Which statement is true about the relationships between the number sets?

all intergers are whole numbers
not all natural numbers are rational
some irrational numbers are rational
all natural numbers are integers

Bot GPT 3.5 Bot GPT 3.5 answered

The statement "all integers are whole numbers" is true.

The statement "not all natural numbers are rational" is also true. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, while natural numbers are only positive integers. Therefore, not all natural numbers can be expressed as a rational number (e.g. โˆš2 is a natural number but is irrational).

The statement "some irrational numbers are rational" is false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Therefore, by definition, irrational numbers cannot be rational numbers.

The statement "all natural numbers are integers" is true. Natural numbers include all positive integers, and integers include all positive and negative whole numbers.

nono nono answered

Which of the following is true about the number 1/6 ?

it's a rational number but not a real number
it's both an integer and a rational number
It's both an irrational number and a real number
It's a rational number but not a whole number

Bot GPT 3.5 Bot GPT 3.5 answered

The statement "it's a rational number but not a real number" is false. The number 1/6 is both a rational number and a real number.

The statement "it's both an integer and a rational number" is false. Integers are whole numbers (negative, zero, and positive) and do not include fractions like 1/6. Therefore, 1/6 is not an integer.

The statement "it's both an irrational number and a real number" is also false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Since 1/6 can be expressed as a fraction, it is not an irrational number. However, it is a real number as it can be plotted on the number line.

The statement "it's a rational number but not a whole number" is true. Rational numbers can be expressed as a fraction or ratio of two integers, which 1/6 is. Whole numbers are integers that are greater than or equal to zero. Since 1/6 is a fraction, it is not a whole number.

nono nono answered

A sign in a gas station advertises gas at the rate listed below. How many dollars does a gallon cost, writing the price strictly as a decimal?

$4.12 9/10

Bot GPT 3.5 Bot GPT 3.5 answered

To write the price strictly as a decimal, we need to convert the fraction 9/10 to a decimal. To do this, we divide 9 by 10:

9 รท 10 = 0.9

Now we can write the price strictly as a decimal:

$4.12 + 0.9 = $4.129

Therefore, a gallon of gas costs $4.129.

nono nono answered

Which set of numbers is always rational

Bot GPT 3.5 Bot GPT 3.5 answered

The set of numbers that is always rational is the set of integers. Integers include all whole numbers (positive, negative, and zero) and can be expressed as a ratio of two integers.

nono nono answered

The height of an equilateral triangle equals โˆš3/2 times the side length. What is the approximate height in meters of an equilateral triangle with a side length of 16 meters?

Bot GPT 3.5 Bot GPT 3.5 answered

To find the height of an equilateral triangle with a side length of 16 meters, we can use the formula given, which states that the height is equal to (โˆš3/2) times the side length.

First, let's calculate (โˆš3/2) times 16:

(โˆš3/2) * 16 = (1.732/2) * 16 = 0.866 * 16 = 13.856

Therefore, the approximate height of the equilateral triangle is approximately 13.856 meters.

nono nono answered

The diagonal of a square equals โˆš2 times the side length. Using 1.4 for โˆš2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 300 feet on a side?

Bot GPT 3.5 Bot GPT 3.5 answered

To find the length from one corner to an opposite corner of a square park with a side length of 300 feet, we can use the formula given, which states that the diagonal is equal to โˆš2 times the side length.

First, let's calculate โˆš2 times 300 using 1.4 as an approximation for โˆš2:

1.4 * 300 = 420

Therefore, the approximate length from one corner to an opposite corner of the square park is approximately 420 feet.

nono nono answered

What whole number and rational number to the nearest half is โˆš128 between?

Bot GPT 3.5 Bot GPT 3.5 answered

To find the whole number and rational number to the nearest half that โˆš128 falls between, we can calculate the square root of 128 and identify the two numbers it lies between.

โˆš128 โ‰ˆ 11.3137

To the nearest half, โˆš128 falls between:

11 and 11.5,
or
11.5 and 12.

Therefore, the whole number to the nearest half is 11 and the rational number to the nearest half is 11.5.

nono nono answered

hat whole number and rational number to the nearest half is โˆš8 between?

Bot GPT 3.5 Bot GPT 3.5 answered

To find the whole number and rational number to the nearest half that โˆš8 falls between, we can calculate the square root of 8 and identify the two numbers it lies between.

โˆš8 โ‰ˆ 2.8284

To the nearest half, โˆš8 falls between:

2 and 2.5,
or
2.5 and 3.

Therefore, the whole number to the nearest half is 2 and the rational number to the nearest half is 2.5.

nono nono answered

Using rational approximations, what is an inequality statement comparing โˆš72 and โˆš76?

Bot GPT 3.5 Bot GPT 3.5 answered

To compare โˆš72 and โˆš76 using rational approximations, we can calculate the square roots and compare the results:

โˆš72 โ‰ˆ 8.4853
โˆš76 โ‰ˆ 8.7178

Since 8.4853 is less than 8.7178, we can write the inequality statement as:

โˆš72 < โˆš76

nono nono answered

Write 5,143 in expanded form

Bot GPT 3.5 Bot GPT 3.5 answered

5,143 in expanded form is:

5,000 + 100 + 40 + 3.

nono nono answered

Express 8/27 as a repeating decimal.

Bot GPT 3.5 Bot GPT 3.5 answered

To express 8/27 as a repeating decimal, we need to perform long division. Here's the process:

0.296296...
----------------
27 | 8.0000000000000
- 7.56
0.440
- 0.405
0.350
- 0.324
0.260
- 0.243
0.170
- 0.162
0.080
- 0.081
-0.001

The division keeps repeating from where the remainder becomes zero. Therefore, 8/27 as a repeating decimal is approximately 0.296296...

nono nono answered

Which of the following is a rational number between 3 and 3 1/6

Bot GPT 3.5 Bot GPT 3.5 answered

To find a rational number between 3 and 3 1/6, we can determine the average of these two numbers.

The average is calculated as follows:

(3 + 3 1/6) รท 2

Converting 3 1/6 to an improper fraction:

3 1/6 = (3 * 6 + 1) / 6 = 19/6

Now, calculating the average:

(3 + 19/6) รท 2 = (18/6 + 19/6) รท 2 = 37/6 รท 2 = 37/12

Therefore, a rational number between 3 and 3 1/6 is 37/12.

nono nono answered

What is a rational number with a denominator of 7 that is between โˆš11 and โˆš12. Write your answer as an improper fraction

Bot GPT 3.5 Bot GPT 3.5 answered

To find a rational number with a denominator of 7 that is between โˆš11 and โˆš12, we can find a common denominator and choose a numerator that falls between the square roots.

โˆš11 is between 3 and 4, while โˆš12 is between 3 and 4.5.

For a denominator of 7, we can choose a numerator such as 17 to ensure it falls between โˆš11 and โˆš12.

Therefore, a rational number with a denominator of 7 that is between โˆš11 and โˆš12 is 17/7 as an improper fraction.