Answer:
x = 45°
Step-by-step explanation:
We can tell that "x + 115" and 160° are vertically opposite angles, which means that they are equal. (Refer to image)
⇒ x + 115 = 160
⇒ x = 160 - 115
⇒ x = 45°
Learn more about vertically opposite angles: brainly.com/question/68367
<h3>Image:</h3>
It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
<h3>How to prove a Line Segment?</h3>We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Read more about Line segment at; brainly.com/question/2437195
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Answer:
The probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.
Step-by-step explanation:
Let <em>X</em> = time between calls made to Amazon's customer service.
The average time between calls is, <em>β</em> = 10 minutes.
The random variable <em>X</em> follows an Exponential distribution with parameter
The probability distribution function of <em>X</em> is:
Compute the probability that the time between the next two calls is between 3 minutes and 7 minutes as follows:
Thus, the probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.
