1. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = x 3 i⃗ + (4y − z 3y 3 )j⃗ + 2xk⃗⃗ and S is the portion of z = x 2 + y 2 − 3 below z = 1 with orientation in the negative z-axis direction. 2. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = 2yi⃗ + 3xj⃗ + (z − x)k⃗⃗ and S is the portion of y = 11 − 3x 2 − 3z 2 in front of y = 5 with orientation in the positive y-axis direction. 3. Use Stokes’ Theorem to evaluate ∫ F⃗ ∙ dr⃗ C where F⃗ = (zx 3 − 3z)i⃗ + xzj⃗ + yxk⃗⃗ and C is the triangle with vertices (0,0,4), (0,2,0), and (2,0,0). C has the orientation seen in the sketch below.

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

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