The ratio of boys to girls in a computer class is 5:3. There are 27 girls in the class. How many boys are in the class
1 answer:
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Answer:
a) 0.951
b) 2,800,000
c)
Step-by-step explanation:
Let R be a bounded and measurable region in the forest and denote with
|R| = area of R in acres
Let T(R) be a discrete random variable that measures the number of trees in the region R.
If the trees are distributed according to a two-dimensional Poisson process with the expected number of trees per acre equals to 40, then
(a) What is the probability that in a certain quarter-acre plot, there will be at most 15 trees?
In this case R is a region with an area of 1/4 acres,
We can compute this with a spreadsheet and we get
(b) If the forest covers 70,000 acres, what is the expected number of trees in the forest?
Given that the expected number of trees per acre equals 40, the expected number of trees in 70,000 acres equals
40*70,000 = 2,800,000 trees.
(c) Suppose you select a point in the forest and construct a circle of radius 0.1 mile. Let X = the number of trees within that circular region. What is the pmf of X?
Now R is a circle of radius 0.1 mile, so its area equals
Since 1 squared mile = 640 acres,
0.0314 squared miles = 0.0314*640 = 20.106 acres, so the pmf of R would be
The graph from which the position of the point <em>A</em> can determined following
the multiplication with a scalar is attached.
Responses:
- If <em>A</em> is in quadrant I and is multiplied by a negative scalar, <em>c</em>, then c·A is in <u>quadrant III</u>
- If A is in quadrant II and is multiplied by a positive scalar, <em>c</em>, then c·A is in <u>quadrant II</u>
- If <em>A</em> is in quadrant II and is multiplied by a negative scalar, <em>c</em>, then c·A is in <u>quadrant IV</u>
- If <em>A</em> is in quadrant III and is multiplied by a negative scalar, <em>c</em>, then c·A is in <u>quadrant I</u>
Background information;
The question relates to the coordinate system with the abscissa represent the real number and the ordinate representing the imaginary number.
Solution:
If A is in quadrant I; A = a + b·i
When multiplied by a negative scalar, <em>c</em>, we get;
c·A = c·a + c·b·i
Therefore;
c·a is negative
c·b is negative
- c·A = c·a + c·b·i is in the <u>quadrant III</u> (third quadrant)
If A is quadrant II, we have;
A = -a + b·i
When multiplied by a positive scalar <em>c</em>, we have;
c·A = c·(-a) + c·b·i = -c·a + c·b·i
-c·a is negative
c·b·i is positive
Therefore;
- c·A = -c·a + c·b·i is in <u>quadrant II</u>
Multiplying <em>A</em> by negative scalar if <em>A</em> is in quadrant II, we have;
c·A = -c·a + c·b·i
-c·a is positive
c·b·i is negative
Therefore;
c·A = -c·a + c·b·i is in <u>quadrant IV</u>
If A is in quadrant III, we have;
A = a + b·i
a is negative
b is negative
Multiplying <em>A</em> with a negative scalar <em>c</em> gives;
c·A = c·a + c·b·i
c·a is positive
c·b is positive
Therefore;
- c·A = c·a + c·b·i is in<u> quadrant I</u>
Learn more about real and imaginary numbers here;
