Its actually f(x) = -(x

A regular polygon has sides that are perpendicular. What is the measurement of each angle?

Radda [10]

They are 90* because perpendicular sides form a right angle hope this helped have a great day!!!

5 0

3 years ago

Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the fiv

Nesterboy [21]

Answer:

a) It is probability distribution

b) mean = 2.5

c) Standard Deviation = 1.11

Step-by-step explanation:

We are given the following in the question:

x 0 1 2 3 4 5

P(x) 0.033 0.149 0.318 0.318 0.149 0.033

Probability distribution:

$\displaystyle\sum P_i(x_i) = 0.033+ 0.149 +0.318+ 0.318+ 0.149 +0.033 = 1$

Since, the summation of all the probabilities is 1 and each value of probability is between 0 and 1, the given is a probability distribution.

Mean of probability distribution:

$E(x) = \displaystyle\sumx_iP(x_i)\\E(x) = 0(0.033)+ 1(0.149)+2(0.318)+3(0.318) +4(0.149) + 5(0.033)\\E(x) = 2.5$

Thus, the mean of distribution is 2.5

Standard deviation of probability distribution:

$E(x^2) = 0^2(0.033)+ 1^2(0.149)+2^2(0.318)+3^2(0.318) +4^2(0.149) + 5^2(0.033)\\E(x^2) = 7.492\\\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 7.492 - (2.5)^2 = 1.242\\\sigma= \sqrt{1.242} = 1.11$

Thus, the standard deviation of the probability distribution is 1.11

5 0

4 years ago

. A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x + 0.25x 2 d

kirza4 [7]

So for each unit they get $100, so if they sell "x" units, they intake 100x, that's just the gross income, and therefore the Revenue.

Now, they have a cost of 20x + 0.25x² if they "x" units, now, bearing in mind that if you pluck out the costs out of the incoming revenue, what's leftover, is a surplus amount, namely the Profit. Therefore, profit p(x) = revenue - costs, or 100x - (20x + 0.25x²), which is p(x) = -0.25x² +80x.

a)
now, what's the highest profit they can make? check the picture below.

$\bf p(x)=-0.25x^2+80x\\\\
-------------------------------\\\\
\textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lcclll}
p(x) = &{{ -0.25}}x^2&{{ +80}}x&{{ +0}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left( -\cfrac{80}{-0.50}~,~0-\cfrac{80^2}{-1} \right)\implies \left( \stackrel{\textit{quantity}}{160}~,~\stackrel{\textit{profit value}}{6400} \right)$

b)

well, if a tax is imposed on them, and say, they take it out of the revenue, then their new revenue is not 100x, is 90x, thus $\bf p(x)=-0.25x^2+70x$

and you can use the same formula as above to get the x-coordinate for that vertex.

$\bf p(x)=-0.25x^2+70x\\\\
-------------------------------\\\\
\textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lcclll}
p(x) = &{{ -0.25}}x^2&{{ +70}}x&{{ +0}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left( -\cfrac{70}{-0.50}~,~0-\cfrac{70^2}{-1} \right)$