Answer:
a) ![82251](https://tex.z-dn.net/?f=82251)
b) ![2.91038 \cdot 10^{24}](https://tex.z-dn.net/?f=2.91038%20%5Ccdot%2010%5E%7B24%7D)
c) ![1](https://tex.z-dn.net/?f=1)
d) ![3.17746\cdot 10^{21}](https://tex.z-dn.net/?f=3.17746%5Ccdot%2010%5E%7B21%7D)
Step-by-step explanation:
a) If the coins are all the same, we have a combination of 35 identical coins in 5 persons.
The amount of combinations is
![\binom{n+r-1}{r-1}=\binom{35+5-1}{5-1}=\binom{39}{4}=\frac{39!}{4!35!} =82251](https://tex.z-dn.net/?f=%5Cbinom%7Bn%2Br-1%7D%7Br-1%7D%3D%5Cbinom%7B35%2B5-1%7D%7B5-1%7D%3D%5Cbinom%7B39%7D%7B4%7D%3D%5Cfrac%7B39%21%7D%7B4%2135%21%7D%20%3D82251)
being n the number of coins and r the number of grandchildren.
b) If the coins are different, the number of combinations can be calculated as:
![r^n=5^{35}=2.91038 \cdot 10^{24}](https://tex.z-dn.net/?f=r%5En%3D5%5E%7B35%7D%3D2.91038%20%5Ccdot%2010%5E%7B24%7D)
c) If the coins are all the same, and each grandchild gets the same number of coins, there is only one combination for that (everyone gets 35/5=7 coins)
d) If the coins are all distinct, but each of the grandchildren get the same numer of coins, the expression to calculate this is:
![\frac{n!}{(n/r)!^r} =\frac{35!}{(35/5)!^5}=\frac{35!}{7!^5}=\frac{1.03331\cdot 10^{40}}{3.25202\cdot 10^{18}} =3.17746\cdot 10^{21}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B%28n%2Fr%29%21%5Er%7D%20%3D%5Cfrac%7B35%21%7D%7B%2835%2F5%29%21%5E5%7D%3D%5Cfrac%7B35%21%7D%7B7%21%5E5%7D%3D%5Cfrac%7B1.03331%5Ccdot%2010%5E%7B40%7D%7D%7B3.25202%5Ccdot%2010%5E%7B18%7D%7D%20%3D3.17746%5Ccdot%2010%5E%7B21%7D)
The answer is 36 all you do is divide the answer choices by 3 to get your answer
Answer:
D
Step-by-step explanation:
the amount of money she gets DEPENDS on the number of hours she works
Answer:
The hypothesis test is right-tailed.
Step-by-step explanation:
We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.
Let p = <u><em>proportion of adults who are in favor of raising the voting age to 21</em></u>
So, Null Hypothesis,
: p
50%
Alternate Hypothesis,
: p > 50%
As we know that the majority is there when we have more 50% chance of happening of that event.
Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.
On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.
This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.
Answer: n= −3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
8(4n+3)=−72
(8)(4n)+(8)(3)=−72(Distribute)
32n+24=−72
Step 2: Subtract 24 from both sides.
32n+24−24=−72−24
32n=−96
Step 3: Divide both sides by 32.
32n/32 = −96/32
n=−3