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4 years ago

what is the algebraic expression for the following word phrase: the quotient of 8 and the difference of x and y?

Mathematics

1 answer:

Kruka [31]4 years ago

5 0

Answer:

8 / (x-y)

Step-by-step explanation:

The key words in this problem are quotient and difference of.

Quotient means division. Difference of means subtraction.

The quotient of 8 AND the diff. of (x and y).

8 / the quantity of x minus y.

YOU GOT IT! YAY!!!

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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

Alex Ar [27]

Answer:

$y=-2.86 x +228.84$

Step-by-step explanation:

We assume that the data is this one:

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

y: 152, 53, 22, 35, 38, 166, 13, 185, 25

Find the least-squares line appropriate for this data.

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:

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

$\sum_{i=1}^n y_i =152 + 53 + 22 + 35 + 38 + 166 + 13 + 185 + 25=689$

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

$\sum_{i=1}^n y^2_i =152^2 + 53^2 + 22^2 + 35^2 + 38^2 + 166^2 + 13^2 + 185^2 + 25^2=91641$

$\sum_{i=1}^n x_i y_i =50*152+ 55*53+ 50*22+ 79*35+ 44*38+ 37*166 +70*13+ 45*185+ 49*25=32654$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.56$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=32654-\frac{479*689}{9}=-4016.11$

And the slope would be:

$m=-\frac{4016.11}{1403.56}=-2.86$

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

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.22$

$\bar y= \frac{\sum y_i}{n}=\frac{689}{9}=76.56$

And we can find the intercept using this:

$b=\bar y -m \bar x=76.56-(-2.86*53.22)=228.84$

So the line would be given by:

$y=-2.86 x +228.84$

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4 years ago