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
__
(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
For this problem, I believe you would just have to plug in for x.
For example, -17 divided by 10 and so on.
The answer should be C, -70. -70 divided by 10 equals -7.
Answer:
He must survey 123 adults.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of
.
The margin of error is:

Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that 
90% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So






Rounding up:
He must survey 123 adults.
If we have 2 coordinates say: (x1,y1) and (x2,y2)
Then the formula for the midpoint is:
((x1+x2)/2,(y1+y2)/2)
And the formula for the distance is:
Sqrt((x2-x1)^2+(y2-y1)^2)
So here we have (-1,-4) and (-7,4)
The midpoint is:
((-1+-7)/2,(-4+4)/2) = (-8/2,0/2) = (-4,0)
The distance is:
Sqrt((-7- -1)^2+(4- -4)^2)
= sqrt((-6^2)+(8^2))
=sqrt(36+64)
=sqrt(100)
=10