What would happen if the water in the dish were replaced with a denser liquid? What would be different about the refracted angle?

/in /by

 

  1. Graph the index of refraction by plotting sinθ1 over sinθ2 and determining the slope of the line.
  2. Try repeating the experiment with the dish empty. What is different about the refraction of the light passing through the empty dish from the refraction of light passing through the dish filled with water?
  3. What would happen if the water in the dish were replaced with a denser liquid? What would be different about the refracted angle?
  1. In the juice and wine industry, a device called a refractometer is used to measure the sugar level in juice. How would the refraction of light be used to determine the sugar content of a solution?

Describe the class for which you developed the activity, the activity, what relationships the students would identify, and how the graph(s) would help them identify each relationship.

/in /by

Question #1-Geometric Thinking and Geometric Concepts (pp. 402-433) chapter 20

What are some of the most important characteristics of proportional reasoning?

Assignment Guidelines
Write a brief paragraph concerning the most important characteristics of proportional reasoning. Pick an activity for helping students develop proportional thought processes. You can select or modify any activity in chapter 18 (except the Lemonade Activity) or any activity from the text you use in your classroom, or you can create your own. Be specific in your description of the activity. Describe what you will do while the students work through the activity. Make a list of the hints you might need to give students who need help. Describe how you would ask students to reflect on the activity. Describe how you would assess student learning. What is the CCLS connection? How would you assess student learning?

Question 2.
Review the activities from the reading and the video. Select one activity and, Reflect on the experience, Include the following responses in the assignment.

Describe the activity.
List the Common Core Learning Standards that are addressed by this activity
Do you think students will develop understanding of the key concepts as a result of the activity? What are these key concepts?
How would you adapt the activity for different ability levels?
Were the logistics of the activity reasonable to implement (for example, were materials easy to obtain/create and manage)?
What would you do differently if you administered this activity again?

Questions 3
If you have graphing calculators available for your class or an overhead graphing calculator available for demonstrations, conduct a data analysis activity with at least one of your classes by using the graphical features of the calculator and requiring students to analyze the relationship(s) between two sets of attributes or phenomena. If possible, conduct the activity. If it is not possible to conduct the activity, anticipate the end result(s) of the activity. Describe the class for which you developed the activity, the activity, what relationships the students would identify, and how the graph(s) would help them identify each relationship.

Assignment Guidelines
First, describe the class for which you designed the activity. Second, describe the activity and the corresponding CCLS. Be sure you identify the type of graph the activity requires. You may wish to attach a copy of the student activity sheet(s) to clarify the activity procedure and reduce the amount of written explanation. Third, list any relationships between the two sets of data the students should be able to determine, and be sure to explain how the graph(s) would help the students justify each relationship.

What did they this person do to help influence the field of mathematics or the world.

/in /by

The report should be two-three pages typed, no more than double spaced and font no larger than 12 pt. You must cite at least 3 sources, two of which must be published books or professional journal articles. What did they this person do to help influence the field of mathematics or the world. Include important mathematician names, dates, theories, discoveries, diagrams, formulas, cultural implications, and anecdotes.

Determine the change in volume and pressure in pneumatic systems

/in /by

Parameters of Pneumatic and
Hydraulic Systems –
Determine the change in volume and pressure in pneumatic systems
Using Bernoulli’s Equation, calculate values at stationary incompressible
flow

Explain in your own words what the meaning of domain is.

/in /by

Discussionhttps://ashford.instructure.com/coursesExplain in your own words what the meaning of domain is. Also, explain why a denominatorcannot be zero.Find the domain for each of your two rational expressions.Write the domain of each rational expression in set notation (as demonstrated in the example).Do both of your rational expressions have excluded values in their domains? If yes, explain whythey are to be excluded from the domains. If no, explain why no exclusions are necessary.Incorporate the following five math vocabulary words into your discussion. Use bold font toemphasize the words in your writing. Do not write definitions for the words; use themappropriately in sentences describing your math work.DomainExcluded valueSetFactorReal numbers

Reflect on the richness/depth of the mathematics you experienced in this exercise, then write your own definition of “doing mathematics.”

/in /by

Van de Walle asks his readers to experience the doing of mathematics. Four problem opportunities appear on pages 15-19 of Elementary and Middle School Mathematics.
1. Describe a learning experience as you work through one of these problems.
2. what you think about not having an answer book (see p. 19) to check your answer.
3. Reflect on the richness/depth of the mathematics you experienced in this exercise, then write your own definition of “doing mathematics.”

Determine the type of function and give the regression equation. Find the value of y when x=10.

/in /by

 

Complete and submit. Determine the type of function and give the regression equation. Find the value of y when x=10.

What value of x will yield a y value in excess of 10,000?

1.

x       0            1             2             3                4

y       3            6            12           24              48

 

2.

(0,5)     (2,10)        (4,15)         (6,20)          (8,25)

 

3.

(0,4)          (2,13)          (4,40)            (6,139)               (8,421)

 

 

Rewrite in simplest rational exponent form x • x4. Show each step of your process.

/in /by

Question 1
Is the expression x3•x3•x3 equivalent to x3•3•3? Why or why not? Explain your reasoning.
Question 2
Rewrite in simplest radical form 1x−36. Show each step of your process.
Question 3
Rewrite in simplest rational exponent form x • x4. Show each step of your process.
Question 4
Rewrite in simplest radical form x56x16. Show each step of your process.
Question 5
Which of the following expressions are equivalent? Justify your reasoning.
34
1x−1
x5•x4•x210
x13•x13•x13
Individual Rubric (10 points possible)
Category Excellent Good Satisfactory Needs Improvement
Mathematical Reasoning All questions were answered completely with required supporting evidence and work.
(5 points) Most questions were answered completely with required supporting evidence and work.
(4–3 points) Some questions were answered completely with required supporting evidence and work.
(2 points) Few questions were answered completely with required supporting evidence and work.
(1 point)
Accuracy All questions were answered correctly.
(5 points) Most questions were answered correctly.
(4–3 points) Some questions were answered correctly.
(2 points) Few questions were answered correctly.
(1 point)

Describe the set of assumptions underlying the mathematical regression model in terms of the error term.

/in /by

Course 2

Answer 3 out of 5

1.

  1. Describe the set of assumptions underlying the mathematical regression model in terms of the error term.
  2. Explain why the above assumptions are necessary.
  3. Explain what is meant by the residual standard error, how it is calculated, and why it is a useful measure.
  4. Explain, using a graph, what it means if in the 2-variable regression model the estimator of B2 is biased.
  5. Explain, using a graph, what it means if in the 2-variable regression model the estimator of B2 is unbiased but inefficient.
  6. Explain what is meant by the coefficient of determination and how it is related to the F-statistic.
  7. The following data relates to the demand for a homogeneous product sold by seven firms:

Sales (units)                      112      120      120      192      104      72        176

Price ($)                             26        24        22        20        23        25        21

 

  1. Estimate the linear relationship between price and sales.
  2. Does price significantly affect sales?
  3. Forecast sales next month, with 95% confidence limits, for a firm charging a price of $24; state any assumptions that you need to make.
  5. a) Explain what is meant by an ANOVA table and its purpose.
  6. b) Using the data in the previous question, construct an ANOVA table and interpret it.
  7. c) Explain in general terms how the addition of another explanatory variable would affect the ANOVA table.
  8. The following regression results have been obtained for aggregate final energy demand in 7 OECD countries (US, UK, Canada, Germany, France, Italy and Japan) for the period 1960-82, using annual data:

lnQ = 1.594 + 0.9972lnY – 0.3315lnP

t             17.17      52.09                        13.61

R2  = 0.994

F = 1688

Where

Q = measure of energy consumption in BTU

Y = aggregate real GDP in $

P = real energy price in $

  1. Comment on the goodness of fit of the model and the overall significance of the explanatory variables.
  2. Explain whether the signs of the coefficients of the variables are what you would expect.
  3. Interpret the coefficients of the variables.
  4. Comment on the significance of the variables.
  5. Is demand elastic or inelastic? Is the result what you would expect?
  6. 5. Explain why multiple regression analysis is superior to simple regression analysis, giving two examples.