Answer:
? ≈ 24°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin? =
=
, then
? -
(
) ≈ 24° ( to the nearest degree )
Given that, the time (t) taken to complete a journey varies directly as the distance (d) and inversely as the average speed (s).
Hence, we can set an equation as following:
t = k\frac{d}{s}
Other information is that it takes 3 hours to complete a 280km trip at 80km/h.
So, plug in t = 3, d = 280 and s = 80 in the above equation to get the value of k. Therefore,
Divide each sides by 3.5.
k = 0.857142857
So, k = 0.857
Now we need to find the time when d= 546 and s = 65. So, plug in these values in the above equation to get the value of t. Hence,
t = 0.857*\frac{546}{65}
= 0.857 * 8.4
= 7.1988
= 7 hours ( Rounded to nearest integer).
So, it will take 7 hours.
Hope this helps you!
Answer:
x is 135°
Step-by-step explanation:
They are both the same angle.
Answer:
Replacement time of 10.064 years.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 8.6, \sigma = 1.6](https://tex.z-dn.net/?f=%5Cmu%20%3D%208.6%2C%20%5Csigma%20%3D%201.6)
Find the replacement time that separates the top 18% from the bottom 82%.
This is the value of X when Z has a pvalue of 0.82. So it is X when Z = 0.915.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.915 = \frac{X - 8.6}{1.6}](https://tex.z-dn.net/?f=0.915%20%3D%20%5Cfrac%7BX%20-%208.6%7D%7B1.6%7D)
![X - 8.6 = 0.915*1.6](https://tex.z-dn.net/?f=X%20-%208.6%20%3D%200.915%2A1.6)
![X = 10.064](https://tex.z-dn.net/?f=X%20%3D%2010.064)
Replacement time of 10.064 years.