5. Name a pair of supplementary angles.
2 answers:
Problem 5
<h3>Answer: Angle EGF and angle FGB</h3>Explanation:
The straight line EGB can be decomposed into the angle pieces of angle EGF and angle FGB. Another way we can break this straight angle down is to break it into angle EGA and angle AGB. Whichever route you go for, the smaller angles add back to 180 degrees. There are other possible answers you could go for. Check out the diagram below for a visual of these angles (shown in red)
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Problem 6
Answer: Angle AGB and angle EGD
Explanation:
Focus on lines AD and EB. They intersect at point G. The two lines form the opposite angles AGD and EGD which are considered vertical angles. Whenever we have an X shape like this, we'll have vertical angles in the opposite positions like this. Vertical angles are always congruent. There are other pairs of vertical angles shown in this diagram. Check out the diagram below for a visual of these angles (shown in blue)
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Problem 7
<h3>Answer: Angle BGC and Angle CGD</h3>Explanation:
The angles BGC and CGD are right next to each other, so we consider them adjacent. They share the common ray GC. Think of it like two neighbors sharing a common wall in an apartment building. There are other possible answers you could go with as long as the two angles share a common ray or line, and also share a common vertex as well. Check out the diagram below for a visual of these angles (shown in green)
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Answer:
Jennifer's height is 63.7 inches.
Step-by-step explanation:
Let <em>X</em> = heights of adult women in the United States.
The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 65 inches and standard deviation <em>σ</em> = 2.4 inches.
To compute the probability of a normal random variable we first need to convert the raw score to a standardized score or <em>z</em>-score.
The standardized score of a raw score <em>X</em> is:
These standardized scores follows a normal distribution with mean 0 and variance 1.
It is provided that Jennifer is taller than 70% of the population of U.S. women.
Let Jennifer's height be denoted by <em>x</em>.
Then according to the information given:
P (X > x) = 0.70
1 - P (X < x) = 0.70
P (X < x) = 0.30
⇒ P (Z < z) = 0.30
The <em>z</em>-score related to the probability above is:
<em>z</em> = -0.5244
*Use a <em>z</em>-table.
Compute the value of <em>x</em> as follows:
Thus, Jennifer's height is 63.7 inches.