The probability is 56/100, or 14/25 = 0.56.
These events are not mutually exclusive, meaning they can happen at the same time. This means we use
P(A or B) = P(A) + P(B) - P(A and B)
P(carpool or full time) = P(carpool) + P(full time) - P(carpool & full time)
There are 6+9=15 people out of 100 that carpool.
There are 7+4+30+6=47 people out of 100 that work full time.
There are 6 people out of 100 that carpool and work full time.
This gives us
15/100 + 47/100 - 6/100 = 56/100
Answer:
a. 0.6899
b. 0.1642
Step-by-step explanation:
a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:
-Each attempt is independent and therefore the probability of the events is calculated as:
![P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.94\times0.94\times0.94\times0.94\times0.94\times0.94\\\\=0.6899](https://tex.z-dn.net/?f=P%28A%20%5C%20and%20%5CB%20%29%3DP%28A%29%5Ctimes%20P%28B%29%5C%5C%5C%5CP%286%29%3D0.94%5Ctimes0.94%5Ctimes0.94%5Ctimes0.94%5Ctimes0.94%5Ctimes0.94%5C%5C%5C%5C%3D0.6899)
Hence, the probability of correctly identifying the 6 matches is 0.6899
b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:
-Each attempt is independent and therefore the probability of the events is calculated as:
![P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.74\times0.74\times0.74\times0.74\times0.74\times0.74\\\\=0.1642](https://tex.z-dn.net/?f=P%28A%20%5C%20and%20%5CB%20%29%3DP%28A%29%5Ctimes%20P%28B%29%5C%5C%5C%5CP%286%29%3D0.74%5Ctimes0.74%5Ctimes0.74%5Ctimes0.74%5Ctimes0.74%5Ctimes0.74%5C%5C%5C%5C%3D0.1642)
#Hence, the probability of correctly identifying the 6 matches is 0.1642
*I have used the sample size of 6(due to conflicting info/question size).
90 hazelnuts = 125g
Therefore, the mass of one hazelnut is this...
90 / 90 = 125 / 90
1 hazelnut = 25/18 grams
630 calories = 100 grams
100 divided by 25/18 = 72
Therefore...
630 / 72 = 1 hazelnut
AND THE ANSWER IS
8.75 calories = 1 hazelnut
Answer:
![V_{s} = \frac{\pi}{4}\cdot D_{out}^{2} \cdot h -\frac{\pi}{4}\cdot (D_{out}-2\cdot t)^{2}\cdot (h-t)](https://tex.z-dn.net/?f=V_%7Bs%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ccdot%20D_%7Bout%7D%5E%7B2%7D%20%5Ccdot%20h%20-%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ccdot%20%28D_%7Bout%7D-2%5Ccdot%20t%29%5E%7B2%7D%5Ccdot%20%28h-t%29)
Step-by-step explanation:
The geometric description of the vase is described in the image attached below. The volume of the solid part of the vase is:
![V_{s} = V_{out} - V_{in}](https://tex.z-dn.net/?f=V_%7Bs%7D%20%3D%20V_%7Bout%7D%20-%20V_%7Bin%7D)
![V_{s} = \frac{\pi}{4}\cdot D_{out}^{2} \cdot h -\frac{\pi}{4}\cdot (D_{out}-2\cdot t)^{2}\cdot (h-t)](https://tex.z-dn.net/?f=V_%7Bs%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ccdot%20D_%7Bout%7D%5E%7B2%7D%20%5Ccdot%20h%20-%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ccdot%20%28D_%7Bout%7D-2%5Ccdot%20t%29%5E%7B2%7D%5Ccdot%20%28h-t%29)
Where:
- Outer diameter, in centimeters.
- Vase thickness, in centimeters.
Answer:
If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:
![X \sim Binom(n=234, p=0.75)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Binom%28n%3D234%2C%20p%3D0.75%29)
And the mean for this case would be:
![E(X) =np = 234*0.75= 175.5](https://tex.z-dn.net/?f=%20E%28X%29%20%3Dnp%20%3D%20234%2A0.75%3D%20175.5)
And the standard deviation would be given by:
![\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624](https://tex.z-dn.net/?f=%20%5Csigma%20%3D%5Csqrt%7Bnp%281-p%29%7D%3D%20%5Csqrt%7B234%2A0.75%2A%281-0.75%29%7D%3D%206.624)
Step-by-step explanation:
If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:
![X \sim Binom(n=234, p=0.75)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Binom%28n%3D234%2C%20p%3D0.75%29)
And the mean for this case would be:
![E(X) =np = 234*0.75= 175.5](https://tex.z-dn.net/?f=%20E%28X%29%20%3Dnp%20%3D%20234%2A0.75%3D%20175.5)
And the standard deviation would be given by:
![\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624](https://tex.z-dn.net/?f=%20%5Csigma%20%3D%5Csqrt%7Bnp%281-p%29%7D%3D%20%5Csqrt%7B234%2A0.75%2A%281-0.75%29%7D%3D%206.624)