Eighty-five mall customers were randomly surveyed across the state to determine if the live entertainment provided had increased the amount of money they spent. can the probability be found by using the binomial probability formula? a. no. the trials are fixed, but the events are independent and the 5% guideline does not apply to this situation. b. yes. the events are dependent; however, the 5% guideline can be applied to this situation. c. yes. the outcomes can be classified into two categories: the trials are fixed, and the events are independent. d. no. the events are dependent.

c. Yes. The outcomes can be classified into two categories: the trials are fixed, and the events are independent.

Since we can calculate the following probabilities:

p= probability that live entertainment had increased the amount of money they spent

q =probability that live entertainment had not increased the amount of money they spent

n = 85

And independence is satisfied.

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

In order to apply the binomial distirbution we need to satisfy some conditions given here:

1) Independence between the trials of the experiment

2)  The number of observations n is fixed for this case n=85

3) Each observation represents one of two outcomes "success" or "failure" and the probability of success is defined.

So then based on this and on the information given we can conclude that the best option for this case is:

c. Yes. The outcomes can be classified into two categories: the trials are fixed, and the events are independent.

Since we can calculate the following probabilities:

p= probability that live entertainment had increased the amount of money they spent

q =probability that live entertainment had not increased the amount of money they spent

n = 85

And independence is satisfied.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: