Asked by Justin

Which statement is true about the relationships between the number sets?
(1 point)
O All rational numbers are also integers.
• Not all natural numbers are reall numbers.
O Whole numbers include all natural numbers and 0.
• Some irrational numbers are also integers.
Answered by Justin
Which of the following is true about - 9?
(1 point)
Ot is an integer but not a rational number.
itteg whole number but not an
O t is an integer but not a whole
number.
It is both an integer and a whole
number.
Answered by Justin
A sign in a gas station advertises gas at the rate of $3.39% per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal? (1 point)
• 3.399
• .339910
• 3.0339
• 0.3399
Answered by Justin
Which set of numbers is always rational?
(1 point)
• positive numbers
• decimals
• negative numbers
• integers
Answered by Justin
The height of an equilateral triangle
V3
equals
times the side length. Using
I for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters? m
Answered by Justin
The diagonal of a square equals V2 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)
ft.
Answered by GPT-4o mini
The true statement about the relationships between the number sets is:

**Whole numbers include all natural numbers and 0.**

Here's a brief explanation of the other statements:

- **All rational numbers are also integers.** (False: Rational numbers include fractions, while integers are whole numbers without fractional parts.)
- **Not all natural numbers are real numbers.** (False: All natural numbers are indeed real numbers.)
- **Some irrational numbers are also integers.** (False: By definition, irrational numbers cannot be expressed as a fraction of two integers, so none can be integers.)

Thus, the correct option is about whole numbers.
Answered by GPT-4o mini
The correct statement about \(-9\) is:

**It is an integer but not a whole number.**

Here's why:

- **-9 is an integer**: Integers include all positive whole numbers, zero, and all negative whole numbers.
- **-9 is not a whole number**: Whole numbers include all non-negative integers (0 and positive integers) but do not include negative numbers.

Therefore, the statement that correctly describes \(-9\) is that it is an integer but not a whole number.
Answered by GPT-4o mini
The price of gas is advertised as $3.39 per gallon.

To express this strictly as a decimal, it should be written as:

**3.39**

However, looking at the provided options, it appears they are specifically attempting to show formats that may not exactly represent what we understand as a clear dollar amount.

The closest option, maintaining the correct format for the price as a decimal is:

**3.399**

This option reflects three decimal places, which might imply a context where prices could be extended beyond typical cents but still indicates the price of $3.39 per gallon.

Therefore, the correct choice from the options is **3.399**.
Answered by GPT-4o mini
The set of numbers that is always rational is:

**integers**

### Explanation:
- **Positive numbers**: This set includes both rational (like 1, 2, 3) and irrational numbers (like √2, π).
- **Decimals**: This set can include terminating decimals (which are rational) and non-terminating decimals (which can be irrational).
- **Negative numbers**: This set includes both rational (like -1, -2) and irrational numbers (like -√2).
- **Integers**: This set includes whole numbers such as -2, -1, 0, 1, 2, etc., which are always rational because they can be expressed as the ratio of the number to 1 (e.g., -2 can be written as -2/1).

Thus, the correct answer is **integers**.
Answered by GPT-4o mini
The height \( h \) of an equilateral triangle can be calculated using the formula:

\[
h = \frac{\sqrt{3}}{2} \times \text{side length}
\]

Given that the side length is \( 8 \) meters, we can substitute this value into the formula:

\[
h = \frac{\sqrt{3}}{2} \times 8
\]

Now, if we approximate \( \sqrt{3} \) as \( 1.732 \):

\[
h \approx \frac{1.732}{2} \times 8
\]

Calculating this step-by-step:

1. Calculate \( \frac{1.732}{2} \):

\[
\frac{1.732}{2} \approx 0.866
\]

2. Now multiply by \( 8 \):

\[
h \approx 0.866 \times 8 \approx 6.928
\]

Therefore, the approximate height of the equilateral triangle with a side length of \( 8 \) meters is:

**6.93 meters** (if rounded to two decimal places).
Answered by GPT-4o mini
To find the diagonal \( d \) of a square given its side length \( s \), we use the formula:

\[
d = \sqrt{2} \times s
\]

Given that the side length \( s \) of the square park is \( 700 \) feet and using \( 1.4 \) for \( \sqrt{2} \), we substitute the values into the formula:

\[
d = 1.4 \times 700
\]

Now, calculate the product:

\[
d = 1.4 \times 700 = 980
\]

Thus, the approximate length in feet from one corner to the opposite corner of the square park is:

**980 feet.**