A braid was bought to put around a blanket that measures 23 inches by 24 inches. At $0.60 per yard how much was paid for the bra
1 answer:
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Carry out the binomial expansion in the numerator:
Then the 9⁴ terms cancel each other, so in the limit we have
Since <em>h</em> is approaching 0, that means <em>h</em> ≠ 0, so we can cancel the common factor of <em>h</em> in both numerator and denominator:
Then when <em>h</em> converges to 0, each remaining term containing <em>h</em> goes to 0, leaving you with
or choice C.
Alternatively, you can recognize the given limit as the derivative of <em>f(x)</em> at <em>x</em> = 9:
We have <em>f(x)</em> = <em>x</em> ⁴, so <em>f '(x)</em> = 4<em>x</em> ³, and evaluating this at <em>x</em> = 9 gives the same result, 2916.
Answer:
(a) The probability density function of <em>X</em> is:
(b) The value of P (129 ≤ X ≤ 146) is 0.3462.
(c) The probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.
Step-by-step explanation:
The random variable <em>X</em> is defined as the flight time between the two cities.
Since the random variable <em>X</em> denotes time interval, the random variable <em>X</em> is continuous.
(a)
The random variable <em>X</em> is Uniformly distributed with parameters <em>a</em> = 10 minutes and <em>b</em> = 154 minutes.
The probability density function of <em>X</em> is:
(b)
Compute the value of P (129 ≤ X ≤ 146) as follows:
Apply continuity correction:
P (129 ≤ X ≤ 146) = P (129 - 0.50 < X < 146 + 0.50)
= P (128.50 < X < 146.50)
Thus, the value of P (129 ≤ X ≤ 146) is 0.3462.
(c)
It is provided that a randomly selected flight between the two cities will be at least 3 minutes late, i.e. <em>X</em> ≥ 128 + 3 = 131.
Compute the value of P (X ≥ 131) as follows:
Apply continuity correction:
P (X ≥ 131) = P (X > 131 + 0.50)
= P (X > 131.50)
Thus, the probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.