# Math

## Constructing and Implementing Hypothesis Tests

Write a minimum of 250 words for each of the discussion questions below:When constructing and implementing hypothesis tests, what reasoning is used behind the statement of the null and alternative hypotheses? Why are hypothesis tests set up in this way? Can a confidence interval obtained for estimating a population parameter be used to reject the null hypothesis? If your answer is yes, explain how. If your answer is no, explain why.When performing a hypothesis testing, two types of errors can be made: Type I and Type II. Explain in your opinion which of these errors would be a more serious error. Use specific examples to support your argument and reasoning.In your two replies to classmates, provide remedies to simultaneously minimize both types of errors mentioned in question 2 above.

## Positive Integers

1. A positive integer is twice another. The sum of the reciprocals of the two positive integers is . Find the two integers.2. A positive integer is twice another. The difference of the reciprocals of the two positive integers is Find the two integers.3. John can jog twice as fast as he can walk. He was able to jog the first 5 miles to his grandmother’s house, but then he tired and walked the remaining 2 miles. If the total trip took 0.9 hours, then what was his average jogging speed?4. A bus? averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle? to travel 155 miles, then what is the speed of each?5. Jane can paint the office? by herself in 7 hours. Working with an associate, she can paint the office in 3 hours. How long would it take her associate to do it working alone?

## The Mathematics of Trigonometry

The science of physics, specifically projectile motion, goes hand in hand with the mathematics of trigonometry. We need the math of trigonometry to model the flight path of an object moving through the air. Describe another connection between a math topic and a non-math topic, where the math topic is needed to explain and model the non-math topic.

## Algae Bloom Equations

A biologist is studying a certain type of algae. She starts with only 1 algae bloom and observes that the number of algae blooms triples every hour. Which equation can be used to find the number of hours, h, it will take for the population to reach 6,561 algae blooms?

## A Relative Frequency Table

Suppose that you have two sets of data to work with. The first set is a list of all the injuries that were seen in a clinic in a month’s time. The second set contains data on the number of minutes that each patient spent in the waiting room of a doctor’s office. You can make assumptions about other information or variables that are included in each data set.For each data set, propose your idea of how best to represent the key information. To organize your data would you choose to use a frequency table, a cumulative frequency table, or a relative frequency table? Why?What type of graph would you use to display the organized data from each frequency distribution? What would be shown on each of the axes for each graph? Including two apa citations

## Math Assessement

Two coils which are made by winding copper wire of different gauges and length have the same mass.The first coil is made by winding 270 metres of wire with cross sectional diameter 2.8 mm while the second coil is made by winding a certain length of wire with cross sectional diameter of 2.1 mm.Find the length of the wire in the second coil.

## Causation vs. Correlation

Need questions 1-3 answered with a paragraph for each question. I copied and pasted the findings at the bottom if the link doesnt work.”Causation vs. Correlation.” You have probably heard this before, at least in my own lectures or lecture slides for this course. When studies are performed and show that two or more variables share a relationship with each other can we be sure one is actually causing the other, or is it just correlation?Terms and ConsiderationsCorrelation is a mutual relationship or connection between two or more variables.Causation occurs when changes in one variable CAUSE changes in another variable to occur in response.The difference is thatcorrelation is just an observed pattern between two or more variables and we cannot always pin downcausation unless we do our studies in a carefully designed experiment that takes into account potential lurking and confounding variables.Typically speaking, causation can only be declared when the cause and effect (1) makes sense, (2) is significantly strong, and (3) the cause occurs before the effect in time. However, because of many lurking variablescausation can never be derived from an OBSERVATIONAL study!Discussion TasksFor this discussion, first read the findings of this recent study from researchers at Ohio State University:Click Here to Read the Findings of the Study(Links to an external site.)In the study, researchers found an interesting link between absenteeism (missing class) in grade school (K-8) and measures of socio-economic status of students in their early twenties (22-23).Read the study and then respond to the following three questions:Do you believe that this study provides enough evidence to declare that absenteeism in grade school causes poorer socio-economic outcomes in student’s early twenties? Or do you believe this is just an interesting correlation?What otherlurking variables may be able to explain the correlation found in this study?Give your own personal opinion. Do you think absenteeism in grade school causes poorer outcomes in students early twenties? Or do you believe there are other factors at play?Kids who miss a lot of school from kindergarten to eighth grade may suffer unexpected costs as young adults, a new study finds.Researchers found that those who were more regularly absent in these early years of school were less likely to vote, reported having greater economic difficulties and had poorer educational outcomes when they were 22 to 23 years old.The results suggest early school absenteeism should be taken more seriously, said Arya Ansari, lead author of the study and assistant professor of human sciences at The Ohio State University.Theres this misconception, especially among parents, that it doesnt matter as much if kids miss school early on that it only becomes important when they get to middle or high school, said Ansari, who is also a researcher at Ohio States Crane Center for Early Childhood Research and Policy.Arya AnsariThis study shows that those early absences do matter, and in ways that many people dont consider.The study was published online recently in the Journal of Youth and Adolescence.Ansari and his colleagues used data from the Study of Early Child Care and Youth Development, which is run by the National Institute of Child Health and Human Development.This study included data on 648 students from 10 cities across the United States who were followed from birth through young adulthood. Researchers had information on the number of days the children were absent from school between kindergarten and eighth grade.In 2013 and 2014, when the participants were 22 or 23 years old, they reported on a variety of outcomes, from criminal or deviant behavior to parenthood, political participation and economic hardship.Results showed that school absenteeism didnt have any relation with criminal, risky or deviant behavior, Ansari said. But it was linked to political engagement and educational and economic success.Students who were more frequently absent from school were 4.7 percentage points less likely to have voted in the 2012 election.They also reported experiencing greater economic hardship (such as difficulty paying bills), were more likely to say they used government assistance such as food stamps, were less likely to have a job and reported poorer educational outcomes, such as a lower high school GPA and a lower likelihood of going to college.Absenteeism in those early years of school has pretty far-reaching consequences, Ansari said. It goes beyond just affecting your education and how well you do in high school.Ansari said showing up less to school in those early years may set dangerous precedents.If you start out being disengaged with school, you may end up being less engaged with society more broadly. Youre less likely to vote, less likely to go to college, less likely to be employed, he said.We believe disengagement may be one of the key mechanisms linking early school absences to poorer outcomes in early adulthood.Ansari said the participants in this study were mostly from middle-class families, so results may be different for those from a more disadvantaged background.If were seeing these negative outcomes of absenteeism in this largely middle-class sample, the associations may be even more pronounced among disadvantaged families, he said.In 2020, parents may be wondering how widespread school closings during the pandemic may be affecting their children. Ansari said this situation is different from what they studied here.These really are unprecedented times. All kids are absent. With that said, the differential access to supports and resources will likely result in even greater variability in outcomes when students return to school after the pandemic.Ansari said he hopes this study will make parents more aware of the importance of school attendance, even for young children.What this work suggests is that we should take absenteeism and its consequences more seriously.Co-authors on the study were Tara Hofkens, a research assistant professor in education, and Robert Pianta, dean of the School of Education and Human Development, both at the University of Virginia.Share thisPeople who missed more school from kindergarten to 8th grade were less likely to vote, reported having greater economic difficulties and had poorer educational outcomes when they were 22 to 23 years old, a new study found.

Use Promo Code: TOP15

**TOP15**and enjoy expert help with any task at the most affordable price.