A reasonable estimate of the moment of inertia of an ice skater spinning with her arms at her sides can be made by modeling most of her body as a uniform cylinder. Suppose the skater has a mass of 64 kg . One eighth of that mass is in her arms, which are 60 cm long and 20 cm from the vertical axis about which she rotates. The rest of her mass is approximately in the form of a 20-cm-radius cylinder.

Step-by-step explanation:

Given data:

Mass of the one arm of the skater, m = (1/16) x 64 = 4 kg

Rest mass of the skater in the form of cylinder, M = (7 / 8) x 64 kg = 56 kg

Radius of the cylinder, R = 20 cm = 0.20 m

The parallel axis theorem:

The only statement that is NOT true is option A.

- If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

Step-by-step explanation:

Complete Question

Ellen is opening. Cookie shop eat a local middle school . She randomly surgery’s students to determine The types of cookies they would buy at the cookie shop the results of the surveys are below based on the survey. Which statement is not true?

Cookie Survey

Type of Cookie | Number of Students

Chocolate Chip | 25

Oatmeal Raisins | 15

Peanut Butter | 22

Sugar | 18

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

B) 22½% of the students surveyed would buy a sugar cookie.

C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

Solution

First of, we obtain the proportion or percentages of students surveyed that buy each type of cookie.

Each of that is the number of students that buy the type of cookie in the sample divided by the Total number of students sampled.

Total number of students sampled = 25 + 15 + 22 + 18 = 80

Type of Cookie | N | proportion | %

Chocolate Chip | 25 | 0.3125 | 31.25%

Oatmeal Raisins | 15 | 0.1875 | 18.75%

Peanut Butter | 22 | 0.2750 | 27.50%

Sugar | 18 | 0.2250 | 22.50%

Now, taking the statements one by one

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

Proportion of students that buy sugar cookie in the sample = 0.225

Number of students that will buy sugar cookie amongst 160 students = np = 160 × 0.225 = 36 students.

This statement is false, that is, NOT true.

B) 22½% of the students surveyed would buy a sugar cookie.

From the table, 22.5% of the students surveyed bought a sugar cookie. Hence, no matter the number of students, the percentage of students that will buy a sugar cookie will approximately be 22.5%.

This statement is True.

C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

Proportion of students that buy peanut butter cookie in the sample = 0.275

Number of students that will buy peanut butter cookie amongst 240 students = np = 240 × 0.275 = 66 students.

This statement is true.

D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

Proportion of students that buy chocolate chips or oatmeal raisin cookies in the sample = 0.3125 + 0.1875 = 0.50

0.50 is half of the distribution.

Hence, this statement too, is True.

Hope this Helps!!!