A towns population has been growing literally

Mathematics

1 answer:

Tresset [83]3 years ago

6 0

$\bf \begin{array}{ccll}
\stackrel{\textit{years since 2000}}{t}&\stackrel{population}{p}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&29400\\
5&36000
\end{array}\\\\
-------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 29400}})\quad 
% (c,d)
&({{ 5}}\quad ,&{{ 36000}})
\end{array}$

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{36000-29400}{5-2}\implies \cfrac{6600}{3}
\\\\\\
2200
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies \stackrel{y}{p}-29400=2200(\stackrel{x}{t}-2)
\\\\\\
p-29400=2200t-4400\implies p(t)=2200t+27200$

how many in 2007? well, 2007 is 7 years after 2000, thus set t = 7,to get p(t).

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What is the probability that a point chosen at random in the given figure will be inside the larger square and outside the small

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Answer:

P(inside larger square and outside smaller) = $\frac{51}{100}$

Step-by-step explanation:

Probability is the result of the division of the number of possible outcome by the number of an event.

In the question, for a point chosen, the point can be in the small square only or in the area or region between the small square and the big square as such,

Area of larger square = area of region between both squares + area of smaller square

Where the area of a square is S × S where S is the side of a square

Area of larger square = 10 × 10

= 100 cm square

Area of smaller square = 7 × 7

= 49 cm square

Area of the region between both squares

= 100 - 49

= 51 cm square

The probability that a dot selected is inside the larger square and outside the smaller is

P(inside larger square and outside smaller) = Area of region between both square/ Area of larger square

P(inside larger square and outside smaller) = $\frac{51}{100}$