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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Using the Multiplication Rule for Counting and your answers to the earlier parts of this exercise, how many ways are there for your friends to sort yourselves into rows to board the roller coaster?You and 5 of your friends are at an amusement park, and are about to ride a roller coaster. The cars
How many different committees of 4 are possible, assuming all of the duties are shared equally?The University Combinatorics Club has 18 members. Four of them will be selected to form a committee.
Instead of sharing responsibility equally, one person will be chosen to be the committee chair. How many different committees are possible? Count these by selecting a chair first, then selecting the remaining 3 members of the committee from the remaining club members and use the Multiplication Rule
Let's count the number of committees with chairs a different way: First, choose 4 people for the committee (as in the first question), then choose 1 of the 4 to be chair. Show your work. Do you get the same number?The University Combinatorics Club has 18 members. Four of them will be selected to
How many different ways are there to choose the white balls? Players who match these 5 numbers exactly (but not the Powerball) win \(\$ 1\) million.Powerball \({ }^{\circledR}\) is a multistate lottery game, which costs \(\$ 2\) to play. Players fill out a ticket by choosing 5 numbers between 1 and
How many ways are there to choose the Powerball? Players who correctly pick the Powerball win \(\$ 4\).Powerball \({ }^{\circledR}\) is a multistate lottery game, which costs \(\$ 2\) to play. Players fill out a ticket by choosing 5 numbers between 1 and 69 (these are the white balls) and then a
How many ways are there to play the game altogether? Players who match all 5 white balls and the Powerball win (or share) the grand prize. (The grand prize starts at \(\$ 40\) million; if no players win the grand prize, the value goes up for the next drawing. The highest value it has ever reached
You are in charge of programming for a music festival. The festival has a main stage, a secondary stage, and several smaller stages. There are 40 bands confirmed for the festival. Five of those will play the main stage, and 8 will play the secondary stage. How many ways are there for you to
You note the number.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a brown \(D\), an
You note the letter.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a brown \(D\), an
You note the color of the number.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a
You note the color of the letter.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a
You note the number and letter.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a brown
You note the number and its color.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a
You note the letter and its color.You are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue \(A\), a red 1 and a green \(A\), an orange 1 and a green \(B\), an orange 2 and a red \(C\), a purple 3 and a
\(G G\) and \(g 9\)In Example 7.13, we used a table to identify the possible genetic result when two pea plants are bred; offspring plants get one of the two genes from each parent. Use tables to identify the sample space of offspring for the parents listed in the following exercise.Data from
\(\mathrm{GG}\) and \(\mathrm{Gg}\)In Example 7.13, we used a table to identify the possible genetic result when two pea plants are bred; offspring plants get one of the two genes from each parent. Use tables to identify the sample space of offspring for the parents listed in the following
\(\mathrm{Gg}\) and \(\mathrm{Gg}\)In Example 7.13, we used a table to identify the possible genetic result when two pea plants are bred; offspring plants get one of the two genes from each parent. Use tables to identify the sample space of offspring for the parents listed in the following
Make a table that shows the sample space for your choices.You're visiting a pasta bar, where you have your choice of pasta types (cavatappi, ziti, or penne) and sauce (marinara, alfredo, or pesto).
Write out the sample space for the pasta bar.You're visiting a pasta bar, where you have your choice of pasta types (cavatappi, ziti, or penne) and sauce (marinara, alfredo, or pesto).
Make a table that shows the sample space for your choices.You have a new art print that you'd like to get framed. You have 3 good choices for the material of the frame: oak, maple, and cherry. You'll also choose a framing mat, for which there are 4 possible colors that will work with your print:
Write out the sample space for the framing choices.You have a new art print that you'd like to get framed. You have 3 good choices for the material of the frame: oak, maple, and cherry. You'll also choose a framing mat, for which there are 4 possible colors that will work with your print: plum,
Make a table that shows the sample space for your choices.You are shopping for a new laptop. The brand you're considering offers laptops with screen sizes 11", 13", 14", 15", and 17". It also offers five memory choices: 4GB, 8GB, 12GB, 16GB, and 32GB.
Write out the sample space for the laptop choices.You are shopping for a new laptop. The brand you're considering offers laptops with screen sizes 11", 13", 14", 15", and 17". It also offers five memory choices: 4GB, 8GB, 12GB, 16GB, and 32GB.
Siobhan and Tristan are trying to decide where they will have dinner. Siobhan wants to go to Antoine's, Burger Hut, or the Chowder Palace. Tristan prefers Burger Hut, Chowder Palace, or Duck Duck Taco. They will flip a coin to decide who gets to choose, then that person selects a restaurant from
On the TV game show The Price Is Right, contestants play games to try to win prizes. One of these games is called "Let 'Em Roll." In this game, players roll five 6-sided dice. These dice each have 3 faces labeled with a car; the other 3 faces are labeled with prize money amounts (one each of \(\$
In the game Rock, Paper, Scissors, each of 2 players secretly chooses 1 of the 3 title objects. The players reveal their choices simultaneously using hand signals. If the players choose the same object, the game is a tie; if they choose different objects, the winner is determined by the following
Paul is at the racetrack and is about to place a daily double bet, where he will try to predict the winner of 2 consecutive races. The stages of the experiment are the two races.Decide whether the described two-stage experiments have independent or dependent stages.
Mishka is looking for a song to play on a jukebox. The machine requires the user to choose an artist first, then choose a song from among that artist's songs. The stages of the experiment are choosing the artist and choosing the song.Decide whether the described two-stage experiments have
Create a tree diagram to display the possible outcomes of this game.John is playing a game that involves flipping a coin and rolling dice. The coin flip happens first. If the outcome is heads, the player rolls a 4-sided die. If the outcome is tails, the player rolls a 6-sided die.
Give the sample space for the game.John is playing a game that involves flipping a coin and rolling dice. The coin flip happens first. If the outcome is heads, the player rolls a 4-sided die. If the outcome is tails, the player rolls a 6-sided die.
Draw a tree diagram that shows the possible color outcomes for 3 spins of the wheel.In the casino game roulette, a wheel with colored and numbered pockets is spun. At the same time, a marble is spun in the opposite direction in such a way that after a minute or so the marble drops into one of the
Give the sample space for the three-stage experiment.In the casino game roulette, a wheel with colored and numbered pockets is spun. At the same time, a marble is spun in the opposite direction in such a way that after a minute or so the marble drops into one of the pockets. Players try to guess
Siobhan and Tristan are trying to decide where they will have dinner. Siobhan wants to go to Antoine's, Burger Hut, or the Chowder Palace. Tristan prefers Burger Hut, Chowder Palace, or Duck Duck Taco. They will flip a coin to decide who gets to choose, then that person selects a restaurant from
On the TV game show The Price Is Right, contestants play games to try to win prizes. One of these games is called "Let 'Em Roll." In this game, players roll five 6 -sided dice. These dice each have 3 faces labeled with a car; the other 3 faces are labeled with prize money amounts (one each of \(\$
In the game Rock, Paper, Scissors, each of 2 players chooses 1 of the 3 title objects. The players reveal their choices simultaneously using hand signals. Jim and Eva are gearing up to play the game. List the sample space of all the possible outcomes of the first round of their game as ordered
45 is what percent of 180 ?
Find \(47 \%\) of 31 . Round to two decimal places.
What is the sale price of a \(\$ 90\) shirt if there is a \(25 \%\) discount for the shirt?
A small boutique buys purses for \(\$ 27.50\) per purse. What is the boutique's retail price for the purses if they add a \(90 \%\) markup
What was the discount on a computer is the retail price was \(\$ 1,200\) and the sale price is \(\$ 950\) ? Round to two decimal places if necessary.
A \(15 \%\) simple interest loan of \(\$ 2,000\) is taken out for 75 days. How much is owed when the loan is due?
What is the future value of a \(\$ 15,000\) investment made at \(4.65 \%\) interest compounded yearly for 10 years?
Apply the \(50-30-20\) budget philosophy to a monthly income of \(\$ 3,920\).
\(\$ 2,500\) is deposited in an account that bears \(5.25 \%\) interest compounded quarterly for 15 years. What is the return on investment for that investment? Round to two decimal places if necessary.
How much per month must be paid into an ordinary annuity so its future value is \(\$ 150,000\) after 10 years if the annuity earns \(3.85 \%\) interest compounded monthly?
Bethanie's employer matches up to \(7 \%\) of annual salary for deposits into the company sponsored IRA. Bethanie earns \(\$ 62,400\) annually. She deposits \(\$ 8,000\) annually inter her IRA. How much does the company deposit in Bethanie's IRA?
If \(\$ 360\) is deposited monthly in a mutual fund that is expected to earn \(9.35 \%\) compounded monthly, how much will the mutual fund be worth after 23 years?
A \(\$ 14,250,4\)-year loan is taken out at \(9.15 \%\) interest. What are the monthly payments for the loan?
Using the amortization table below, how much total interest has been paid after payment 20 ? Loan Amount Interest Rate (annual) Term (Years) Monthly Payment Amortization Schedule Calculator $17,500.00 8.25% 5 $356.93 Month Payment Principal Interest Total Interest Balance $17,500.00 1 $356.93
What is the maximum amount of federal subsidized and unsubsidized loans per year for an independent student in a graduate program?
Braden takes out a private student loan for \(\$ 6,250\) in his second year of his undergraduate IT program. He begins paying the loan after 39 months. If Braden's interest rate was \(8 \%\), how much is his balance when he begins to pay off the loan?
The billing cycle for Therese's credit card is July 7 to August 6 (31 days). The interest rate on the card is \(17.9 \%\). The balance on her card at the start of the billing cycle is \(\$ 925.00\). The table below has her transactions for the billing cycle. What is her balance due at the end of
The cost of a car is \(\$ 45,750\). The residual price after 2 years is \(\$ 28,822.50\). What is the monthly depreciation for the car?
Find the payment for a 3 -year lease on a car if the price of the car is \(\$ 30,000\), the residual price of the car is \(\$ 20,000\), and the APR is \(8.5 \%\).
What are the monthly payments, excluding escrow, for a 20 -year mortgage for \(\$ 131,500\) at \(5.15 \%\) interest?
What are the monthly payments, including escrow, for a 20 -year mortgage for \(\$ 131,500\) at \(5.15 \%\) interest, with property taxes of \(\$ 3,170\) per year and homeowner's insurance of \(\$ 715\) every 6 months?
If a person earns \(\$ 2700\) gross on a paycheck, how much is taken out in FICA taxes?
Find the taxable income for a person who has \(\$ 81,200\) in earnings, \(\$ 1,250\) reported on a 1099 -INT for a savings account, \(\$ 5,400\) reported on a 1099-MISC for a contract job they did, paid \(\$ 5,250\) in mortgage interest, paid \(\$ 4,700\) in property taxes, and has \(\$ 4,200\) in
Find the federal income tax owed by a person filing single who has a taxable income of \(\$ 114,750\). Use the table below to determine the taxes. Bracket Lower Income Limit Upper Income Limit Tax Rate 1 0 $10,275 10% 2 $10,276 $41,775 12%
If a person owes \(\$ 20,000\) in federal income tax, but qualifies for \(\$ 4,000\) in child tax credit and \(\$ 8,000\) for child and dependent care credit, how much federal tax does the person actually pay?
How many different basic sundaes are possible?An ice-cream parlor sells 26 different flavors of ice cream. A basic sundae has one scoop of any flavor of ice cream, your choice of one of 3 sauces, and any one of 8 different toppings.
The ice-cream parlor also sells a medium sundae. The options are the same except it starts with 2 scoops of ice cream, which can be the same flavor or different flavors. How many different medium sundaes are there?An ice-cream parlor sells 26 different flavors of ice cream. A basic sundae has one
The ice-cream parlor also sells a large sundae. The choice of a large sundae allows you to choose any 3 scoops of ice cream, any 2 sauces (they can be the same, or you can choose 2 different ones), and any 3 toppings (that might be 3 servings of the same topping, or 2 servings of one topping and a
A company that builds custom computers offers 4 hard drive sizes, 4 memory sizes, 3 graphics cards, and 3 display options. How many computer configurations do they offer, if customers choose one of each customization?
A video game allows users to customize their avatars. There are 12 hair styles that users may choose from, as well as 5 hair colors, 8 skin tones, 24 shirts, 12 pants, and 8 shoes. How many different avatars are possible?
A small company has 3 divisions: Sales, Research and Development, and Manufacturing. One person from each division will be chosen to create an advisory board for the management group. If there are 8 people in Sales, 15 in Research and Development, and 48 in Manufacturing, how many different
A multiple-choice quiz has 5 questions, each of which has 4 possible answers. How many different ways are there to respond to this quiz?
The teacher decides to make the quiz from above a little harder by offering 5 responses on each of the 5 questions. How many ways are there to respond to this quiz?
In the United States, radio and television broadcast stations are assigned unique identifiers known as call signs. Call signs consist of 4 letters. The first is either \(\mathrm{K}\) or \(\mathrm{W}\) (generally speaking, stations with a \(\mathrm{K}\) call sign are west of the Mississippi River
Little sister has asked big brother to play a new game she's invented. It uses a modified deck of cards with 3 suits and only the numbered cards (those with rank 2 through 10). How many cards are in her deck?
The board game Mastermind has 2 players. One of them is designated the codemaker who creates a code that consists of a series of 4 colors (indicated in the game with 4 colored pegs), which may contain repeats. The other player, who is the codebreaker, tries to guess the code. If there are 6 colors
3 !Give a whole number that's equal to the given expression.
9 !Give a whole number that's equal to the given expression.
\(\frac{7!}{2!2!3!}\)Give a whole number that's equal to the given expression.
\(\frac{8!}{5!2!}\)Give a whole number that's equal to the given expression.
\(\frac{21!}{18!2!}\)Give a whole number that's equal to the given expression.
\(\frac{28!}{26!2!}\)Give a whole number that's equal to the given expression.
\(\frac{34!}{30!3!}\)Give a whole number that's equal to the given expression.
\(\frac{17!}{12!5!}\)Give a whole number that's equal to the given expression.
\({ }_{4} P_{3}\)Give a whole number that's equal to the given expression.
\({ }_{7} P_{5}\)Give a whole number that's equal to the given expression.
\({ }_{12} P_{10}\)Give a whole number that's equal to the given expression.
\(14 P_{10}\)Give a whole number that's equal to the given expression.
\({ }_{10} P_{8}\)Give a whole number that's equal to the given expression.
\({ }_{15} P_{11}\)Give a whole number that's equal to the given expression.
A euchre hand contains 5 cards. How many ways are there to receive a 5 -card hand (where the order in whichThe following exercise is about the card game euchre, which uses a partial standard deck of cards: It only has the cards with ranks \(9,10, \mathrm{~J}, \mathrm{Q}, \mathrm{K}\), and A for a
After all 4 players get their hands, the remaining 4 cards are placed facedown in the center of the table. How many arrangements of 4 cards are there from this deck?The following exercise is about the card game euchre, which uses a partial standard deck of cards: It only has the cards with ranks
Euchre is played with partners. How many ways are there for 2 partners to receive 5 -card hands (where the order in which the cards are received matters)?The following exercise is about the card game euchre, which uses a partial standard deck of cards: It only has the cards with ranks \(9,10,
How many different arrangements of the full euchre deck are possible (i.e., how many different shuffles are there)?The following exercise is about the card game euchre, which uses a partial standard deck of cards: It only has the cards with ranks \(9,10, \mathrm{~J}, \mathrm{Q}, \mathrm{K}\), and A
How many possible complete orders of finish are there?Involve a horse race with 13 entrants.
An exacta bet is one where the player tries to predict the top two finishers in order. How many possible exacta bets are there for this race?Involve a horse race with 13 entrants.
A trifecta bet is one where the player tries to predict the top three finishers in order. How many possible trifecta bets are there for this race?Involve a horse race with 13 entrants.
A superfecta bet is one where the player tries to predict the top four finishers in order. How many possible superfecta bets are there for this race?Involve a horse race with 13 entrants.
Convert 0.45 to percent form.
What is \(70 \%\) of 200 ?
Rewrite the fraction \(\frac{240}{100}\) as a percentage.
20 is what percent of 500 ?
An item with a retail price of \(\$ 250.00\) is on sale for \(30 \%\) off. What is the sale price of the item? Round to the nearest penny.
The sales price of an item is \(\$ 38.50\) after a \(40 \%\) discount. What was the retail price of the item? Round to the nearest penny.
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