Tell which rule applies to each expression
2 answers:
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Answer:
Step-by-step explanation:
We are finding the probability, which is a percentage, of each of these intervals on our standard bell curve. In order to find this percentage, we need to find the z-score that provides this percentage. To find the z-score:
which is the number in question minus the mean, all divided by the standard deviation. We're first looking for the probability that the gas mileage on a certain model of car is less than 26 mpg.
To find this z-score:
Depending upon which table you look at for the z-score determines how you will find it. The z-score that measure from the value and to the left of it is what we need. This decimal is .3085375, or 30.8538%.
Onto b., which is for the percentage of cars that have gas mileage over 34 mpg. Find the z-score, and this time, we look to the right of the value for the percentage:
and to the right of 1.5 standard deviations we will find .0668072, or 6.68072%
Then finally c., which wants the probability that the gas mileage on one of these cars is greater than 22 but less than 34 mpg. To do this we have to find the z-scores of each and then do some subtracting. First the z-scores:
The percentage of data that lies to the right of that z-score is .9331927
The z-score for the other value, 34, was already found as 1.5, having .0668072 of the data to the right of that z-score. We subtract the smaller from the larger to determine what's left in-between:
.9331972 - .0668072 = .86639, or as a percentage, 86.639% of the cars fall into this interval for gas mileage.
Answers:
- Shortest Length = LN
- Middle Length = LM
- Longest Length = MN
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Explanation:
Let's find the missing angle.
For any triangle, the three interior angles always add to 180
L+M+N = 180
75+50+N = 180
N+125 = 180
N = 180-125
N = 55
So we know the three angles of the triangle are
- L = 75
- M = 50
- N = 55
We see that M = 50 is the smallest angle, so the smallest side is the segment opposite this angle. The smallest side is LN. The smallest side is always opposite the smallest angle.
Similarly, the largest side is always opposite the largest angle. The largest angle here is L = 75, so the largest side is MN.
The middle side must therefore be LM.
The diagram below shows a visual summary.
