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natali 33 [55]
3 years ago
8

what is the smallest number of integer kilogram weights needed to weigh every whole kilogram between 1kg and 40kg?​

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
6 0

9514 1404 393

Answer:

  4

Step-by-step explanation:

We assume you are using a balance, and that weights can be put in either pan. In that case, weight values can be either added or subtracted, so there are 3 possibilities for the contribution each weight makes. In other words, we need to find how many digits are required to count to 40 in base 3.

The largest 3-digit number in base 3 is ...

  3^2 +3^1 + 3^0 = 13 (base 10)

The largest 4-digit number adds 3^3 = 27 to this: 27 +13 = 40.

Hence, we can weigh values 0 to 40 using 4 weights, of sizes 1, 3, 9, 27.

__

Some example weights are ...

  5 = 9 - 3 - 1

  38 = 27 + 9 + 3 - 1

where the "negative" weights are placed in the same pan as the unknown.

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Help please and simplify answer in radical form if needed
deff fn [24]

Answer:

16\sqrt{3}\:\mathrm{units^2}

Step-by-step explanation:

The area of an equilateral triangle with side length s is equal to \frac{\sqrt{3}}{4}s^2. Since the perimeter is 24 units and there are three equal sides to an equilateral triangle, each side is 24\div 3=8 units.

Substituting in this value, we get:

\frac{\sqrt{3}}{4}8^2=\frac{64\sqrt{3}}{4}=\boxed{16\sqrt{3}}

6 0
3 years ago
Last year the cost of Mr. patten’s car insurance was 86.80 per month. This year it inscreased by 5 percent. What was the cost of
marissa [1.9K]

Answer:4.34

Step-by-step explanation:

3 0
3 years ago
The rectangular prism shown has a surface area of 488 square inches. What is the length of the prism?
BigorU [14]

Answer:

length of the prism = 244 - (width x height) / width + height)

Step-by-step explanation:

Let length be a and width be b and height be c

2 (a * b) + 2 (b* c) + 2 (a * c) = 488

2ab+ 2bc + 2ac = 488

ab + bc + ac = 244

ab + ac = 244 - ac

a (b + c) = 244-ac

a = 244-bc / b + c

Therefore the length of the prism = 244 - (width x height) / width + height)

8 0
3 years ago
Please help i have 2 questions thank you very much.
Rudik [331]
Hello!

Question 1
We first have to convert everything to yards since the concrete is charged by the cubic yards

15 feet = 5 yards
15 feet = 5 yards
3 inches = 0.08333

Multiply these to find the volume

5 * 5 * 0.08333 = 2.08325

Multiply this by the cost

2.08325 * 46 = 95.83

The answer is C) $95.83
------------------------------------------------------------------------------------------------------
Question 2

You have to find the volume of the first pyramid

The equation we use is V = \frac{lwh}{3}

V is volume
l is length
w is width
h is height

Put in the values we know

V =  \frac{16 * 16 * 28}{3}

Multiply

V =  \frac{7168}{3}

Divide

V = 2389.3333

Now we use this to find the side length of the second pyramid

2389.333 =  \frac{lw * 112}{3}

Multiply both sides by 3

<span>7167.999 = lw * 112
</span>
Divide both sides by 112

63.9999 = lw

Since it is a square pyramid we know that sides are equal

63.999 = l^2

Take the square root of both sides

8 = l

The answer is B) 8in

Hope this helps!
8 0
3 years ago
PLEASE HELP I WILL MARK YOU BRAINIEST AND SHOW YOUR WORK PLEASE
iris [78.8K]

Answer:

D 30 square units

Step-by-step explanation:

count all the squares inside the triangle including the non full squares

8 0
3 years ago
Read 2 more answers
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