The point (6, -5) is reflected across the x axis. What is the coordinates of the reflected point.
2 answers:
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<h3>Answer: 154</h3>
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Explanation:
I'll be using the formula
which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.
While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".
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If you ride r = 15 coasters, then we have the following number of combinations
There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.
We'll use this result later, so let x = 136.
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If r = 16, then we follow the same steps as above. You should get 17C16 = 17
There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"
Let y = 17 so we can use it later
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Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.
Let z = 1
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Add up the values of x, y, and z to get the final answer
x+y+z = 136+17+1 = 154
Answer: The required number of quarters in the collection is 11.
Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.
If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.
We are to find the number of quarters in the collection.
Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.
We will be using the following values of nickels, dimes and quarters in form of dollar :
1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.
Then, according to the given information, we have
Substituting the value of x from equation (i) in equations (ii) and (iii), we have
and
Comparing the values of y from equations (iv) and (v), we get
Thus, the required number of quarters in the collection is 11.