Answer:

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

And replacing we got:


We can find the probability of interest using the normal standard table and with the following difference:

Step-by-step explanation:
Let X the random variable who represent the expense and we assume the following parameters:

And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

And replacing we got:


We can find the probability of interest using the normal standard table and with the following difference:

5) Obtuse triangle because the top angle is more than 90 degrees
Given:


To find:
The quadrant of the terminal side of
and find the value of
.
Solution:
We know that,
In Quadrant I, all trigonometric ratios are positive.
In Quadrant II: Only sin and cosec are positive.
In Quadrant III: Only tan and cot are positive.
In Quadrant IV: Only cos and sec are positive.
It is given that,


Here cos is positive and sine is negative. So,
must be lies in Quadrant IV.
We know that,



It is only negative because
lies in Quadrant IV. So,

After substituting
, we get





Therefore, the correct option is B.
Answer and explanation:
Given : The position of an object moving along an x axis is given by
where x is in meters and t in seconds.
To find : The position of the object at the following values of t :
a) At t= 1 s




b) At t= 2 s




c) At t= 3 s




d) At t= 4 s




(e) What is the object's displacement between t = 0 and t = 4 s?
At t=0, x(0)=0
At t=4, x(4)=14.24
The displacement is given by,



(f) What is its average velocity from t = 2 s to t = 4 s?
At t=2, x(2)=-1.76
At t=4, x(4)=14.24
The average velocity is given by,




108÷6 = 18 and 84÷6=14 last one is 184÷8=23