Formula for midpoint between two points is M(x,y)
x=(x1+x2)/2 and y=(y1+y2)/2
In our case (x1,y1)=(m,b) and (x2,y2)=(0,0)
x=(m+0)/2=m/2 and y=(b+0)/2=b/2 M(m/2,b/2)
Good luck!!!
13. (a-b)^2=a^2-2ab+b^2
B is the answer
14. B is the answer
( x+9)(x-3)= x^2+6x-27
15. B is the answer
(x+6)(x-5)=x^2+x-30
16. D is the answer
(x-6y)(x-4y)=x^2-10xy+24y^2
17. C is the answer
(2x+5)(3x-4)=6x^2+7x-20
18. B is the answer
(5x+7)(x-2)=5x^2-3x-14
We want to find a scalar function

such that

.
So we need to have

Integrating both sides with respect to

gives

Differentiating with respect to

gives



So we find that

By the fundamental theorem of calculus, we then know the line integral depends only on the values of

at the endpoints of the path. Therefore
Answer:
c
Step-by-step explanation:
Answer:
0.6154 = 61.54% probability that the student is an undergraduate
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Foreign
Event B: Undergraduate.
There are four times as many undergraduates as graduate students
So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.
Probability the student is foreign:
10% of 80%
25% of 20%. So

Probability that a student is foreign and undergraduate:
10% of 80%. So

What is the probability that the student is an undergraduate?

0.6154 = 61.54% probability that the student is an undergraduate