The perimeter of the park is (125+150)*2=550 yards. Then, to walk a million years, you would need to walk 1000000/550=1818.18 perimeters. Since we're looking for the amount of times we have to walk around the park fully to hit 1,000,000 yards, though, we must round up (even though normally with a decimal of .18 we'd round down) to 1819 times.
Answer:
Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.
Step-by-step explanation:
Consider the provided information,
Let X is the number of defective bulbs.
Ten light bulbs are randomly selected.
The likelihood that a light bulb is defective is 5%.
Therefore sample size is = n = 10
Probability of a defective bulb = p = 0.05.
Therefore, q = 1 - p = 1 - 0.05 = 0.95
Mean of binomial random variable: 
Therefore, 
Variance of binomial random variable: 
Therefore, 
Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.
Answer:
A <u>postulate</u> is accepted to be true without proof, while a <u>theorem </u>is an assertion that can be proven using the rules of logic.
Explanation:
In mathematics, a postulate is a statement that is considered to be true without looking for any proof of that statement. Other hypotheses or statements can be tested using a postulate as a standard. A postulate is not only significant in mathematics but also plays an important role in understanding the concept of physics.
A theorem can be described as a statement that can be proved right by using logical pieces of evidence.
I’m pretty sure the answer is C
A.
If she will choose 8 from 12 photos, the total number of ways she can choose is given by a combination of 12 choose 8, since the order of the photos doesn't matter.
The formula for a combination of n choose p is:

For n = 12 and p = 8, we have:

So there are 495 ways.
B.
If she wants to arrange the 12 photos, the total number of ways is given by the factorial of 12:

There are 479,001,600 ways.
C.
Since 10 photos already have specific places, we need to calculate the number of ways to arrange the other two photos in the two remaining places.
In this case, there are only 2 ways of organizing the remaining two photos:
Photo 1 first, photo 2 last, or photo 1 last and photo 2 first.