A local television station for a city with a population of 500,000 recently conducted a poll where they invited viewers to call in and voice their support or opposition to a controversial referendum that was to be voted on in an upcoming election. Over 10,000 people responded, with 67% opposed to the referendum. The TV station announced that they are convinced that the referendum will be defeated in the election. Select the answer below that indicates whether the TV station's announcement is valid or invalid, and why.

a. Valid, because 67% is far enough above 50% to predict a majority vote.
b. Invalid, because the sample may not be representative of the population.
c. Valid, because the sample size is large enough to represent the population.
d. Invalid, because the sample is too small given the size of the population.

b. Invalid, because the sample may not be representative of the population.

Step-by-step explanation:

A sample of around 10% of the population is needed to be representative.

In this question:

We have a population of 500,000, and a sample of 10,000.

10,000/500,000 = 1/50 = 0.02 = 2% of the population, so not representative, and option b is correct.

y=x+2 hope this jdjxhdnzbdjdo

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: