This document is notes from a mathematics lesson on equivalent ratios. It includes examples of equivalent and non-equivalent ratios, and defines that equivalent ratios have the same value. The value of a ratio is represented as a fraction using the largest possible units. The document includes practice problems applying this concept, such as analyzing a runner's training ratios and determining if specific ratios are equivalent based on their values.
The end of our short metric history unit, this was designed as an overview to the basic themes of why we use metric (or should). A stress on science and the democratic nature of science and ten-based measurements is my cornerstone. I like the stuff about the metric calendar best.
The end of our short metric history unit, this was designed as an overview to the basic themes of why we use metric (or should). A stress on science and the democratic nature of science and ten-based measurements is my cornerstone. I like the stuff about the metric calendar best.
ScoreWeek 5 Correlation and Regressio.docxpotmanandrea
Score:
Week 5
Correlation and Regression
<1 point>
1.
Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)
a.
Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?
b. Place table here (C8):
c.
Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are
significantly related to Salary?
To compa?
d.
Looking at the above correlations - both significant or not - are there any surprises -by that I
mean any relationships you expected to be meaningful and are not and vice-versa?
e.
Does this help us answer our equal pay for equal work question?
<1 point>
2
Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint,
age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both used in the same regression.)
Plase interpret the findings.
Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not significant
Note: technically we have one for each input variable.
Ha: The regression coefficient for each variable is significant
Listing it this way to save space.
Sal
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9915591
R Square
0.9831894
Adjusted R Square
0.9808437
Standard Error
2.6575926
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
6
17762.3
2960.38
419.1516
1.812E-36
Residual
43
303.7003
7.0628
Total
49
18066
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-1.749621
3.618368
-0.4835
0.631166
-9.046755
5.5475126
-9.04675504
5.54751262
Midpoint
1.2167011
0.031902
38.1383
8.66E-35
1.1523638
1.2810383
1.152363828
1.28103827
Age
-0.004628
0.065197
-0.071
0.943739
-0.136111
0.1268547
-0.13611072
0.1268547
Performace Rating
-0.056596
0.034495
-1.6407
0.108153
-0.126162
0.0129695
-0.12616237
0.01296949
Service
-0.0425
0.084337
-0.5039
0.616879
-0.212582
0.1275814
-0.2125.
Math 009 Final Examination Spring, 2015 1 Answer Sheet M.docxandreecapon
Math 009 Final Examination Spring, 2015 1
Answer Sheet
Math 009 Introductory Algebra Name______________________________
Final Examination: Spring, 2015 Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam and
you may use a calculator. Record your answers and show your work on this document. You must show your
work to receive credit: answers given with no work shown will not receive credit. You may type your work
using plain-text formatting or an equation editor, or you may hand-write your work and scan it. If you choose
to scan your work, note that most scanners have a setting that will allow you to create one PDF document from
all of the pages of your Answer Sheet – please make use of this option if it is available on your scanner.
Whether you type your work or write it by hand, show work neatly and correctly, following standard
mathematical conventions. Each step should follow clearly and completely from the previous step. If
necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed.
Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I have completed this final examination myself, working independently and not consulting
anyone except the instructor. I have neither given nor received help on this final examination.
Name _______________ Date___________________
Math 009 Final Examination Spring, 2015 2
Answer Sheet
Problem
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Solution
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ANSWE ...
2. Module 1 Lesson 8.notebook
2
September 18, 2014
Module 1
Ratios and Unit Rates
Topic A: Representing and Reasoning About Ratios
Lesson 8: Equivalent Ratios Defined
Through the Value of a Ratio
3. Module 1 Lesson 8.notebook
3
September 18, 2014
Classwork
Exercise 1
Circle any equivalent ratios from the list below.
Ratio: 1:2
Ratio: 5:10
Ratio: 6:16
Ratio: 12:32
Find the value of the following ratios, leaving your answer as a fraction, but re‐write the
fraction using the largest possible unit.
Ratio: 1:2 Value of the Ratio:
Ratio: 5:10 Value of the Ratio:
Ratio: 6:16 Value of the Ratio:
Ratio: 12:32 Value of the Ratio:
What do you notice about the value of the equivalent ratios?
The value of the ratio is the same for equivalent ratios.
4. Module 1 Lesson 8.notebook
4
September 18, 2014
Note that 1:2 is not the same ratio as 5:10, so we do not say they are equal.
The ratios are not the same, but their values are equal.
Would this always be the case? Would the values of equivalent ratios always
be equal?
Exercise 2
Here is a theorem:(a theorem is a statement that is always true)
If two ratios are equivalent, then they have the same value.
Can you provide any counter‐examples to the theorem above?
5. Module 1 Lesson 8.notebook
5
September 18, 2014
Exercise 3
Taivon is training for a duathlon, which is a race that consists of running and cycling. The
cycling leg is longer than the running leg of the race, so while Taivon trains, he rides his bike
more than he runs. During training, Taivon runs 4 miles for every 14 miles he rides his bike.
a. Identify the ratio associated with this problem and find its value.
6. Module 1 Lesson 8.notebook
6
September 18, 2014
Use the value of each ratio to solve the following.
b. When Taivon completed all of his training for the duathlon, the ratio of total number of
miles he ran to total number of miles he cycled was 80:280.
Is this possible according to Taivon’s training schedule? Explain why or why not.
This is possible because the ratio of the number of miles he
ran to the number of miles he biked, 80:280, has the value of
which is the same value as the ratio 4:14
27
7. Module 1 Lesson 8.notebook
7
September 18, 2014
c. In one training session Taivon ran 4 miles and cycled 7 miles. Did this training session
represent an equivalent ratio of the distance he ran to the distance he cycled? Explain why or
why not.
The training session does not represent an equivalent ratio of the
distance he ran to the distance he cycled because the value of the
ratio in this instance is which is not equal to 47
27
8. Module 1 Lesson 8.notebook
8
September 18, 2014
Closing
How is the value of a ratio related to the ratio?
Please take out your exit ticket for Lesson 1, close your
binder, and complete the exit ticket. This will be collected.