We know that
applying the law of cosines
a² = b²+ c²<span> – 2*b*c*cos(A)
cos (A)=[b</span>²+c²-a²]/[2*b*c]
in this problem
a=10
b=17
c=18
so
cos (A)=[17²+18²-10²]/[2*17*18]-----> cos (A)=0.8382
A=arc cos (0.8382)-----> A=33.05°-----> A=33°
the answer is
33 degrees
Answer:
We don't have sufficient evidence to support the claim
Step-by-step explanation:
Null hypothesis:

Alternate hypothesis:

The P-value is 0.3064
0.3064 probability of finding a sample proportion lower than the one found.
The p-value is higher than the significance level of 0.05, which means that there is no sufficient evidence to support the claim.
9900 because you divide 99000 by 10
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>
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Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.