Assume MATH 12 Students' happiness function is given by H = C2Q + 2E
Where,
H is the students' happiness
C is the students' happiness due to going to Math 12 class
Q is the students' happiness due to taking Math 12 Quizzes
E is the students' happiness dues to taking Math 12 Exams
Assume that at the end of the semester:
1. Students' happiness due to going to class is 5 utils/week, and is decreasing by 2 utils/week.
2. Students' happiness due to taking Math 12 Quizzes is 10 utils/week, and decreasing by 1 util/week.
3. Students' happiness due to taking the Exams is 2 utils/week and is decreasing by 1 util/week.
QUESTION: By how much is Students' happiness increasing/decreasing at the end of the quarter. (Note: This problem does not correspond to reality) HINT: Use implicit differentiation with respect to time.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!