Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the t
op of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°.
A.) Find the height, h, of the lighthouse.
B.) Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse.
C.) To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations
A.) Find the height, h, of the lighthouse.
B.) Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse.
C.) To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations
1 answer:
To find the height of the lighthouse, use 
to get that h = 14 (the tangent of 45 is 1). Now for the next question, you have to use the height you just solved for to find angle y. Use 
and the inverse tangent button on your calculator tells us that the angle is 28.3. Now for the last question, use the supplement of 45 to get that the angle adjacent to y is 135. 180 - 135 - 28.3 = 16.7 That's your x value.
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Answer:
3. The mean will increase more than median, but both will increase.
Step-by-step explanation:
We have been given a dot plot. We are asked to find the true statement, if a new data point at 12 is added to our given dot plot.
Since we know that an large valued outlier affects mean more than median, so mean will increase more than median.
Let us check this using our given information. Our data set before adding 12 is:
1, 2, 2, 2, 3, 4, 4, 4, 5.
We can see that our data set has odd number (9) of data points, so median will be the value of 5th term, that is 3.
Therefore, mean of our data set is 3.
Upon adding a data point at 12, our new data set will be:
1, 2, 2, 2, 3, 4, 4, 4, 5, 12.
Now our data set has 10 terms, so median will be the average of 5th and 6th term.
Therefore, the median of new data set will be 3.5.
Therefore, mean of new data set will be 3.9.
Upon looking at our given statements we can see that 3rd statement is true as mean and median both increased after adding 12 to our data set, but mean increased more that median. Mean and median before adding 12 was 3; but after adding 12 median became 3.5, while mean became 3.9 (which is greater than mean).