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marusya05 [52]
2 years ago
7

I need help on this problem. I don’t understand it at all. Please help me.

Mathematics
1 answer:
Inessa [10]2 years ago
5 0

When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.

Similarly, we will factor the polynomials first:

x^4+3x^3 = x^3(x+3)

x^2-9 = (x+3)(x-3)

x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2

The following factors emerged:

  • x,\ x^3 We will choose x^3 because it has the higher exponent
  • x-3
  • x+3,\ (x+3)^2 We will choose (x+3)^2 because it has the higher exponent.

So, the LCM is

x^3(x-3)(x+3)^2

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PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!<br><br><br><br> :(
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Montano1993 [528]
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3 years ago
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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2 years ago
In how many ways can 3 cards from a deck of 52 cards can be laid in a row face up?
tresset_1 [31]
Ok slot method
3 slots
1st slot has 52 options
2nd slot has 51 optoins (1 went to first slot)
3rd slot has 50 options (1 went to previous slot)

number of ways=52*51*50=132600 ways
4 0
3 years ago
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