Choose which group of sets the following number belongs to. Be sure to account for ALL sets. 9/10
The number 9/10 belongs to the following sets:
1. Rational numbers: The number 9/10 can be expressed as a fraction and is therefore a rational number.
2. Real numbers: The set of real numbers includes rational and irrational numbers, and since 9/10 is a rational number, it is also a real number.
3. Integers: The set of integers includes whole numbers and their negatives. Although 9/10 is not an integer itself, it can be written as the fraction 9/10 or the decimal 0.9, which is very close to 1. Thus, it can be rounded up to the nearest integer, which is 1. Therefore, 9/10 can also be considered an integer in a broader sense.
4. Natural numbers: The set of natural numbers is a subset of whole numbers and includes positive integers only. Since 9/10 is not a positive integer, it does not belong to the set of natural numbers.
Therefore, the number 9/10 belongs to the sets of rational numbers, real numbers, and integers.
try again
Apologies for the oversight. Let's reassess the sets to which the number 9/10 belongs:
1. Rational numbers: The number 9/10 can be expressed as a fraction, making it a rational number.
2. Real numbers: The set of real numbers comprises both rational and irrational numbers. Since 9/10 is rational, it is also a real number.
3. Integers: Integers consist of positive and negative whole numbers, as well as zero. The number 9/10 is not an integer since it lies between 0 and 1.
4. Natural numbers: Natural numbers are positive integers, starting from 1. The number 9/10 is not a natural number either.
Therefore, the number 9/10 belongs to the sets of rational numbers and real numbers. It does not fall within the sets of integers or natural numbers.
Choose which group of sets the following number belongs to. Be sure to account for ALL sets. 3
The number 3 belongs to the following sets:
1. Rational numbers: The number 3 can be expressed as a fraction, specifically 3/1. Therefore, it is a rational number.
2. Real numbers: The set of real numbers comprises both rational and irrational numbers. Since 3 is a rational number, it is also a real number.
3. Integers: Integers are the set of whole numbers and their negatives, including zero. Since 3 is a positive whole number, it is also an integer.
4. Natural numbers: Natural numbers are positive integers, starting from 1. Given that 3 is a positive integer, it is a natural number as well.
Therefore, the number 3 belongs to the sets of rational numbers, real numbers, integers, and natural numbers.
Choose which set or sets the following number belongs to. Be sure to account for ALL sets. \sqrt{2}
The number √2 belongs to the following sets:
1. Irrational numbers: The square root of 2, denoted as √2, is an irrational number. This means that it cannot be expressed as a fraction or a terminating or repeating decimal. Irrational numbers include numbers like √2, π, and e.
2. Real numbers: The set of real numbers includes both rational and irrational numbers. As √2 is an irrational number, it is also a real number.
3. Complex numbers: Complex numbers consist of a real part and an imaginary part, where the imaginary part is a multiple of the imaginary unit i. Since √2 is a real number (√2 + 0i), it can also be considered a complex number.
Therefore, the number √2 belongs to the sets of irrational numbers, real numbers, and complex numbers.
Order the numbers below from least to greatest. 1/2, -3, \sqrt{6}, - 5/4, 4.2
Ordering the numbers from least to greatest:
1. -3
2. -5/4
3. 1/2
4. √6 (approximately 2.449)
5. 4.2
Choose the property illustrated by the following statement. (4 x y) x 3 = 4 x (y x 3)
The property illustrated by the statement "(4 x y) x 3 = 4 x (y x 3)" is the associative property of multiplication.
Name the property that the following statement illustrates. 84+4=4+84
The property illustrated by the statement "84 + 4 = 4 + 84" is the commutative property of addition.
Name the property that the following statement illustrates. 57 x 3.14 = 3.14 x 57
The property illustrated by the statement "57 x 3.14 = 3.14 x 57" is the commutative property of multiplication.
The sign at the right shows the costs for a deep-sea fishing trip. How much will the total cost be for 1 adult, 2 children, and 1 senior citizen to go on a fishing trip? Use mental math.
DEEP-SEA FISHING
Adults
Children (12 & under)
Seniors (65 & up)
$53
$35
$47
To calculate the total cost for 1 adult, 2 children, and 1 senior citizen to go on a fishing trip using mental math, you can add the individual costs together:
1 adult: $53
2 children: $35 x 2 = $70
1 senior citizen: $47
Adding these costs together:
$53 + $70 + $47 = $170
Therefore, the total cost for 1 adult, 2 children, and 1 senior citizen to go on a fishing trip would be $170.
Simplify by using the associative property of multiplication. 10(4y)
Using the associative property of multiplication, we can simplify the expression 10(4y) as follows:
10(4y) = (10 * 4) * y
= 40 * y
= 40y
Therefore, 10(4y) simplifies to 40y using the associative property of multiplication.
Use the commutative and associative properties as needed to simplify the expression. (12+a)+13
Using the commutative and associative properties, we can simplify the expression (12+a)+13 as follows:
First, using the commutative property of addition, we can rearrange the terms:
(12+a)+13 = (a+12)+13
Next, using the associative property of addition, we can group the terms differently without changing the value:
(a+12)+13 = a+(12+13)
Simplifying further, we have:
a+(12+13) = a+25
Therefore, the expression (12+a)+13 simplifies to a+25 using the commutative and associative properties.
Use deductive reasoning to tell whether the statement shown below is true or false. If it is true, indicate which property or properties of real numbers are needed to show the expressions are equivalent. For all real numbers r, s, and t, (r x s) x t = t x (s x r)
The statement "(r x s) x t = t x (s x r)" is true, and the property that shows the expressions are equivalent is the commutative property of multiplication.
According to the commutative property of multiplication, the order of multiplication does not affect the result. In other words, when multiplying three real numbers, reordering the terms will not change the final product.
In the given statement, we have the expression (r x s) x t on the left side and t x (s x r) on the right side. By applying the commutative property of multiplication, we can rearrange the terms on the right side of the equation:
t x (s x r) = t x (r x s)
Now, we can observe that the expressions on both sides of the equation are the same: (r x s) x t and t x (r x s). Therefore, the statement is true, and the commutative property of multiplication justifies their equivalence.
1. Write an algebraic expression for the word phrase: the quotient of r and 12.(1 point)
Responses
r – 12
r – 12
r • 12
r • 12
r + 12
r + 12
r ÷ 12
r ÷ 12
Question 2
2. Write a word phrase for the algebraic expression 3x – 7.(1 point)
Responses
the difference of three times a number x and seven
the difference of three times a number x and seven
the difference of seven and three times a number x
the difference of seven and three times a number x
three times a number x fewer than seven
three times a number x fewer than seven
the quotient of three times a number x and seven
the quotient of three times a number x and seven
Question 3
3. What is the 2nd step in simplifying the expression 4² + 8 ÷ 2 ?(1 point)
Responses
Divide 8 by 2
Divide 8 by 2
Add 16 and 8
Add 16 and 8
Square 4
Square 4
Divide 24 by 2
Divide 24 by 2
Question 4
4. 5 is the square root of what expression(s)? Check all that apply.
10
10
25
25
5+5
5+5
5²
5²
5. The square root of 0.81 is
6. Name the subset(s) of real numbers to which the number zero belongs. Choose all that apply.
Responses
irrational numbers
irrational numbers
integers
integers
whole numbers
whole numbers
natural numbers
natural numbers
7. Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the Expression.
7+3⋅(9−6)2
1. The algebraic expression for the word phrase "the quotient of r and 12" is r ÷ 12.
2. The word phrase for the algebraic expression 3x – 7 is "the difference of three times a number x and seven".
3. The 2nd step in simplifying the expression 4² + 8 ÷ 2 is to divide 8 by 2.
4. 5 is the square root of the expressions 25 and 5².
5. The square root of 0.81 is 0.9.
6. The subset(s) of real numbers to which the number zero belongs are the integers, whole numbers, and natural numbers.
7. To simplify the expression 7 + 3⋅(9−6)², we start by evaluating the expression inside the parentheses:
9 - 6 = 3
Now, substitute that value back into the expression:
7 + 3⋅(3)²
Next, simplify the exponent:
7 + 3⋅(9)
Then, perform the multiplication:
7 + 27
Finally, add the numbers:
7 + 27 = 34
Therefore, the simplified expression is 34.
8. Homer and Bart plan to buy one computer for 499.00 strictly for gaming purposes. Games cost $49.99 each.
Part A: Define each variable and write an algebraic expression to describe how much they will spend before sales tax, based on purchasing the computer and the number of games?
(2 points)
0Word(s)
Question 9
Part B: If they purchase one computer and five games, how much do they spend before sales tax? Show your work below.
(3 points)
Part A:
Let's define the variables:
C = cost of the computer (499.00)
G = number of games
The algebraic expression to describe how much they will spend before sales tax, based on purchasing the computer and the number of games, is:
C + (G * 49.99)
Part B:
If they purchase one computer and five games, we can substitute the values into the expression and calculate the total cost before sales tax:
C + (G * 49.99) =
499.00 + (5 * 49.99) =
499.00 + 249.95 =
748.95
Therefore, they will spend $748.95 before sales tax.