Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5
2 answers:
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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:
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<h2>Answer with explanation:</h2>
By considering the given information, we have
Null hypothesis :
Alternative hypothesis :
Since the alternative hypothesis is two-tailed , so the test is a two-tailed test.
Given : Sample size : n= 20, since sample size is less than 30 so the test applied is a t-test.
;
Test statistic :
i.e.
Degree of freedom : n-1 = 20-1=19
Significance level = 0.01
For two tailed, Significance level
By using the t-distribution table, the critical value of t =
Since , the observed t-value (7.25) is greater than the critical value (2.861) .
So we reject the null hypothesis, it means we have enough evidence to support the alternative hypothesis.
We conclude that there is some significance difference between the mean score for sober women and 35.0.