To answer this question, let's analyze the given equation and the relationship between the variables:

Given: A/B = C and C > D

We are asked to determine which of the following statements is true.

Option A) A is always greater than D: This statement is not necessarily true. Since A and B are not explicitly defined, we cannot conclude any specific relationship between A and D. The given equation A/B = C does not provide enough information to make this statement always true.

Option B) C is always greater than D: This statement is true. Since C is greater than D, any value of A/B that equals C will also be greater than D. This is because if A/B = C and C > D, then multiplying both sides of the equation by B gives us A = BC. Since C > D, A will always be greater than D.

Option C) B is always less than D: This statement is not necessarily true. Similar to Option A, we don't have enough information about the relationship between B and D. Therefore, we cannot conclude that B is always less than D.

Option D) None of the above: This option is incorrect, as we have concluded that Option B is true.

Therefore, the correct answer is Option B) C is always greater than D.

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To determine whether a number is divisible by 3, we need to check if the sum of its digits is divisible by 3.

Let's go through each option to see if it is divisible by 3:

Option A) (ii) only - The number 5967013 has digits 5, 9, 6, 7, 0, 1, and 3. The sum of these digits is 5+9+6+7+0+1+3 = 31. Since 31 is not divisible by 3, option A is incorrect.

Option B) (i) only - The number 541326 has digits 5, 4, 1, 3, 2, and 6. The sum of these digits is 5+4+1+3+2+6 = 21. Since 21 is divisible by 3 (21/3 = 7), option B is correct.

Option C) both (i) and (ii) - Since we have already determined that option A is incorrect, option C is also incorrect.

Option D) None - Since option B is correct, option D is incorrect.

Therefore, the correct answer is B.

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To find the value of the given expression, let's simplify it step by step:

(21/4 - 1)(23/4 + 21/2 + 21/4 + 1)

First, let's simplify the expression inside the brackets:

23/4 + 21/2 + 21/4 + 1

To add fractions, we need to have a common denominator. In this case, the common denominator is 4.

23/4 + 21/2 + 21/4 + 1 = 23/4 + (2*21)/4 + 21/4 + 4/4

= (23 + 42 + 21 + 4)/4

= 90/4

= 45/2

Now, let's substitute this value back into the original expression:

(21/4 - 1)(45/2)

= (21/4 - 4/4)(45/2)

= (17/4)(45/2)

To multiply fractions, multiply the numerators together and multiply the denominators together:

= (17 * 45)/(4 * 2)

= 765/8

Therefore, the value of the expression is 765/8.

However, none of the given options match this value. So, the correct answer should be "None".

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To answer this question, we can calculate the time taken for each part of the journey separately and then add them together.

Let's calculate the time taken for the first part of the journey, which is two-thirds of the total distance of 15 miles. The speed for this part is given as 40 mph.

Distance for the first part = 2/3 * 15 miles = 10 miles Speed for the first part = 40 mph

To calculate the time taken for the first part, we can use the formula:

Time = Distance / Speed

Time taken for the first part = 10 miles / 40 mph = 0.25 hours

Next, let's calculate the time taken for the second part of the journey, which is the remaining one-third of the total distance. The speed for this part is given as 60 mph.

Distance for the second part = 1/3 * 15 miles = 5 miles Speed for the second part = 60 mph

Time taken for the second part = 5 miles / 60 mph = 0.083 hours

Finally, we can add the times taken for both parts of the journey to get the total time taken:

Total time taken = Time taken for the first part + Time taken for the second part = 0.25 hours + 0.083 hours = 0.333 hours

To convert this time to minutes, we multiply by 60:

Total time taken = 0.333 hours * 60 mins/hour = 20 mins

Therefore, the correct answer is D) 20 mins.

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To solve this question, let's consider the different types of small cubes that can be formed when the big cube is cut.

The big cube is made up of 6 x 6 x 6 = 216 small cubes.

1. The corner small cubes: There are 8 corner small cubes in the big cube. Each corner small cube has 3 faces painted.
2. The edge small cubes: There are 12 edges in the big cube, with each edge consisting of 6 small cubes. So, there are a total of 12 x 6 = 72 edge small cubes. Each edge small cube has 2 faces painted.
3. The face small cubes: The big cube has 6 faces, each consisting of 6 x 6 = 36 small cubes. So, there are a total of 6 x 36 = 216 face small cubes. Each face small cube has 1 face painted.

Now, let's calculate the number of small cubes that are painted on at least 2 sides:

1. Corner small cubes: 8 x 3 = 24 cubes (since each corner small cube has 3 faces painted).
2. Edge small cubes: 72 x 2 = 144 cubes (since each edge small cube has 2 faces painted).
3. Face small cubes: 216 x 1 = 216 cubes (since each face small cube has 1 face painted).

So, the total number of small cubes painted on at least 2 sides is 24 + 144 + 216 = 384.

Therefore, the correct answer is A) 56.

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To answer this question, let's go through each option to understand why it is correct or incorrect:

Option A) 1,2,3,4 - This option is incorrect because it includes options 1 and 2, which are contradictory. Option 1 states that you can see all pages of your document, while option 2 states that you can only see the page you are currently working on. These two options cannot both be true at the same time.

Option B) 1,3,4 only - This option is incorrect because it includes option 1, which is contradictory. Option 1 states that you can see all pages of your document, while option 2 states that you can only see the page you are currently working on. These two options cannot both be true at the same time.

Option C) Only 4 - This option is correct. In page preview mode, you can only see pages that do not contain graphics. This means that you cannot see pages with graphics in page preview mode.

Option D) None of the above - This option is incorrect because option C (Only 4) is the correct answer.

The correct answer is C) Only 4. This option is correct because in page preview mode, you can only see pages that do not contain graphics.

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