Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
31 answers
Not all natural numbers are real numbers.
A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
A gallon costs $3.39910.
Which set of numbers is always rational?(1 point)
Responses
integers
integers
decimals
decimals
positive numbers
positive numbers
fractions
Responses
integers
integers
decimals
decimals
positive numbers
positive numbers
fractions
fractions
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, the approximate height in meters of an equilateral triangle with a side length of 8 meters can be calculated as follows:
Height = 3√2 * side length
= 3 * 74 * 2 * 8
= 3 * 148 * 8
= 3 * 1184
≈ 3552 meters.
Height = 3√2 * side length
= 3 * 74 * 2 * 8
= 3 * 148 * 8
= 3 * 1184
≈ 3552 meters.
The height of an equilateral triangle equals √3/2 times the side length. Using 7/4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
The height of an equilateral triangle equals (√3/2) times the side length. Using 7/4 for the square root of 3, the approximate height in meters of an equilateral triangle with a side length of 8 meters can be calculated as follows:
Height = (√3/2) * side length
= (7/4) * 8
= 7 * 2
= 14 meters.
Height = (√3/2) * side length
= (7/4) * 8
= 7 * 2
= 14 meters.
Using a number line, what whole number and rational number to the nearest half is √40 between?(1 point)
√40 is between 6 and 7 on the number line. To the nearest half, the whole number is 6 and the rational number is 6.5.
Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.(1 point)
Using rational approximations, we can compare √81 and √88 as follows:
√81 ≈ 9
√88 ≈ 9.4
Therefore, the inequality statement would be:
√81 < √88.
√81 ≈ 9
√88 ≈ 9.4
Therefore, the inequality statement would be:
√81 < √88.
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 1 5/8 in., 1 11/16 in., 1 3/4in ., and 1 1/2 in. What is the width of the widest stamp?(1 point)
To find the width of the widest stamp, we need to compare the given measurements and find the largest value.
The measurements are as follows:
1 5/8 in. = 13/8 in.
1 11/16 in. = 17/16 in.
1 3/4 in. = 7/4 in.
1 1/2 in. = 3/2 in.
To compare these values, we can convert them to a common denominator:
13/8, 17/16, 7/4, and 3/2 all have a common denominator of 16.
Converting the fractions to have a denominator of 16:
13/8 = 26/16
17/16 remains the same
7/4 = 28/16
3/2 = 24/16
Now, we can see that the widest stamp has a width of 28/16 in.
Simplifying this fraction:
28/16 = 7/4
Therefore, the width of the widest stamp is 7/4 inches.
The measurements are as follows:
1 5/8 in. = 13/8 in.
1 11/16 in. = 17/16 in.
1 3/4 in. = 7/4 in.
1 1/2 in. = 3/2 in.
To compare these values, we can convert them to a common denominator:
13/8, 17/16, 7/4, and 3/2 all have a common denominator of 16.
Converting the fractions to have a denominator of 16:
13/8 = 26/16
17/16 remains the same
7/4 = 28/16
3/2 = 24/16
Now, we can see that the widest stamp has a width of 28/16 in.
Simplifying this fraction:
28/16 = 7/4
Therefore, the width of the widest stamp is 7/4 inches.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
7.07 miles
7.07 miles
63.59 miles
63.59 miles
14.13 miles
14.13 miles
14.2 miles
.(1 point)
Responses
7.07 miles
7.07 miles
63.59 miles
63.59 miles
14.13 miles
14.13 miles
14.2 miles
To find the circumference of a circle, we can use the formula:
Circumference = π * diameter
Given that the diameter is 4.5 miles and using 3.14 for π, we can calculate the circumference as follows:
Circumference = 3.14 * 4.5
≈ 14.13 miles
Therefore, the circumference of a circle with a diameter of 4.5 miles is approximately 14.13 miles.
Circumference = π * diameter
Given that the diameter is 4.5 miles and using 3.14 for π, we can calculate the circumference as follows:
Circumference = 3.14 * 4.5
≈ 14.13 miles
Therefore, the circumference of a circle with a diameter of 4.5 miles is approximately 14.13 miles.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we divide 8 by 11 using long division:
0.72...
- 11| 8.00...
- 7.26...
- 2.74...
- 2.42...
- 3.20...
- 3.02...
- 0.18...
As we can see, the decimal representation of 8/11 is a repeating decimal with a cycle of 72. Therefore, we can express 8/11 as 0.72 (with the 72 repeating).
0.72...
- 11| 8.00...
- 7.26...
- 2.74...
- 2.42...
- 3.20...
- 3.02...
- 0.18...
As we can see, the decimal representation of 8/11 is a repeating decimal with a cycle of 72. Therefore, we can express 8/11 as 0.72 (with the 72 repeating).
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert 0.72¯¯¯¯¯ to a rational number, we can set it up as an equation:
Let x = 0.72¯¯¯¯¯
Multiplying both sides of the equation by 100 to remove the repeating bar, we get:
100x = 72.7272¯¯¯¯¯
Subtracting the original equation from the multiplied equation, we have:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99, we find:
x = 72/99
The rational number in simplest form is 8/11.
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11.
Let x = 0.72¯¯¯¯¯
Multiplying both sides of the equation by 100 to remove the repeating bar, we get:
100x = 72.7272¯¯¯¯¯
Subtracting the original equation from the multiplied equation, we have:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99, we find:
x = 72/99
The rational number in simplest form is 8/11.
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11.
Convert 0.72 to a rational number in simplest form.(1 point)
To convert 0.72 to a rational number in simplest form, we can write it as a fraction.
Let x = 0.72
We know that 0.72 is equal to 72/100, because the decimal point is two places to the right.
Simplifying the fraction 72/100, we can divide the numerator and denominator by the greatest common divisor, which is 8:
72 ÷ 8 = 9
100 ÷ 8 = 12
So, x = 9/12.
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
9 ÷ 3 = 3
12 ÷ 3 = 4
Therefore, 0.72 as a rational number in simplest form is 3/4.
Let x = 0.72
We know that 0.72 is equal to 72/100, because the decimal point is two places to the right.
Simplifying the fraction 72/100, we can divide the numerator and denominator by the greatest common divisor, which is 8:
72 ÷ 8 = 9
100 ÷ 8 = 12
So, x = 9/12.
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
9 ÷ 3 = 3
12 ÷ 3 = 4
Therefore, 0.72 as a rational number in simplest form is 3/4.
Which of the following is a rational number between √5 and √15?(1 point)
To find a rational number between √5 and √15, we can take the average of the two values:
√5 ≈ 2.24
√15 ≈ 3.87
Taking the average between 2.24 and 3.87:
(2.24 + 3.87)/2 = 6.11/2 = 3.055
Therefore, 3.055 is a rational number between √5 and √15.
√5 ≈ 2.24
√15 ≈ 3.87
Taking the average between 2.24 and 3.87:
(2.24 + 3.87)/2 = 6.11/2 = 3.055
Therefore, 3.055 is a rational number between √5 and √15.
Which of the following is a rational number between √5 and √15?(1 point)
Responses
√9
√10
√12
√6
Responses
√9
√10
√12
√6
To find a rational number between √5 and √15, we can identify the perfect squares that lie between 5 and 15.
We find that √9 is a perfect square and lies between √5 and √15.
Therefore, √9 is a rational number between √5 and √15.
We find that √9 is a perfect square and lies between √5 and √15.
Therefore, √9 is a rational number between √5 and √15.
What are three irrational numbers between √15 and √30?(1 point)
Responses
4, √18, √19
√20, √22, √25
√16, √17, √18
√17, √21, √27
Responses
4, √18, √19
√20, √22, √25
√16, √17, √18
√17, √21, √27
To find three irrational numbers between √15 and √30, we can identify the perfect squares that lie between 15 and 30 and take their square roots.
The perfect squares between 15 and 30 are 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29.
Taking the square roots of these numbers, we find the following:
√16 = 4
√17
√18
√19
√20
√21
√22
√23
√24
√25
√26
√27
√28
√29
Of these, √17, √18, and √19 are irrational numbers between √15 and √30.
Therefore, √17, √18, and √19 are three irrational numbers between √15 and √30.
The perfect squares between 15 and 30 are 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29.
Taking the square roots of these numbers, we find the following:
√16 = 4
√17
√18
√19
√20
√21
√22
√23
√24
√25
√26
√27
√28
√29
Of these, √17, √18, and √19 are irrational numbers between √15 and √30.
Therefore, √17, √18, and √19 are three irrational numbers between √15 and √30.
What are three irrational numbers between √15 and √30?(1 point)
Responses
1. 4, √18, √19
2. √20, √22, √25
3. √16, √17, √18
4. √17, √21, √27
Responses
1. 4, √18, √19
2. √20, √22, √25
3. √16, √17, √18
4. √17, √21, √27
The correct response is:
1. 4, √18, √19
Therefore, 4, √18, and √19 are three irrational numbers between √15 and √30.
1. 4, √18, √19
Therefore, 4, √18, and √19 are three irrational numbers between √15 and √30.
9 answers