The average length a band spends on stage in a rock concert is normally distributed with a mean of 55 minutes. The American band Manowar, who have been playing dozens of concerts every year for about 40 years, claims that their shows are more cost-effective for their fans because their concerts, on average, last longer than the typical rock concert. To test this, a magazine takes a random sample of 24 Manowar concerts and find the average length Manowar spends on stage to be 74 minutes with a standard deviation of 16 minutes Check the conditions for this Hypothesis Test and set up the Hypotheses:

Conditions:

1. The sample is

2. The sample size is

3. Select is likely less than 5% of ..

(Independent sample) Hypotheses: H : Select H : Select Based on the conditions, should this Hypothesis Test be conducted by the magazine in its current state?

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°