Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
It is both an integer and a whole number.
The price of gas is $3.39 9/10 per gallon. To write this as a decimal, we can ignore the fraction and consider the decimal part. 9/10 is equivalent to 0.9.
So, a gallon costs $3.39 + $0.9 = $<<3.39+0.9=4.29>>4.29.
The length of the diagonal of a square is given by the formula:
diagonal = √2 * side length
Given that √2 is approximately 1.4, we can substitute this value into the formula:
diagonal = 1.4 * 700
diagonal = 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park that is 700 feet on a side is 980 feet.
Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.(1 point)
Using rational approximations, we can approximate √81 to be 9 and √88 to be approximately 9.38.
So, the inequality statement comparing √81 and √88 would be:
√81 < √88
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 perform long division:
0. 72
11|8
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
The cycle of repeating digits is 72, indicating that 8/11 as a repeating decimal is approximately 0.72 (or 0.7272... with the 72 part repeating).
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number, we can use a variable to represent the repeating decimal. Let's say x = 0.72¯¯¯¯¯.
Multiplying both sides of the equation by 100 (to remove the decimal):
100x = 72.7272¯¯¯¯¯
Subtracting the original equation from the multiplied equation:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
Simplifying:
99x = 72.0072
Dividing both sides by 99:
x = 72.0072/99
To express x as a simplified rational number, we can reduce the fraction 72.0072/99 by dividing both the numerator and denominator by their greatest common divisor:
x = 7200.72/9900
x = 36/50
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 36/50, which can be further simplified to 18/25 by dividing both the numerator and denominator by their greatest common divisor of 2.
So, 0.72¯¯¯¯¯ is equivalent to the rational number 18/25 in simplest form.
Which of the following is a rational number between 5 and 5 1/4
To find a rational number between 5 and 5 1/4, we can use the average of these two numbers.
The average of 5 and 5 1/4 can be calculated as follows:
(5 + 5 1/4) / 2
First, let's convert 5 1/4 to an improper fraction:
5 1/4 = (4 * 5 + 1) / 4 = 21/4
Now, we can calculate the average:
(5 + 21/4) / 2 = (20/4 + 21/4) / 2 = 41/4 / 2 = 41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
Among the given options, the rational number between 5 and 514 is 5 1/3.
Which of the following is true about −9?(1 point)
Responses
It is a whole number but not an integer.
It is an integer but not a rational number.
It is an integer but not a whole number.
It is both an integer and a whole number.
A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
Which set of numbers is always rational?(1 point)
Responses
fractions
positive numbers
decimals
integers
The set of numbers that is always rational is fractions.
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 is given by the formula:
height = √3/2 * side length
Given that √3 is approximately 7/4, we can substitute this value into the formula:
height = (7/4)/2 * 8
Simplifying further:
height = 7/4 * 4
height = 7 meters
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 7 meters.
The diagonal of a square equal √2 times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?(1 point)
Using a number line, what whole number and rational number to the nearest half is 40√ between?(1 point)
To find the whole number and rational number to the nearest half that 40√ lies between, we need to approximate 40√ and determine its position on the number line.
Approximating √40, we can estimate it to be approximately 6.32.
To find the whole number and rational number to the nearest half, we can round 6.32 to the nearest half:
Nearest whole number: 6
Nearest half: 6.5
Therefore, 40√ is between the whole number 6 and the rational number 6.5 on the number line.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 7.5 and 8
between 8 and 8.5
between 7 and 7.5
between 8.5 and 9
To find the whole number and rational number to the nearest half that 58⁻√ lies between, we need to approximate 58⁻√ and determine its position on the number line.
Approximating 58⁻√, we can estimate it to be approximately 7.64.
To find the whole number and rational number to the nearest half, we can round 7.64 to the nearest half:
Nearest whole number: 8
Nearest half: 7.5
Therefore, 58⁻√ is between the whole number 8 and the rational number 7.5 on the number line.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
5 1/3
√26
5 1/7
5 2/5
What is a rational number with a denominator of 7 that is between 7√ and 8√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that is between 7√ and 8√, we need to find the average of these two numbers.
The average of 7√ and 8√ can be calculated as follows:
(7√ + 8√) / 2
We can simplify this expression by factoring out the square root (√):
√(7^2 + 8^2) / 2
√(49 + 64) / 2
√113 / 2
To make this a rational number with a denominator of 7, we multiply the numerator and denominator by 7:
(√113 / 2) * (7 / 7)
(7√113) / 14
Therefore, a rational number with a denominator of 7 that is between 7√ and 8√ is (7√113) / 14 written as an improper fraction.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
Rational numbers and whole numbers are related, but they are not the same.
Not all rational numbers are whole numbers. Whole numbers include all the natural numbers (positive integers) and zero, but rational numbers can also include fractions and decimals. For example, the rational number 2/3 is not a whole number because it is a fraction between 0 and 1.
However, all whole numbers are rational numbers. Whole numbers can be expressed as fractions with a denominator of 1. For example, the whole number 5 can be written as the rational number 5/1.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
What is a rational number with a denominator of 7 that is between 7√ and 8√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that is between 7√ and 8√, we can find the average of these two numbers.
The average of 7√ and 8√ can be calculated as follows:
(7√ + 8√) / 2
We can simplify this expression by factoring out the square root (√):
√(49 + 64) / 2
√113 / 2
To make this a rational number with a denominator of 7, we can multiply the numerator and denominator by 7:
(√113 / 2) * (7 / 7)
(7√113) / 14
Therefore, a rational number with a denominator of 7 that is between 7√ and 8√ is (7√113) / 14 written as an improper fraction.
will the bot respond to me?
Again guys! Do your own research. The Bot is wrong in many of the answers! Be careful!!!
For example, you can use this example to do your approx. calculations:
Find a rational number between 2 and 2 1/4 (2 1/4 change it to improper)
**You can use the method of adding the numbers together and dividing by 2**
1. You add 2/1 + 9/4 (look for c. denominator) you get: 17/4
2. 17/4 you will divide 17 / 4= 4.25 or 4 1/4 and
3. You do division of 4 1/4 (or 4.25) by 2 and you get: 2 1/8