Answer:
m = -8 (Two points slope form)
Step-by-step explanation:
y = -8x + 6
Answer:
a) 1/2 (50%)
b) 1/2 (50%)
c) 3/4 (75%)
d) 3/4 (75%)
Step-by-step explanation:
for a uniform distribution
P(X=x)= x-A/(B-A) , for A≤x≤B
then
P(X=x)= (x+8)/16 , for -8≤x≤8
a) P(X<0)= interval chosen / total interval = (0-(-8))/(8-(-8)) = 1/2 (50%)
b) P(-4<X<4)= interval chosen / total interval =(4-(-4))/(8-(-8)) = 1/2 (50%)
c) P(-5<X<7)= interval chosen / total interval =(7-(-5))/(8-(-8)) = 3/4 (75%)
d) for −8 < k and k + 4 < 8 → k < 4 , then -8<k<4 , thus k
P(X=k)= P(-8<X<4) = interval chosen / total interval =(4-(-8))/(8-(-8)) = 3/4 (75%)
Let x be the population distribution.
p(25 ≤ x ≤ 33) = p((25 - 29)/4 ≤ z ≤ (33 - 29)/4) = p(-1 ≤ z ≤ 1) = p(z ≤ 1) - p(z ≤ -1) = p(z ≤ 1) - [1 - p(z ≤ 1)] = 2p(z ≤ 1) - 1 = 2(0.84134) - 1 = 0.68268 = 68%
p(21 ≤ x ≤ 25) = p((21 - 29)/4 ≤ z ≤ (25 - 29)/4) = p(-2 ≤ z ≤ -1) = p(z ≤ -1) - p(z ≤ -2) = [1 - p(z ≤ 1)] - [1 - p(z ≤ 2)] = p(z ≤ 2) - p(z ≤ 1) = 0.97725 - 0.84134 = 0.13591 = 13.5%
Answer:
True for all values of a, b and c.
Step-by-step explanation:
(a–3c)(4c+2a)+3c(a+3c)=(2a–c)(3c+5a)–8a^2
Left side:
(a–3c)(4c+2a)+3c(a+3c)
= 4ac + 2a^2 - 12c^2 - 6ac + 3ac + 9c^2
= 2a^2 + ac - 3c^2
Right side:
(2a–c)(3c+5a)–8a^2
= 6ac + 10a^2 - 3c^2 - 5ac - 8a^2
= 2a^2 + ac - 3c^2.
So we see that the left side is identical to the right side so it is true for all values of the variables.
