A Rectangle is removed from a right triangle to create the shaded region below. Find the area of the shaded region be sure to in
clude the correct unit in your answer
1 answer:
The given shapes area is found to be 4 square yards.
Step-by-step explanation:
Step 1; To determine the area of an indefinite shape we must divide it into the shapes that we know. The shape that is given can be split into a triangle with a rectangle in it.
Step 2; Any given triangles area is half the multiplication of its base value and its height value. In the given diagram, the base of the triangle measures a length of 5 yards and the length from base to top is 4 yards
Area of the triangle = * base * height =
* 5 * 4 = 10 square yards.
The given rectangle measures a length of 3 yards and a width of 2 yards. The area of any given rectangle is the multiplication of its length and width.
Area of the rectangle = Length * Width = 3 yards * 2 yards = 6 square yards.
Step 3; To find the total area of the shape we must subtract the the rectangle's area from the triangle's area.
Area of given shape = Area of the triangle - Area of the rectangle.
Area of given shape = 10 square yards - 6 square yards = 4 square yards.
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Answer:
The probability mass function for the items sold is
The mean is 96.667
The variance is 22.222
b) The probability mass function for the unfilled demand due to lack of stock is
The mean is 3.333
The variance is 33.333
Step-by-step explanation:
If the demand is higher than 100, then you will sell 100 items only. Thus, there is a probability of 1/3+1/3 = 2/3 that you will sell 100 items, while there is a probability of 1/3 that you will sell 90.
The probability mass function for the items sold is
The mean is 1/3 * 90 + 2/3 * 100 = 290/3 = 96.667
The variance is V(X) = E(X²)-E(X)² = (1/3*90² + 2/3*100²) - (290/3)² = 200/9 = 22.222
b) If order to be unfilled demand, you need to have a demand of 110, which happens with probability 1/3. In that case, the value of the variable, lets call it Y, that counts the amount of unfilled demand due to lack of stock is 110-100 = 10. In any other case, the value of Y is 0, which would happen with probability 1-1/3 = 2/3. Thus
The mean is 2/3 * 0 + 1/3 * 10 = 10/3 = 3.333
The variance is 2/3*0² + 1/3*10² = 100/3 = 33.333