Answer:
Option C is correct.
Ratio of longer leg to hypotenuse is; 
Step-by-step explanation:
This is the special right angle triangle 30°-60°-90° as shown below in the figure.
- The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.
- The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.
- Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.
In 30°−60°−90° right triangle,
- the length of the hypotenuse is twice the length of the shorter leg,also
- the length of the longer leg is
times the length of the shorter leg.
Then:
the sides are in proportion i.e, 
Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is:
Mean = 12000
Standard Deviation = 2000
We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score
Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.
z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score =
This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
From the graph it appears that S′(5) 2 ≈ and S′(25) 2 ≈ − . The important
thing is that they do have opposite signs. The first means that at about 5ºC
the Coho gains about 2 cm/sec while at 25ºC it loses about 2 cm/sec in
maximum sustainable speed.
Answer: b. 0.8413
Step-by-step explanation:
Given : The average time taken to complete an exam, X, follows a normal probability distribution with 
and 
.
Then, the probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-
![P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z-z)=P(Z](https://tex.z-dn.net/?f=P%28x%3E30%29%3DP%28z%3E%5Cdfrac%7B30-60%7D%7B30%7D%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%5C%5C%5C%5C%3DP%28z%3E-1%29%3DP%28z%3C1%29%5C%20%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%3E-z%29%3DP%28Z%3Cz%29%5D%5C%5C%5C%5C%3D%200.8413)
[using z-value table]
Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam = 0.8413
Answer:
Length of x+3= 6.75
Length of 4x=15
Length of 3x-1=10,25
Step-by-step explanation:
- First make an equation and find x x+3+3x+1+4x=34
- Then solve for x, answer will be 3,75
- 3,75 represents x
