Answer:
The probability of SFS and SSF are same, i.e. P (SFS) = P (SSF) = 0.1311.
Step-by-step explanation:
The probability of a component passing the test is, P (S) = 0.79.
The probability that a component fails the test is, P (F) = 1 - 0.79 = 0.21.
Three components are sampled.
Compute the probability of the test result as SFS as follows:
P (SFS) = P (S) × P (F) × P (S)

Compute the probability of the test result as SSF as follows:
P (SSF) = P (S) × P (S) × P (F)

Thus, the probability of SFS and SSF are same, i.e. P (SFS) = P (SSF) = 0.1311.
Note this pattern: Mult. 24 by (-1/4) produces -6.
Mult -6 by (-1/4) produces 6/4 = 3/2
Mult. 3/2 by (-1/4) produces 3/8
Looks as though you copied the problem down incorrectly. You wrote 32 for 3/2 and -38 for -3/8.
The common ratio is -1/4.
Answer:
Second point (-5/2, -7/2)
First point (3/2, 17/2)
Step-by-step explanation:
We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.
4x2+ 7x -11=y
3x+4=y
Lets use substitute method
4x2+7x-11=3x+4
This can be re arrange as the following eq:
4x2+4x-15=0
A quadratic equation, its solution can be obtained using the below eq.

where a=4, b=4, c=-15.
Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.
By doing the above, we have x=-5/2 and x=3/2
By using x=3/2 in equation of line (3x+4=y) we have y=17/2
First point (3/2, 17/2)
By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2
Second point (-5/2, -7/2)
Those points are the ones where the line and the parabola intercept.
Solving the inequality for g
Move the 6 over by subtraction and you have:
4.5g ≤ 34
Then divide each side by 4.5
g = 7.55555
So Ellis can purchase at lease 7 gallons but not 8 (D)