Order the numbers below from least to greatest. 1/4, -1, Square Root 5, -5/2, 3.7
Choose the correct answer below.
1/4, -1, 3.7, Square Root 5, -5/2
-5/2, -1, 1/4, Square Root 5, 3.7
-1, 5/2, 1/4, 3.7, Square Root 5
-5/2, -1, 1/4, 3.7, Square Root 5
-5/2, -1, 1/4, 3.7, Square Root 5
Translate the algebraic expression to a word phrase.
6a
Choose the correct answer below.
A.
six plus a
B. the difference between six and a
C. six divided by a
D. six times a
D. six times a
Plot the points on a real number line.
(b) Write the numbers in ascending order.
(c) List the numbers that are integers.
(d) List the numbers that are rational numbers.
Question content area bottom
Part 1
(a) Plot the points on a real number line. Choose the correct answer below
A.
An infinite number line, labeled from negative 10 to 10 , has tick marks in increments of 1. Labeled points are plotted at negative 6.5, negative 4, negative three tenths, two thirds, 4, and 7.8; StartAbsoluteValue negative 9 EndAbsoluteValue is plotted to the right of 0.
-10
10
0
-3/10
2/3
4
-4
-6.5
7.8
B.
An infinite number line, labeled from negative 10 to 10 , has tick marks in increments of 1. Labeled points are plotted at negative 7.8, negative 4, negative two thirds, three tenths, 4, and 6.5; StartAbsoluteValue negative 9 EndAbsoluteValue is plotted to the right of 0.
-10
10
0
3/10
-2/3
-4
4
6.5
-7.8
C.
An infinite number line, labeled from negative 10 to 10 , has tick marks in increments of 1. Labeled points are plotted at negative 7.8, negative 4, negative two thirds, three tenths, 4, and 6.5; StartAbsoluteValue negative 9 EndAbsoluteValue is plotted to the left of 0.
-10
10
0
3/10
-2/3
-4
4
6.5
-7.8
B. An infinite number line, labeled from negative 10 to 10, has tick marks in increments of 1. Labeled points are plotted at negative 7.8, negative 4, negative two thirds, three tenths, 4, and 6.5; |-9| is plotted to the right of 0.
(a) Plot the points on a real number line.
(b) Write the numbers in ascending order.
(c) List the numbers that are integers.
(d) List the numbers that are rational numbers.
{3/10, -4, -2/3, 4, 6.5, |-9|, -7.8}
(b) Write the numbers in ascending order. Choose the correct answer below.
-7.8, -4, -2/3, 3/10, 4, 6.5, |-9|
-4, -7.8, -2/3, 3/10, 4, 6.5, |-9|
-7.8, -4, -2/3, 4, 3/10, 6.5, |-9|
|-9|, 6.5, 4, 3/10, -2/3, -4, -7.8
-7.8, -4, -2/3, 3/10, 4, 6.5, |-9|
List the numbers that are integers.
{3/10, -4, -2/3, 4, 6.5, |-9|, -7.8}
(Use a comma to separate answers as needed. Use ascending order.)
-9, -4, 4
d) List the numbers that are rational numbers.
-7.8, -4, -2/3, 3/10, 4, 6.5, |-9|
-4, 4, |-9|
-4, 4
-7.8, -4, 4, 6.5, |-9|
-7.8, -2/3, 3/10, 4, |-9|
Determine if the given number belongs to the set. 20/10
Question content area bottom
Part 1
Natural
Whole
Integers
Rational
Irrational
Real
▼
▼
No
Yes
▼
Yes
No
▼
No
Yes
▼
Yes
No
▼
No
Yes
Yes
Determine if the given number belongs to the set. 20/10
Natural Whole Integers Rational Irrational Real
▼
▼
No
Yes
▼
Yes
No
▼
No
Yes
▼
Yes
No
▼
No
Yes
Yes, 20/10 belongs to the set of rational numbers.
what about natural?
No, 20/10 does not belong to the set of natural numbers. Natural numbers are the counting numbers, starting from 1 and not including fractions or decimals.
ah, i see. then what about whole numbers?
Yes, 20/10 belongs to the set of whole numbers. Whole numbers include all the natural numbers (counting numbers) and also include zero.
and integers?
Yes, 20/10 belongs to the set of integers. Integers include all whole numbers (including zero) and their corresponding negative counterparts. In this case, 20/10 simplifies to 2, so it is an integer.
okay, what about irrational?
No, 20/10 does not belong to the set of irrational numbers. Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. Since 20/10 simplifies to 2, which can be expressed as the ratio of two integers (2/1), it is not considered irrational.
alright, what about real numbers?
Yes, 20/10 belongs to the set of real numbers. Real numbers include all rational and irrational numbers, so any number that is not imaginary is considered a real number. Since 20/10 is a rational number (2), it is also considered a real number.
In a week, a man received a paycheck for $425.50. The withholding for taxes was $96.50. If he worked 29 hours in that week, what is his hourly pay rate?
His hourly pay rate is $ [ ]
(Type an integer or a decimal.)
To find the hourly pay rate, we need to divide the total paycheck amount by the number of hours worked.
Hourly pay rate = (Paycheck amount - Withholding amount) / Number of hours worked
= ($425.50 - $96.50) / 29
= $329 / 29
Now, dividing $329 by 29 gives approximately $11.34.
Therefore, his hourly pay rate is $11.34.
Perform the indicated operation.
17/24 - 3/16
17/24 - 3/16 = [ ] (Type an integer or a fraction. Simplify your answer.)
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 48.
17/24 - 3/16 = (17/24) * (2/2) - (3/16) * (3/3)
= 34/48 - 9/48
Now, subtracting the numerators gives 25/48.
Therefore, 17/24 - 3/16 = 25/48.
Find the product.
4.7 • 5.4
4.7 • 5.4 = [ ] (Type an integer or a decimal.)
To find the product of 4.7 and 5.4, simply multiply these two numbers:
4.7 * 5.4 = 25.38
Therefore, 4.7 • 5.4 = 25.38.
State the property of real numbers that is being illustrated.
7/8 • ( - 12/35) • 8/7 = 7/8 • 8/7 • ( -12/35)
Choose the correct answer below.
multiplication property of zero
associative property of multiplication
multiplicative identity
multiplicative inverse property
commutative property of multiplication
The property of real numbers being illustrated in this equation is the commutative property of multiplication.
The commutative property of multiplication states that the order of the factors does not affect the product. This property allows us to rearrange the factors in a multiplication expression without changing the result.
In the given equation, we can see that the order of the factors 7/8 and -12/35 is reversed in the second expression, but the product remains the same. Thus, it demonstrates the commutative property of multiplication.
State the property of real numbers that is being illustrated.
8.09 + 6.42 + (- 8.09) = 8.09 + (-8.09) + 6.42
Choose the correct answer below.
associative property of addition
commutative property of addition
additive inverse property
identity property of addition
The property of real numbers being illustrated in this equation is the additive inverse property.
The additive inverse property states that for any real number "a," there exists an additive inverse "-a" such that "a + (-a) = 0". In other words, adding a number to its additive inverse results in the additive identity, which is 0.
In the given equation, we can see that the number 8.09 is added to its additive inverse (-8.09) in both expressions. This illustrates the additive inverse property.
Evaluate the following exponential expression.
(-1/6)^2
(-1/6)^2 = [ ] (Type an integer or a simplified fraction.)
To evaluate the expression (-1/6)^2, we simply square the numerator and denominator separately:
(-1/6)^2 = (-1)^2 / 6^2
= 1/36
Therefore, (-1/6)^2 is equal to 1/36.
Evaluate the following expression.
20 - 12 ÷ 2 + (-30)
_______________
16 • 4 - 8 • 0
20 - 12 ÷ 2 + (-30)
_______________ = [ ] (Type an integer or a simplified fraction.)
16 • 4 - 8 • 0
To evaluate the expression, we follow the order of operations (PEMDAS):
20 - 12 ÷ 2 + (-30) / (16 • 4 - 8 • 0)
First, we perform the multiplication and division inside the parentheses:
20 - 12 ÷ 2 + (-30) / (64 - 0)
Next, we perform the division:
20 - 6 + (-30) / (64 - 0)
Now, we perform the addition and subtraction from left to right:
20 - 6 + (-30) / 64
= 14 + (-30) / 64
To evaluate (-30) / 64, we divide -30 by 64:
14 - 30/64
To simplify the fraction 30/64, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
14 - (30 ÷ 2) / (64 ÷ 2)
= 14 - 15/32
Now, to perform the subtraction and simplify further, we find a common denominator of 32:
14(32/32) - 15/32
= 448/32 - 15/32
To subtract the fractions, we subtract the numerators and keep the common denominator:
(448 - 15)/32
= 433/32
Therefore, the expression simplifies to 433/32.
20 - 12 ÷ 2 + (-30) / (16 • 4 - 8 • 0)
Evaluate the following expression.
20 - 12 ÷ 2 + (-30) / (16 • 4 - 8 • 0) = [ ] (Type an integer or a simplified fraction.)
To evaluate the expression, we follow the order of operations (PEMDAS):
20 - 12 ÷ 2 + (-30) / (16 • 4 - 8 • 0)
First, we perform the multiplication and division inside the parentheses:
20 - 12 ÷ 2 + (-30) / (64 - 0)
Next, we perform the division:
20 - 6 + (-30) / 64
Now, we perform the addition and subtraction from left to right:
20 - 6 + (-30) / 64
To evaluate (-30) / 64, we divide -30 by 64:
20 - 6 - 30/64
To simplify the fraction 30/64, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
20 - 6 - (30 ÷ 2) / (64 ÷ 2)
= 20 - 6 - 15/32
Now, to perform the subtraction and simplify further, we get:
14 - 15/32
To subtract the fractions, we find a common denominator of 32:
(14 * 32)/32 - 15/32
= 448/32 - 15/32
To subtract the fractions, we subtract the numerators and keep the common denominator:
(448 - 15)/32
= 433/32
Therefore, the expression simplifies to 433/32.
Evaluate the following expression.
1/2 h(b + B); h = 6, b = 5, B = 16
The value of the expression for the given values of the variables is [ ]
To evaluate the expression 1/2 h(b + B) when h = 6, b = 5, and B = 16, we substitute these values into the expression:
1/2 * 6(5 + 16)
First, we simplify the expression inside the parentheses:
1/2 * 6(21)
Next, we multiply 6 by 21:
1/2 * 126
To find 1/2 of 126, we divide 126 by 2:
126/2
= 63
Therefore, the value of the expression for the given values of the variables is 63.
Evaluate the expression when a = 7, b = 6 c = -5 and d = - 2.
a - b / c - d
a - b / c - d = [ ] when a = 7, b = 6, c = - 5, and d = - 2. (Simplify your answer. Type an integer or a fraction.)
To evaluate the expression (a - b) / (c - d) when a = 7, b = 6, c = -5, and d = -2, we substitute these values into the expression:
(7 - 6) / (-5 - (-2))
First, we simplify the expression inside the parentheses:
1 / (-5 + 2)
Next, we simplify the addition inside the parentheses:
1 / -3
To find the reciprocal of -3, we invert the fraction:
-1/3
Therefore, the value of the expression when a = 7, b = 6, c = -5, and d = -2 is -1/3.
The cost of renting a truck from Hamilton Auto Rental is $58. 50 per day plus $0.25 per mile. The expression 58.50 + 0.25m represents the cost of renting a truck for one day and driving it for m miles. Evaluate 58.50 + 0.25m for m = 150.
The cost of renting a truck for one day and driving it 150 miles is $ [ ]
To evaluate 58.50 + 0.25m for m = 150, we substitute the value of m into the expression:
58.50 + 0.25 * 150
First, we perform the multiplication:
58.50 + 37.50
Next, we perform the addition:
= 96.00
Therefore, the cost of renting a truck for one day and driving it 150 miles is $96.00.
The Center for Science and Industry sells adult tickets for $13 and children's tickets for $9. The expression 13a +9c represents the total revenue from selling a adult tickets and c children's tickets. Evaluate the algebraic expression 13a + 9c for a = 165 and c = 467.
The total revenue for a = 165 and c = 467 is $ [ ]
To evaluate 13a + 9c for a = 165 and c = 467, we substitute the values of a and c into the expression:
13 * 165 + 9 * 467
First, we perform the multiplication:
2145 + 4203
Next, we perform the addition:
= 6348
Therefore, the total revenue for selling 165 adult tickets and 467 children's tickets is $6,348.
The total revenue for a = 165 and c = 467 is $ [ ]
The
The Center for Science and Industry sells adult tickets for $13 and children's tickets for $9. The expression 13a +9c represents the total revenue from selling a adult tickets and c children's tickets. Evaluate the algebraic expression 13a + 9c for a = 165 and c = 467.
The total revenue for a = 165 and c = 467 is what?