On your own paper, plot the Points E(−2,2) and F(8,10). Use the vertical and horizontal grid lines to draw a right triangle with
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The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:
- P(X < 6) = 0.9545
- P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
The mean and the variance are:
We have that:
5 + 7 = 12 rocks, which means that
9 are chosen, which means that
7 are granite, which means that
Question a:
Thus:
Question b:
Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:
In which
Thus
So P(X < 6) = 0.9545.
Question c:
5 of basaltic and 4 of granite: 0.1591 probability.
7 of granite is P(X = 7), in which
0.1591 + 0.0455 = 0.2046, thus:
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
A similar question is found at brainly.com/question/24008577
Answer:
Step-by-step explanation:
The question is to find the equation of the line going through the points (3,-1) and has a slope of -1.
First, the equation of a line is given as:
Equation = y = mx + b
Where
m is the slope
b is the y-intercept (y-axis cutting point)
We know the slope, so the equation becomes:
y = mx + b
y = -1x + b
y = -x + b
Now the point given is in the form (x,y), so
x = 3
y = -1
We substitute and find b:
y = -x + b
-1 = -3 + b
-1 + 3 = b
b = 2
Final Equation:
y = -x + 2