math 113 exam 3 hw questions

Using the following tax bracket, how much tax would be owed on $200,000 in taxable income? (2nd tax schedule on doc)

$200,000 into three parts: $50,000, and $100,000. One $50,000 part gets charged 10%, the other $50,000 gets charged 20%, and the $100,000 part gets charged 30%. (0.10)($50,000)+(0.20)($50,000)+(0.30)($100,000)= $5,000+$10,000+$30,000=$45,000

Using the following tax bracket, how much tax would be owed on $60,000 in taxable income? Note: This is not a tax schedule (1st tax schedule on doc)

$60,000 into two parts: $50,000 and $10,000. The $50,000 part gets charged 10%, and the $10,000 part gets charged 20%. (0.10)($50,000)+(0.20)($10,000)=$5,000+$2,000=$7,000

You wish to offer a short-term disability insurance policy to your company's 50 employees. You have some statistics about the likelihood of such a need among male and female populations. Twenty of your employees are female, and there is a 18% chance that each female employee might file a claim in the coming year. Thirty are male, and there is a 14% chance that each male employee might file a claim in the coming year. If each disability claim will cost you $5,000, how much should you have in the fund in order to cover the typical expected claims in the coming year?

(.18)(5000)(30)+(0.14)(5000)(30)= $39000

Homeowners' insurance offers policies that can be purchased by the homeowner. For example, a roof policy might cover roof replacement in the event of major total roof damage. Suppose you have the choice whether to purchase a roof policy or not. The policy costs $300 per year. You consult with local meteorologists and determine that the likelihood that your roof will be destroyed this year due to hurricanes, hail, or tornadoes is 2%. The cost of a new roof for your house is $13,000. In order to decide whether or not to purchase this policy this year, you need to determine whether the price of this policy is more or less than the expected value of your roof's replacement. Which one of the following statements is true?

(0.02)(13000)=260 260-300 40 less

You and your friend have started a tutoring service, in which you prepare students to pass a licensure exam. You would like to advertise a guarantee that your clients will pass their exam. If they complete your training session and still do not pass the exam, then you will pay them $75. You plan to have 60 clients complete the training this year. For each client who completes the training, you have found there is a 85% chance that they will pass the exam. How much should you add to your training fees, per person, to make sure you bring in enough extra funds to cover this guarantee for those who do not pass?

(0.15)(75)=11.25

Let's suppose you manage a simple insurance policy in which you replace vehicles that are "totalled" in an accident. For the sake of simplicity, suppose you do not have any deductible for your policy. If a client totals their car, your policy will cover the entire cost to replace their vehicle. There is a 23% chance that your client Karen will total her car within the next year, and her car would cost $16,830 to replace. There is a 9% chance that your client Sam will total his $5,600 car. There is a 12% chance that your client Renee will total her $8,920 car. How much should you have in a fund to cover the expected cost of these three clients this year?

(0.23)($16,830)+(0.09)($5,600)+(0.12)($8,920)= $3,870.90+$504.00+1070.4 = 5,445.30

Suppose you plan to flip five coins. Determine the probability that all five will result in heads. Round your answer to the nearest percentage.

(1/2)^5 =3%

Purchasing your first home can be scary. After finding a great home for your family, you talk to the real estate agent about the price. The agent discloses that the sellers still have a mortgage on it, and they will be happy if they can simply pay off the mortgage at the sale. They need to have $130,000 for the mortgage payoff after a 6% commission and $200 in title expenses are deducted. You now have enough information to figure out how much to offer for the home.

(P−0.06)P−200=130,000 $138,510.64

What is your AGI if you owe 20,000 in taxes? (number 6)

-falls into 4th bracket 20,000=14,605.50 + (0.24)(amount beyond) =22,477.08 add back 22,477.08+85,525 =108,002.08

percentage decrease steps

-subtract 2nd number from 1st -divide by 2nd number

Percentage increase steps

-subtract 2nd number from 1st -divide by the 1st number

Suppose you will flip one coin, and you will roll one 12-sided die that has the numbers 1 through 12 on its sides. Determine each probability and round to the nearest percentage.

1/12 x 1/2 1/24 =4%

Here's a riddle. I have some money in my wallet. I won't tell you how much. I will tell you, though, that after an n% decrease, I will have no money and no debt. What number is n?

100%

A man walked into a pawn shop and told the broker, "I'm here to redeem my rifle. 78 days ago I pawned it for $60. How much do I need to pay you for you to return it to me today?" The broker reported that he must pay $72. Determine what annual percent interest this is equivalent to. Use the 30-day banker's months and 360-day banker's years. Round to the nearest percent.

72-60=12 12=60 x r x (78/360) =0.92, 92%

A researcher finds that a 23-foot-wide redwood tree's diameter has increased by 12% over a span of 200 years. Determine its width 200years ago. Round to the nearest tenth of a foot.

ADD w+(0.12w)=23 1.12w=23 23/1.12 =20.5

A candidate says, "Most of the voters chose me as their first choice, but I wasn't the winner of the election! I don't think that is fair!" Which one of the following vote-counting methods must have been used?

Borda count

Which mode of communication is the most popular, if you use Borda count? (table 3 on doc)

Borda count: each row counts as a different number of points, add them all up -email with 106

Eight years ago, a friend loaned you $60 and you forgot to pay him back. Once you remember, you want to repay him with a fair amount of interest. How much should you pay him if you want to include interest accrued at a rate of 5% simple interest.

I=(60)(0.05)(8) =24 60+24 =84

You offer private tutoring and babysitting services to local families. After surveying your customers and potential customers, you figure out that you could do 2% more business, on average, if you were able to accept credit card payments. Also, all your current customers express that they would pay you with a credit card if it were an option. After investigating buying a credit card reader, you learn that the credit card reading service charges 2% of all transactions. Which of the following would be the best description of this business decision?

If you buy a card reader, less money will come in. Even though your revenue will increase by 2%, the 2% taken out by the card reader services will be greater than the increase in revenue that you will see. -Let's call the original revenue R. If you get the card reader, the business will increase by 2% of R, bringing the revenue up to 1.02R. However, the credit card reader service is going to charge 2% of that, which would bring the revenue down to (0.98)(1.02R), and this is 0.9996R, which is slightly less than the original revenue R.

A candidate says, "I would have won the election, but because one of the other candidates withdrew, I wasn't chosen as the winner." Which of the following fairness criteria was violated?

Independence criterion

Imagine you have an insurance policy for three people, and this policy would solely offer completed coverage for a $10,000 heart surgery. In the upcoming year, Jillian has a 6% chance of needing this surgery, Saul has a 4% chance of needing this surgery, and Aaron has a 9% chance of needing this surgery. Calculate the expected value for each client.

Jillian: (0.06)(10,000)=600 Saul: 400 Aaron: 900

candidate says, "I was going to win the election, but then some of the voters changed their votes. Even though they moved me higher in their rankings when they changed their votes, it caused me to not win the election."

Monotonicity criterion

In the conversation shown in the following image, someone offers to sell their friend's guitar for a 10% commission. Determine what the lowest sales price can be if she wants it to sell for at least 230

P-(0.10P)=230 (1-.10)p=230 230/0.90 $255.56

A candidate says, "I was going to win the election, but then some of the voters changed their votes. Even though they moved me higher in their rankings when they changed their votes, it caused me to not win the election." which vote must have been used?

Plurality with elimination

User Answer Correct The global population of wild giant pandas was 1,596 in 2003 and was 1,864 in 2015. What was the percent increase from 2003 to 2015? Round to the nearest percentage

The increase was 1,864−1,596=268 To determine this as a percentage of the earlier value, divide 268/1,596 = 17%

I have a drawer full of colored pencils. Each one may or may not have an eraser on it. If I choose one of these pencils at random, the probability that it has an eraser on it is 0.3 However, with the same drawer full of pencils, the probability that the chosen pencil has an eraser on it, given that it is a red pencil, is also 0.3 Which of the following statements would be true?

The proportion of erasers within the population of red pencils is the same as the proportion of erasers within the general population of pencils, indicating that the color of the pencil and the presence of an eraser are independent.

Determine the probability that a random dart lands on yellow. Assume it hits the board. Assume this was separated into symmetric partitions (doc graph 5)

divided into 6 pieces in all and those 6 pieces are divided further. multipy 1/6 by how much of that piece is yellow (1/6)+(1/2 x 1/6)+(2/3 x 1/6) (6/36)+(3/36)+(4/36) =36%

Which mode of communication is the most popular, if you use pairwise comparison?

pairwise comparison: pit two together, count points up from where one is higher than the other, do this with all of them and see which one wins the most -email

Which mode of communication is the most popular, if you use plurality with elimination? (table 3 on doc)

plurality with elimination: get rid of the option with the least votes and use the second row for the ones you eliminated\ email with 25

Which mode of communication is the most popular, if you use plurality vote-counting? (table 3 on doc)

plurality: add top row up and the one with the most wins Email

If you invest $9,230 into an account, which earns simple interest at an annual rate of 5%, then how much will you have at the end of seven years?

use I=Prt I=(9230)(0.05)(7) =3230.50 +9230 =12,460.50

there is a circle with a radius of 4, and a smaller circle inside with a radius of 1, what is the probability a dart would land in the smaller circle

whole circle: pie(4)^2 smaller circle: pie (1)^2 pie(1)^2/Pie(4)^2 =6.2%