(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:
For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:
which reduces to
<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2
(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):
<h2>Answer:</h2>
<h2>Explanation:</h2>
Given the equation expressed as:
First, we need to calculate the value of "x" from the given expression.
Step 1: Given the equation 2x + 5 = 8x
Step 2: Subtract 5 from both sides:
Step 3: Subtract 8x from both sides
Step 4: Divide both sides by -6
Step 5: Get the value of 12x. Substitute x = 5/6 into the expression to have:
Therefore the value of 12x is 10
Answer:
a
x
2
+
b
x
+
c
=
0
the two roots of the equation take the form
x
1
,
2
=
−
b
±
√
b
2
−
4
a
c
2
a
So, start by adding
−
5
to both sides of the equation to get
2
x
2
+
x
−
5
=
5
−
5
2
x
2
+
x
−
5
=
0
Notice that you have
a
=
2
,
b
=
1
, and
c
=
−
5
. This means that the two solutions will be
x
1
,
2
=
−
1
±
√
1
2
−
4
⋅
2
⋅
(
−
5
)
2
⋅
2
x
1
,
2
=
−
1
±
√
41
4
You can simplify this if you want to get
x
1
=
−
1
+
√
41
4
≅
1.35078
and
x
2
=
−
1
−
√
41
4
≅
−
1.85078
Answer:
√2.37+ 3 √9 = √5. 3 is the last one
x+9 =+25
Step-by-step explanation:
(x+9)2= 25 This means x= 3.5 and the square root of x = √3.5 = 1.87 square root of 9 x 2 = √18 =4.24
We can also see 18+7 =25
√5.65 √5
this is 25 = 5 so it's the last one.
as 2.37+ 3 √9 = √5. 3
Answer:
It would be 490 or 108
Step-by-step explanation:
multiply the perimeter thats all
