(20 PTS!!)
2 answers:
Answer:
The correct option is C.
Step-by-step explanation:
In a dot plot, the number of dots above a number represents the frequency of that number.
From the given dot plot it is clear that number of dots for group R is 21 and the time taken by the students of groups R are
45, 50, 50, 55, 60, 60, 70, 75, 80, 85, 90, 90, 95, 100, 100, 105, 110, 110, 115, 120, 120
The average of the data is
From the given dot plot it is clear that number of dots for group S is 17 and the time taken by the students of groups S are
50, 55, 60, 60, 65, 70, 70, 80, 90, 90, 95, 100, 105, 110, 110, 115, 120
The average time of both groups are same.
Since both groups show about the same average time, therefore the correct option is C.
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Answer:
27 degrees
Step-by-step explanation:
The easy way is by remembering the formula (a-b)/2=c, where a is the larger angle, and b is the smallest angle. (90-36)/2=27.
The longer, more drawn out answer goes as follows. See the image to understand the notation I use:
- AOE + BOD + BOA + DOE = 360
- AOE + BOD = 90 + 36 = 126
- BOA + DOE = 360 - AOE - BOD = 234
- Since the sum of a triangle's angles is 180, ODE = (180 - DOE) / 2
- Likewise, OBA = (180 - BOA) / 2
- Since CDE is 180, CDO = 180 - ODE = 180 - (180 - DOE) / 2
- Likewise, CBA is 180, so CBO = 180 - OBA = 180 - (180 - BOA) / 2
- The interior angles of the irregular polygon CBOD add up to 360, so CBO + CDO + BOD + BCD = 360.
- Substituting what we already found, 180 - (180 - BOA)/2 + 180 - (180 - DOE)/2 + 36 + BCD = 360
- Cleaning it all up, we get 180 + (BOA + DOE)/2 + 36 + BCD = 360
- As we found in line 3, BOA + DOE = 234, so substituting that in, 180 + 117 + 36 + BCD = 360
- Finally, solving for BCD (360 - 36 - 117 - 180) we get our answer, 27
Note: The long drawn out method shown above is a way to derive the formula for the secant theorem. You do not need to use this method every time. Just remember, large angle minus small angle, all divided by 2. That is it.
