Practice for Exam 1

Suppose corn chips cost 21.5 cents per ounce. If a bag costs $2.91, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.

$0.215/1oz = $2.91/xoz 13.53oz

Suppose potato chips cost 34.5 cents per ounce. What would a bag of chips cost if it contained 24oz? Round your answer to the nearest cent, if necessary.

$0.345/1oz = $x/24oz x=8.28

If the ratio of tourists to locals is 2:7 and there are 7070 tourists at an arts festival, how many locals are in attendance?

245 locals 2/7 70/x? 70x7=490 divided by 2 is 245

Which of the following is not an example of a mathematical statement?

Chocolate milkshakes are delicious

Consider the following statement: "If the dog got loose, then the door was left open." Rewrite this statement using the alternative phrasing "q whenever p."

The door was left open whenever the dog got loose.

Which of the given sentences is an example of a mathematical statement?

Whole milk has 146 calories per cup.

Suppose corn chips cost 34.5 cents per ounce. What would a bag of chips cost if it contained 25oz? Round your answer to the nearest cent, if necessary.

$0.345/1oz = $x/25oz a bag of corn chips that weighs 25oz will cost $⁢8.63.

Your dinner bill was $41.00 If you leave a 15% tip, how much will the tip be?

$6.15

Katie is about to list her house as For Sale By Owner. What is the minimum she can list the house if she wants to receive a minimum of $195,900 on the sale while still allowing for a 3% commission for the buyer's realtor? Round to the nearest hundred dollars.

(1−0.03)=$195,900 0.97x=$195,900 $201,958.76 or $202,000, rounded to the nearest hundred dollars.

Lindsay is about to list her house as For Sale By Owner. She would like to receive a minimum of $222,300 on the sale, but she also needs to allow for a 6% commission for the buyer's realtor. What is the minimum Lindsay can list the house to accommodate both of these requirements? Round to the nearest hundred dollars.

(1−0.06)x = 222300 .94x = 222300 $236,489.36, or $236,500 rounded to the nearest hundred dollars.

Suppose the probability of a soccer team winning a playoff game is 0.20 What are the odds of winning? Express your answer in the form a:b

.20/1-.20 .20/.80 .25 or 1/4 or 1:4

Suppose corn chips cost 36.5 cents per ounce. If a bag costs $4.71, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.

.365/1oz = 4.71/xoz x=4.71/.365 x=12.90oz

Suppose the probability of winning a raffle item is 0.02. What are the odds of winning? Express your answer in the form a:ba:b.

0.02/1−0.02 1/49, 1:49

If 32 of the 108 people who swim at the YMCA are adults, what is the ratio of children to adults who swim at the YMCA? Write the ratio in lowest terms as a fraction or with a colon.

108−32=76 76/32 19/8 or 19:8

Julia sets up a passcode on her smart phone, which allows only six-digit codes. A spy sneaks a look at Julia's smart phone and sees her fingerprints on the screen over six numbers. What is the probability the spy is able to unlock the smart phone on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

6P6=6!=720 1/720

Argument that rests on the assumption that there are only two choices as a solution.

False Dilemma

There are 4 sets of balls numbered 1 through 8 placed in a bowl. If 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

To calculate the total number of combinations of choosing four balls randomly, we use the value of the total number of balls in the bowl, n=4⋅8=32, along with number of balls being chosen, r=4 32!/4!(32−4)!=35960 8/35960=1/4495

Consider the following statement: "If I get $100$⁢100 for Christmas, then I will be able to buy a laptop." Rewrite this statement using the alternative phrasing "p will lead to q."

Getting $100 for Christmas will lead to me being able to buy a laptop.

Which of the following is an example of a mathematical statement?

My boyfriend was born in Atlanta.

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two aces in succession from a standard deck of 5252 cards without replacing the first card, you give him $70 Otherwise, he pays you $10. If the same bet was made 15 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

We know that 2 cards are drawn in succession from a standard deck of 52 cards without replacing the first card. We are going to find the probability of drawing two aces. There are 52 cards and 4 of those are aces. This means the probability of drawing two aces is as follows. 4/52⋅3/51≈0.004525 The probability of not drawing two aces is the complement of 0.004525, which is 1−0.004525=0.995475. ($10)(0.995475)+(−$70)(0.004525) ≈$9.95−$0.32 =$9.63 To find the expected value after 15 times, multiply the expected value by 15 (15)($9.63)=$144.45,WIN

A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible four-topping pizzas (4 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with spicy Italian sausage, beef, jalapeño peppers, and sausage. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Pizza Toppings: Green Peppers, Onions, Kalamata Olives, Sausage, Mushrooms, Black Olives, Pepperoni, Spicy Italian Sausage, Roma Tomatoes, Green Olives, Ham, Grilled Chicken, Jalapeño Peppers, Banana Peppers, Beef

15!/4!(15−4)! = 1365 1/1365

If three out of every seven trick-or-treaters that came to your house last Halloween were dressed as Buzz Lightyear, what proportion of trick-or-treaters were not dressed as Buzz Lightyear?

1−3/7=4/7

If four out of every fifteen trick-or-treaters that came to your house last Halloween were dressed as witches, what proportion of trick-or-treaters were not dressed as witches?

1−4/15 = 11/15

A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible two-topping pizzas (2 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham and artichoke hearts. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Pizza Toppings: Green Peppers, Onions, Kalamata Olives, Sausage, Mushrooms, Black Olives, Pepperoni, Spicy Italian Sausage, Roma Tomatoes, Green Olives, Ham, Grilled Chicken, Jalapeño Peppers, Banana Peppers, Beef, Chicken Fingers, Red Peppers, Spinach, Bacon, Anchovies, Artichoke Hearts, Sundried Tomatoes, Canadian Bacon, Extra Cheese

24!/2!(24−2)! = 276 1/276≈0.003623

Finn, John, Andrew, and Eddie are going to have a movie night this weekend. Together, they have 30 movies. If they decide to randomly choose four movies, what is the probability that the four they choose will consist of each of their favorite movies? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

30!/4!(30−4)!=27405 1/27405

There are 2 sets of balls numbered 1 through 17 placed in a bowl. If 2 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

34!/2!(34−2)! = 561 17/561 = 1/33

Liam and John are going to play video games this afternoon. Together, they have 47 video games. If they decide to randomly choose two video games, what is the probability that the two they choose will consist of each of their favorite video games? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

47!/2!(47−2)! = 1081 1/1081 = 0.000925

Julia sets up a passcode on her smart phone, which allows only four-digit codes. A spy sneaks a look at Julia's smart phone and sees her fingerprints on the screen over four numbers. What is the probability the spy is able to unlock the smart phone on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

4P4=4!=24 1/24

Which of the following is the negation for the given statement? None of the customers are not satisfied.

At least one of the customers is not satisfied.

Determine whether the given argument uses inductive or deductive reasoning. If deductive, determine whether the reasoning is valid or invalid. If it is sunny, we are not watching tv. We are watching tv. So, it must not be sunny.

Deductive, valid

Determine whether the given argument uses inductive or deductive reasoning. If deductive, determine whether the reasoning is valid or invalid. This store is known for having sales. My friends were talking about a big sale, so it must be at this store.

For deductive reasoning to be a valid argument, the conclusion must be guaranteed from the premise. Consider whether the conclusion, "My friends were talking about a big sale, so it must be at this store," follows from the premise, "This store is known for having sales" regardless of the truth of the premise. If so, we have a valid argument, otherwise it is invalid. However, in this case, the argument is invalid, so we have an invalid argument that uses deductive reasoning. Correct Answer:Deductive, invalid

It was recently estimated that domestic vehicles outnumber foreign vehicles by about eight to seven. If there are 5595 vehicles in a county, how many of them are domestic?

In this situation, the ratio eight to seven indicates how to partition every set of 8+7=15 vehicles. Each set of 15 vehicles should have, on average, 8 domestic vehicles and 7 foreign vehicles, as shown in the following ratios. Domestic vehicles: 8/15 and Foreign vehicles: 7/15 8/15 = x/5595 x = 2984

It was recently estimated that females outnumber males by about three to two. If there are 1770 people in a county, how many of them are females?

In this situation, the ratio three to two indicates how to partition every set of 3+2=5 people. Each set of 5 people should have, on average, 3 females and 2 males, as shown in the following ratios. Females: 3/5 and Males: 2/5 We can use these ratios to set up a proportional equation for the category of interest, females, and solve to find the amount of females that would be expected in 1770 people. 3/5=x/1770 1770*3 = 5310 5310 divided by 5 = 1062 females

Which of the following is not an example of a mathematical statement?

Nobody drives on Highway 16; there is too much traffic.

Which of the following is the negation for the given statement? None of the girls are not dancing.

Not all of the girls are dancing.

There was a cupcake in the kitchen before you went in there. Therefore, you must have taken the cupcake.

Post Hoc, Ergo Propter Hoc

Identify the type of fallacy being used in the statement. My opponent wants to shorten the city curfew. If we let kids run wild all night, they'll all end up in jail.

STRAW MAN

The buildup of a distortion of someone's ideas or beliefs so that they can easily be knocked down.

STRAW MAN

non sequitur

The conclusion has nothing to do with the premise.

If 22 of the 92 people who swim at the YMCA are children, what is the ratio of adults to children who swim at the YMCA? Write the ratio in lowest terms as a fraction or with a colon.

To calculate the ratio of adults to children, we can use the number of children to find the number of people who are not children and are therefore adults. The problem tells us that there are 22 children and that there are 92 people altogether. We can find the number of those who are adults by finding the difference between the total number of people and those who are children. 92-22 = 70 not children 70/22 35/11 35:11

Suppose that you and a friend are playing cards and decide to make a bet. If you draw three non-face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacement, you win $10. Otherwise, you pay your friend $20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

We are going to find the probability of drawing three non-face cards, where a face card is a Jack, a Queen, or a King. There are 52 cards and 40 of those are non-face cards. This means the probability of drawing three non-face cards, where a face card is a Jack, a Queen, or a King, is as follows. 40/52⋅39/51⋅38/50≈0.447059 The probability of not drawing three non-face cards, where a face card is a Jack, a Queen, or a King, is the complement of 0.447059, which is 1−0.447059=0.552941 ($10)(0.447059)+(−$20)(0.552941) ≈$4.47−$11.06 =−$6.59

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three non-face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards with replacement, you give him $50$. Otherwise, he pays you $50. If the same bet was made 30 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

We are going to find the probability of drawing three non-face cards, where a face card is a Jack, a Queen, or a King. There are 52 cards and 40 of those are non-face cards. This means the probability of drawing three non-face cards, where a face card is a Jack, a Queen, or a King, is as follows. 40/52⋅40/52⋅40/52≈0.455166 The probability of not drawing three non-face cards, where a face card is a Jack, a Queen, or a King, is the complement of 0.455166, which is 1−0.455166=0.544834 ($50)(0.544834)+(−$50)(0.455166) ≈$27.24−$22.76 =$4.48 To find the expected value after 30 times, multiply the expected value by 30. (30)($4.48)=$134.40, WIN

Suppose that you and a friend are playing cards and decide to make a bet. If you draw two clubs in succession from a standard deck of 52 cards without replacing the first card, you win $40$⁢ Otherwise, you pay your friend $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

We know that 2 cards are drawn in succession from a standard deck of 52 cards without replacing the first card. We are going to find the probability of drawing two clubs. There are 52 cards and 13 of those are clubs. This means the probability of drawing two clubs is as follows. 13/52⋅12/51≈0.058824 The probability of not drawing two clubs is the complement of 0.058824, which is 1−0.058824=0.941176. ($40)(0.058824)+(−$10)(0.941176) ≈$2.35−$9.41 =−$7.06