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MTH 213 Week 5 Studyplan

The five top swimmers in an event had the following times.

Start 6 By 2 Table 1st Row 1st Column Swimmer 2nd Column Time 2nd Row 1st Column Emily 2nd Column 60.86 3rd Row 1st Column Molly 2nd Column 60.51 4st Row 1st Column Martha 2nd Column 61.76 5st Row 1st Column Kathy 2nd Column 61.71 6st Row 1st Column Rhonda 2nd Column 62.12 EndTable Swimmer Time Emily 60.86 Molly 60.51 Martha 61.76 Kathy 61.71 Rhonda 62.12

In order of how they placed, they were ___.

A.

Molly comma Emily comma Rhonda comma Kathy comma MarthaMolly, Emily, Rhonda, Kathy, Martha

B.

Molly comma Emily comma Kathy comma Martha comma RhondaMolly, Emily, Kathy, Martha, Rhonda

Your answer is correct.C.

Kathy comma Martha comma Molly comma Emily comma RhondaKathy, Martha, Molly, Emily, Rhonda

D.

Rhonda comma Molly comma Emily comma Kathy comma Martha

Classify each of the following as true or false. Complete parts a through e below.

a. If a number is divisible by 66, then it is divisible by 22 and 33.

This statement is

true.

b. If a number is divisible by 22 and 33, then it is divisible by 66.

This statement is

true.

c. If a number is divisible by 33 and 66, then it is divisible by 1212.

This statement is

false.

d. If a number is divisible by 1212, then it is divisible by 33 and 66.

This statement is

true.

e. A number is divisible by 1212, if and only if, it is divisible by 33 and 66.

This statement is

false.

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In the following, write an expression in terms of the given variables that represents the indicated quantity. Complete parts a through g.

a. The cost of having a plumber spend h hr at your house if the plumber charges $6060 for coming to the house and $x per hour for labor.

The expression for the cost of the plumber coming to the house is

60 plus xh60+xh dollars.

(Simplify your answer.)

b. The amount of money in cents in a jar containing some nickels and d dimes and some quarters if there are 66 times as many nickels as dimes and twice as many quarters as nickels.

The expression for the amount of money in the jar is

340 d340d cents.

(Simplify your answer.)

c. The sum of fourfour consecutive integers if the greatest integer is x

The expression for the sum of the fourfour consecutive integers is

4 x minus 64x−6.

(Simplify your answer.)

d. The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 1010 sec. (Hint: The answer should contain q as well as n)

The expression for the amount of bacteria is

q left parenthesis 3 Superscript 6 n Baseline right parenthesisq36n.

(Simplify your answer.)

e. The temperature t hr ago if the present temperature is 4040degrees°F and each hour it drops by 33degrees°F.

The expression for the temperature is

40 plus 3 t40+3tdegrees°F.

(Simplify your answer.)

f. Pawel’s total earnings after 3 yr if the first year his salary was s dollars, the second year it was $30003000 higher and the third year it was twice as much as the first year.

The expression for Pawel’s total earnings is

4 s plus 30004s+3000 dollars.

(Simplify your answer.)

g. The sum of threethree conscecutive even whole numbers if the greatest is x.

The expression for the sum of threethree consecutive even whole numbers is

3 x minus 63x−6.

(Simplify your answer.)

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Explain whether the following could be true: In a survey of 285285 students, 175175 were taking algebra, 8787 were taking biology, and 2323 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 2323 students are taking neither of the two subjects then the distribution of students implies there will have to be more than 285285 total students.

B.

Yes this could be true if there were

175175 students taking algebra but not biology, and there were

8787 students taking biology but not algebra.

How many ways can you make change for 6565cents¢ using only nickels, dimes, and quarters?

1414 (Type a whole number.)

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Place parentheses, if needed, to make each of the following equations true.

a. 99plus+55 times •33equals=4242

c. 5plus+4plus+9 divided by ÷66equals=33

b. 1515 divided by ÷33plus+1equals=66

d. 5plus+6 divided by ÷2plus+33equals=1111

a. Choose the correct answer below.

A.

Parentheses are needed. The corrected equation is left parenthesis 9 plus 5 right parenthesis times 3 equals 42(9+5)•3=42.

Your answer is correct.B.

Parentheses are needed. The corrected equation is 9 plus left parenthesis 5 times 3 right parenthesis equals 429+(5•3)=42.

C.

Parentheses are needed. The corrected equation is left parenthesis 9 plus 5 times 3 right parenthesis equals 42(9+5•3)=42.

D.

Parentheses are not needed to make the equation true.

b. Choose the correct answer below.

A.

Parentheses are needed. The corrected equation is left parenthesis 15 divided by 3 right parenthesis plus 1 equals 6(15÷3)+1=6.

B.

Parentheses are needed. The corrected equation is left parenthesis 15 divided by 3 plus 1 right parenthesis equals 6(15÷3+1)=6.

C.

Parentheses are needed. The corrected equation is 15 divided by left parenthesis 3 plus 1 right parenthesis equals 615÷(3+1)=6.

D.

Parentheses are not needed to make the equation true.

Your answer is correct.

c. Choose the correct answer below.

A.

Parentheses are needed. The corrected equation is left parenthesis 5 plus 4 plus 9 right parenthesis divided by 6 equals 3(5+4+9)÷6=3.

Your answer is correct.B.

Parentheses are needed. The corrected equation is 5 plus left parenthesis 4 plus 9 right parenthesis divided by 6 equals 35+(4+9)÷6=3.

C.

Parentheses are needed. The corrected equation is left parenthesis 5 plus 4 right parenthesis plus left parenthesis 9 divided by 6 right parenthesis equals 3(5+4)+(9÷6)=3.

D.

Parentheses are not needed to make the equation true.

d. Choose the correct answer below.

A.

Parentheses are needed. The corrected equation is left parenthesis 5 plus 6 right parenthesis divided by 2 plus 3 equals 11(5+6)÷2+3=11.

B.

Parentheses are needed. The corrected equation is left parenthesis 5 plus 6 right parenthesis divided by left parenthesis 2 plus 3 right parenthesis equals 11(5+6)÷(2+3)=11.

C.

Parentheses are needed. The corrected equation is 5 plus 6 divided by left parenthesis 2 plus 3 right parenthesis equals 115+6÷(2+3)=11.

D.

Parentheses are not needed to make the equation true.

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Use the number-line model to show that 5 left parenthesis Superscript minus Baseline 3 right parenthesis equals Superscript minus Baseline 15.5−3=−15.

Choose the correct answer below.

A.

A number line is labeled from negative 1 to 19 in increments of 1. Above the number line, arrows connect numbers as follows: from 0 to 3, from 3 to 6, from 6 to 9, from 9 to 12, from 12 to 15. The number 15 is circled.

B.

A number line is labeled from negative 18 to 1 in increments of 1. Above the number line, arrows connect numbers as follows: from 0 to negative 3, from negative 3 to negative 6, from negative 6 to negative 9, from negative 9 to negative 12, from negative 12 to negative 15. The number negative 15 is circled.

Your answer is correct.C.

A number line is labeled from negative 18 to 1 in increments of 1. Above the number line, arrows connect numbers as follows: from negative 15 to negative 12, from negative 12 to negative 9, from negative 9 to negative 6, from negative 6 to negative 3, from negative 3 to 0. The number negative 15 is circled.

D.

A number line is labeled from negative 1 to 19 in increments of 1. Above the number line, arrows connect numbers as follows: from 15 to 12, from 12 to 9, from 9 to 6, from 6 to 3, from 3 to 0. The number 15 is circled.

Use the information in the table to answer the following questions. Complete parts (a) through (c) below.

a. Which team won more than one half

1

2 of its games and was closest to winning one half

1

2 of its games?

Dolphins

b. Which team won less than one half

1

2 of its games and was closest to winning one half

1

2 of its games?

Eagles

c. Which team won more than one third

1

3 of its games and was closest to winning one third

1

3 of its games?

Hawks

A seventh-grade student does not believe that minus−5less than<minus−2. The student argues that a debt of $5 is greater than a debt of $2. How do you respond?

Which response is correct?

A.

The student is correct that a debt of $5 is greater than a debt of $2. This means that minus−5 is farther to the left than minus−2. Therefore, minus−2less than<minus−5.

B.

The student is incorrect that a debt of $5 is greater than a debt of $2. This means that minus−5 is farther to the left than minus−2. Therefore, minus−5less than<minus−2.

C.

The student is incorrect that a debt of $5 is greater than a debt of $2. This means that minus−2 is farther to the left than minus−5. Therefore, minus−2less than<minus−5.

D.

The student is correct that a debt of $5 is greater than a debt of $2. However, this means that minus−5 is farther to the left than minus−2. Therefore, minus−5less than<minus−2.

Cookies are sold singly or in packages of 22 or 66. With this packaging, how many ways can you buy 1212 cookies?

There are

1212 different ways to buy 1212 cookies.

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A student computes Superscript minus−8minus−2(Superscript minus−3) by writing Superscript minus−10(Superscript minus−3)equals=30. How would you help this student?

Select the correct answer below.

A.

The student does not fully understand the order of operations. The teacher should emphasize that in order to avoid ambiguity, mathematicians agree that multiplication is performed only before addition, and that division is performed only before subtraction. A few simpler examples like 10plus+2 times •3 and 10minus−6 divided by ÷2 should be helpful.

B.

The student does not fully understand the necessity of parentheses. The teacher should emphasize that in order to avoid ambiguity, mathematicians agree that parentheses should always be placed so that ambiguity is eliminated.

C.

The student does not understand that the expression is necessarily ambiguous. The student must determine, from the context, the appropriate order of operations in order to determine the correct answer. Using the same expression in different contexts should be helpful.

D.

The student does not fully understand the order of operations. The teacher should emphasize that in order to avoid ambiguity, mathematicians agree that multiplication is performed before addition or subtraction. A simple example like 10minus−2 times •3 should be helpful.

In each of the following, order the decimals from greatest to least.

a. 17.1568717.15687, 17.15717.157, 17.156917.1569, 17.1569217.15692

b. minus−3.7933.793, minus−3.70233.7023, minus−3.723.72, minus−3.7233.723

a. Order the decimals 17.1568717.15687, 17.15717.157, 17.156917.1569, and 17.1569217.15692 from greatest to least.

17.15717.157

greater than>

17.1569217.15692

greater than>

17.156917.1569

greater than>

17.1568717.15687

b. Order the decimals minus−3.7933.793, minus−3.70233.7023, minus−3.723.72, and minus−3.7233.723 from greatest to least.

negative 3.7023−3.7023

greater than>

negative 3.72−3.72

greater than>

negative 3.723−3.723

greater than>

negative 3.793

Read each measurement as shown on the following ruler.

Image of a partial ruler showing 3 inches, with tick marks every one eighth of an inch. There are questions about four measurements on the ruler: Question A points to a line 7 tick marks past 2 inches. Question B points to a line 1 tick mark past 2 inches. Question C points to a line 4 tick marks past 1 inch. Question D points to a line 7 tick marks past 0.

1

2

3

a.

b.

c.

d.

0

a.

2 and seven eighths2

7

8 in. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

b.

2 and one eighth2

1

8 in. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

c.

1 and one half1

1

2 in. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

d.

seven eighths

7

8 in. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

A car trip took 99 hours at an average speed of 6868 mph. Mentally compute the total number of miles traveled.

What is the number of miles traveled?

612612 miles

a. Fill in the missing numbers in the factor tree.

b. How could you find the top number without finding the other two numbers?

a. Fill in the missing numbers in the factor tree below.

441441

A short line segment rises from left to right.

A short line segment falls from left to right.

33

147147

A short line segment rises from left to right.

A short line segment falls from left to right.

77

2121

A short line segment rises from left to right.

A short line segment falls from left to right.

33

77

b. Choose the correct answer below.

A.

Count the total number of divisors and then multiply that number by the largest prime factor.

B.

Find the sum of all four prime factors determined from the tree.

C.

Find the product of all four prime factors determined from the tree.

Your answer is correct.D.

Subtract the product of the prime factors from the product of the composite factors.

10 years from now a girl’s age will be 66 times her present age. Find the girl’s age now.

The girl is currently

22 years old.

Indicate whether the statement is true or false.

negative StartRoot 16 EndRoot−16 is an irrational number.

Choose the correct answer below.

FalseFalse

Your answer is correct.

True

Simplify the expression.

Superscript minus−44minus−(33minus−44x)

Superscript minus−44minus−(33minus−44x)equals=

negative 7 plus 4 x

Rewrite each of the following as a base ten numeral.

a. 4 times 10 cubed plus 1 times 10 squared plus 4 times 104•103+1•102+4•10

b. 6 times 10 Superscript 6 Baseline plus 4 times 10 plus 36•106+4•10+3

a. 4 times 10 cubed plus 1 times 10 squared plus 4 times 104•103+1•102+4•10equals=

41404140 (Simplify your answer.)

b. 6 times 10 Superscript 6 Baseline plus 4 times 10 plus 36•106+4•10+3equals=

6,000,0436,000,043 (Simplify your answer.)

State the name of the property illustrated.

22plus+[44plus+(88)]equals=2 plus left bracket left parenthesis 8 right parenthesis plus 4 right bracket2+[(8)+4]

The expression is an example of which property?

A.

Commutative property of additionCommutative property of addition

Your answer is correct.B.

Identity property of additionIdentity property of addition

C.

Associative property of addition

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Which of the following are functions from the set StartSet x comma y comma z comma w EndSet to the set StartSet a comma b comma c comma d EndSet? If the set of ordered pairs is not a function, explain why not.

a. StartSet left parenthesis x comma a right parenthesis comma left parenthesis y comma b right parenthesis comma left parenthesis z comma c right parenthesis comma left parenthesis w comma d right parenthesis EndSet{(x,a),(y,b),(z,c),(w,d)}

b. StartSet left parenthesis x comma a right parenthesis comma left parenthesis y comma b right parenthesis comma left parenthesis z comma c right parenthesis comma left parenthesis w comma b right parenthesis EndSet{(x,a),(y,b),(z,c),(w,b)}

a. Is the set of ordered pairs StartSet left parenthesis x comma a right parenthesis comma left parenthesis y comma b right parenthesis comma left parenthesis z comma c right parenthesis comma left parenthesis w comma d right parenthesis EndSet{(x,a),(y,b),(z,c),(w,d)} a function?

It is

a function

because

each input maps to exactly one output.each input maps to exactly one output.

b. Is the set of ordered pairs StartSet left parenthesis x comma a right parenthesis comma left parenthesis y comma b right parenthesis comma left parenthesis z comma c right parenthesis comma left parenthesis w comma b right parenthesis EndSet{(x,a),(y,b),(z,c),(w,b)} a function?

It is

a function

because

each input maps to exactly one output.

Test whether the number 115115 is prime.

Is 115115 prime?

Convert to decimal notation.

8.68.6 times •10 Superscript negative 810−8

8.68.6 times •10 Superscript negative 810−8equals=

0.0000000860.000000086

(Simplify your answer. Type an integer or a decimal.)

Rewrite the following using mathematical symbols.

a. Q is equal to the set whose elements are mm, nn, and qq.

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 mm, nn, and qq.

Qequals=StartSet nothing EndSet

m,n,q

(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 proper subset of⊂StartSet nothing EndSet

nothing

B.

is a subset of⊆StartSet nothing EndSet

nothing

C.

is an element of∈StartSet nothing EndSet

nothing

D.

almost equals≈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

1,3,4

Your answer is correct.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

nothing

E.

is not an element of∉StartSet nothing EndSet

nothing

F.

is not a subset of⊈StartSet nothing EndSet

nothing

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

Set A contains the letters in the word beerbeer.

Set B contains the letters in the word babybaby.

Set C contains the letters in the word badbad.

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

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Solve for x in each of the following.

a. five sixths equals StartFraction x Over 13 EndFraction

5

6=

x

13

b. two thirds equals StartFraction Superscript minus Baseline 18 Over x EndFraction

2

3=

−18

x

a. xequals=

StartFraction 65 Over 6 EndFraction

65

6 (Simplify your answer. Type an integer or a simplified fraction.)

b. xequals=

negative 27−27 (Simplify your answer. Type an integer or a simplified fraction.)

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