinks together to get the total drinks
(5 + 3 + 7 + 8 = 23)

3 / 23 is your probability

This ratio cannot be simplified into lowest terms

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