Answer:
Step-by-step explanation:
a. $360
The total surplus of Q1 is found within triangle abc. The base is a ($70) to c ($10), and the height is the x value of b, or Q1 (12 bags). The total length of the base is 60 (70-10). Multiply that by the height of the triangle (12), and divide the total by 2. (60 x 12) / 2 = 360
a1. $144
The consumer surplus for Q1 is found within the triangle formed by point a, point b, and the y intercept of the equilibrium. The problem says equilibrium = 46, so the third is point (0, 46). The base is point a ($70) to the equilibrium intercept ($46). The height is Q1 (12). The total base is 24 (70-46). (24 x 12) / 2 = 144
b. $62.50
The deadweight loss for Q2 is found is found within triangle dbe. The base is d ($56) to e ($31). The height of the triangle is Q2 (7) to Q1 (12). The total base is 25 (56-31), and the total height is 5 (12-7). (25 x 5) / 2 = 62.5
b1. $297.50
The total surplus of Q2 is found by subtracting the deadweight loss from the total surplus. 360 - 62.5 = 297.5
c. $122.50
The deadweight loss for Q3 is found within triangle bfg. The base is f (67) to g (32). The height is Q1 (12) to Q3 (19). The total base is 35 (67-32) and the total height is 7 (19-12). (35 x 7) / 2 = 122.5
c1. $237.50
The total surplus for Q3 is found by subtracting the deadweight loss from the total surplus. 360 - 122.5 = 237.5
2x - 4(x-4) = -2 + 3x + 3
2x - 4x + 16 = 3x + 1
-2x + 16 = 3x + 1
5x = 15
x = 3
Answer:
<h2> 3p</h2>
Step-by-step explanation:
4p - p = 4p - 1p = (4 - 1)p = 3p
Let 
be the 20 marks of the boys, and 
be the 10 marks of the girls.
We know that the global mean was 70, meaning that
Multiplying both sides by 30 we deduce that the sum of the scores of the whole classroom is
By the same logic, we work with the marks of the boys alone: we know the average:
And we deduce the sum of the marks for the boys:
Which implies that the sum of the marks of the girls is 
And finally, the mean for the girls alone is
Answer:
The radius of the water bottle is 2.72cm
Step-by-step explanation:
In this question, we are concerned with calculating what the radius of the cylindrical water bottle is given its volume and height.
Mathematically, the volume of a cylinder is V = pi * r^2 * h
From the question, we know that V = 179 cm^3. , h = 7.7cm while r = ?
we substitute these values into the volume equation.
179 = pi * r^2 * 7.7
179 = 3.14 * r^2 * 7.7
179 = 24.178 * r^2
r^2 = 179/24.178
r^2 = 7.403
r = square root 7.403
r = 2.72 cm
