Answer:
1771 possible ways
Step-by-step explanation:
In this case, we need to know first how many candidates are in total:
10 + 3 + 10 = 23 candidates in total.
Now, we need to choose 3 of them to receive an award. In this case, we have several scenarios, but as it's an award we can also assume that the order in which the candidates are chosen do not matter, so, the formula to use is the following:
C = m! / n! (m - n)!
Where m is the total candidates and n, is the number of candidates to be chosen. Replacing this data we have:
C = 23! / 3! (23 - 3)!
C = 2.59x10^22 / 6(2.43x10^18)
C = 1771
So we have 1771 ways of choose the candidates.
A) 6
Replace the y with 6
4(6)+13=37
Multiply
24+13=37
Add
37=37
I hope this helps :)
If you have any questions about my answer please feel free to ask:)
Answer:
The variable 8. Equation is 16 + 12x = 112.
Step-by-step explanation:
We know that she spent $16 dollars on magazines, so we can put it in the equation (16 + x= ?). We also know that the total is $112, so we can also add that (16+ x= 112). We don't know how many books she got, but we do know how much they cost (16 + 12x=112. So that makes the books the variable (X).
To find the variable we need to take out the magazines from the price. 112-16=96. Now we're left with 12x=96. Now all we have to do is divide 96 by 12, which equals 8.
Sorry everything is so long, I tried to make it short as possible
Answer:
34 mph.
Step-by-step explanation:
Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.
Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.
Now we will use formula 
. Upon using our given information we will get two equation and two unknowns as:
Upon substituting 
in 1st equation we will get,
Upon multiplying both sides of our equation by 5 we will get,
Upon substituting y=170 in 2nd equation we will get,
Therefore, Charlene's speed is 34 miles per hour.
Every line that does not have the slope of 2/7 is perpendicular to this line.
In order to find this fact, we first must find what is perpendicular. To do that, we first have to find the slope of this line. We can do this by solving for y.
7x + 2y = 3
2y = -7x + 3
y = -7/2x + 3/2
Now we can take the slope of -7/2 and flip and negate it. This will give us the perpendicular slope (2/7). Now we know any line that does not have this slope is not perpendicular to this line.
