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

Question

A)Whole numbers include all natural numbers and 0.
B)not all natural numbers are real numbers.
C)some irrational numbers are also integers.
D)All rational numbers are also integers

Answer 1

Let's analyze each statement one by one:

A) Whole numbers include all natural numbers and 0.

• This statement is true. Whole numbers are defined as all natural numbers (1, 2, 3, ...) plus 0.

B) Not all natural numbers are real numbers.

• This statement is false. All natural numbers are real numbers, as real numbers include all rational and irrational numbers.

C) Some irrational numbers are also integers.

• This statement is false. By definition, integers are whole numbers that can be positive, negative, or zero, while irrational numbers cannot be expressed as a fraction and are not whole numbers.

D) All rational numbers are also integers.

• This statement is false. Rational numbers include all integers, but they also include fractions and decimals that can be expressed as a ratio of integers.

Based on this analysis, the true statement is A: Whole numbers include all natural numbers and 0.

Answer 2

Which of the following is true about -9?
A)it is an integer but not a whole number.
B)it is an integer but not a rational number.
C)it is both and integer and a whole number
D)its a whole number but not an integer

Answer 3

Let's analyze each statement regarding -9:

A) It is an integer but not a whole number.

• This statement is true. -9 is an integer, but whole numbers are defined as non-negative integers (0, 1, 2, ...). Therefore, -9 is not a whole number.

B) It is an integer but not a rational number.

• This statement is false. -9 is an integer, and all integers are also rational numbers (because they can be expressed as a fraction, e.g., -9/1).

C) It is both an integer and a whole number.

• This statement is false. While -9 is an integer, it is not a whole number.

D) It is a whole number but not an integer.

• This statement is false. -9 is an integer, but it is not a whole number.

The correct statement is A: it is an integer but not a whole number.

Answer 4

A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cast, writing the price strictly as a decimal?
A)3.399
B).339910
C)3.0339
D)0.3399

Answer 5

The price advertised is $3.39 9/10 per gallon, which means it is $3.39 plus 9/10 of a cent. To convert this to a decimal:

1. The whole number part is $3.39.
2. The fractional part, 9/10 cent, is equal to 0.009 (since 9/10 of a cent is 0.009 dollars).

Now, add them together:

\[ 3.39 + 0.009 = 3.399 \]

Therefore, the price strictly as a decimal is $3.399.

The answer is A) 3.399.

Answer 6

which set of numbers is always rational?
A)negative number.
B)positive numbers.
C) decimals
D) integer

Answer 7

To determine which set of numbers is always rational, let's analyze each option:

A) Negative numbers.

• This set includes numbers like -1, -2, -0.5, etc. While some negative numbers are rational (like -1 and -0.5), not all negative numbers are rational (irrational numbers like -√2 are also negative).

B) Positive numbers.

• This set includes numbers like 1, 2, 0.5, etc. Similar to negative numbers, while some positive numbers are rational (like 1 and 0.5), not all positive numbers are rational (irrational numbers like √2 are also positive).

C) Decimals.

• This set includes both terminating decimals (like 0.5) and non-terminating, repeating decimals (like 0.333...), which are rational numbers. However, it also includes non-terminating, non-repeating decimals (like π or e), which are irrational. Thus, this set is not always rational.

D) Integers.

• This set includes whole numbers such as -3, -2, -1, 0, 1, 2, 3, etc. All integers can be expressed as a fraction (e.g., 1 can be written as 1/1, -3 as -3/1), making all integers rational.

Based on this analysis, the correct answer is D) integer. Integers are always rational numbers.

Answer 8

The height of an equilateral triangle equals square root of 3/2 times the side length. Using 7/4 for the square root of 3 what Is the approximate height in meters of an equilateral triangle with the side length of 8 meters?
____m

Answer 9

To find the height \( h \) of the equilateral triangle, you can use the formula:

\[ h = \left(\frac{\sqrt{3}}{2}\right) \times \text{side length} \]

Given the side length is 8 meters, we can substitute this into the formula. We're also given that \( \sqrt{3} \) is approximately \( \frac{7}{4} \).

Substituting the values into the formula gives:

\[ h = \left(\frac{7/4}{2}\right) \times 8 \]

First, simplify \( \frac{7/4}{2} \):

\[ \frac{7/4}{2} = \frac{7/4}{2/1} = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \]

Now, multiply \( \frac{7}{8} \) by 8 meters:

\[ h = \frac{7}{8} \times 8 = 7 \]

Thus, the approximate height of the equilateral triangle is 7 meters.

Answer 10

The diagonal of a square equals square root of 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?
_____ft.

Answer 11

To find the diagonal \( d \) of the square, you can use the formula:

\[ d = \sqrt{2} \times \text{side length} \]

Given that the side length of the square park is 700 feet, we can substitute this into the formula. We are also given that \( \sqrt{2} \) is approximately 1.4.

Substituting the values gives:

\[ d = 1.4 \times 700 \]

Now, performing the multiplication:

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

Therefore, the approximate length from one corner to the opposite corner of the square park is 980 feet.