Mechanics paper/Math (please helpp!!!)
1 answer:
Answer:
(i) 15 m, 6 m/s
(ii) 90 m
Step-by-step explanation:
(i) For some acceleration (a) from rest, the distance covered (d) in time t is ...
d = (1/2)at^2
The distance covered by Ben in the 5 seconds he is accelerating is ...
d = (1/2)(1.2 m/s²)(5 s)² = 15 m
Of course, Ben's speed at that point is ...
s = (1.2 m/s²)(5 s) = 6 m/s
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(ii) When Ben has been walking 5 s, Alan has been walking 10 s, so Alan has covered (10 s)(4 m/s) = 40 m. Their distance difference of 40 -15 = 25 m is being made up at the rate of their speed differences: (6 m/s) -(4 m/s) = 2 m/s.
It will take (25 m)/(2 m/s) = 12.5 s additional time for Ben to catch Alan. In the 22.5 s that Alan has been walking before they meet, he will have walked ...
(22.5 s)(4 m/s) = 90 m . . . the distance OP
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Answer:
Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.
Step-by-step explanation:
We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.
If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.
The above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 20 children
r = number of success = none of the 20 children
p = probability of success which in our case is probability that
children are unvaccinated, i.e; p = 13.5%
<u><em>Let X = Number of children that are unvaccinated</em></u>
So, X ~ Binom(n = 20, p = 0.135)
Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)
P(X = 0) =
=
= 0.055
<em>Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.</em>
A dilation is a transformation 
, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.
In a dilation of
, the scale factor, 
is mapping the original figure to the image in such a way that the
distances from O to the vertices of the image are half the distances
from O to the original figure. Also the size of the image is half the
size of the original figure.
Therefore, <span>If is a dilation of △ABC, the truth about the image △A'B'C'</span> are:
<span>AB is parallel to A'B'.
The distance from A' to the origin is half the distance from A to the origin.</span>
In a dilation of
Therefore, <span>If
<span>AB is parallel to A'B'.
The distance from A' to the origin is half the distance from A to the origin.</span>