Answer:
Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S
Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.
Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because
of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.
Step-by-step explanation:
<u>Answer(1):</u>
Law of Cosines.
<u>Answer(2):</u>
since side "c" is missing so we will write formula used for side "c"
![c^2=a^2+b^2-2ab\cdot\cos\left(C\right)](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2-2ab%5Ccdot%5Ccos%5Cleft%28C%5Cright%29)
<u>Answer(3):</u>
First lets write both sine and cosine formulas:
Check the attached picture for the list of formulas:
From given picture we see that two angles A and B are missing. Also 1 side "c" is missing.
Sine formula uses two angles while cosine formula uses only one angles.
Hence cosine formula will be best choice to find the missing values.
Let
be the random variable representing the winnings you get for playing the game. Then
![W=\begin{cases}10-1=9&\text{if the dice sum is odd}\\5-1=4&\text{if the dice sum is 4 or 8}\\50-1=49&\text{if the dice sum is 2 or 12}\\-1&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=W%3D%5Cbegin%7Bcases%7D10-1%3D9%26%5Ctext%7Bif%20the%20dice%20sum%20is%20odd%7D%5C%5C5-1%3D4%26%5Ctext%7Bif%20the%20dice%20sum%20is%204%20or%208%7D%5C%5C50-1%3D49%26%5Ctext%7Bif%20the%20dice%20sum%20is%202%20or%2012%7D%5C%5C-1%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
- The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)
- The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.
- The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.
- There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.
So the probability mass function for this game is
![P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=P%28W%3Dw%29%3D%5Cbegin%7Bcases%7D%5Cfrac12%26%5Ctext%7Bfor%20%7Dw%3D9%5C%5C%5Cfrac29%26%5Ctext%7Bfor%20%7Dw%3D4%5Ctext%7B%20or%20%7Dw%3D-1%5C%5C%5Cfrac1%7B18%7D%26%5Ctext%7Bfor%20%7Dw%3D49%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
The expected value of playing the game is then
![E[W]=\displaystyle\sum_ww\,P(W=w)=\frac92+\frac89-\frac29+\frac{49}{18}=\frac{71}9](https://tex.z-dn.net/?f=E%5BW%5D%3D%5Cdisplaystyle%5Csum_ww%5C%2CP%28W%3Dw%29%3D%5Cfrac92%2B%5Cfrac89-%5Cfrac29%2B%5Cfrac%7B49%7D%7B18%7D%3D%5Cfrac%7B71%7D9)
or about $7.89.
Answer:
ewwwww
Step-by-step explanation:
black people play basketball