Which statement is true about the relationships between the number sets?(1 point)
Responses
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
All rational numbers are also integers.
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Not all rational numbers are also integers.
Which of the following is true about −9?(1 point)
Responses
It is a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a whole number.
It is an integer but not a whole number.
It is both an integer and a whole number.
It is both an integer and a whole number.
It is an integer but not a rational number.
It is an integer but not 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)
$
3.39910
Which set of numbers is always rational?(1 point)
Responses
positive numbers
positive numbers
integers
integers
fractions
fractions
decimals
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)
To find the approximate height of an equilateral triangle with a side length of 8 meters, we can multiply the side length (8) by the given value of the square root of 3 (74) and then divide by 2.
Height = (Side length * √3) / 2
Height = (8 * 74) / 2
Height = 592 / 2
Height = 296 meters
Therefore, the approximate height of the equilateral triangle is 296 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)
To find the approximate length from one corner to an opposite corner of a square park with a side length of 700 feet, we can multiply the side length (700) by the given value of 2–√ (1.4).
Length = Side length * (2–√)
Length = 700 * 1.4
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)
To locate the value of √40 on a number line, we can approximate it to the nearest whole number and the nearest half.
√40 is approximately equal to 6.32.
Nearest whole number to 6.32 is 6.
Nearest half to 6.32 is 6.5.
Therefore, √40 is between the whole number 6 and the rational number 6.5 on a number line.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 7 and 7.5
between 7 and 7.5
between 7.5 and 8
between 7.5 and 8
between 8.5 and 9
between 8.5 and 9
between 8 and 8.5
To locate the value of √58 on a number line, we can approximate it to the nearest whole number and the nearest half.
√58 is approximately equal to 7.62.
Nearest whole number to 7.62 is 7.
Nearest half to 7.62 is 7.5.
Therefore, √58 is between the whole number 7 and the rational number 7.5 on a number line.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
To compare 81−−√ and 8–√8 using rational approximations, we can approximate both values:
81−−√ is approximately equal to 9.
8–√8 is approximately equal to 8.
Since 9 is greater than 8, the inequality statement would be:
81−−√ > 8–√8
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 811 as a repeating decimal, we divide 811 by 99 (because 811 is divisible by 9 and 11, and 9 * 11 = 99).
The result is 8 with a remainder of 53.
We then take the remainder (53) and put it as the numerator over the divisor (99).
53/99 = 0.53535...
The digits 53 repeat indefinitely, so the decimal representation of 811 is 0.53¯¯¯¯¯.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can assign a variable to the repeating part and solve for it.
Let x = 0.72¯¯¯¯¯
Multiply both sides of the equation by 1000 to remove the repeating bar:
1000x = 720.727272...
Subtract the equation x from 1000x to eliminate the repeating part:
999x = 720
Divide both sides of the equation by 999:
x = 720/999
The fraction 720/999 is a rational number in simplest form. It cannot be simplified further since the numerator and the denominator do not share any common factors other than 1. Therefore, the rational representation of 0.72¯¯¯¯¯ is 720/999.
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
The rational number between 5 and 514 would be 513.
Which of the following is a rational number between 5 and 5/14?(1 point)
Responses
26−−√
start root 26 end root
5/13
5 Start Fraction 1 over 3 end fraction
5/25
5 Start Fraction 2 over 5 end fraction
5/17
The rational number between 5 and 5/14 would be 5/13.
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 calculate the value of √7 and √8 to better understand the range.
Approximately, √7 is equal to 2.646 and √8 is equal to 2.828.
So, we need to find a rational number between 2.646 and 2.828.
A rational number that could fit this criteria is 53/20, which is equal to approximately 2.65.
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 53/20.
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 that every whole number is a rational number, but not every rational number is a whole number.
A rational number is any number that can be expressed as a fraction (where the numerator and denominator are integers). This includes whole numbers since they can be written as fractions with a denominator of 1. For example, 3 can be written as 3/1, making it a rational number.
However, not all rational numbers are whole numbers. Rational numbers also include fractions and decimals that are not whole numbers. For instance, 1/2 is a rational number, but it is not a whole number. Similarly, 0.75 is a rational number, but it is not a whole number.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
well that sucked
are you a robot gpt
what are the answers to the whole test tho and are all of these correct??
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, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
Write 6,739 in expanded form.(1 point)
Responses
(9×1,000)+(3×100)+(7×10)+(6×1)
(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(0×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
Question
Which of the following is a rational number between 5 and 514?(1 point)
Responses
5 1/7
5 2/5
5 1/3
26−−√
Rita buys four different types of fruits for a fruit salad. Her costs for the fruits are $2.31, $6.45, $3, and $1.23. If she draws a Venn diagram to classify these numbers, which circle will include all of the numbers?(1 point)
Which of the following number sets consists only of integers?(1 point)
Responses
{−12,−3,0,1,52}
left brace negative 12 comma negative 3 comma 0 comma 1 comma 52 right brace
{0,12,1,8,56}
left brace 0 comma Start Fraction 1 over 2 End Fraction comma 1 comma 8 comma 56 right brace
{−79100,−0.63,0,78,9.92}
left brace negative Start Fraction 79 over 100 End Fraction comma negative 0.63 comma 0 comma Start Fraction 7 over 8 End Fraction comma 9.92 right brace
{−12,−3.2,0,12,47}