Answer:
Final answer is
Step-by-step explanation:
We need to find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3).
So first we need to find the slope of given line.
rewirite x=6y-5 in y=mx+b form
x+5=6y
Compare given equation with y=mx+b
we get: m=1/6
We know that parallel equations has equal slope.
Then slope of required line m=1/6
Now plug the given point (5,-3) and slope m=1/6 into point slope formula:
Now we need to rewrite that equation in standard form. Ax+By=C.
6y=x-23
x-23=6y
x-6y=23
Hence final answer is
Answer:
Step-by-step explanation:
(-1, 5) (-5, 8)
(8-5)/(-5+1) = 3/-4 = -3/4
y - 8 = -3/4(x + 5)
y - 32/4 = -3/4x - 15/4
y = -3/4x + 17/4
Answer and Step-by-step explanation: This function is a probability density function of a random variable X:
and to calculate probabilities, we will have to integrate it:
Solving:
Then:
a. P(X < 5)
P(X < 5) = 0.683
b. P(X < 9)
Since density function's upper limit is 8, probability of x < 9 is 100% or 1.
So, P(X < 9) = 1
c. P(5 < X < 7)
P(5 < X < 7) = 0.273
d. P(X > 3)
P (X > 3) = 0.683
e. P(X < x) = 0.95
Solving this cubic equation, we have three values for x:
x₁ = -3.909
x₂ = 8.992
x₃ = 6.917
The value of x will the one between 0 and 8, which are the limits of the function. So, value of x which gives a probability of 0.95 is x = 6.917.