A brother and a sister are in the same math class. there are 8 boys and 10 girls in the class. one boy and one girl are randomly
2 answers:
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Answer:
0.62% probability that randomly chosen salary exceeds $40,000
Step-by-step explanation:
Problems of normally distributed distributions 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 question:
What is the probability that randomly chosen salary exceeds $40,000
This is 1 subtracted by the pvalue of Z when X = 40000. So
has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that randomly chosen salary exceeds $40,000
Answer: 7 centimeters
Explanation:
Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x
Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.
Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.
Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.
Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:
- angle BAC and angle CED
- angle ACB and angle ECD
By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.
In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,
(1)
Since
, we can substitute these values to equation (1). So, equation (1) becomes
(2)
SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that
x = 42(1/6)
x = 7 centimeters
Explanation:
Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x
Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.
Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.
Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.
Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:
- angle BAC and angle CED
- angle ACB and angle ECD
By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.
In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,
Since
SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that
x = 42(1/6)
x = 7 centimeters