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mathematics
a survey of mathematics with applications

Questions and Answers of A Survey of Mathematics with Applications

Write the Roman numeral as a Hindu–Arabic numeral.L̅MCMXLIV
Multiply in the indicated base. 223× 23
Write the Roman numeral as a Hindu–Arabic numeral.X̅MMDCLXVI
Convert each of the following to a numeral in the base indicated.2921 to base 8
Write the Roman numeral as a Hindu–Arabic numeral.X̅C̅I̅X̅CMXCIX
Use an Euler diagram to determine whether the syllogism is valid or invalid.All kangaroos are marsupials.Bounder is a kangaroo.∴ Bounder is a marsupial.
Use a truth table to determine whether the two statements are equivalent.p → q, ~p ∨ q
If you did not submit your application, then you will not be accepted to school. You did not submit your application. Therefore, you will not be accepted to school.Translate the argument into
a) If the dress is a Prada, then it is not a Gucci.b) It is not true that the dress is a Prada and it is not a Gucci.c) The dress is not a Prada or it is a Gucci.Determine which, if any, of the three
Convert the numeral to a Hindu–Arabic numeral.MMCDLXXIX
Fill in the blanks with an appropriate word, phrase, or symbol(s).The most common place-value system is the decimal number system that uses a base of ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).In base 5, 35 + 45 = ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the numeral 2345, the 5 is called the _______.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When determining the product 39 × 73, using duplation and mediation,a) The 39 is first ________ by 2, and thenb) The 73 is ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).A number is a quantity, and it answers the question “_______ ?”
Fill in the blanks with an appropriate word, phrase, or symbol(s).When we write 789 as (7 × 102) + (8 × 10) + (9 × 1) the number is written in ________ form.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In base 6, 26 + 56 = ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When using duplation and mediation, when you divide the number on the left by two you disregard the _________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the numeral 234, the 2 represents 2 ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).When subtracting in base 5, when we borrow, we must borrow one group of ________ from the preceding column.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the numeral 2345, the 3 represents 3 × _______.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When determining the product 327 × 45, using lattice multiplication, first construct a rectangle consisting of _________ columns and
Fill in the blanks with an appropriate word, phrase, or symbol(s).The system of numeration that we presently use is the _______ system.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the numeral 234, the 3 represents 3 ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).When subtracting in base 8, when we borrow, we must borrow one group of ________ from the preceding column.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When using lattice multiplication, after using multiplication to complete the boxes in the rectangle, add the numbers along the
Fill in the blanks with an appropriate word, phrase, or symbol(s).The Egyptian hieroglyphic system and the Roman numeration system are examples of _______ numeration systems.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the numeral 234, the 4 represents 4 ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).In base 5, 35 × 45 = ________.
Multiply using duplation and mediation.11 × 19
Fill in the blanks with an appropriate word, phrase, or symbol(s).As you read a Roman numeral from left to right, if a smaller number comes before a larger number, you should _______ the smaller
Fill in the blanks with an appropriate word, phrase, or symbol(s).The Babylonian system is not considered a true place-value system because it lacked a symbol for ________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).In base 9, 39 × 79 = ________.
Multiply using duplation and mediation.15 × 21
Fill in the blanks with an appropriate word, phrase, or symbol(s).A bar above a Roman numeral means to multiply that numeral by______.
Add in the indicated base. 213+ 203
Convert the given numeral to a numeral in base 10.4126
Multiply using duplation and mediation.29 × 35
Fill in the blanks with an appropriate word, phrase, or symbol(s).The Chinese numeration system is an example of a _______ numeration system.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The base used in the Babylonian numeration system is ________ .
Add in the indicated base. 234+ 134
Convert the given numeral to a numeral in base 10.5236
Fill in the blanks with an appropriate word, phrase, or symbol(s).The Ionic Greek numeration system is an example of a _______ numeration system.
Write the Egyptian numeral as a Hindu–Arabic numeral. 9900
Convert the given numeral to a numeral in base 10.2418
Write the Roman numeral as a Hindu–Arabic numeral.XIV
Fill in the blanks with an appropriate word, phrase, or symbol(s).It is believed that the Mayans used 18 × 20 instead of 202 so that their numeration system would conform to their ________ , which
Convert the given numeral to a numeral in base 10.7658
Write the Roman numeral as a Hindu–Arabic numeral.CXLII
Write the Hindu–Arabic numeral in expanded form.25
Convert the given numeral to a numeral in base 10.30912
Write the Roman numeral as a Hindu–Arabic numeral.MMCDXXXVII
Do research and write a report on the life and achievements of Augustus De Morgan. Indicate in your report his contributions to sets and logic.
Review the Mathematics Today box regarding fuzzy logic and Exercise 75. Do additional research and write a report on how fuzzy logic is used in many devices we encounter in our everyday lives.Data
Solve the following puzzle. Pablo has four cats. The parents are Tiger and Boots, and the kittens are Sam and Sue. Each cat insists on eating out of its own bowl. To complicate matters, each cat will
Determine whether ~[~(p ∨ ~q)] ⇔ p ∨ ~q.Explain the method(s) you used to determine your answer.
Construct a truth table fora) (p ∨ q) → (r ∧ s).b) (q → ~p) ∨ (r ↔ s).
If the meeting is in Las Vegas, then we can see a show or we can go to the casino.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
Determine whether the argument is valid or invalid.If Lynn wins the contest or strikes oil, then she will be rich.If Lynn is rich, then she will stop working.∴ If Lynn does not stop working, then
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
a) The spacecraft was made by SpaceX, or it was not made by Orbital and it was made by Boeing.b) The spacecraft was made by Boeing if and only if, it was made by SpaceX or it was not made by
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.q → (p ↔ r)
In Exercise, read the requirements and each applicant’s qualifications for obtaining a loan.a) Identify which of the applicants would qualify for the loan.b) For the applicants who do not qualify
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(q ^ r) → p
a) Akemi plays Star Stable if and only if she plays Just Dance.b) If Akemi plays Star Stable, then she plays Just Dance, and if Akemi plays Just Dance, then she plays Star Stable.c) Akemi does not
In Exercise, read the requirements and each applicant’s qualifications for obtaining a loan.a) Identify which of the applicants would qualify for the loan.b) For the applicants who do not qualify
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.~r → (q ^ p)
a) The grass grows and the trees are blooming.b) If the trees are blooming, then the grass does not grow.c) The trees are not blooming or the grass does not grow.Determine which, if any, of the three
In Exercise, letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is run by electric power.Translate each statement into symbols. Then construct a truth table for each
a) LeBron did not play for the Bucks or Giannis did not play for the Cavaliers.b) If LeBron played for the Bucks, then Giannis played for the Cavaliers.c) It is not true that Giannis played for the
In Exercise, letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is run by electric power.Translate each statement into symbols. Then construct a truth table for each
a) The shoes are not on sale but the purse is on sale.b) If the shoes are not on sale then the purse is not on sale.c) It is false that the shoes are on sale or the purse is not on sale.Determine
All bears are furry.Teddy is furry.∴ Teddy is a bear.Use an Euler diagram to determine whether the argument is valid or invalid.
Quentin Tarantino is a movie director, or if Halle Berry is a school teacher then Denzel Washington is a circus clown.Determine the truth value for each simple statement. Then, using the truth
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.If the air conditioner is working, then the temperature is 90° if and
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.Snickers is a brand of watches and Hershey’s is a brand of
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.The apartment is vacant if and only if the air conditioner is working,
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.The temperature is not 90° if and only if the air conditioner is not
If the two lines are perpendicular, then the two lines are not parallel.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or
All marigolds are annuals.Some tulips are annuals.∴ Some tulips are marigolds.Use an Euler diagram to determine whether the argument is valid or invalid.
If the United States has 60 states or the United States capital is Washington, D.C., then the capital of Mexico is Philadelphia.Determine the truth value for each simple statement. Then, using the
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.If the apartment is vacant and the air conditioner is working, then
If Xiomara runs a dance school, then Jane becomes an author. Jane becomes an author. Therefore, Xiomara runs a dance school.Translate the argument into symbolic form. Then determine whether the
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.If 72 = 49, then √49 = 7.
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.If the temperature is 90°, then the air conditioner is working or the
If the number is not a natural number, then the number is not a positive number.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is
If it rains on Monday, then we will go shopping. It does not rain on Monday. Therefore, we will not go shopping.Translate the argument into symbolic form. Then determine whether the argument is valid
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.If 1 + 1 = 3, then 5 - 2 = 3.
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.The temperature is 90° and the air conditioner is working, or the
If p is true, q is false, and r is false, determine the truth value of the statement.~[(p ∨ q) ↔ (p → ~r)]
Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The apartment is vacant.The temperature is not 90° and the air conditioner is working, but
If p is true, q is false, and r is false, determine the truth value of the statement.(~p ↔ r) ∨ (~q ↔ r)
The area of the United States is not larger than the area of Russia but the area of Canada is larger than the area of China.Use the table to determine the truth value of each simple statement. Then
The area of Brazil and China combined is larger than the area of Russia, and the area of the United States and Canada combined is not larger than the area of Russia.Use the table to determine the
Javier is a police officer or Javier is a little league coach.If Javier is a police officer, then Javier is a community leader.∴ Javier is a little league coach if and only if Javier is a community
The United States is over twice as large as Brazil or Canada is over twice as large as China.Use the table to determine the truth value of each simple statement. Then determine the truth value of the
Determine which, if any, of the three statements are equivalent.a) The screwdriver is on the workbench if and only if the screwdriver is not on the counter.b) If the screwdriver is not on the

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