On a sunny day, your friend Issac was daydreaming under an apple tree. All of a sudden, an apple dropped from the tree and hit Issac's head. From there Issac had the idea that the apple was dragged down from the tree by a "force". He contemplated an equation to describe this "force": F = m*g Where F is the force exerted onto the apple (in unit N), m is the mass of the apple (in unit kg), and g is a fundamental constant of nature, Issac named it the gravitational constant. Issac was intrigued by this idea and he wanted to measure the gravitational constant. He designed a simple experiment to do this: 1. Collect 5 apples 2. Measure the mass of each of them and put them into a dataset M 3. Put each apple onto the tree branch, and let 4. Measure the force exerted on each apple F = it drop from the tree [6.9, 7.3, 9.8, 9.0, 10} = {0.7, 0.7, 0.9, 0.8, 1.0} Issac carefully prepared his dataset so that there is one-to-one correspondence between each element in M and F. (i.e., the 1st apple with measured mass 0.7 has an measured force 6.9, and the 3rd apple with measured mass 0.9 has measured force of 9.8, etc.). Issac would like you to help him analyze these data to obtain the gravitational constant. a) Calculate the Mean and Median for both Dataset M and F, make sure to show your work. b) Given Mean(F), Mean(M), Median(F), Median(M), Issac went ahead and reported: Mean(g) Median (g) = = Mean(F) Mean(M) Median (F) Median(M) Issac's friend Albert does not agree with Issac on the reported values. Use the mathematical experssion of Mean(), to help Albert prove that Issac's report of Mean(g) is incorrect. State whether the following statements are True or False and give reasons for your answer:
On a sunny day, your friend Issac was daydreaming under an apple tree. All of a sudden, an apple dropped from the tree and hit Issac's head. From there Issac had the idea that the apple was dragged down from the tree by a "force". He contemplated an equation to describe this "force": F = m*g Where F is the force exerted onto the apple (in unit N), m is the mass of the apple (in unit kg), and g is a fundamental constant of nature, Issac named it the gravitational constant. Issac was intrigued by this idea and he wanted to measure the gravitational constant. He designed a simple experiment to do this: 1. Collect 5 apples 2. Measure the mass of each of them and put them into a dataset M 3. Put each apple onto the tree branch, and let 4. Measure the force exerted on each apple F = it drop from the tree [6.9, 7.3, 9.8, 9.0, 10} = {0.7, 0.7, 0.9, 0.8, 1.0} Issac carefully prepared his dataset so that there is one-to-one correspondence between each element in M and F. (i.e., the 1st apple with measured mass 0.7 has an measured force 6.9, and the 3rd apple with measured mass 0.9 has measured force of 9.8, etc.). Issac would like you to help him analyze these data to obtain the gravitational constant. a) Calculate the Mean and Median for both Dataset M and F, make sure to show your work. b) Given Mean(F), Mean(M), Median(F), Median(M), Issac went ahead and reported: Mean(g) Median (g) = = Mean(F) Mean(M) Median (F) Median(M) Issac's friend Albert does not agree with Issac on the reported values. Use the mathematical experssion of Mean(), to help Albert prove that Issac's report of Mean(g) is incorrect. State whether the following statements are True or False and give reasons for your answer:
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:On a sunny day, your friend Issac was daydreaming under an apple tree. All of a sudden, an apple dropped
from the tree and hit Issac's head. From there Issac had the idea that the apple was dragged down from the
tree by a "force". He contemplated an equation to describe this "force":
F = m*g
Where F is the force exerted onto the apple (in unit N), m is the mass of the apple (in unit kg), and g is a
fundamental constant of nature, Issac named it the gravitational constant.
Issac was intrigued by this idea and he wanted to measure the gravitational constant. He designed a simple
experiment to do this:
1. Collect 5 apples
2. Measure the mass of each of them and put them into a dataset M
3. Put each apple onto the tree branch, and let
4. Measure the force exerted on each apple F
=
it drop from the tree
[6.9, 7.3, 9.8, 9.0, 10}
=
{0.7, 0.7, 0.9, 0.8, 1.0}
Issac carefully prepared his dataset so that there is one-to-one correspondence between each element in M
and F. (i.e., the 1st apple with measured mass 0.7 has an measured force 6.9, and the 3rd apple with measured
mass 0.9 has measured force of 9.8, etc.). Issac would like you to help him analyze these data to obtain the
gravitational constant.
a)
Calculate the Mean and Median for both Dataset M and F, make sure to show your work.
b)
Given Mean(F), Mean(M), Median(F), Median(M), Issac went ahead and reported:
Mean(g)
Median (g) =
=
Mean(F)
Mean(M)
Median (F)
Median(M)
Issac's friend Albert does not agree with Issac on the reported values. Use the mathematical experssion
of Mean(), to help Albert prove that Issac's report of Mean(g) is incorrect.
State whether the following statements are True or False and give reasons for your answer:
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