130 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:

Cumulative Frequency

# of times floss per week

0

1

12

Frequency

12

21

13

Relative Frequency

0.0923

0.1615

0.1

0.1385

33

2

46

64

20

0.1538

100

0.1308

117

0.1

130

a. The answers obtained are as follows:

Frequency for flossing 7 times per week = 24

Relative frequency for flossing 4 times per week = 0.1231

Cumulative Frequency at flossing 1 time per week = 22

b. The Cumulative Relative Frequency at flossing 7 time per week is 100%.

Step-by-step explanation:

Note: This question is not complete and the data in it are merged together. The complete question is therefore provided with the sorted data before answering the question. See the attached pdf file for the complete question.

The explanation to the answers is now provided as follows:

a. Complete the table (Use 4 decimal places when applicable)

Note: See part a of the attached excel for the complete table (answers are in bold red color)

Frequency is the rate at which something or an event occurs in a particular sample.

Since we already have frequency for others flossing times per week and we have 130 adults as the sample, the frequency for flossing 7 times per week is calculated by deducting the frequencies of others from 130 as follows:

Frequency for flossing 7 times per week = 130 – 10 – 12 – 14 – 18 – 16 – 21 – 15 = 24

Relative Frequency refers to the fraction of times an event occurs. The relative frequencies in this question are calculated by dividing each frequency by the total number of adults in the sample, i.e. 130. The relative frequency for flossing 4 times per week is therefore calculated as follows:

Relative frequency for flossing 4 times per week = Frequency for flossing 4 times per week / Total number of adults in the sample = 16 / 130 = 0.1231

Cumulative Frequency is calculated by adding the current frequency to the previous Cumulative Frequency. The Cumulative Frequency at flossing 1 time per week is therefore calculated as follows:

Cumulative Frequency at flossing 1 time per week = Cumulative Frequency at flossing 0 time per week + Frequency at flossing 1 time per week = 10 + 12 = 22

b. What is the cumulative relative frequency for flossing 7 times per week? %

Note: See part b of the attached excel for the complete table (answer is in bold red color)

The cumulative relative frequency refers to the accumulation of the previous relative frequencies.

Cumulative Relative Frequency is calculated by adding the current relative frequency to the previous Cumulative Relative Frequency. It should be noted that the first cumulative relative frequency equal to the first relative frequency.

The Cumulative Relative Frequency at flossing 7 time per week is therefore calculated in the attached excel file as follows:

Cumulative Relative Frequency at flossing 1 time per week = Cumulative Relative Frequency at flossing 6 times per week + Relative Frequency at flossing 7 times per week = 0.8154 + 0.1846 = 1.0000

Since the question indicates that the Cumulative Relative Frequency at flossing 7 time per week should be stated in percentage term, we therrefore have:

Cumulative Relative Frequency at flossing 7 time per week = 1.0000 * 100 = 100%.

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option