Answer:
0.25
Step-by-step explanation:
72% of courses have final exams and 46% of courses require research papers which means probability of 0.72 for courses that have final exams and 0.46 for courses that require research papers.
31% of courses have a research paper and a final exam, which means probability of 0.31 for both courses with exams and research papers, using Venn diagram approach, find picture attached to the solution.
P(R or E) = P(R) + P(E) - P(R and E), which gives:
P(R or E) = 0.15 + 0.41 - 0.31
P(R or E) = 0.25.
Answer:
y = -x + 2
Step-by-step explanation:
Use the point-slope formula y - k = m(x -h):
y - [-1] = -1(x - 3), or
y + 1 = -x + 3, or
y = -x + 2
Answer:
3sqrt(2)
Step-by-step explanation:
The upper triangle is a 30-60-90 triangle. The hypotenuse is twice the length of the small leg.
30-60-90 triangle
hypotenuse = 6
small leg = 3
The small leg of the 30-60-90 triangle is the leg of the lower triangle.
The lower triangle is a 45-45-90 triangle. The hypotenuse is sqrt(2) times the length of the leg.
45-45-90 triangle
leg = 3
hypotenuse = 3sqrt(2)
x is the hypotenuse of the 45-45-90 triangle.
x = 3sqrt(2)
Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0
=> For general solution of equation,
Solve D4 - 5D3 + 5D2 + 5D - 6 = 0
=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0
=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0
=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)
Now
D2 - 1 = (D - 1)(D + 1) and
Factors of D2 - 5D + 6
D2 - 5D + 6 = D2 - 2D - 3D + 6
= D(D - 2) - 3(D - 2)
= (D - 3)(D - 2)
Therefore, equation (1) implies
(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0
=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3
=> General solution of differential equation is,<span>
=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
Hope it helps
</span>
Step-by-step explanation:
59/8=7.375
So that's mean wxyz is bigger than the ABCD for 7.375
So YZ = 7.375×4 = 29.5
