Find the area of the polygon with the given vertices x(2,4) y(0,-2) z(2,-2)
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a (i) The number of standard size is 288 eggs
a (ii) The number of medium size is 1,476 eggs
a (iii) The number of large size is 36 eggs
b (i) The expected profit made from selling the standard size is Gh¢43.2
b (ii) The expected profit made from selling the medium size is Gh¢516.6
b (iii) The expected profit made from selling the large size is Gh¢16.2
The given parameters:
the mean of the distribution, m = 0.06 kg
standard deviation (std) of the distribution, d = 0.009 kg
number of the samples, n = 1800 eggs
(i) Find the position of "less than 0.052 kg (standard size)":
- 1 standard deviation below the mean = m - d
- m - d = 0.06 kg - 0.009 kg = 0.051 kg
(<em>the </em><em>standard size</em><em> is 1 standard deviation below the mean</em>)
- less than 1 standard deviation below the mean in a normal distribution is equal to 16% of the data samples
- Number of standard size = 0.16 x 1800 = 288 eggs
(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":
- 0.052 kg is 1 standard deviation below the mean
- 2 standard deviation above the mean = m + 2d
- m + 2d = 0.06 + 2(0.009) = 0.078 kg
(<em>the </em><em>medium size</em><em> is between 1 std below the mean and 2 std above the mean</em>)
- Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%
- Number of medium size = 0.82 x 1800 = 1,476 eggs
(iii) Find the position of "Greater than 0.075 kg (large size)":
- 0.078 kg is 2 standard deviation below the mean
- greater than 2 std above the mean in a normal distribution = 2 % of the data samples
- Number of large size = 0.02 x 1800 = 36 eggs
<u>Check:</u> <em>288 eggs + 1476 eggs + 36 eggs = 1,800 eggs</em>
(b) the cost of production of an egg = Gh¢0.45
the selling price of the standard size = Gh¢0.60
the selling price of the medium size = Gh¢0.80
the selling price of the large size = Gh¢0.95
(i) The expected profit made from selling the standard size:
Profit = total revenue - cost of production
Profit = 288(0.6) - 288(0.45) = Gh¢43.2
(ii) The expected profit made from selling the medium size:
Profit = total revenue - cost of production
Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6
(iii) The expected profit made from selling the large size:
Profit = total revenue - cost of production
Profit = 36(0.9) - 36(0.45) = Gh¢16.2
Learn more here: brainly.com/question/22520030
we have
Convert to vertex form
we know that
the equation of a vertical parabola in vertex form is equal to
where
(h,k) is the vertex
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
therefore
<u>the answer is </u>
The y-value of the vertex is