Question

1. during a particular experiment, 2 events, a and b, can each occur or not occur. a and b are mutually - exclusive during this experiment. which of the following probabilities is 0?

f. p(a)
g. p(b)
h. p(a or b)
j. p(a and b)

1. the polynomial function defined by (p(x)=x^{3}+x^{2}-8x - 12) has ((x - 3)) as one of its linear factors. what are all and only the zeros of (p)?

a. - 2 and 3
b. - 3 and 2
c. - 2 and - 3
d. 2 and 3

1. jonathan rode his bike every day for 18 days. the table shows each of the distances he rode. the table also shows the number of days he rode each of those distances.

distance (in miles)	number of days
3	4
4	3
5	6
7	3

what is the median daily distance, in miles, that jonathan rode his bike for the 18 days?
f. 3
g. 3.5
h. 4
j. 4.5

1. a tourism organization randomly selected 100 tourists finishing their summer visit to spain. the organization asked them how many cities they had toured in the country. the table shows the results. based on these data, for the population of tourists that visited spain during the summer, what is the best estimate of the mean number of cities toured?

number of cities	1	2	3
number of tourists	10	40	50

a. 0.8
b. 2
c. 2.4
d. 3

Explanation:

36.

Step1: Recall mutual - exclusivity property

If two events A and B are mutually exclusive, then \(P(A\cap B)=0\). By the addition rule of probability, \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Since \(P(A\cap B) = 0\) for mutually - exclusive events, \(P(A\cup B)=P(A)+P(B)\).

Step1: Use factor - theorem

If \((x - 3)\) is a factor of \(p(x)=x^{3}+x^{2}-8x - 12\), then \(p(3)=0\). First, we can use synthetic division or long - division to divide \(p(x)\) by \((x - 3)\). Using synthetic division:

3	1 1 - 8 - 12
	3 12 12
	----------------
	1 4 4 0

The quotient is \(x^{2}+4x + 4=(x + 2)^{2}\).

Step2: Find the zeros

Set \(p(x)=(x - 3)(x + 2)^{2}=0\). Then \(x=3\) and \(x=-2\) are the zeros of \(p(x)\).

Step1: Organize the data

We have the following data set based on the table:
\(1,1,3,3,3,3,4,4,4,5,5,5,5,5,5,7,7,7\)
There are \(n = 18\) data points.

Step2: Calculate the median

Since \(n = 18\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data values. \(\frac{n}{2}=9\) and \(\frac{n}{2}+1 = 10\). The 9th value is \(4\) and the 10th value is \(5\). The median is \(\frac{4 + 5}{2}=4.5\).

Answer:

H. \(P(A\ or\ B)\)

37.