Category: Mathematics Homework Help

I’m studying for my Calculus class and need an explanation.

Determine whether each of the following statements is true or false, and explain why.

1. The absolute maximum of a function always occurs where the derivative has a critical number.
2. A continuous function on a closed interval has an absolute maximum and minimum.
3. A continuous function on an open interval does not have an absolute maximum or minimum.
4. Demand for a product is elastic if the elasticity is greater than 1.
5. Total revenue is maximized at the price where demand has unit elasticity.
6. Implicit differentiation can be used to find dy/dx when x is defined in terms of y.
7. In a related rates problem, all derivatives are with respect to time.
8. In a related rates problem, there can be more than two quantities that vary with time.
9. A differential is a real number.
10. When the change in x is small, the differential of y is approximately the change in y.

I’m working on a statistics discussion question and need an explanation and answer to help me learn.

After reading the example above where one can see how probability values can be used in managerial decision-making to establish a product guarantee, post a comment where you think probability could be used to help solve other management-type questions/problems. Think of something at work, past or present, where you could apply the techniques in the example to assist in making the best decision. If you can’t draw on life experience, then think of a product/issue where this process could be applied. 

I’m working on a geometry discussion question and need a sample draft to help me learn.

1. Give a model of an incidence geometry (i.e. all of IA1, IA2, IA3 are satisfied) which does
   not satisfy any of the parallel postulates. (Hint: I came up with an example on five points.)
2. Give a model of an incidence geometry with a finite number of points which satisfies the
   Hyperbolic Parallel Postulate and not every line has the same number of points. (Hint: I
   came up with an example on six points.)
3. Give a model of an incidence geometry with a finite number of points which satisfies the
   Elliptic Parallel Postulate and not every line has the same number of points. (Hint: I came
   up with an example on four points.
4. (i) Is it possible for there to exist a model of incidence geometry on 6 points such that every line
   contains exactly 3 points. (ii) Create a version of “Spot-it” in which each card has three symbols. It must have the property
   that every pair of cards has exactly one symbol in common and the number of cards must be
   equal to the total number of symbols.

I’m trying to study for my Statistics course and I need some help to understand this question.

1. Using the information from the table above, calculate the murder rates (per 100,000) for each of the five cities (include 2 decimal places in the rates. For example, 50.00).

• Copy the table into a Word doc and add a column that is titled Murder Rate (see example above). Then enter the murder rate for each city.

2. What is the lowest murder rate in the table? What is the city that has the lowest murder rate?

3. What is the highest murder rate in the table? What is the city that has the highest murder rate?

4. Were you surprised by these results? Why or why not? Explain your answer.

You are studying with one of your classmates who is acing this class. She displays the following picture.

Then she pulls out a new deck of cards. She removes the plastic wrap from the deck of new cards, opens the box, and pulls out the cards. She removes the jokers and any other cards not displayed in the picture above. Then she starts shuffling the cards – which is difficult because the cards are brand new and slippery. She continues to shuffle and reshuffle until you agree that the deck is well-shuffled. Then she sets the deck down.

To verify that you know how to calculate various probabilities for a randomly drawn card, she asks the following questions which you answer correctly.

• If I randomly select a card, what is the probability of drawing a red card?
  YOUR ANSWER: 26/52 = 0.5 or 50%
• If I randomly select a card, what is the probability of drawing a 9?
  YOUR ANSWER: 4/52 ?? 0.0769 or 7.69%

• If I randomly select a sample of two cards, what is the probability that both cards are red?
  YOUR ANSWER: (26/52)(25/51) ?? 0.2451 or 24.51%

• In the above calculation you multiplied, (26/52)(25/51). Why?
  YOUR ANSWER: Randomly selecting a sample of two cards means we draw two cards – one at a time without replacement. So a random sample of two red cards means the first card is red and the second card is red. When we randomly select the first card, the probability we draw a red card is  26 red cards out of 52 total cards, or 26/52. We set that first red card aside. So, when we randomly select the second card, there are only 25 red cards out of a total of 51 cards, so the probability we get a red card is 25/51. We need to calculate the probability that the first card is red AND the second card is red. So we multiply the two fractions together, (26/52)(25/51).

Then your classmate says, “O.K. Let’s make a little bet. If you draw a black card, I will help you with all remaining homework in this class.” If not, you must wash and wax my car for me. Since she opened a brand new deck of cards right in front of you and you verified they were well-shuffled, you know the probability of drawing a black card is 0.5 or 50%, so you agree to the bet.

She picks up the deck of cards, fans them out (face down of course), and asks you to randomly select a card. You select a card and turn it over. It’s red – not black.

You set the card aside and ask to try again. She reluctantly agrees and warns that if you lose, you will have to wash and wax her car twice. But if you win, you will not have to wash and wax her car, and she will help you with your homework as promised. You draw another card. It’s red – not black. 

You set the card on top of the previously drawn red card and ask to try a third time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You must now wash and wax her car three times. You decide to quickly calculate the probability of randomly selecting a sample of three red cards.

2652?2551?2450?0.11762652?2551?2450?0.1176  or 11.76%

You set the card on top of the previously drawn red cards and think, “The next card has to be black.” You ask to try a fourth time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You now have a random sample of 4 red cards, and you must wash and wax her car four times.

You set the card on the stack of previously drawn red cards, and ask to try again. Once again, she reluctantly agrees, and you draw another card.

Prompt

1. What is the probability of drawing a random sample of 4 red cards (write the probability as a decimal and a percentage)? Would you consider the random sample of 4 red cards unusual? Why or why not?
2. What is the probability of drawing a random sample of 5 red cards (write the probability as a decimal and a percentage)? Would you consider the random sample of 5 red cards unusual? Why or why not?
3. When your classmate began shuffling the deck of cards, what obvious assumption did you believe was true? If you draw a random sample of 5 red cards from the deck, should you reject that assumption? Why or why not?
4. Based on your responses to the previous question, what will you infer about the deck of cards?

Instructions

Williams, A. (2012). Worry, intolerance of uncertainty, and statistics anxiety.

Click on the following link to retrieve the article.

https://iase-web.org/documents/SERJ/SERJ12(1)_Williams.pdf

Keiko wins the lottery! She has a choice between

Option A: $13,000,000.00 received today.

Option B: 21 payments of $871,624.41 at the start of every year for 21 years, with the first payment today.

The nominal annual interest rate is i(4) = 6.000%. Keiko wants you to advise them which option to choose.

a) Build a spreadsheet (see the posted example) to compare the present value of the 2 options. Which would you recommend?

b) Suppose instead you assumed they would never spend any of the money, instead saving it all until the time of the last payment of Option B. Find the future value of both options at this time. Would this calculation change your recommendation?

c) If the interest rate were i(4) = 1.000% instead, would that change which option you recommend?

d) Obviously there is some interest rate i(4) at which the present value of the two options is the same. Find that value (accurate to 3 decimal places, e.g. 3.456%) using either trial and error or goal seek. (Warning: if you are using trial and error using only 3 decimal places for the interest rate, the present values you compute might not match exactly!)

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem.

Find the odds in favor and the odds against a randomly selected person from Country X, age 25 and over, with the stated amount of education.

Four years (or more) of college

Can you please explain how you would do this problem? The hint is to use a Taylor Expansion to make the problem easier but I don’t know how to use it for this question.