Explanation

Explanation

Explanation

The degree of a vertex in a graph is the count of edges connected to it.

It represents the number of direct connections the vertex has.

Explanation

Explanation

When a pair of dice are tossed, there are 36 possible outcomes.

The combinations that result in a total of 7 or 11 are:

Total 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes

Total 11: (5,6), (6,5) = 2 outcomes

Total favorable outcomes = 6 + 2 = 8

Probability = (Number of favorable outcomes) / (Total possible outcomes)

Probability = 8/36 = 2/9

Explanation

Only a few of the sounds produced by insects can be heard by humans.

کیڑوں سے پیدا ہونے والی صرف چند آوازیں انسانوں کے ذریعہ سنی جاسکتی ہیں۔

"Only" correctly emphasizes the limited number of sounds.

Explanation

To find ∫ln(x)dx, we use integration by parts:

Let u = ln(x) and dv = dx

Then du = 1/x dx and v = x

∫ln(x)dx = uv - ∫v du

= x_ln(x) - ∫x * 1/x dx

= x_ln(x) - ∫1 dx

= x*ln(x) - x + C

The answer is xlnx – x + c.

Explanation

Lagrange's Mean Value Theorem is a special case of Cauchy's Mean Value Theorem when one function is f(x) and the other is g(x) = x.

Cauchy’s theorem is more general and applies to two functions.

Explanation

Explanation