Find the slope of the line. The slope is ___
2 answers:
You might be interested in
Answer:
a) 3.56% probability that both adults think most celebrities are good role models.
b) 65.74% probability that neither adult thinks most celebrities are good role models.
c) 34.26% probability that at least one of the two adults thinks most celebrities are good role models.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the adults are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
(a) Find the probability that both adults think most celebrities are good role models.
Desired outcomes:
Think most celebrities are good role models, so 2 from a set of 208. Then
Total outcomes:
Two adults from a set of 1100. Then
Probability:
3.56% probability that both adults think most celebrities are good role models.
(b) Find the probability that neither adult thinks most celebrities are good role models.
Desired outcomes:
2 from a set of 1100 - 208 = 892. Then
Total outcomes:
Two adults from a set of 1100. Then
Probability:
65.74% probability that neither adult thinks most celebrities are good role models.
(c) Find the probability that at least one of the two adults thinks most celebrities are good role models.
Either neither think, or at least one does. The sum of the probabilities of these events is 100%.
From b), 65.74% probability that neither think.
So
65.74 + p = 100
p = 100 - 65.74
p = 34.26
34.26% probability that at least one of the two adults thinks most celebrities are good role models.
The coefficients of the binomial expansion 
, where n is the row number, is given in the Pascal's triangle shown below.
First, to find the <span>coefficient of the fourth term of (x+2)^5 we look at row 5, term 4. The coefficient there is 10.
But, we must also remember that the term 2 also is taken to a certain power here. Mainly , for each term, the power of 2 is as follows:
2^0, 2^1, 2^2, 2^3=8.
So, in total we have: 10*8=80.
Second, to find </span><span> the coefficient of the third term of (3x-1)^5 we again go to the row 5, this time term 3 and we have 10 there. Now we must check how each of (3x) and 1 expand, now being careful about the sign as well.
we have:
(3x)^5 (1) -(3x)^4 (1) (3x)^3(1)=27x^3.
Thus, the coefficient of the third term is 27*10=270.
Third, we want to find </span><span>the coefficient of the third term of (a+5b^2)^4. We look at row 4, term 3. There we have 6.
The terms a and 5b^2 are as follows:
a^4 (5b^2)^0 </span> a^3 (5b^2)^1 a^2 (5b^2)^2=25a^2b^4
Thus, the coefficient is 25*6=150.
Answer:
80; 270; 150
First, to find the <span>coefficient of the fourth term of (x+2)^5 we look at row 5, term 4. The coefficient there is 10.
But, we must also remember that the term 2 also is taken to a certain power here. Mainly , for each term, the power of 2 is as follows:
2^0, 2^1, 2^2, 2^3=8.
So, in total we have: 10*8=80.
Second, to find </span><span> the coefficient of the third term of (3x-1)^5 we again go to the row 5, this time term 3 and we have 10 there. Now we must check how each of (3x) and 1 expand, now being careful about the sign as well.
we have:
(3x)^5 (1) -(3x)^4 (1) (3x)^3(1)=27x^3.
Thus, the coefficient of the third term is 27*10=270.
Third, we want to find </span><span>the coefficient of the third term of (a+5b^2)^4. We look at row 4, term 3. There we have 6.
The terms a and 5b^2 are as follows:
a^4 (5b^2)^0 </span> a^3 (5b^2)^1 a^2 (5b^2)^2=25a^2b^4
Thus, the coefficient is 25*6=150.
Answer:
80; 270; 150