We have the area of the base of a triangular prism= a*b
the volume of triangular prism =a*b*c( where c is the height) so that 210=a*b*14 ==> 210= base area*14==> base area= 210/14
-1 < c + 2 < 3....subtract 2 from all sections
-1 - 2 < c + 2 - 2 < 3 - 2...simplify
-3 < c < 1
==============================
32 > 16 - 4g > 12....subtract 16 from all sections
32 - 16 > 16 - 16 - 4g > 12 - 16....simplify
16 > -4g > -4 ...now divide all sections by -4, and change inequality signs
16/-4 < (-4/-4)g < -4/-4...simplify
-4 < g < 1
============================
6y + 1 > = 10
6y > = 10 - 1
6y > = 9
y > = 9/6 which reduces to 3/2 or 1 1/2
-3/2y > = 9 ....multiply both sides by -2/3, cancelling the -3/2 on the left...and change the inequality sign
y < = 9 * -2/3
y < = -18/3 which reduces to - 6
so y > = 9/6(or 1 1/2) or y < = -6
Answer:
(a)
and
are indeed mutually-exclusive.
(b)
, whereas
.
(c)
.
(d)
, whereas 
Step-by-step explanation:
<h3>(a)</h3>
means that it is impossible for events
and
to happen at the same time. Therefore, event
and
are mutually-exclusive.
<h3>(b)</h3>
By the definition of conditional probability:
.
Rearrange to obtain:
.
Similarly:
.
<h3>(c)</h3>
Note that:
.
In other words,
and
are collectively-exhaustive. Since
and
are collectively-exhaustive and mutually-exclusive at the same time:
.
<h3>(d)</h3>
By Bayes' Theorem:
.
Similarly:
.
We are given that there are a total of 78 students. If we set the following variables:

Then, the sum of all of these must be 78, that is:

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

Simplifying:

Now we solve for P by subtracting 62 on both sides:

Therefore, there are 16 students in physics
Answer:
Step-by-step explanation: