If 0.139 + 0.75 + 2.105 − (1.001) × 1.1 = 2 − k, then the value of k is

The correct answer is 0.1071 (which corresponds to Option 3).

To find the value of $$_k, we set up the given equation:

$0.139\; +\; 0.75\; +\; 2.105\; -\; (1.001)\; \times \; 1.1\; =\; 2\; -\; k$

Step 1: Simplify the left-hand side of the equation using the order of operations (BODMAS/PEMDAS).

First, perform the multiplication:

$1.001\; \times \; 1.1\; =\; 1.1011$

Next, perform the addition of the terms on the left:

$0.139\; +\; 0.75\; +\; 2.105\; =\; 2.994$

Now, subtract the result of the multiplication from the sum:

$2.994\; -\; 1.1011\; =\; 1.8929$

Step 2: Solve for $$_k.

Substitute the simplified left-hand side back into the equation:

$1.8929\; =\; 2\; -\; k$

Rearrange the equation to isolate $$_k:

$k\; =\; 2\; -\; 1.8929$

Perform the subtraction:

$k\; =\; 0.1071$

Thus, the value of $$_k is 0.1071.