To find the population of a town after 3 years with a 10% annual increase:

1. Current Population: 10,000
2. Growth Rate: 10% (or 0.10)

Formula:
Future Population = Current Population × (1 + Growth Rate) ^ Number of Years

Calculation:
Future Population  = 10,000 × (1 + 0.10)^3
                              = 10,000 × (1.10)^3
                              = 10,000 × 1.331
Future Population ≈ 13,310

So, after 3 years, the population will be 13,310.

To find the value of 0.09+1.69 0.09 + 1.69

0.09+1.69=1.78

Therefore, the correct answer is (A) 1.78.

Let's addition of the binary numbers 11 and 10 .

First, let's break down the binary numbers:

- The binary number 11 is equal to 3 in decimal (base 10).

- The binary number 10 is equal to 2 in decimal (base 10).

Now, let's add them in decimal to check our work:

    3 (from 11)

+ 2 (from 10)

= 5 in decimal.

Next, we need to convert the decimal result (5) back into binary.

To convert 5 to binary:

- 5 divided by 2 is 2, remainder 1.

- 2 divided by 2 is 1, remainder 0.

- 1 divided by 2 is 0, remainder 1.

Now, we read the remainders from bottom to top: 101.

So, in binary, 3 (11) + 2 (10) equals 101.

Thus, the correct answer is: A. 101

Solution:

1. Angles Ratio: Let the angles be 1x,3x,5x.

2. Sum of Angles: In a triangle, the sum is 180∘:

   1x+3x+5x=180∘  ⟹  9x=180∘

3. Solve for x:

   x=20∘

4. Calculate Angles:

   • First angle: 1x=20∘
     
   • Second angle: 3x=60∘
     
   • Largest angle: 5x=100∘
     

So, the largest angle is 100°.

Final Answer: (D) 100°.

The sum of the roots of the quadratic equation 2x²−5x+3=0

 is calculated using the formula:

Sum of roots=−b/a​

where a=2, $b=-5$.

Substituting in those values:

Sum of roots=−5/2​

To solve this, we need to consider two parts of the person's journey:

1. The person moves from P to Q along a semi-circular path.
2. The person returns to P from Q by the shortest route, which is the diameter of the circle and is given as 4 km.

Understanding the circular path

• The shortest route between P and Q is the diameter, which means the diameter of the circle is 4 km.
• The radius rr of the circle can be found using the formula r=diameter2r = \frac{\text{diameter}}{2}​, so r=42=2r = \frac{4}{2} = 2 km.

Semi-circular path

• The distance traveled from P to Q along the semi-circular path is half the circumference of the circle.
• The formula for the circumference of a circle is 2πr2\pi r.
• For the semi-circular path, the distance is half the circumference:
• Distance from P to Q=πr=π×2=2π km

Total distance covered

• The person first covers the semi-circular path from P to Q (which is 2π2\pi km).
• Then they return along the diameter, which is 4 km.
• The total distance traveled is = 2π+4 km