Answer:
0 = 6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(m−1)=5m+3−2m
(3)(m)+(3)(−1)=5m+3+−2m (Distribute)
3m+−3=5m+3+−2m
3m−3=(5m+−2m)+(3) (Combine Like Terms)
3m−3=3m+3
3m−3=3m+3
Step 2: Subtract 3m from both sides.
3m−3−3m=3m+3−3m
−3=3
Step 3: Add 3 to both sides.
−3+3=3+3
0=6
To determine the probability that one or the other circumstances will occur, you will count the number of possible outcomes and divide it by all the possible outcomes.
#of female teaching assistants + # of male teaching assistants + # of female professors
6 + 16 + 11 = 33
Total = 41
33/41 = 80
There is a approximate 80% probability that one or the other will occur.
Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for 
such that 
is maximized. Once we have that , we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes 
, just on a smaller scale. So, we really want to maximize . To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of such that the inner part of the square term is equal to 
.
.
So, the answer to part a is 
.
We can then plug 
into the equation for p to find the answer to part b.
.
So, the answer to part b is 
.
And we're done!
Answer:
3 hours
Step-by-step explanation:
The difference between the initial temperature and the temperature after an hour is an increase of 5 degrees. Since we need to calculate the time it would take for the temperature to rise to 60 degrees we need to find the difference in degrees from the current temperature to 60 degrees.
60 - 45 = 15 degrees
Since 1 hour equals an increase of 5 degrees we need to divide 15 by 5 to calculate how many hours before the temperature increases to 60 degrees
15 / 5 = 3 hours
Answer:
x = 4
Step-by-step explanation:
An angle bisector divides an angle into two equal parts. This means that you can set the two parts equal to each other and solve for x.
8x + 35 = 11x + 23
(8x + 35) - 35 = (11x + 23) - 35
8x = 11x - 12
8x - 11 x = (11x - 12) - 11x
-3x = -12
(-3x)/-3 = -12/-3
x = 4
