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.
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.
Not all natural numbers are real numbers.
Which of the following is true about −9?(1 point)
Responses
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 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 an integer but not a rational 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?
A gallon costs $3.39910.
Which set of numbers is always rational?(1 point)
Responses
integers
integers
decimals
decimals
fractions
fractions
positive numbers
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?
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, we can substitute the values into the formula to find the approximate height.
Approximate Height = (3√2) * Side Length
= (3 * 74) * 8
= 222 * 8
= 1776 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 1776 meters.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
To determine the whole number and rational number that 40−−√ is between on a number line, we can round the square root value to the nearest half.
The square root of 40 is approximately 6.32. Rounded to the nearest half, it becomes 6.5.
Therefore, 40−−√ is between the whole number 6 and the rational number 6.5 on a 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.
To compare 81−−√ and 8–√8 using rational approximations, we can find the decimal or rational approximations of each square root.
The square root of 81 is exactly 9.
To approximate the square root of 8, we can use rational approximations:
√8 ≈ 2.83
Therefore, the inequality statement comparing 81−−√ and 8–√8 is:
9 > 2.83
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 158in., 11116in., 134in., and 112in. What is the width of the widest stamp?(1 point)
in.
The width of the widest stamp is 1 5/16 inches.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
63.59 miles
63.59 miles
7.07 miles
7.07 miles
14.2 miles
14.2 miles
14.13 miles
The circumference of a circle is calculated using the formula C = π * d, where C is the circumference and d is the diameter.
Given a diameter of 4.5 miles and using the approximation of π as 3.14, we can estimate the circumference:
C = 3.14 * 4.5
C ≈ 14.13 miles
Therefore, the estimated circumference of a circle with a diameter of 4.5 miles is 14.13 miles.
Write 6,739 in expanded form.(1 point)
Responses
(6×1,000)+(7×100)+(3×10)+(0×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 0 times 1 right parenthesis
(7×100)+(3×10)+(9×1)
left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
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 the divisor of 999 to obtain the repeating decimal form.
811 ÷ 999 ≈ 0.811811...
In this case, the repeating pattern is 811, so we can express it as 0.8̅1̅1̅.
Therefore, 811 can be expressed as a repeating decimal as 0.8̅1̅1̅.
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 set a variable equal to the repeating part (72¯¯¯¯¯) and subtract the variable from the whole decimal:
x = 0.72¯¯¯¯
100x = 72.72¯¯¯¯
Now, we subtract the first equation from the second equation:
100x - x = 72.72¯¯¯¯ - 0.72¯¯¯¯
99x = 72
x = 72/99
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 9:
x = (72/9)/(99/9)
x = 8/11
Therefore, 0.72¯¯¯¯ can be converted to the rational number 8/11 in simplest form.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 2 over 5 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 can identify the whole number part and the decimal part of the square roots.
The whole number part of 7–√ is 7, and the decimal part is less than 1.
The whole number part of 8–√ is 8, and the decimal part is also less than 1.
To find a rational number between them with a denominator of 7, we can take the average of these two whole numbers:
(7 + 8) / 2 = 15 / 2
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 15/2, which is 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 that all whole numbers are rational numbers, but not all rational numbers are whole numbers.
To understand this, we need to define rational numbers and whole numbers.
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
A whole number, on the other hand, is a non-negative integer, including zero.
All whole numbers can be expressed as the ratio of two integers, where the denominator is 1. For example, 2 can be written as 2/1, which is a ratio of two integers. Therefore, all whole numbers are rational numbers.
However, not all rational numbers are whole numbers. Rational numbers can include fractions and decimals. For instance, 1/2 and 0.5 are rational numbers, but they are not whole numbers because they are not integers.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.