Answer: 
or 
.
Step-by-step explanation:
Given : A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards.
The total number of cards in a deck 52
Number of faces cards in a deck = 12
Number of cards not face cards = 40
The total number of combinations of drawing 9 cards out of 52 cards = 
Now , the combination of 9 cards such that exactly 6 of them are face cards = 
Now , the probability that the hand contains exactly 6 face cards will be :-
![=\dfrac{\dfrac{12!}{6!6!}\times\dfrac{40!}{3!37!}}{\dfrac{52!}{9!\times43!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{228}{91885}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Cdfrac%7B12%21%7D%7B6%216%21%7D%5Ctimes%5Cdfrac%7B40%21%7D%7B3%2137%21%7D%7D%7B%5Cdfrac%7B52%21%7D%7B9%21%5Ctimes43%21%7D%7D%5C%20%5C%20%5B%5Cbecause%5C%20%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%5D%5C%5C%5C%5C%3D%5Cdfrac%7B228%7D%7B91885%7D)
Hence, the probability that the hand contains exactly 6 face cards. is .
Given:
The arithmetic sequence is −15, −33, −51, −69.
To find:
The nth term of the arithmetic sequence.
Solution:
We have,
−15, −33, −51, −69
Here,
First term: a = -15
Common difference is
Now, nth term of an arithmetic sequence is
Substitute a=-15 and d=-18.
Therefore, the nth term of the given arithmetic sequence is .
The dependent is the childrens hospital
<em><u>An inequality that shows the distance Johnathan could of ran any day this week is:</u></em>
<em><u>Solution:</u></em>
Let "x" be the distance Johnathan can run any day of this week
Given that,
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles
Therefore,
Number of days ran = 5
The most he ran in 1 day = 3.5 miles
Thus, the maximum distance he ran in a week is given as:
The maximum distance he ran in a week is 17.5 miles
If we let x be the distance he can run any day of this week then, we get a inequality as:
If we let y be the total distance he can travel in a week then, we may express it as,
Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
Group like terms
Add like terms
Now let's set the sum of exterior angles to 360
Subtract 2 from both sides
Divide both sides by 23
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
