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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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31.5 square feet of counter top

Step-by-step explanation:

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The following figures are not drawn to scale but AB and CD are straight lines.<br> Find x.
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Answer:

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Step-by-step explanation:

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Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit
Phantasy [73]

Answer:

y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

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