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MTH 213 Week 1 Checkpoint

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Shown to the right is a magic square (all rows, columns, and diagonals sum to the same number). Find the value of each letter.

Explain whether the following could be true: In a survey of 214214 students, 104104 were taking algebra, 9090 were taking biology, and 2020 were taking neither of the two subjects.

Choose the correct answer below and, if necessary, fill in any answer boxes to complete your choice.

A.

No this could not be true because if 2020 students are taking neither of the two subjects then the distribution of students implies there will have to be more than 214214 total students.

B.

Yes this could be true if there were

104 students taking algebra but not biology, and there were

90 students taking biology but not algebra.

Cookies are sold singly or in packages of 44 or 1212. With this packaging, how many ways can you buy 2424 cookies?

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Rewrite the following using mathematical symbols.

a. Q is equal to the set whose elements are aa, bb, and cc.

b. The set containing 33 and 55 is equal to the set containing 55 and 33.

c. The set containing 33 and 55 only is not a proper subset of .

a. Q is equal to the set containing aa, bb, and cc.

Qequals=StartSet nothing EndSet

a,b,c

(Use a comma to separate answers as needed.)

b. The set containing 33 and 55 is equal to the set containing 55 and 33. Select the correct choice below and fill in the answer box to complete your choice.

(Use a comma to separate answers as needed.)

A.

is a subset of⊆StartSet nothing EndSet

nothing

B.

is an element of∈StartSet nothing EndSet

nothing

C.

almost equals≈StartSet nothing EndSet

nothing

D.

is a proper subset of⊂StartSet nothing EndSet

nothing

E.

equals=StartSet nothing EndSet

5,3

Your answer is correct.F.

congruent≅StartSet nothing EndSet

nothing

c. The set containing 33 and 55 only is not a proper subset of . Select the correct choice below and fill in the answer box to complete your choice.

(Use a comma to separate answers as needed.)

A.

is not a proper subset of⊄StartSet nothing EndSet

nothing

B.

is not an element of∉StartSet nothing EndSet

nothing

C.

is not a subset of⊈StartSet nothing EndSet

nothing

D.

is not a proper subset of⊄StartSet nothing EndSet

1,3,4

Your answer is correct.E.

is not a subset of⊈StartSet nothing EndSet

nothing

F.

is not an element of∉StartSet nothing EndSet

nothing

A student asks, “If A = and B = , why isn’t it true that A union∪ B = ?” What is your response?

Choose the correct answer below.

A.

It is not true that A union∪ B = because A union∪ Bequals=.

B.

It is not true that A union∪ B = because the union of two sets always consists of less elements than either of the sets.

C.

It is not true that A union∪ B = because A union∪ Bequals=empty set∅.

D.

It is not true that A union∪ B = because A union∪ Bequals=. Elements are not repeated in sets.

In each of the following, list three terms that continue the arithmetic or geometric sequences. Identify the sequences as arithmetic or geometric.

a. 11, 1111, 2121, 3131, 4141

b. 22, 44, 88, 1616, 3232

c. 99, 1313, 1717, 2121, 2525

a. The next three terms of 11, 1111, 2121, 3131, 4141 are

5151,

6161, and

7171. (Use ascending order.)

Is the sequence arithmetic or geometric?

A.

ArithmeticArithmetic

Your answer is correct.B.

GeometricGeometric

b. The next three terms of 22, 44, 88, 1616, 3232 are

6464,

128128, and

256256. (Use ascending order.)

Is the sequence arithmetic or geometric?

A.

GeometricGeometric

Your answer is correct.B.

ArithmeticArithmetic

c. The next three terms of 99, 1313, 1717, 2121, 2525 are

2929,

3333, and

3737. (Use ascending order.)

Is the sequence arithmetic or geometric?

A.

Geometric

B.

Arithmetic

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Assume the following pattern with terms built of square tile figures continues and complete parts (a) through (c) below.

A figure consists of 2 equal sized squares in a column.

A figure consists of 5 equal sized squares. In the center is a column of 3 squares. From the bottom square, 1 more square extends to the left. From the top square, 1 more square extends to the right.

A figure consists of 8 equal sized squares. In the center is a column of 4 squares. From the bottom square, 2 more squares extend to the left. From the top square, 2 more squares extend to the right.

A figure consists of 11 equal sized squares. In the center is a column of 5 squares. From the bottom square, 3 more squares extend to the left. From the top square, 3 more squares extend to the right.

a. How many square tiles are there in the ninthninth figure?

2626

b. How many square tiles are in the nth figure?

A.

There are 3nplus+1 square tiles in the nth figure.

B.

There are 3n square tiles in the nth figure.

C.

There are 3 n minus 13n−1 square tiles in the nth figure.

Your answer is correct.D.

The figures do not appear to follow any predictable pattern.

c. Is there a figure that has exactly 338338 square tiles? If so, which one? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

Yes. Figure number

113113 has 338338 square tiles.

Your answer is correct.B.

No. There does not exist a figure with exactly 338338 square tiles.

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Which of the following sets are equal?

Aequals={bb, ff, j}

Jequals={x vertial line x equals 2 n and n is an element of set of whole numbers Wx∣x=2n and n∈?}

Bequals={x, y}

Kequals={22, 44, 66, 88, 1010, 1212, …}

Cequals={j, ff, bb}

Lequals={x vertial line x equals 2 n minus 4 and n is an element of set of natural numbers Nx∣x=2n−4 and n∈ℕ}

Dequals={x vertial line 3 less than or equals x less than or equals 5 and x is an element of set of natural numbers Nx∣3≤x≤5 and x∈ℕ}

Select all that apply.

A.

Jequals=L

B.

Jequals=K

C.

Cequals=D

D.

Aequals=B

E.

Dequals=L

F.

Aequals=C

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Write the letters in the appropriate sections of the following Venn diagram using the following information.

Set A contains the letters in the word fussfuss.

Set B contains the letters in the word fatfat.

Set C contains the letters in the word footfoot.

The universal set U contains the letters in the word facetiousfacetious.

Choose the correct answer below.

The 14 digits of a credit card are written in the boxes shown. If the sum of any three consecutive digits is 1919, what is the value of A?

A

44

44

77

Aequals=

8

Explore the Color Patterns eManipulative and then study this pattern.

The following pattern of shapes is shown from left to right: yellow plus sign, yellow plus sign, green plus sign with arrows, orange sun, yellow plus sign, green plus sign with arrows, green plus sign with arrows, orange sun, orange sun, yellow plus sign, yellow plus sign.

What are the next two elements in the pattern?

A.

The following pattern of shapes is shown from left to right: green plus sign with arrows, green plus sign with arrows.

B.

The following pattern of shapes is shown from left to right: orange sun, yellow plus sign.

C.

The following pattern of shapes is shown from left to right: orange sun, orange sun.

D.

The following pattern of shapes is shown from left to right: green plus sign with arrows, orange sun.

How many ways can you make change for 4040cents¢ using only nickels, dimes, and quarters?

7 (Type a whole number.)

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