Answer:
See explanation
Step-by-step explanation:
1. Angles AOM and MOC are supplementry angles. If m∠MOC = 135°, then
m∠AOM = 180° - 135° = 45°
2. OM − angle bisector of ∠AOB, then
m∠AOM = m∠MOB = 45°
3. Now
m∠BOC = m∠MOC - m∠MOB
m∠BOC = 135° - 45° = 90°
4. Since m∠BOC = 90°, BO is perpendicular to AC.
5. Consider isosceles triangle ABC (because AB ≅ BC). BO is the height drawn to the base, so it is an angle B bisector too, thus
∠ABO ≅ ∠CBO
Answer:
22.86% probability that the persons IQ is between 110 and 130
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 problem, we have that:

If one person is randomly selected what is the probability that the persons IQ is between 110 and 130
This is the pvalue of Z when X = 130 subtracted by the pvalue of Z when X = 110.
X = 130



has a pvalue of 0.9772
X = 110



has a pvalue of 0.7486
0.9772 - 0.7486 = 0.2286
22.86% probability that the persons IQ is between 110 and 130
Answer:
Width = 4.8 inches
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:

Where
P is perimeter
l is length
w is width
Given length = 3.6 and perimeter = 16.8, we plug them in into the formula and figure out the width, w. Process shown below:

Hence, the width is 4.8 inches
Your answer would be B
When you have two angles, and want to know which lines must be congruent, you have to look at the transversal first. The two angles will share a side which is the transversal, and then their other side is one of the parallel lines.
The converse of the corresponding angles theorem states that If corresponding angles are congruent, then the lines are parallel.