What is 125 centimeters to 87.5 centimeters
2 answers:
You might be interested in
From the given information,
a. The length of the belt is 180.28 ft
b. The height of the window from the ground is 100 ft
c. The length of the ramp needed is 141.42 ft
<h3>What is the Pythagorean theorem's formula?</h3>The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²
<h3>Calculation:</h3>It is given that,
The height of the silo is 150 feet
The distance from the belt to the silo is 100 feet
With the given measurements, a right-angled triangle is formed.
a. Finding the length of the belt:
From the diagram,
The height of the silo, sh = 150 ft
The base distance, sb = 100 ft
So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.
On applying the Pythagorean theorem,
bh² = sb² + sh²
⇒ bh² = (100)² + (150)²
⇒ bh² = 32500
⇒ bh = √32500 = 50√13
∴ bh = 180.28 ft
Thus, the length of the belt is 180.28 ft.
b. Finding the height of the window from the ground:
It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.
This creates a special right-angled triangle. I.e.,
The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)
So, the new triangle has angles of 90°- 45°- 45°
Thus, the new triangle is said to be an isosceles right angled triangle.
So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft
Therefore, the height of the window from the ground(sw) is 100 ft
c. Finding the length of the ramp(bw) to the window:
Since we have
sw = 100 ft and sb = 100 ft
On applying Pythagora's theorem,
bw² = sb² + sw²
⇒ bw² = (100)² + (100)²
⇒ bw = √20000 = 141.42 ft
Therefore, the length of the ramp to the window is 141.42 ft.
Learn more about the Pythagorean theorem here:
#SPJ1
Answer:
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
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:
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 question:
The z-score when x=187 is ...
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.