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Step-by-step explanation:
Angles in the same segment. The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.
Picture 1 a° = a° they are the same
Picture 2 p= 52° q= 40° Angles in the same segment are equal. if they ask you to calculate you just show both angles p= 52 and q=40.
Picture 3 + 4 Let the obtuse angle MOQ = 2x.
Using the circle theorem, the angle at the centre is twice the angle at the circumference.
Therefore picture 4 tells us and proves;
Angle MNQ = x and angle MPQ = x.
Picture 5
A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every corner of the quadrilateral must touch the circumference of the circle.
The second shape is not a cyclic quadrilateral. One corner does not touch the circumference.
Picture 6
The opposite angles in a cyclic quadrilateral add up to 180°.
a + c = 180°
b + d = 180°
Picture 7
Example
Calculate the angles a and b.
The opposite angles in a cyclic quadrilateral add up to 180°.
This is a picture that couldn't be added but has a quadrilateral occupying half the triangle consisting of 3 arcs the middle one was 140 and proved part of one triangle. The x (a) missing angle showed below a = 180-60 = 120 °
So hopefully this will help you remember the format here for quadrilateral shapes within a circle.
b = 180 - 140 = 40°
a = 180 - 60 = 120°
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is <u>one subtracted by the p-value of Z when X = 4</u>, hence:
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
More can be learned about the normal distribution at brainly.com/question/24663213
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