Answer:
B. 60 ft²
Step-by-step explanation:
The overall area of the parallelogram is the product of its base length (15 ft) and height (8 ft), so is ...
overall area = (15 ft)(8 ft) = 120 ft²
The area of the quadrilateral in the middle of the parallelogram is the area of two triangles, each with a base equal to 15 ft (the horizontal line in the diagram), and heights that total 8 ft. If we let x represent the height of one of those triangles, then the other has a height of (8-x) and the sum of their areas is ...
quadrilateral area = (1/2)(15 ft)(x) +(1/2)(15 ft)(8 ft -x)
= (1/2)(15 ft)(x + 8 ft - x) = (1/2)(15 ft)(8 ft) = 60 ft²
Then the shaded area is the difference between the parallelogram area and the quadrilateral area:
shaded area = parallelogram area - quadrilateral area
= (120 ft²) - (60 ft²)
= 60 ft²
The area of the shaded region is 60 ft².
Answer:
(a) The probability of the event (<em>X</em> > 84) is 0.007.
(b) The probability of the event (<em>X</em> < 64) is 0.483.
Step-by-step explanation:
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 64.
The probability mass function of a Poisson distribution is:
(a)
Compute the probability of the event (<em>X</em> > 84) as follows:
P (X > 84) = 1 - P (X ≤ 84)
![=1-\sum _{x=0}^{x=84}\frac{e^{-64}(64)^{x}}{x!}\\=1-[e^{-64}\sum _{x=0}^{x=84}\frac{(64)^{x}}{x!}]\\=1-[e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{84}}{84!}]]\\=1-0.99308\\=0.00692\\\approx0.007](https://tex.z-dn.net/?f=%3D1-%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D84%7D%5Cfrac%7Be%5E%7B-64%7D%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3D1-%5Be%5E%7B-64%7D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D84%7D%5Cfrac%7B%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5D%5C%5C%3D1-%5Be%5E%7B-64%7D%5B%5Cfrac%7B%2864%29%5E%7B0%7D%7D%7B0%21%7D%2B%5Cfrac%7B%2864%29%5E%7B1%7D%7D%7B1%21%7D%2B%5Cfrac%7B%2864%29%5E%7B2%7D%7D%7B2%21%7D%2B...%2B%5Cfrac%7B%2864%29%5E%7B84%7D%7D%7B84%21%7D%5D%5D%5C%5C%3D1-0.99308%5C%5C%3D0.00692%5C%5C%5Capprox0.007)
Thus, the probability of the event (<em>X</em> > 84) is 0.007.
(b)
Compute the probability of the event (<em>X</em> < 64) as follows:
P (X < 64) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 63)
![=\sum _{x=0}^{x=63}\frac{e^{-64}(64)^{x}}{x!}\\=e^{-64}\sum _{x=0}^{x=63}\frac{(64)^{x}}{x!}\\=e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{63}}{63!}]\\=0.48338\\\approx0.483](https://tex.z-dn.net/?f=%3D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D63%7D%5Cfrac%7Be%5E%7B-64%7D%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3De%5E%7B-64%7D%5Csum%20_%7Bx%3D0%7D%5E%7Bx%3D63%7D%5Cfrac%7B%2864%29%5E%7Bx%7D%7D%7Bx%21%7D%5C%5C%3De%5E%7B-64%7D%5B%5Cfrac%7B%2864%29%5E%7B0%7D%7D%7B0%21%7D%2B%5Cfrac%7B%2864%29%5E%7B1%7D%7D%7B1%21%7D%2B%5Cfrac%7B%2864%29%5E%7B2%7D%7D%7B2%21%7D%2B...%2B%5Cfrac%7B%2864%29%5E%7B63%7D%7D%7B63%21%7D%5D%5C%5C%3D0.48338%5C%5C%5Capprox0.483)
Thus, the probability of the event (<em>X</em> < 64) is 0.483.
Answer:
Yes, it does. A way to confirm this is you can divide 16/8 which is 2 and 2/1 which is also 2 to get your answer.
Step-by-step explanation:
Answer:
Distributive property
Step-by-step explanation:
