7. you are planning a camping trip. the campsite you want to rent charges a $15 fee to reserve the site, plus an extra $3 per day. part i: define your variables and write a linear equation in slope-intercept form to represent the cost of the campsite. (4 points) part ii: find the intercepts and interpret them. (4 points) part iii: graph the equation for the cost of renting the campsite. label three points on your graph and indicate the slope. (5 points) part iv: how much would it cost to camp for a week? if you had $40 to spend, how long could you stay? (3 points)

PART: I--

Let x represent the number of days of camping.

and y represent the camping fees.

Now, it is given that:

The campsite you want to rent charges a $15 fee to reserve the site, plus an extra $3 per day.

This means that the slope is: 3

( since it represent the cost per day)

and the y-intercept is 15 since it represent the fixed cost.

Hence, we have:

          y=3x+15

( since the slope-intercept of a line is given by:

       y=mx+c where m is slope and c is intercept of line)

PART II--

We know that the y-intercept of a graph is the value of y at the point where the x-value is zero and the x-intercept of a graph is the x-value at the point where y-value is zero.

From the given linear equation i.e.

               y=3x+15

when x=0 we have:

y=15

This means that y-intercept is: 15

and when y=0 we have:

3x= -15

⇒   x= -5

This means that x-intercept is: -5

PART III--

We know that the slope of a graph is calculated as:

If the graph passes through two distinct points i.e. (a,b) and (c,d) then:

Hence, from the graph the graph passes through (0,15) and (1,18)

This means that:

PART IV--

The cost to camp for a week means we have to find the value of y such that x=7

( since there are 7 days in a week )

Hence,

y=3×7+15

y=36

Hence, the cost to camp for a week is:  $ 36

Now, we are asked to find the value of x when  y=40

i.e.   3x+15=40

i.e.  3x=25

i.e. x=8.33≈8 days

Hence, the number of days one could stay if he had $ 40 is: 8.33≈8 days

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

ddd

step-by-step explanation: