Which statement is true about the relationships between the number sets?(1 point)%0D%0AResponses%0D%0A%0D%0AAll rational numbers are also integers.%0D%0AAll rational numbers are also integers.%0D%0A%0D%0AWhole numbers include all natural numbers and 0.%0D%0AWhole numbers include all natural numbers and 0.%0D%0A%0D%0ANot all natural numbers are real numbers.%0D%0ANot all natural numbers are real numbers.%0D%0A%0D%0ASome irrational numbers are also integers.%0D%0ASome irrational numbers are also integers.

Question

2. Which of the following is true about −9%0D%0A−%0D%0A9%0D%0A?(1 point)%0D%0AResponses%0D%0A%0D%0AIt is both an integer and a whole number.%0D%0AIt is both an integer and a whole number.%0D%0A%0D%0AIt is an integer but not a rational number.%0D%0AIt is an integer but not a rational number.%0D%0A%0D%0AIt is a whole number but not an integer.%0D%0AIt is a whole number but not an integer.%0D%0A%0D%0AIt is an integer but not a whole number.

3. A sign in a gas station advertises gas at the rate of $3.39910%0D%0A$%0D%0A3.39%0D%0A9%0D%0A10%0D%0A per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal? (1 point)%0D%0AResponses%0D%0A%0D%0A3.399%0D%0A3.399%0D%0A%0D%0A.339910%0D%0A.339910%0D%0A%0D%0A3.0339%0D%0A3.0339%0D%0A%0D%0A0.3399

4. Which set of numbers is always rational?(1 point)%0D%0AResponses%0D%0A%0D%0Apositive numbers%0D%0Apositive numbers%0D%0A%0D%0Aintegers%0D%0Aintegers%0D%0A%0D%0Anegative numbers%0D%0Anegative numbers%0D%0A%0D%0Adecimals

5. The height of an equilateral triangle equals 3√2%0D%0A3%0D%0A2%0D%0A times the side length. Using 74%0D%0A7%0D%0A4%0D%0A for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)

6. The diagonal of a square equals 2–√%0D%0A2%0D%0A 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)%0D%0A$$ ft.

7. Using a number line, what whole number and rational number to the nearest half is 40−−√%0D%0A40%0D%0A between?(1 point)%0D%0A40−−√%0D%0A40%0D%0A is between and .

8. Using a number line, what whole number and rational number to the nearest half is 58−−√%0D%0A58%0D%0A between?(1 point)%0D%0AResponses%0D%0A%0D%0Abetween 8.5 and 9%0D%0Abetween 8.5 and 9%0D%0A%0D%0Abetween 8 and 8.5%0D%0Abetween 8 and 8.5%0D%0A%0D%0Abetween 7 and 7.5%0D%0Abetween 7 and 7.5%0D%0A%0D%0Abetween 7.5 and 8

9. Using rational approximations, what is an inequality statement comparing 81−−√%0D%0A81%0D%0A and 8–√8%0D%0A8%0D%0A8%0D%0A? Enter <, >, or =.(1 point)%0D%0AThe inequality is: 81−−√%0D%0A81%0D%0A 8–√8%0D%0A8%0D%0A8%0D%0A.

11. Express 811%0D%0A8%0D%0A11%0D%0A as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)

12. Convert 0.72¯¯¯¯¯%0D%0A0.%0D%0A72%0D%0A¯%0D%0A to a rational number in simplest form.(1 point)

13. Which of the following is a rational number between 5 and 514%0D%0A5%0D%0A1%0D%0A4%0D%0A ?(1 point)%0D%0AResponses%0D%0A%0D%0A525%0D%0A5%0D%0A2%0D%0A5%0D%0A5 Start Fraction 2 over 5 end fraction%0D%0A%0D%0A26−−√%0D%0A26%0D%0Astart root 26 end root%0D%0A%0D%0A517%0D%0A5%0D%0A1%0D%0A7%0D%0A5 Start Fraction 1 over 7 end fraction%0D%0A%0D%0A513

14. What is a rational number with a denominator of 7 that is between 7–√%0D%0A7%0D%0A and 8–√%0D%0A8%0D%0A. Write your answer as an improper fraction.(1 point)

Answer 1

Here are the answers to the provided questions based on the descriptions:

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

   • Response: Whole numbers include all natural numbers and 0.

2. Which of the following is true about −9?

   • Response: It is an integer but not a whole number.

3. How many dollars does a gallon cost, writing the price strictly as a decimal?

   • Response: 3.399

4. Which set of numbers is always rational?

   • Response: Integers

5. What is the approximate height in meters of an equilateral triangle with a side length of 8 meters? (Using \( \sqrt{3} \approx 1.732 \))

   • Height: \( \text{Height} = \frac{\sqrt{3}}{2} \cdot \text{side length} = \frac{1.732}{2} \cdot 8 \approx 6.928 , \text{meters} \)

6. 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? (Using \( \sqrt{2} \approx 1.4 \))

   • Diagonal: \( \text{Diagonal} = \sqrt{2} \cdot \text{side length} \approx 1.4 \times 700 = 980 , \text{feet} \)

7. Using a number line, what whole number and rational number to the nearest half is \( \sqrt{40} \) between?

   • Response: \( \sqrt{40} \) is between 6.3 and 6.4, so it is approximately between 6.3 and 6.4.

8. Using a number line, what whole number and rational number to the nearest half is \( \sqrt{58} \) between?

   • Response: Between 7.5 and 8.

9. Using rational approximations, what is an inequality statement comparing \( \sqrt{81} \) and \( \sqrt{8} \)?

   • The inequality is: \( \sqrt{81} > \sqrt{8} \).

10. Express \( \frac{811}{8} \) as a repeating decimal.

• Answer: \( 101.375 \)

12. Convert \( 0.72\overline{72} \) to a rational number in simplest form.

• Answer: \( \frac{8}{11} \)

13. Which of the following is a rational number between \( 5 \) and \( 5\frac{1}{4} \)?

• Response: \( \frac{26}{5} \)

14. What is a rational number with a denominator of 7 that is between \( \sqrt{7} \) and \( \sqrt{8} \)?

• Response: \( \frac{16}{7} \) (since it is approximately 2.285, which is indeed between approximately \( 2.645 \) and \( 2.828 \)).

If you need help with any specific calculations or further clarification, feel free to ask!

Answer 2

what is it for 5 6 7 13 and 14? say the answer as a number or word it out like all of it like for example 37. thirty seven

Answer 3

Sure! Here are the answers to questions 5, 6, 7, 13, and 14 with the answers clearly stated:

5. The approximate height in meters of an equilateral triangle with a side length of 8 meters is:

   • Answer: 6.93 meters. Six point nine three meters.

6. The approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side is:

   • Answer: 980 feet. Nine hundred eighty feet.

7. Using a number line, \( \sqrt{40} \) is between:

   • Answer: 6.3 and 6.4. Six point three and six point four.

8. A rational number between 5 and \( 5\frac{1}{4} \) is:

• Answer: \( 5\frac{2}{5} \). Five and two fifths.

14. A rational number with a denominator of 7 that is between \( \sqrt{7} \) and \( \sqrt{8} \) is:

• Answer: \( \frac{16}{7} \). Sixteen sevenths.

If you have any more questions or need further assistance, feel free to ask!