Mathematics, 12.10.2020 22:01 Victor3756

The equation y= 3.2x represents the cost y ( in dollars ) for a taxi ride during peak hours that costs x dollars during off peak hours a) Solve the equation for x
b) What is a range of cost for a taxi during off peak hours that cost between $64 and $80 during peak hours?

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Answer from: Quest

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Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

answer: (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$

here given table is,

price ($), x : 18 23 25 29 30 33

pairs sold, y : 16 13 10 8 6 2

so, $\sum x = 158$ , $\sum y = 55$ , $\sum xy = 1315$ ,

$\sum x^2 = 4308$ and $\sum y^2 = 629$ ,

thus, slop of the given line is,

$a = \frac{55\times 4308-158\times 1315}{6\times 4308-(158)^2}$

⇒ $a = \frac{29170}{884}$

⇒ $a =32.9977375566$ ≈ 33

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