Answer:
a) E(X) = 71
b) V(X) = 20.59
Sigma = 4.538
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015).
</em>
<em>
Suppose we randomly select 100 tweets.
</em>
<em>a) What is the expected number of these tweets with no reaction?
</em>
<em>b) What are the variance and standard deviation for the number of these tweets with no reaction?</em>
This can be modeled with the binomial distribution, with sample size n=100 and p=0.71, as the probability of no reaction for each individual tweet.
The expected number of these tweets with no reaction can be calcualted as the mean of the binomial random variable with these parameters:

The variance for the number of these tweets with no reaction can be calculated as the variance of the binomial distribution:

Then, the standard deviation becomes:

There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,
S = (a1 + an)(n/2)
and substituting,
S = (2 + 998)(500/2)
we get,
S = 250,000
Therefore, the sum of all even numbers between 1 and 1000 is 250,000.
Answer:

Step-by-step explanation:

If you sum it up, she works a total of 29 hours
29 x 12.5 = 362.5
Her gross pay is $362.5
Answer:
m =-4
Step-by-step explanation:
-12m-10=-5m+18
add 5m to both sides
-7m-10=18
add 10 to both sides
-7m=28
divide both sides by -7
m= -4