Which statement is true about the relationships between the number sets?(1 point)
Responses
All integers are also rational numbers.
All integers are also rational numbers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Whole numbers include all positive integers and negative integers.
All integers are also rational numbers.
Which of the following is true about 9?(1 point)
Responses
It is an integer but not a whole number.
It is an integer but not a whole number.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is both an integer and a whole number.
It is both an integer and a whole number.
It is a whole number but not an integer.
It is both an integer and a whole number.
Four people have found the distance in kilometers across a small bridge using different methods.
Their results are given in the table. Order the distances from least to greatest
512, 28−−√, 5.5¯¯¯, 234
512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 512
28−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
28−−√, 5.5¯¯¯, 234, 512
Which set of numbers is always irrational?(1 point)
Responses
positive decimals
positive decimals
non-terminating, non-repeating decimals
non-terminating, non-repeating decimals
repeating decimals
repeating decimals
terminating decimals
non-terminating, non-repeating decimals
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 70 feet on a side?(1 point)
ft.
The length of the diagonal can be calculated by multiplying the side length of the square by 2–√ (or 1.4).
Diagonal length = side length * 1.4
Diagonal length = 70 ft * 1.4
Diagonal length = 98 ft
Therefore, the approximate length from one corner to an opposite corner of the square park is 98 feet.
Using a number line, what whole number and rational number to the nearest half is 30−−√
between?(1 point)
30−−√ is between
and
To find the whole number and rational number to the nearest half that 30−−√ lies between, we can estimate its value.
Let's approximate 30−−√ by using 5.5 for the square root of 30.
To the nearest half, we can say that 30−−√ is between 5 and 6.
Therefore, 30−−√ is between 5 and 6 on the number line.
Using a number line, what whole number and rational number to the nearest half is 68−−√
between?(1 point)
Responses
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 8 and 8.5
between 8 and 8.5
between 9 and 9.5
To find the whole number and rational number to the nearest half that 68−−√ lies between, we can estimate its value.
Let's approximate 68−−√ by using 8.2 for the square root of 68.
To the nearest half, we can say that 68−−√ is between 8 and 8.5.
Therefore, 68−−√ is between 8 and 8.5 on the number line.
Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
To compare 91−−√ and 98−−√ using rational approximations, we can use 9.5 as the approximate value for the square root of 91 and 9.9 as the approximate value for the square root of 98.
Based on these approximations, we can see that 91−−√ is less than 98−−√.
Therefore, the inequality is: 91−−√ < 98−−√.
Write 2,468 in expanded form.(1 point)
Responses
(2 x 1,000) + (4 x 100) + (6 x 10) + (0 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (0 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(4 x 100) + (6 x 10) + (8 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
Express 711
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
The number 711 as a repeating decimal is expressed as 711.000... with the digit "0" repeating infinitely. Therefore, the cycle of repeating digits is indicated by a bar over the "0" in the decimal representation.
Convert 0.09¯¯¯¯¯
to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we can use the concept of geometric series.
Let x = 0.09¯¯¯¯¯
Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 9.999¯¯¯¯¯
Subtracting the original equation from the equation with 100x:
100x - x = 9.999¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.909¯¯¯¯¯
Now, divide both sides of the equation by 99:
x = 9.909¯¯¯¯¯ / 99
Simplifying the fraction 9.909¯¯¯¯¯ / 99:
x = 0.099¯¯¯¯¯
So, 0.09¯¯¯¯¯ is equal to 0.099¯¯¯¯¯ as a rational number in simplest form.
Convert 0.7¯¯¯
to a fraction.(1 point)
The fraction equivalent of 0.7¯¯¯ is
Let's assign a variable to the repeating decimal 0.7¯¯¯, such as x.
x = 0.7¯¯¯
To remove the repeating part, we multiply both sides of the equation by 10:
10x = 7.7¯¯¯
Next, we subtract the original equation from the equation multiplied by 10:
10x - x = 7.7¯¯¯ - 0.7¯¯¯
This simplifies to:
9x = 7
To isolate x, we divide both sides of the equation by 9:
x = 7/9
Therefore, the fraction equivalent of 0.7¯¯¯ is 7/9.
Which of the following is an irrational number between 4 and 8?(1 point)
Responses
12−−√
square root of 12
17−−√
square root of 17
8–√
square root of 8
5–√
The square root of 8, denoted as 8–√, is an irrational number between 4 and 8.
Which of the following rational numbers is not between 3–√ and 6–√
?(1 point)
Responses
1.8
1 point 8
4–√
square root of 4
1.5
1 point 5
2
Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.(4 points)
0 / 10000 Word Limit
Math Short Answer Rubric (4 points)
Points Award Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0
The question is not answered.
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Yes, all integers are also whole numbers.
Integers include all positive and negative whole numbers, as well as zero. So any integer, such as -3 or 7, is also a whole number.
On the other hand, not all whole numbers are integers. The whole numbers include all positive integers and zero, but they do not include negative numbers. For example, 5 is a whole number but not an integer since it is a positive number but not a negative number or zero.
In summary, the relationship between integers and whole numbers is that all integers are also whole numbers, but not all whole numbers are integers.
Question
Type the following sentence and add your name to the end to acknowledge that you have completed this assessment on your own.
"I have neither given nor received any assistance on this assessment."
{Your name here}
(1 point)
0 / 10000 Word Limit
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"I have neither given nor received any assistance on this assessment."
{Your name here}