Answer:
c) -1.75°
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 0, standard deviation of 1:
This means that ![\mu = 0, \sigma = 1](https://tex.z-dn.net/?f=%5Cmu%20%3D%200%2C%20%5Csigma%20%3D%201)
Find the reading that separates the bottom 4% from the others.
This is the 4th percentile, which is X when Z has a p-value of 0.04, so X when Z = -1.75.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.75 = \frac{X - 0}{1}](https://tex.z-dn.net/?f=-1.75%20%3D%20%5Cfrac%7BX%20-%200%7D%7B1%7D)
![X = -1.75*1](https://tex.z-dn.net/?f=X%20%3D%20-1.75%2A1)
![X = -1.75](https://tex.z-dn.net/?f=X%20%3D%20-1.75)
The correct answer is given by option c.
Answer:
6
Step-by-step explanation:
6
triangle MNP and MAB are similar.
MA=46.2-14
=32.2
scale factor=32.2/46.2
=23/33
x/72.6=23/33
x=50.6
<span>4x + 2y = 4
6x - 8 = -2y
Both equations are divisible by 2, so divide both sides of both equations by 2.
</span><span>2x + y = 2
3x - 4 = -y
Since the second equation has -y on one side, we can multiply both sides by -1 to solve for y.
y = -3x + 4
Now we substitute y of the first equation with -3x + 4.
This is the substitution method.
2x + y = 2
2x - 3x + 4 = 2
-x + 4 = 2
-x = -2
x = 2
Now we substitute 2 for x in the first original equation and solve for y.
4x + 2y = 4
4(2) + 2y = 4
8 + 2y = 4
2y = -4
y = -2
The solution is x = 2 and y = -2
</span>
Answer:
52/15 or 3 7/15
Step-by-step explanation:
2 3/5 divide 3/4
13/5 divide 3/4
13 x 4/5 x 3
52/15
3 7/15