Which statement is true about the relationships between the number sets?(1 point)
Responses
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
All rational numbers are also integers.
All rational numbers are also integers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
I mean 5 of them!!
Whole numbers include all natural numbers and 0.
Which of the following is true about −9?(1 point)
Responses
It is an integer but not a rational number.
It is an integer but not a rational number.
It is an integer but not a whole number.
It is an integer but not a whole number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is both an integer and a whole number.
It is both an integer and a whole number.
A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
The price of gas is $3.39910 per gallon. So, the cost of 1 gallon of gas is $3.39910.
9/10 as decimal
To write 9/10 as a decimal, you can divide the numerator (9) by the denominator (10).
9 ÷ 10 = 0.9
So, 9/10 as a decimal is 0.9.
Which set of numbers is always rational?(1 point)
Responses
fractions
fractions
decimals
decimals
positive numbers
positive numbers
integers
integers
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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)
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The height of an equilateral triangle equals 3√2 times the side length. To find the height, we need to multiply the side length by 3√2.
Given that the square root of 3 is approximately 74, we can calculate the height as follows:
Height = 3√2 × side length
Height = 3 × 74 × 2 × 8
Height = 148 × 8
Height = 1184 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 1184 meters.
The diagonal of a square equals 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)
The diagonal of a square equals 2–√ times the side length. To find the length from one corner to an opposite corner, we need to multiply the side length by 2–√.
Given that the square root of 2 is approximately 1.4, we can calculate the diagonal length as follows:
Diagonal length = 2–√ × side length
Diagonal length = 1.4 × 700
Diagonal length = 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between and
To find the whole number and rational number to the nearest half that 40−−√ (also written as √40) is between, we can utilize a number line.
First, let's calculate the value of √40:
√40 ≈ 6.3246
Then, we can find the whole number and the nearest half that √40 falls between on the number line:
On the left side: 6
On the right side: 6.5
Thus, √40 is between 6 and 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 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
To find the whole number and rational number to the nearest half that 58−−√ (also written as √58) is between, we can utilize a number line.
First, let's calculate the value of √58:
√58 ≈ 7.6157
Then, we can find the whole number and the nearest half that √58 falls between on the number line:
On the left side: 7.5
On the right side: 8
Thus, √58 is between 7.5 and 8 on the number line.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√ 8–√8.
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To compare 81−−√ and 8–√8 using rational approximations, we can calculate their approximate decimal values.
Approximating √81:
√81 = 9
Approximating 8–√8:
8–√8 ≈ 8 – 2.8284 ≈ 5.1716
Comparing these values, we have:
9 > 5.1716
Therefore, the inequality statement comparing 81−−√ and 8–√8 is: 81−−√ > 8–√8.
Just give the number that's the answer
9
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
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To express 811 as a repeating decimal, we divide 811 by the appropriate divisor.
811 ÷ 9 = 90 remainder 1
Since we have a remainder of 1, we can express the decimal as a repeating decimal by placing the digit 1 above the bar. Therefore, 811 as a repeating decimal is written as 90.1 with the digit 1 repeating indefinitely after the decimal point: 90.1¯.
Just give me the answer
90.1¯
What is that line after the zero
The line after the zero indicates that the digit 1 repeats indefinitely. It is called a "vinculum" or a "repeating bar."
Thanks for helping her out punk!
You're welcome! If you have any more questions, feel free to ask.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
513
5 Start Fraction 1 over 3 end fraction
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
The rational number between 5 and 514 is 5 Start Fraction 1 over 3 end fraction.
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 convert the square roots to decimals and find the rational number between those values.
First, let's approximate the square roots:
7–√ ≈ 2.6458
8–√ ≈ 2.8284
Now, we need to find a rational number with a denominator of 7 between these decimal values.
Since the irrational numbers are between 2.6458 and 2.8284, we can choose a rational number like 2.7 as an approximation.
So, the rational number with a denominator of 7 that is between 7–√ and 8–√ is:
27/10 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)
The relationship between rational numbers and whole numbers is as follows:
1. Not all rational numbers are whole numbers: Rational numbers include both integers and fractions. While whole numbers are a subset of integers, they do not include fractions. For example, the rational number 4/3 is not a whole number because it is a fraction.
2. All whole numbers are rational numbers: Whole numbers include integers, which are also rational numbers. This is because rational numbers can be expressed as a ratio of two integers, and every whole number can be represented as an integer divided by 1. For example, the whole number 5 can be expressed as 5/1, where both the numerator and denominator are integers.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers. Whole numbers are a subset of rational numbers that include only integers.
Sorry I'm late! That is all incorrect expect 5!!!!
I apologize for any confusion caused by my previous response. Here is the correct information:
The relationship between rational numbers and whole numbers is as follows:
1. All whole numbers are rational numbers: Every whole number can be expressed as a fraction with a denominator of 1. For example, the whole number 5 can be expressed as the fraction 5/1, where both the numerator and denominator are integers.
2. Not all rational numbers are whole numbers: Rational numbers include both integers and fractions. Whole numbers are a subset of rational numbers that exclude fractions. For example, the rational number 4/3 is not a whole number because it contains a fraction.
To summarize, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
I apologize for the misunderstanding. Here are five statements regarding the relationship between rational numbers and whole numbers:
1. All whole numbers are rational numbers: Every whole number can be expressed as a fraction with a denominator of 1. For example, the whole number 5 can be expressed as the fraction 5/1.
2. Not all rational numbers are whole numbers: Rational numbers include both integers and fractions. Whole numbers are a subset of rational numbers that exclude fractions. For example, the rational number 4/3 is not a whole number because it contains a fraction.
3. Whole numbers are a subset of rational numbers: Every whole number is a rational number because it can be expressed as a fraction with a denominator of 1. For example, the whole number 7 can be expressed as the fraction 7/1.
4. Rational numbers can be whole numbers: Some rational numbers can be whole numbers when the denominator is equal to 1. For example, the rational number 10/1 is a whole number because it can be written as the whole number 10.
5. Whole numbers and rational numbers have overlap: There are some rational numbers that are also whole numbers. For example, the rational number 2/1 is both a whole number (2) and a rational number.
I hope this clears up any confusion and provides the information you were looking for.