Explanation

Explanation

Work done by 12 children in 16 days = 1 (full work)

Work done by 1 child in 16 days = 1/12

Work done by 1 child in 1 day = 1/(12 × 16) = 1/192

Work done by 8 adults in 12 days = 1

Work done by 1 adult in 12 days = 1/8

Work done by 1 adult in 1 day = 1/(8 × 12) = 1/96

Work done by 16 adults in 3 days = 16 × 3 × (1/96) = 1/2

Remaining work = 1 - 1/2 = 1/2

Now, 6 adults and 4 children work together:

Work done by 6 adults in 1 day = 6 × 1/96 = 6/96 = 1/16

Work done by 4 children in 1 day = 4 × 1/192 = 4/192 = 1/48

Total work done per day = (1/16 + 1/48) = (3 + 1)/48 = 4/48 = 1/12

Days required = (1/2) ÷ (1/12) = 6 days

Explanation

Given numbers: 8, 13, 25, 43, 11

Step 1: Add the numbers  

8 + 13 + 25 + 43 + 11 = 100

Step 2: Divide by the number of values  

100 ÷ 5 = 20

Explanation

20 men can construct a building in 40 days.

Total work = 20 men × 40 days = 800 man-days.

Time = Total work / Number of men = 800 man-days / 10 men = 80 days.

Explanation

We are told:

• Circumference of a circle = a

• Area of the circle = b

• And a = b

We know the formulas:

• Circumference:

  $$a = 2pi r$$
  

• Area:

  $$b=\pi r^2$$r=0orr=

Since $a = b$, set the formulas equal:

$$2pi r = pi r^2$$

Divide both sides by $pi$:

$$2r = r^2$$

Rearrange:

$$r^2 - 2r = 0 Rightarrow r(r - 2) = 0$$

So the solutions are:

r=0 or r=2

Explanation

We are given:

$$$$h3=64

To find the value of h, take the cube root of both sides:

$$$$h=3^√64 =4

So the value of h is 4.

But the question asks for the value of n, not h.

Since n is never defined, we cannot determine n from the given equation.

Answer: (D) None of these (assuming it's not a typo and the question asked for "n").

If the question meant "the value of h", then the answer would be (B) 4.

Explanation

The probability that someone is between Aviva and Naomi

• Aviva is the 37th person.

• Naomi is the 67th person.

• "Between" refers to people aged 37 to 67, i.e., positions 38 through 66.

Number of people between them = 66 − 38 + 1 = 29 people

There are 100 people total.

So the probability that a randomly chosen person is between them is:

$$\frac{\mathrm{<font\; color="\#0000ff"><span\; style="background-color:\; rgb(255,\; 255,\; 0);">29</span></font>}}{\mathrm{<span\; style="font-size:\; 0.875rem;"><font\; color="\#0000ff"\; style="background-color:\; rgb(255,\; 255,\; 0);">100</font><span\; style="font-family:\; Overpass,\; sans-serif;"></span></span>}}$$

Explanation

We solve: x^2=32

√x^2=+_√32 

x= +_√32

Simplify the square root

x = +_ √16.5

x = +_ √16.√2

x = +_  4√2

Answer: (D) None of these

Explanation

Part=3/8/1/12​​

=3​/8×12/1​

=36/8​

=9/2​

Explanation

 Let's analyze the problem:

• Total marbles in the jar: 5 (red, white, blue, yellow, and 1 more color)

• 4 marbles are removed.

• Find the probability that the yellow marble was removed.

Step 1: Total ways to remove 4 marbles from 5

Step 2: Number of ways to remove 4 marbles, including yellow

To include the yellow marble, we must select the yellow marble and 3 others from the remaining 4 marbles:

Step 3: Probability yellow marble is removed