Which statement is true about the relationships between the number sets?(1 point)
Responses
A. Whole numbers include all natural numbers and 0.
B. Some irrational numbers are also integers.
C. Not all natural numbers are real numbers.
D. All rational numbers are also integers.
im sorry to inform you but most of the answers you had given me were incorrect
Dude at least tell us the incorrect ones!
A. Whole numbers include all natural numbers and 0.
Which of the following is true about −9?(1 point)
Responses
A. It is an integer but not a rational number.
B. It is an integer but not a whole number.
C. It is a whole number but not an integer.
D. It is both an integer and a whole number.
D. It is both an integer and a whole number.
this is wrong, negative numbers cannot be whole numbers.
You are correct; I apologize for the misinformation. The correct answer is B. It is an integer but not a whole number. Negative numbers are considered integers because they are whole numbers that can be expressed as a negative value. However, whole numbers specifically refer to non-negative integers, so -9 would not be considered 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?
To write the price strictly as a decimal, we can convert the fraction 9/10 to a decimal by dividing 9 by 10.
9 ÷ 10 = 0.9
So, the fraction 9/10 is equivalent to the decimal 0.9.
The gas price is given as $3.39 9/10 per gallon. Adding the decimal form of the fraction to $3.39 gives:
$3.39 + 0.9 = $4.29
Therefore, a gallon of gas costs $4.29.
Which set of numbers is always rational?(1 point)
Responses
A. integers
B. decimals
C. positive numbers
D. fractions
D. fractions
please do look over this question one more time
Apologies for the confusion. Upon reviewing the question, I understand that the correct response is A. integers.
Integers, which include whole numbers (positive numbers, negative numbers, and zero), are always rational numbers. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Since integers can be expressed as a fraction with a denominator of 1, they are always rational.
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?
To find the approximate height in meters of an equilateral triangle with a side length of 8 meters, we can use the given formula: height = (3√3/2) * side length.
Given that 7/4 is the approximate value for the square root of 3, we can substitute it into the formula:
height = (3 * (7/4) / 2) * 8
Now, simplify the expression:
height = (21/4) * 8
height = 168/4
height = 42 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 42 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?
To find the approximate length from one corner to an opposite corner of a square park that is 700 feet on each side, we can use the given formula: diagonal = (2 - √2) * side length.
Given that 1.4 is the approximate value for the square root of 2, we can substitute it into the formula:
diagonal = (2 - 1.4) * 700
Now, simplify the expression:
diagonal = (0.6) * 700
diagonal = 420 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 420 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
To find the whole number and rational number to the nearest half that 40−√ is between, we can look at the number line.
Let's first find the whole number. We can approximate the value of √40 as approximately 6.32. Since 6 is the closest whole number to 6.32, we can say that 40−√ is between 6 and 7 on the number line.
Next, let's find the rational number to the nearest half. We know that 6 is equivalent to 6.0 and 7 is equivalent to 7.0. To find the number halfway between 6.0 and 7.0, we can take their average:
(6.0 + 7.0) / 2 = 6.5
Therefore, 40−√ is between 6 and 6.5 on the number line.
So, to the nearest half, 40−√ is between the whole number 6 and the rational number 6.5.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
To find the whole number and rational number to the nearest half that 58−√ is between, we can again look at the number line.
Let's first find the whole number. We can approximate the value of √58 as approximately 7.62. Since 7 is the closest whole number to 7.62, we can say that 58−√ is between 7 and 8 on the number line.
Next, let's find the rational number to the nearest half. We know that 7 is equivalent to 7.0 and 8 is equivalent to 8.0. To find the number halfway between 7.0 and 8.0, we can take their average:
(7.0 + 8.0) / 2 = 7.5
Therefore, 58−√ is between 7 and 7.5 on the number line.
So, to the nearest half, 58−√ is between the whole number 7 and the rational number 7.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.
To compare 81−√ and 8–√8 using rational approximations, we can rewrite the expressions using rational approximations for the square roots.
Approximating √81, we get √81 ≈ 9.
Approximating √8, we get √8 ≈ 2.828.
Therefore, the inequality statement comparing 81−√ and 8–√8 is:
9 < 2.828
So, the correct inequality statement is 9 < 2.828.
Using rational approximations, what is an inequality statement comparing 81−−√ and 88–√? Enter <, >, or =.
To compare 81−√ and 88–√ using rational approximations, we can rewrite the expressions using rational approximations for the square roots.
Approximating √81, we get √81 = 9.
Approximating √88, we get √88 ≈ 9.380.
Therefore, the inequality statement comparing 81−√ and 88–√ is:
9 < 9.380
So, the correct inequality statement is 9 < 9.380.
Write 6,739 in expanded form.
6,739 in expanded form is written as:
6,000 + 700 + 30 + 9
So the expanded form of 6,739 is 6,000 + 700 + 30 + 9.
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 811 as a repeating decimal, we divide 811 by the number of digits that repeat indefinitely. In this case, there are no digits that repeat indefinitely, so 811 cannot be expressed as a repeating decimal. It is already in its simplest form.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 8/11 as a repeating decimal, we divide 8 by 11:
0.727272...
In this case, the digits 72 repeat indefinitely. To represent repeating digits, we can place a bar over them. So, 8/11 can be expressed as 0.72̄.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, let's assign a variable to the repeating portion. Let x = 0.72¯¯¯¯¯.
Next, we multiply both sides of the equation by a power of 10 that will move the decimal point to the right of the repeating portion. In this case, we multiply both sides by 100 to eliminate the repeating decimal:
100x = 72.7272...
Now, we subtract the original equation from the new equation to eliminate the repeating portion:
100x - x = 72.7272... - 0.7272...
99x = 72
Dividing both sides of the equation by 99:
x = 72/99
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
x = (8*9)/(11*9)
x = 8/11
Therefore, the rational number representation in simplest form for the repeating decimal 0.72¯¯¯¯¯ is 8/11.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
Responses
A. 5 1/3
B. 5 2/5
C. 5 1/7
D. 26−−√
To determine which of the given options is a rational number between 5 and 5 1/4, we need to find the option that falls within this range.
First, let's convert 5 1/4 to an improper fraction:
5 1/4 = (5 * 4 + 1) / 4 = 21/4
Now, let's compare the given options to this fraction:
A. 5 1/3 = 16/3, which is greater than 21/4
B. 5 2/5 = 28/5, which is greater than 21/4
C. 5 1/7 = 36/7, which is greater than 21/4
D. 26−√ = approximately 5.099, which is less than 5 1/4
After evaluating each option, we observe that all of them are either greater than or less than the range of 5 to 5 1/4. Therefore, none of the given options is a rational number between 5 and 5 1/4.
one has to be correct please check again
Apologies for the mistake. Let's reassess the given options and determine the correct answer.
First, let's convert 5 1/4 to an improper fraction:
5 1/4 = (5 * 4 + 1) / 4 = 21/4
Now, let's compare the remaining options to this fraction:
A. 5 1/3 = 16/3, which is greater than 21/4
B. 5 2/5 = 28/5, which is greater than 21/4
C. 5 1/7 = 36/7, which is greater than 21/4
D. 26−√ is a non-repeating decimal and does not fall between 5 and 5 1/4
After reconsidering the options, it appears that none of the given options is a rational number between 5 and 5 1/4.
please check one more time
Apologies for the confusion. Let's reassess the given options and determine the correct answer.
To find a rational number between 5 and 5 1/4, we need to find a fraction between the two values.
The fraction 5 1/3 is greater than 5 1/4, so it is not between the given range.
The fraction 5 2/5 is also greater than 5 1/4 and is not between the given range.
The fraction 5 1/7 is less than 5 1/4 and is not between the given range.
We are left with the option D. √26 (approximated to 5.099), which is greater than 5 but less than 5 1/4. Therefore, D. 26−√ is the correct answer.
Apologies for the previous incorrect responses. The correct answer is D. 26−√.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we need to approximate the values of 7–√ and 8–√.
Approximating √7, we can use the fact that √9 = 3. Since 7 is between 4 and 9, we can estimate that √7 is between 2 and 3.
Approximating √8, we can use the fact that √9 = 3. Since 8 is between 4 and 9, we can estimate that √8 is between 2 and 3 as well.
Therefore, a rational number with a denominator of 7 that falls between 7–√ and 8–√ is 2 and 5/7.
To write it as an improper fraction, we can convert it:
2 and 5/7 = (2 * 7 + 5) / 7 = 19/7
So, the rational number with a denominator of 7 that is between 7–√ and 8–√ is 19/7.
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.
The relationship between rational numbers and whole numbers is that every whole number is a rational number. This is because rational numbers include all integers (which includes whole numbers) and can be expressed as a fraction of two integers.
For example, the whole number 5 is also a rational number since it can be expressed as 5/1.
However, not all rational numbers are whole numbers. Rational numbers can include fractions and decimals as well.
For example, the rational number 3/4 is not a whole number as it is a fraction between 0 and 1.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.