Triangle IJK, with vertices I(3,-8), J(9,-7), and K(5,-4), is drawn inside a rectangle, as shown below. What is the area, in squ
are units, of triangle IJK?
1 answer:
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Answer:
(a) P (Y = 3) = 0.0844, P (Y ≤ 3) = 0.8780
(b) The probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.
Step-by-step explanation:
The random variable <em>Y</em> is defined as the number of consecutive time intervals in which the water supply remains below a critical value <em>y₀</em>.
The random variable <em>Y</em> follows a Geometric distribution with parameter <em>p</em> = 0.409<em>.</em>
The probability mass function of a Geometric distribution is:
(a)
Compute the probability that a drought lasts exactly 3 intervals as follows:
Thus, the probability that a drought lasts exactly 3 intervals is 0.0844.
Compute the probability that a drought lasts at most 3 intervals as follows:
P (Y ≤ 3) = P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3)
Thus, the probability that a drought lasts at most 3 intervals is 0.8780.
(b)
Compute the mean of the random variable <em>Y</em> as follows:
Compute the standard deviation of the random variable <em>Y</em> as follows:
The probability that the length of a drought exceeds its mean value by at least one standard deviation is:
P (Y ≥ μ + σ) = P (Y ≥ 1.445 + 1.88)
= P (Y ≥ 3.325)
= P (Y ≥ 3)
= 1 - P (Y < 3)
= 1 - P (X = 0) - P (X = 1) - P (X = 2)
Thus, the probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.
Answer:
1) Change the length of side AB to 2 feet
Step-by-step explanation:
Given that both structures are similar, it follows that the ratio of their corresponding lengths are equal.
To find out what should be the correct length of AB that she should change to, set up the proportion showing the ratio of 2 corresponding lengths of both structures. Thus:
We will assume AB is unknown.
PR = 7.5 ft
AC = 2.5 ft
PQ = 6 ft
Plug in the values into the equation
Cross multiply
Divide both sides by 7.5
The architect should change the length of AB to 2 ft