Explanation

Let's analyze the given relationships:

• P is the brother of Q and R.
• S is the mother of R.
• T is the father of P.

From this, we can deduce:

• T is also the father of Q (since P and Q are siblings).
• P is also the son of S (since S is R's mother and P and R are siblings).
• S is also the mother of P (as explained above).

Therefore, all the statements except (D) Q is T's son are true.

Explanation

We are given four words:

1. Apparent
2. Apostate
3. Appoint
4. Apparel

Let's arrange them in the order they appear in a dictionary:

• First, compare the first letter of each word (all start with "A").
• Next, compare the second letters:
  • "p" (for "Apparent", "Appoint", "Apparel", "Apostate")
  • Then, compare the third letter:
    • "p" (Apparent, Appoint, Apparel)
    • "o" (Apostate)
  • "Apparel" comes after "Appoint" and before "Apparent"
  • "Appoint" comes after "Apparent"

So, the correct order is:

1. Apparent
2. Apparel
3. Appoint
4. Apostate

Explanation

There are:

• 8 red toys
• 6 green toys
• 7 blue toys

The total number of toys is:

$$8+6+7=21\text{toys}$$

We are asked to find the probability that the toy picked is neither red nor green, which means it must be blue.

The number of blue toys is 7, so the probability is:

17​/21=1/3​

Explanation

We are given:

• 27 bicycles passed the lights test.
• 21 bicycles passed the brakes test.
• 1 bicycle failed both tests.
• There are 30 bicycles in total.

Let:

• $L$ be the set of bicycles that passed the lights test.
• $B$ be the set of bicycles that passed the brakes test.

We need to find how many bicycles passed both tests, which is the intersection of sets $L$a nd $B$, or $L cap B$.

The formula for the union of two sets is:

$$|L\cup B|=|L|+|B|-|L\cap B|$$

We know:

• $|L cup B| = 30 - 1 = 29$ (since 1 bicycle failed both tests).
• $|L|=27$
• $|B| = 21$

Substitute the values into the formula:

$$29 = 27 + 21 - |L cap B|$$ $$29 = 48 - |L cap B|$$ $$|L cap B| = 48 - 29 = 19$$

Explanation

we use the formula:

$$\text{Total Surface Area}=2\pi r(h+r)$$

Where:

• $r$ is the radius of the cylinder.
• $\mathrm{<span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><font\; color="\#0000ff">h\; is\; the\; height\; of\; the\; cylinder.</font></span>}$

• Radius $r = 3.5 , text{cm}$
• Height $h = 5.5 , text{cm}$

1. Plug values into the formula:
   $$\text{Total Surface Area}=2\pi \times 3.5\times (5.5+3.5)$$ $$= 2pi times 3.5 times 9$$=2×3.1416×3.5×9
   =2×3.1416×31.5
   =6.2832×31.5
   ≈198.0cm2

Explanation

To find the perimeter of a semi-circle, we need to consider two parts:

1. The half of the circumference of the circle, which is $frac{1}{2} times 2pi r = pi r$.
2. The diameter of the circle, which is $2r$.

• The radius $r = 700$ meters.

1. Calculate the curved part (half of the circumference):

   $$text{Curved part} = pi times r = pi times 700 approx 3.1416 times 700 approx 2199.12 , text{m}$$

2. Add the diameter:

   $$text{Diameter} = 2 times r = 2 times 700 = 1400 , text{m}$$

3. Total perimeter:

   $$text{Perimeter} = text{Curved part} + text{Diameter} = 2199.12 , text{m} + 1400 , text{m} = 3599.12 , text{m}$$

4. Convert the result to kilometers:

   $$3599.12 , text{m} = 3.6 , text{km}$$

Explanation

Let the number of sweets Roni gives to Tony be x.

After giving x sweets: Roni will have 2 25−x sweets.

Tony will have 55+x sweets.

We want Tony to have four times as many sweets as Roni, so: 55 + x = 4 ( 25 − x )

1. Expand the equation:

   $$55 + x = 100 - 4x$$
   

2. Add $4x$ to both sides to combine the $x$-terms:

   $$55 + 5x = 100$$
   

3. Subtract 5 from both sides:

   $$\mathrm{<font\; color="\#0000ff">5</font>}\mathrm{<font\; color="\#0000ff">x</font>}<font\; color="\#0000ff">=</font>\mathrm{<font\; color="\#0000ff">45</font>}$$5x = 45
   

4. Solve for $x$:

   $$$$x=45/5=9x 
   

Explanation

The temperature in Murree at noon was 16.6°C, and at midnight, it was 20.4°C lower.

To find the temperature at midnight, subtract 20.4°C from the noon temperature:

$$16.6°C - 20.4°C = -3.8°C$$

Explanation

We know that:

1. x + y = 45
2. 4x = 5y - 9

From the first equation, we can express y in terms of x:

y = 45 - x

Substitute this into the second equation:

4x = 5(45 - x) - 9

Expand and simplify:

4x = 225 - 5x - 9

9x = 216

x = 24

Now, substitute x = 24 into the first equation:

24 + y = 45

y = 21

Therefore, the two parts are 24 and 21.

Explanation

• The son's current age be $x$
  
• The man's current age is 5 times the son's age, so the man's age is $5x$.

• Four years ago, the product of their age was 52.

Four years ago:

• The son's age was $x - 4$.
• The man's age was $5x-4$.

According to the problem, the product of their ages 4 years ago is 52:

$$(x-4)(5x-4)=52$$

1. Expand the left side: