PART 1.
Going westward:
Distance: 2400 miles
Rate (this is speed): (450-wind_speed) mph
Time: distance / speed = 2400 / (450-wind speed)
Going eastward:
Distance: 2400 miles
Rate (this is speed): (450+wind_speed) mph
Time: distance / speed = 2400 / (450+wind speed)
PART 2
Formula for speed:
speed = distance / time
Now we solve this for time:
time = distance / speed
11h = 2400 / (450+-wind_speed)
+- sign is put because in one case wind increases speed of plane and in other case it decreases speed.
PART 3
To solve for wind_speed we start by rearranging formula so that we have wind_speed on left side:
(450+-wind_speed) = 2400 / 11
(450+-wind_speed) = 218mph
To fly this distance in 11h speed of plane must be 218mph.
The only way to get this solution is if we substract wind speed:
450-wind_speed = 218
wind_speed = 450-218 = 232mph
57. i = -1. so... 2-1/3-(-1) = 1/4
1x 1 inch cube has volume 1in³, so 180 of these cubes can fit in a 180in³ space.
Answer:
c. 0.0142
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
2) Solution to the problem
We want this probability:
The question on this case is ".Find the probability that the average price for 30 gas stations is less than $4.55". So then our value for n=30.
If we apply the formula for the z score to our probability we got this:
And using the normal standard table or the following excel code we calculate the probability "=NORM.DIST(-2.19,0,1,TRUE)"
Intersection means elements both have. Both sets have -1 but they have nothing else in common so the intersection is {-1}
Union means combining the sets so {-1, 1, 2, 3, 7} Note that I only wrote 1 twice. No duplicates allowed!