The scatterplot shows the average miles per gallon versus the age, in years, of a car.

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 without replacement.

(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}$

5 0

3 years ago

Anne and Nancy use a metal alloy that is 20% copper to make jewelry. How many ounces of a 14% and 24% alloy must be mixed to for

Gala2k [10]

copper +copper = copper
0.14x+0.24(100-x) = 0.20*100 = 20

7 0

3 years ago

If a girl read 3/8 of a chapter book and another girl read 3/6 of a chapter book which girl read more pages

fredd [130]

Answer:

The girl which read 3/6 of a chapter book read more pages than the other girl.

Step-by-step explanation:

We need to compare between $\frac{3}{8} \ and \ \frac{3}{6}$

so, the denominator of both fractions should be the same number

Factor of 6 = 1 * 2 * * 3

Factor of 8 = 1 * 2 * 2 * 2

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The common denominator = 1 * 2 * 2 * 2 * 3 = 24

$\frac{3}{8} = \frac{3*3}{3*8} =\frac{9}{24} \\\frac{3}{6} = \frac{4*3}{4*6} =\frac{12}{24}$

Then compare between $\frac{9}{24} \ and \frac{12}{24} \\$

So, the fraction of the great numerator will be the great fraction

$\frac{12}{24} > \frac{9}{24}$

∴ $\frac{3}{6} > \frac{3}{8}$

==================================================

Another solution:

Convert both fractions to decimal:

3/8 = 0.375

3/6 = 0.5

0.5 > 0.375

===================================================

Third Solution:

As the numerators are equal

The fraction of least denominator is the great fraction

So, 3/6 > 3/8

3 0

3 years ago

Use complete sentences to describe how simplifying expressions with multiple logarithms makes evaluating expressions less compli

Andrej [43]

To give you an idea about logarithm, it is the opposite of exponents. Exponents are the repeated multiplication of a number. It is represented by the formula of a^n where a is the number to be repeated and n is the number of times the number is being multiplies by itself. Also include the sign of the number, no matter how it is multiplied, it is still important. In this problem, you have 4 as the repeated number. You can see that it is multiplied by itself by two times. So you have (-4)^2.

7 0

3 years ago

Aiden is grocery shopping and wants to know which packages are cheapest. He is

arlik [135]

Answer:Bottle B

Step-by-step explanation:

Given

Bottle A has 175 fluid ounce and cost $\$19.25$