Answer:
B
Step-by-step explanation:
Find all probabilities:
A. False

B. True

C. False

D. False

Answer:
Step-by-step explanation:
The given postulate If two lines intersect, then they intersect in exactly one point is true because whenever the two lines intersect they intersect at one point only and we know that a postulate is a statement that we accept without proof.
The given theorem If two distinct planes intersect, then they intersect in exactly one line is true as theorem is a statement that has been proved and it has been proved that if two distinct planes intersect, then they intersect in exactly one line.
The figures are drawn to prove them.
3. ∠1+∠2=180° and ∠2+∠3=180°
4. they are supplementary
5. ∠1+∠2=180°=∠2+∠3
6. ∠1+∠2=180°=∠2+∠3
∠2 are same in both side so ∠1=180°-∠2 =∠3=180°-∠2
7.
Answer:
Length = 12 inches
Width = 14 inches
Step-by-step explanation:
Formula for perimeter of a rectangle is;
P = 2(L + W)
Where;
L is length
W is width
We are told that the length is 2 inches shorter than its width. Thus;
L = (W - 2)
Thus,perimeter is now;
P = 2(W - 2 + W)
P = 2(2W - 2)
P = 4W - 4
We are told that the perimeter is 52. Thus;
4W - 4 = 52
4W = 52 + 4
4W = 56
W = 56/4
W = 14 inches
From L = (W - 2) ;
L = 14 - 2
L = 12 inches
Answer: The running time should at least 119.32 seconds to be in the top 5% of runners.
Step-by-step explanation:
Let X= random variable that represents the running time of men between 18 and 30 years of age.
As per given, X is normally distrusted with mean
and standard deviation
.
To find: x in top 5% i.e. we need to find x such that P(X<x)=95% or 0.95.
i.e. 

Since, z-value for 0.95 p-value ( one-tailed) =1.645
So,
Hence, the running time should at least 119.32 seconds to be in the top 5% of runners.