Answer:
x = -2, y = 7
Step-by-step explanation:
Since it's a system of equations, we know that the they use the same variables. To use substitution to solve a system of equation, we must take one equation and solve it for a variable, then you plug the solution into that variable for the other equation:
-2x + y = 11
y = 2x + 11
-------
4x + 4y = 20
4x + 4(2x + 11) = 20
4x + 8x + 44 = 20
12x + 44 = 20
12x = -24
x = -2
Then we can plug "x" into the first equation:
-2x + y = 11
-2(-2) + y = 11
4 + y = 11
y = 7
Answer:
C. $4.38
Step-by-step explanation:
To find out how much paper she covers the box with, you need to find the area of each of the rectangles covered by the box.
First, find the area of the side closest to you.
3 x 8 = 24 in^2
Since the side opposite to it is equivalent, they are both 24 in^2, so multiply 24 by 2:
24 x 2 = 48 in^2
Now, find the sides on the left and right (equal in size).
7 x 3 = 21
21 x 2 = 42 in^2
Finally, find the bottom. There is no top, so there's no need to multiply this one by 2.
8 x 7 = 56 in^2
Add up the sides:
56 + 42 + 48 = 146 ![in^2](https://tex.z-dn.net/?f=in%5E2)
Multiply 146 by 0.03:
146 x 0.03 = 4.38
$4.38
Have a nice day!
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Answers:
- Sam's current age = 24
- The mother's current age = 48
=========================================================
Explanation:
s = Sam's age right now
2s = the mother's age right now, since she is twice as old as Sam currently.
In 12 years time, Sam will be s+12 years old.
12 years ago from this current year, the mother was 2s-12 years old.
Since we're told these future and past ages line up, this means s+12 and 2s-12 are the same value
Set the expressions equal to one another and solve for s.
s+12 = 2s-12
s-2s = -12-12
-s = -24
s = 24
Sam is currently 24 years old.
His mother is currently 2s = 2*24 = 48 years old.
12 years ago, his mother was 2s-12 = 48-12 = 36 years old.
12 years from now, Sam will be s+12 = 24+12 = 36 years old.
Since we get 36 each time, this confirms we have the correct answers.
Given the answers of 100 students surveyed, you have to find the following probability:
<em>P(taken a public speaking class | majoring in business administration)</em>
This is the probability that the student has taken a public speaking class, given that he is majoring in business administration, which is a conditional probability.
We already know that the student is majoring in business administration, so instead of working with the information about the 100 students, you can directly work with the group os students that are doing that major:
You can determine this probability as the quotient between the students that took a public speaking class and are majoring in business and the total number of students that are majoring in business:
![P(public.class|bu\sin ess.major)=\frac{10}{55}](https://tex.z-dn.net/?f=P%28public.class%7Cbu%5Csin%20ess.major%29%3D%5Cfrac%7B10%7D%7B55%7D)
So, the probability is 10/55