WILL MARK BRAINLIEST + 35 POINTS DUE TODAYY The graph below shows a company’s profit f(x), in dollars,

WILL MARK BRAINLIEST + 35 POINTS DUE TODAYY

The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company:

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

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  1. 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

  2. 56.6

    step-by-step explanation:

    the ratio of the perimeters is equal to the scale.

    the ratio of the areas is equal to the square of the scale.

    34 / 20 = k

    a / 19.6 = k²

    substituting:

    a / 19.6 = (34 / 20)²

    a = 19.6 (34 / 20)²

    a ≈ 56.6

    [tex]These figures are similar. the perimeter and area of one are given. the perimeter of the other is al[/tex]

  3. a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

    explanation:

    a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

    using the function, substituting 0 in for w,

    [tex]p(w)=230(1.1)^w\\\\p(0)=230(1.1)^0\\\\p(0)=230(1)=230[/tex]

    this is a difference of 230-190 = 40.

    b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is [tex]p(w)=230(1.1)^w[/tex]; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

    for the new factory, we find the percent of increase to find the growth rate; the formula for this is

    [tex]\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}[/tex]

    between the first two points, the amount of change is 220-190 = 30; this gives us

    30/190 = 0.158 ≈ 0.16 = 16%

    c) at week 0, the old factory has 230 while the new factory has 190.

    at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

    at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

    at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

    at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.

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