There are 140 people in a singing competition. The graph shows the results for the first five rounds

a) The expression is y = 140 - 15 x

b ) There are 5 participants in the 9th round

Step-by-step explanation:

Step 1 :

From the graph we can see that,

Number of people in the singing competition = 140

Number of people in the first round = 125

Number of people in the second round = 110

Number of people in the third round = 95

Number of people in the fourth round = 80

Number of people in the fifth round = 65

Step 2 :

From the given data, We can get that the difference between the number of people participating in each round is 15 less than the previous round .

The first round has 15 people less than the total number 140

Let x represent the number of the round and y represent the number of people participating in each round .

Then the expression to represent this would be

y = 140 - 15 x

Step 3 :

To find the number of participants in the 9th round given the same pattern continues.

For the 9th round x = 9, as x represents the number of the round

Substituting this in the equation obtained in step 2, we get

y = 140 -15 (9) = 140 - 135 = 5

There are 5 participants in the 9th round

Step 4 :

Answer :

a) The expression is y = 140 - 15 x

b ) There are 5 participants in the 9th round

a) Increase the sample size

Step-by-step explanation:

Given that a 95%  confidence interval for μ turns out to be (1,000, 2,100)

The confidence interval is formed as

Margin of error = critical value * std dev/sqrt of sample size

Hence for the same confidence level, we cannot change critical value.

The only available ways are either to decrease std deviation or increase the sample size to make it narrower.

If confidence level becomes higher, then confidence interval would be wider.

Here  out of four options the correct option is

a) Increase the sample size