The range of years would be 493 to 745.
According to the empirical rule, 99.7% of data will fall within 3 standard deviations from the mean. Using this information, we have
619+3(42) and 619-3(42)
619+126 and 619-126
745 and 493
Let h=height where top of ladder touches wall and x be distance from wall to bottom of ladder...
tana=h/x
a=arctan(h/x) and a≤75
arctan(h/x)≤75 now taking tan of both sides :P
h/x≤tan75 now we have an ugly x value that we need to get rid of:
Using the pythagorean theorem we know:
144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x
h/√(144-h^2)≤tan75
h^2/(144-h^2)≤(tan75)^2
h^2≤144(tan75)^2-h^2(tan75)^2
h^2+h^2(tan75)^2≤144(tan75)^2
h^2(1+(tan75)^2)≤144(tan75)^2
h^2≤[144(tan75)^2]/(1+(tan75)^2)
h^2≤134.353829
h≤11.5911
So he cannot have the top of the ladder 11.8 ft above the ground and not exceed a 75° angle with the ground.
I worked it the hard way just to go through the process. However we could have used a simple trig function to see that maximum height of the top of the ladder....
sin75=h/12
h=12sin75
h≈11.59 ft. That would be the maximum height given that we did not want to exceed 75° with the ground.
Answer:
Hi! The answer is E).
Step-by-step explanation:
In order to find the volume, we must multiply, Length x Width x Height.
The length is 9cm and 5cm. The width is 5cm. And the height is 3cm.
We must remember when finding the volume, the answer must be divided by 3.
<em>Hope</em><em> </em><em>this</em><em> </em><em>helped</em><em>!</em>
Answer:
-1
Step-by-step explanation:
-3-8+12+9-15 divided by 5
gives -5/5=5
mean means average total number over frequency
Answer:
a common denominator for 3/7 and 1/3 is 21
