1.1. Find the second-order derivative of the following function:f(x) = log2cosx+ lnπ
2. Using limit definition of derivative, determine whether
definition of derivative, determine whether
1/2(t+ 5),0< t≤1 is differentiable at t= 1
√t+ 2, t >1
3. FM Corporation is a company that manufactures face masks. For everyxthousand pieces of facemask sold, the company’s revenue (in thousand pesos) isR(x) =x(5 +x),x≥0.
a. If the company soldxthousand pieces of face mask, find the company’s marginal revenue.Note: Marginal revenue is the increase in revenue that results from the sale of one additionalunit of output.
b. Find the number of face mask sold if the company has a marginal revenue of Php 25,000.
2.1) (Ch. 7) Explain what a residual is (also known as residual of prediction).
e idea of “least squares” in regression (you need to fully read pp. 200-208 to understand).
3) What does it mean if b = 0?
4) What does it mean when r-squared is 0? What does it mean when r-squared is 1?
5) What is the difference in an unstandardized regression coefficient and the standardized regression coefficient?
6) If a report says test performance was predicted by number of cups of coffee (b = .94), what does the .94 mean? Interpret this. (For every one unit increase in ___,There is an increase in ___ )
7) If F (2,344) = 340.2, p < .001, then what is this saying in general about the regression model? (see p. 217)
8) Why should you be cautious in using unstandardized beta? (p. 218)
9) (Ch. 8) Explain partial correlation in your own words. In your explanation, explain how it is different from zero-order correlation (aka Pearson r).
10) (Ch. 9) What is the F statistic used to determine in multiple regression?
11) What is F when the null hypothesis is true?
12) In Table 9.4, which variable(s) are statistically significant predictors?
13) In Table 9.4, explain what it means if health motivation has b = .36 in terms of predicting number of exercise sessions per week.
14) What is the benefit of interpreting standardized beta weights? (see p. 264).
15) What happens if your predictor variables are too closely correlated?
16) Reflect on your learning. What has been the most difficult? How did you get through it? What concepts are still fuzzy to you? Is there anything you could share with me that would help me address how you learn best?
3.Part I. Reaction Paper
Read and understand the text below. Follow outline in writing your reaction paper at least 250-750
paper at least 250-750 words.
2. Thesis Statement
3. Supporting details
The Digital Divide: The Challenge of Technology and Equity
(1) Information technology is influence the way many of us live and work today. We use the internet to look and apply for jobs, shop, conduct research, make airline reservations, and explore areas of interest. We use Email and internet to communicate instantaneously with friends and business associates around the world. Computers are commonplace in homes and the workplace.
(2) Although the number of internet users is growing exponentially each year, most of the worlds population does not have access to computers of the internet. Only 6 percent of the population in the developing countries are connected to telephones. Although more than 94 percent of U.S households have telephones, only 56 percent
have personal computers at home and 50 percent have internet access. The lack of what most of us would consider a basic communication necessity the telephone does not occur just in developing nations. On some Native American reservations only 60 percent of the residents have a telephone. The move to wireless connectivity may eliminate the need for telephone lines, but it does not remove the barrier to equipment costs.
(3) Who has internet access? The digital divide between the populations who have access to the internet and information technology tools and those who dont is based on income, race, education, household type, and geographic location, but the gap between groups is narrowing. Eighty-five percent of households with an income
over $75,000 have internet access, compared with less than 20 percent of the households with income under $15,000. Over 80 percent of college graduates use the internet as compared with 40 percent of high school completers and 13 percent of high school dropouts. Seventy-two percent of household with two parents have internet access; 40 percent of female, single parent households do. Differences are also found among households and families from different racial and ethnic groups. Fifty-five percent of white households, 31 percent of black households, 32 percent of Latino households, 68 percent of Asian or Pacific Islander households, and 39 percent of American Indian, Eskimos, or Aleut households have access to the internet. The number of internet users who are children under nine years old and persons over fifty has more than triple since 1997. Households in inner cities are less likely to have computers and internet access than those in urban and rural areas, but the differences are no more than 6 percent.
(4) Another problem that exacerbates these disparities is that African-American, Latinos, and Native Americans hold few of the jobs in information technology. Women about 20 percent of these jobs and receiving fewer than 30 percent of the Bachelors degrees in computer and information science. The result is that women and members of the most oppressed ethnic group are not eligible for the jobs with the highest salaries at graduation. Baccalaureate candidates with degree in computer science were offered the highest salaries of all new college graduates.
(5) Do similar disparities exist in schools? Ninety-eight percent of schools in the country are wired with at least one internet connection. The number of classrooms with internet connection differs by the income level of students. Using the percentage of students who are eligible for free lunches at a school to determine income level, we see that the higher percentage of the schools with more affluent students have wired classrooms than those with high concentrations of low-income students.
(6) Access to computers and the internet will be important in reducing disparities between groups. It will require higher equality across diverse groups whose members develop knowledge and skills in computer and information technologies. The field today is overrepresented by white males. If computers and the internet are to be used to promote equality, they have to become accessible to schools cannot currently afford the equipment which needs to be updated regularly every three years or so. However, access alone is not enough; Students will have to be interacting with the technology in authentic settings. As technology has become a tool for learning in almost all courses taken by students, it will be seen as a means to an end rather than an end in itself. If it is used in culturally relevant ways, all students can benefit from its power.
6.Show that the following compound propositions are logically equivalent using truth table.
¬p → (q → r) and q → (p
q → r) and q → (p ∨ r).
Q2. Write the converse, inverse and contrapositive of the statement:
“I will score marks whenever I will study”.
Q3. Convert the following compound propositions into English sentences for given
p: It is below freezing.
q: It is snowing.
(i) ¬q → ¬p
(ii) ¬q ∨ (¬p ∧ q )
(iii) p ↔ ¬q
(iv) p ∨ q
(v) ¬q ∧ ¬p
Q4. Determine whether each of the statements is true or false.
(i) If 1 + 1 = 2, then 2 + 2 = 5.
(ii) If 1 + 1 = 3, then 2 + 2 = 4.
(iii) If 1 + 1 = 3, then dogs can fly.
(iv) Monkeys can fly if and only if 1 + 1 = 3.
(v) A number is prime if and only if it is divisible by 1 and itself.