Answer: d. np(1 - p).
Step-by-step explanation:
Let x be any binomial variable which represents the number of success such that , where n is the sample size or the total number of trials and p is the probability of getting success in each trial .
Then, the mean E(x) and the variance Var(x) for the binomial distribution is given by equation :
where n is the sample size or the total number of trials and p is the probability of getting success in each trial .
Therefore , the correct option is option d. np(1 - p) .
Answer:
Step-by-step explanation:
Using Pythagoras theorem , since it is a right angled triangle ,
side 1 = 10cm
side 2 = x cm
side 3 = x cm
Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. That is
100 =
divide through by 2 , we have
50 =
find the square root of both sides
Answer:
<h2>Tn = 34+3n</h2>Step-by-step explanation:
The formula for finding the nth term of an arithmetic sequence is expressed as shown;
a is the first term of the sequence
n is the number of terms
d is the common difference
If T₁₂ = 70 and T₃₀ = 124
T₁₂ = a+(12-1)d = 70
T₁₂ = a+11d = 70... (1)
Similarly;
T₃₀ = a + (30-1)d = 124
T₃₀ = a +29d = 124...(2)
Solving equation 1 and 2 simultaneously to get a and d.
Subtracting 2 from 1 we have;
29d - 11d = 124-70
18d = 54
d = 54/18
d = 3
Substituting d = 3 into equation 1 to get a we have;
a + 11(3) = 70
a + 33 = 70
a = 70-33
a = 37
The explicit rule for the nth term of the sequence can be gotten by substituting the value of a and d into the formula Tn = a+(n-1)d
Tn = 37+(n-1)*3
Tn = 37+3n-3
Tn = 34+3n