Answer:
Expected value = 190
Variance = 4000
Step-by-step explanation:
Let X be the number of the trials until the third success of the bad pump.
This implies that X is a negative binomial distribution
having θ = 20% = 0.2.
Now, if for example it will take X trials to use up the three pumps, then the total time is 10 min/trials + extra 10 minutes for the 3 bad pumps
This means the total time is written as;
T = 10X + (10 + 10 + 20)
T = 10X + 40
Mean which is also expected value of X is;
μ_x = 3/0.2 = 15
Variance of X is; σ²_x = 40
Thus;
Mean of T will be;
μ_T = 10μ_x + 40
μ_T = 10(15) + 40
μ_T = 190
Also, variance of T will be;
σ²_T = 10²•σ²_x
σ²_T = 100 × 40
σ²_T = 4000
Answer:
50.24 yards
Step-by-step explanation:
We will use the pythagorean theorem to find hypotenuse of each of the 4 triangles.
Pythagorean Theorem is 
For Spinach area, two of the legs are 8 and 6. Solving for hypotenuse:
For watermelon area, two of the legs are 12 and 8. Solving for hypotenuse:
in red peppers area, the hypotenuse is already given as 15. But we need to find one leg since that will be the leg of the triangle in tomatoes area. Hypotenuse is 15 and one leg is 12, so the other leg is:
So, in tomatoes area, we have one leg 9 and another leg 6. Solving for hypotenuse:
Adding all the four hypotenuses, we get the length of the walkway:
Length of Walkway = 
yards
Answer: 1. False.
2.True.
3.True.
4.False.
5.True.
6.False.
Explanation:
1.∠XFG is lying between the one side and the line extended to the next side of the triangle, therefore it is an exterior angle.
2.∠EFG is lying between the two sides of the ΔEFG, therefore it is an interior angle of the triangle.
3.∠FEZ is lying between the one side and the line extended to the other side of ΔEFG.
4.∠YGE is a straight line it is between the one side and the line extended to the same side ∴ it cannot be an exterior angle of the triangle.
5.∠EGF and FGY lying on the same line YZ ,∴they are linear pair i.e. they are supplementary angles.
6.∠FEG and ∠FGE are both the interior angles of a triangle and we know that for supplementary angles they should lie on the same line.Therefore ∠FEG and ∠FGE are not supplementary angles.
-5abc+10d will be the answer.
