P^3•9^2 (P^4•9^n•R^3/R^4)= P^7 9^5 1^7 What is n?

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

tomika plans to run 84 miles in 4 weeks. If she continues the pattern, how many miles will she run in 1yr.

drek231 [11]

She run in 28 days = 84 miles
So, 1 day, it will be = 84 / 28 = 3 miles

Now, in 1 year it would be = 365 * 3 = 1095

So, your final answer is 1095 miles

Hope this helps!

4 0

3 years ago

If m∠XWY = 20°, m∠XWZ = 40°, and XY = 16, what is the value of YZ?

Jobisdone [24]

YZ = 16. The triangles are congruent. This would be AAS so YZ = 16 because of CPCTC.

7 0

3 years ago

If Charlie liked dogs, and Macy's hat was green, how fast was the car, that the dog's dad was driving?

Likurg_2 [28]

Answer: The car wasn't going fast at all because dogs can't drive

Step-by-step explanation:

4 0

3 years ago

Segments

Kazeer [188]

Given

AB and CD intersect

AC, CB, BD and AD are congruent.

Prove that AB is the bisector of ∠CAD and ray CD is the bisector of ∠ACB.

and AB and CD are perpendicular.

To proof

Bisector

A bisector is that which cut an angle in two equal parts.

In ΔACB and ΔADB

AD = AC ( Given )

AB = AB ( common )

BC = DB ( Given )

by SSS congurence property

we have

ΔACB ≅ΔADB

∠CAB =∠ DAB

∠CBA = ∠DBA

( By corresponding sides of the congurent triangle )

Thus AB is the bisector of the ∠CAD.

InΔ DAC and ΔDBC

AD = DB (Given)

AC = CB ( Given )

CD = CD (common)

By SSS congurence property

ΔDAC≅ Δ DBC

∠ ACD =∠ BCD

∠ADC =∠BDC

( By corresponding sides of the congurent triangle )

Therefore CD is the bisector of the CAD.

In ΔBOC andΔ BOD

BO = BO ( Common )

∠BCO = ∠BDO

( As prove above ΔACB ≅ΔADB

Thus ∠ACB = ∠ADB by corresponding sides of the congurent triangle , CD is a bisector

∠BCO = ∠BDO )

CB = DB ( given )

by SAS congurence property

ΔBOC ≅ ΔBOD

∠BOC =∠ BOD

∠BOC +∠ BOD = 180 °( Linear pair )

2∠ BOC = 180°

∠BOC = 90°

∠BOC =∠ BOD = 90°

also

In ΔCOA and ΔAOD

AO = AO ( Common )

∠ACO =∠ ADO

( As prove above ΔACB ≅ΔADB Thus ACB = ADB by corresponding sides of congurent triangle ,CD is a bisector

thus ∠ACO = ∠ADO )

AC =AD ( given )

by SAS congurence property

Δ COA ≅ ΔAOD

∠AOC = ∠AOD

( By corresponding angle of corresponding sides )

∠AOC + ∠AOD = 180°

2∠ AOC = 180° ( Linear pair )

∠AOC = 90°

∠AOC = ∠AOD = 90 °

Thus AB and CD are perpendicular.

Hence proved

6 0

3 years ago