A) The experimental probability is 1/1 = 1
b) The experimental probability is 2/6 = 1/3
c) The experimental probability is 4/12 = 1/3
d) The theoretical probability is 1/6
r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
Answer: 
<u>Step-by-step explanation:</u>
There is 1 four out of 6 possible numbers = 
A. $90
150 x .40= 60
150-60=90
Answer:
B ; C ; D
Step-by-step explanation:
Number of faces on a number cube = 6
Sample space = (1, 2, 3, 4, 5, 6)
P(1 then 0)
P(1) = 1/6 ; P(0) = 0
P(1 then 0) = 1/6 * 0 = 0
P(even number then odd number) :
P(even number) = 3/6 = 1/2
P(odd) = 3/6 = 1/2
P(even number then odd number) = 1/2 * 1/2 = 1/4
P(6 then 2) :
P(6) = 1/6 ; P(2) = 1/6 = 1/2
P(6 then 2) = 1/6 * 1/6 = 1/36
P(even number then 5) :
P(even) = 3/6 = 1/2
P(5) = 1/6
P(even number then 5) = 1/2 * 1/6 = 1/12
P(odd number then 2) :
P(odd) = 3/6 = 1/2
P(2) = 1/6
P(odd number then 2) = 1/2 * 1/6 = 1/12
