A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.

If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

a. .0330

b. .1318

c. .7844

d. .9624

b. .1318

Step-by-step explanation:

For each freshmen, there are only two possible outcomes. Either they support increased spending on enviromental issues, or they do not. The probabiliy of each freshmen supporting increased spending on environmental issues is independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

25 percent of college freshmen support increased spending on environmental issues. This means that

If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

This is when . So

So the correct answer is:

b. .1318

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis