Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
<em>P(p' ≥ 0.5) = 0.0031</em>
<em></em>
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Answer: 14.73
Step-by-step explanation:
The given triangle is a right angle triangle.
EF^2 + DF^2 = ED^2
The hypotenuse is |ED| while the two shorter legs are |EF| and |DF|.
We can then apply the Pythagoras Theorem to find the length of EF.
(EF)^2 + (DF)^2 = (ED)^2
(EF)^2 + (12)^2 = (19)^2
(EF)^2 + 144 = 361
(EF)^2 = 361 - 144
(EF)^2 = 217
EF = 14.73
Answer:
r = 5
Step-by-step explanation:
To solve for r, plug in the change in x values and change in y values, since the hypotenuse is simply the diagonal of both the y-coordinate and x-coordinates shown via drawing legs on the vertical and horizontal axis. So, since (0,0) is the initial point, r = sqr[(-4-0)^2 + (-3-0)^2 = sqr(16 + 9) = 5.
Now, the angle theta is the angle in which the sine, cosine, and tangent ratios are found. Simply use opposite over hypotenuse for sine, adjacent over hypotenuse for cosine, and opposite over adjacent for tangent using theta as the angle in which these values are obtained.
Answer:
CU = 117
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
= 
substituting in values to the ratios
= 
( cross- multiply )
24(36x - 1) = 3432 ( divide both sides by 24 )
36x - 1 = 143 ( add 1 to both sides )
36x = 144 ( divide both sides by 36 )
x = 4
CU = 36x - 1 - 26 = (36 × 4) - 27 = 144 - 27 = 117
