How many inches are in 8 feet?

Final answer:

Given that Pam spends 80 minutes a day practicing math and dance combined, with dancing taking up 20 minutes more than math, it's mathematically impossible for her to spend 60 minutes on dance. She can only spend 50 minutes on dance and 30 minutes on math.

Explanation:

To answer your question, let's first assume that Pam spends 'x' minutes practicing math. According to the information provided, she spends 20 minutes more dancing than doing math, which means she spends 'x + 20' minutes dancing. The total time she spends practicing both activities is 80 minutes. So, 'x' (math) plus 'x + 20' (dance) equals 80.

This can be represented as the equation: x + x + 20 = 80. By solving this equation, we find that 'x' equals 30. This means that Pam spends 30 minutes practicing math and 50 minutes (30 + 20) practicing dance. Therefore, it is not possible for Pam to have spent 60 minutes practicing dance every day because she only spends 50 minutes practicing dance.

Learn more about time allocation here:

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Answer:

A and D are correct options.

Step-by-step explanation:

Circumscribing some figure means to draw one figure around another in such a way that all the sides should touch the outside figure. Like if we circumscribe a circle around a triangle, all the vertices must touch the circle.

Based on the definition, the following statements are correct answer.

A) One figure is drawn around the other.

D) Circumscribing can be done as a construction.

Many figures can be circumscribed like - a right triangle around a square, a circle around a triangle or a square etc.

Answer:

the solution to the inequality 1/2 + r/-4 ≥ 5/6 is r ≤ -4/3.

Step-by-step explanation:

To solve the inequality 1/2 + r/-4 ≥ 5/6, we need to isolate the variable r.

1. First, let's simplify the expression on the left side of the inequality:

1/2 + r/-4 can be rewritten as 1/2 - r/4.

2. Next, let's find a common denominator for 1/2 and -r/4. The common denominator is 4.

1/2 - r/4 becomes 2/4 - r/4.

3. Now, we can combine the fractions:

2/4 - r/4 = (2 - r)/4.

4. The inequality becomes:

(2 - r)/4 ≥ 5/6.

5. To eliminate the denominator, we can multiply both sides of the inequality by 4:

4 * (2 - r)/4 ≥ 4 * 5/6.

This simplifies to:

2 - r ≥ 20/6.

6. Let's further simplify the right side:

20/6 can be simplified to 10/3.

So the inequality becomes:

2 - r ≥ 10/3.

7. To isolate the variable r, we can subtract 2 from both sides of the inequality:

2 - r - 2 ≥ 10/3 - 2.

This simplifies to:

-r ≥ 4/3.

8. Finally, to solve for r, we need to multiply both sides of the inequality by -1. Since we are multiplying by a negative number, we need to reverse the direction of the inequality:

-r * (-1) ≤ (4/3) * (-1).

This simplifies to:

r ≤ -4/3.

Therefore, the solution to the inequality 1/2 + r/-4 ≥ 5/6 is r ≤ -4/3.

Answer:

3√2

Step-by-step explanation:

Pythagoras says s²+s²=6²

so

2s² = 36

s = √18 = √9·2 = √3²·2 = 3√2

Answer:

C

Step-by-step explanation:

The diagonal splits the square into 2 right triangles with hypotenuse 6

Using Pythagoras' identity in one of the right triangles.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

s² + s² = 6²

2s² = 36 ( divide both sides by 2 )

s² = 18 ( take the square root of both sides )

s = = = × = 3 → C

Answer:

The greatest possible error for the measurement 3.2 cm is 0.05 cm.

Step-by-step explanation:

We have given that,

Bruce measured a buckle as 3.2 cm using the ruler   

We have to find,

What is the greatest possible error?

Solution is given by,

The greatest possible error is defined as the error is half of the measuring unit.

Bruce measured a buckle as 3.2 cm using the ruler.

The measuring unit is nearest tenth of a cm or 0.1 cm.

The  greatest possible error is half of 0.1.

i.e.

Therefore, The greatest possible error for the measurement 3.2 cm is 0.05 cm.