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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.

11 answers

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.

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.

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.

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

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.

Which set of numbers is always rational?
(1 point)
• positive numbers
• decimals
• negative numbers
• integers

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.

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

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 \( \frac{1.732}{2} \):

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

  1. 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).

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.

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.