A standard roulette wheel has 38 numbered slots for a small ball to land in: 36 are marked from 1 to 36, with half of those blac
1 answer:
Answer:
The expected value of betting $500 on red is $463.7.
Step-by-step explanation:
There is not a fair game. This can be demostrated by the expected value of betting a sum of money on red, for example.
The expected value is calculated as:
being G the profit of each possible result.
If we bet $500, the possible outcomes are:
- <em>Winning</em>. We get G_w=$1,000. This happens when the roulette's ball falls in a red place. The probability of this can be calculated dividing the red slots (half of 36) by the total slots (38) of the roulette:
- <em>Losing</em>. We get G_l=$0. This happens when the ball does not fall in a red place. The probability of this is the complementary of winning, so we have:
Then, we can calculate the expected value as:
We expect to win $463.7 for every $500 we bet on red, so we are losing in average $36.3 per $500 bet.
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Answer: The greatest number of rows Li Na can plant is 9.
Step-by-step explanation:
Given: Li Na is going to plant 63 tomato plants and 81 rhubarb plants.
Li Na would like to plant the plants in rows where each row has the same number of tomato plants and each row has the same number of rhubarb plants.
To find the greatest number of rows Li Na can plant, we need to find the GCF of 63 and 81.
Since ,
Clearly, GCF(63,81)=9
Therefore, the greatest number of rows Li Na can plant is 9.
So,, there are 5 different flavors. A total of 180 people were asked. Hence, the hypothesis that there is no significant difference is that every flavor gets 180/5=36 flavors. x^2=
. In this case, mi is the proportion of the hypothesis, thus 36, n=180 and xi is the number of actual observations. Substituting the known quantities, we get that x^2=9. The degree of association is given by 
. This yields around 0.10, much higher than our limit.
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Let
because that is the range of the inverse cosine funcition.
Also,
![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3Dcos%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B5%5C%2Ccos%5C%2C%5Ctheta%3D4%7D)
Square both sides and apply the fundamental trigonometric identity:
But which means 
lies either in the 1st or the 2nd quadrant. So 
is a positive number:
![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Ctherefore~~%5Cmathsf%7Bsin%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%3D%5Cdfrac%7B3%7D%7B5%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
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Let
Also,
Square both sides and apply the fundamental trigonometric identity:
But
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>