8,000 is blank as 800

Solution Procedure

Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:

... C = 2√(πA)

To find ten times this circumference, we calculate:

... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm

Derivation of Formulas

The standard formulas for circumference and area are:

... C = 2πr

... A = πr²

Multiplying the area formula by π and extracting the square root yields:

... πA = (πr)²

... √(πA) = πr

Doubling this value results in the circumference formula:

... C = 2√(πA) = 2πr

Answer: The correct choice is (C) A = {1, 2, 3, 4, 5, 7, 8}.

Step-by-step explanation: We have eight identical slips of paper, each numbered from one to eight, which have been mixed inside a bag.

The sample space, S is as follows:

S = {1, 2, 3, 4, 5, 6, 7, 8}.

Subset A consists of the complement of the event where the number 6 is drawn.

Let 'B' denote the event of drawing the number 6.

Thus, B = {6}.

Since 'A' represents the complement of 'B', it will include all elements in the sample space 'S' that are not part of set 'B'.

Therefore,

A = B' = {1, 2, 3, 4, 5, 7, 8}

So, A = {1, 2, 3, 4, 5, 7, 8}.

Consequently, (C) is the correct choice.

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

Response: 3.2

Detailed explanation:

Answer:

Option 1 is valid, which entails 2 hours of walking and 12 hours of running.

Step-by-step explanation:

The equations provided are:

3w + 6r ≥ 36

3w + 6r ≤ 90

We'll assess which options comply with these equations.

1) 2 hours walking; 12 hours running

w = 2 and r = 12

3w + 6r ≥ 36

3(2) + 6(12) ≥ 36

6+72 ≥ 36

78 ≥ 36

3w + 6r ≤ 90

3(2) + 6(12) ≤ 90

6+72 ≤ 90

78 ≤ 90

Both equations are satisfied. Option 1 is valid.

2) 4 hours walking; 3 hours running

w = 4 and r = 3

3w + 6r ≥ 36

3(4) + 6(3) ≥ 36

12+18 ≥ 36

30 ≥ 36 (this does not hold since 30 < 36)

3w + 6r ≤ 90

3(4) + 6(3) ≤ 90

12+18 ≤ 90

30 ≤ 90

Thus, Option 2 is invalid.

3) 9 hours running; 12 hours walking

w = 9 and r = 12

3w + 6r ≥ 36

3(9) + 6(12) ≥ 36

27+72 ≥ 36

99 ≥ 36

3w + 6r ≤ 90

3(9) + 6(12) ≤ 90

27+72 ≤ 90

99 ≤ 90 (this does not hold since 99 > 90)

Option 3 is invalid.

4) 12 hours walking; 10 hours running

w = 12 and r = 10

3w + 6r ≥ 36

3(12) + 6(10) ≥ 36

36+60 ≥ 36

96 ≥ 36

3w + 6r ≤ 90

3(12) + 6(10) ≤ 90

36 + 60 ≤ 90

96 ≤ 90 (this does not hold since 96 > 90)

So, Option 4 is invalid.