Determine the number of subsets of {sock, shoe, shirt, hat, glove}

(a) Suppose you have 9 gold coins that look identical, but you also know one (and only one) of them is counterfeit. The counterf

alisha [4.7K]

Answer:

Step-by-step explanation:

You can split the coins into 3 groups, each of them has 3 coins. Weigh group 1 vs group 2, if one is lighter, that group has the fake coin. If both groups weigh the same, then group 3 has the fake coin.

Continue to split the group that has the fake coin into 3 groups, each group has 1 coin. Now apply the same procedure and we can identify the fake coin.

Total of scale usage is 2

b) if you have $3^n$ coins then you can apply the same approach and find the fake coin with just n steps. By splitting up to 3 groups each step, after each step you should be able to narrow down your suspected coin by 3 times.

Step 1: you narrow down to group of $\frac{3^n}{3} = 3^{n-1}$ coins

Step 2: you narrow down to group of $\frac{3^{n-1}}{3} = 3^{n-2}$ coins

Step 3: you narrow down to group of $\frac{3^{n-2}}{3} = 3^{n-3}$ coins

...

Step n: Step 1: you narrow down to group of $3^{n-n} = 3^0 = 1$ coin

8 0

3 years ago

I need the volume for 9,11,and 13

mihalych1998 [28]

Hey there!

<h3>Question 1</h3>

Let's use 3.14 for pi during this. It'll make it a lot easier.

The volume for a cone is $\pi r^{2} \frac{h}{3}$ .

The diameter of this cone is 17.6 inches. Since the radius is half the diameter, we can find the radius by dividing this amount by 2.

17.6 ÷ 2 = 8.8

The height of this cone is 23.4 inches.

Plug the values into the equation.

$\pi 8.8^{2} \frac{23.4}{3}$

Next, square 6.8 and divide 23.4 by 3. Also, replace the pi symbol with 3.14.

$3.14 * 77.44 * 7.8$

Multiply the numbers together.

<u>The volume of this cone is approximately 1896.66 cubic inches.</u>

<h3>Question 2</h3>

Finding the volume of a trapezoidal prism can be done by finding the are of the trapezoidal face and multiplying it by the depth.

Formula for finding the area of a trapezoid is $a = \frac{1}{2} h(b_{1} +b_{2} )$

The two bases are 10 and 34, and the height is 24.7 feet. Put these values into the equation.

$a = \frac{1}{2} 24.7(10 +34 )$

Add 10 and 34, then multiply it by 24.7 and 1/2.

a = 543.4

Multiply that value by 19, which is the depth of the figure.

<u>The volume of the prism is 10324.6 cubic feet.</u>

<h3>Question 3</h3>

The formula for volume of a triangular pyramid is v = 1/3ah, with a the area of the base and h the height.

The formula for the area of an equilateral triangle, which is the base, is $a = \frac{\sqrt{3} }{4} s^{2}$

The length of the side is 12, so we can square that to get 144.

Now multiply that by $\frac{\sqrt{3} }{4}$ to get the area of the base.

The area of the base is about 62.35 square meters.

The height of the pyramid is 20 meters. Plug that and the area of the base into the equation.

v = 1/3 x 62.35 x 20

Multiply the numbers together to get the volume.

<u>The volume of the pyramid is approximately 415.67 cubic meters.</u>

Hope this helps!

3 0

3 years ago

Which of the following are examples of expenses:

BartSMP [9]

Answer:

Step-by-step explanation:

Only interest and car payments are expenses.

Student loans are a form of income which must be paid back with interest.

Paychecks are income.

Cash is a subset of Paychecks.

8 0

3 years ago

What is the equator of 40,075,000

kati45 [8]

I'm not even that high level sorry

5 0

3 years ago

What is the value of x ? Enter your answer in the box

Lelu [443]

Answer:

x=65

Step-by-step explanation:

145=2x+15

7 0

3 years ago

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