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Elden [556K]
2 years ago
9

Suppose that x has the density function f(x) = cx 0 < x < 2 identify c

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
4 0

The value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

<h3>What is probability density function?</h3>

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that:

f(x)=cx\ \ at\ 0 < x < 2

Here we can see that the value of x is varies as 0,1,2

So at 0,1,2 the value of the function is

f(1)=c\times 1=c\\\\\\f(2)=c\times 2=2c\\\\

So the probability density function is given as:

\sum f(x)=f(1)+F(2)=1\\\\\sum f(x)=c+2c=1

3c=1\\\\c=\dfrac{1}{3}

Hence the value of C=1/3 for the probability density function f(x)=cx , 0<x<2.

To know more about probability density function follow

brainly.com/question/14214648

#SPJ4

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For the region bounded by y=2x​, the​ x-axis, and x=1​, determine which of the following is​ greater: the volume of the solid ge
telo118 [61]

Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

\int\limits^1_0 {(pi)y^{2} } \, dx

which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

7 0
3 years ago
Five minutes on the clock
Nuetrik [128]

Answer:

15/32 cm²

Step-by-step explanation:

Area of rectangle = l × b

=> 3/4 × 5/8

=> 15/32

Therefore,

Area of rectangle is 15/32 cm²

4 0
2 years ago
Read 2 more answers
How do you find each measure for #7?
Lunna [17]

Step-by-step explanation:

From this figure TUW+WUV=TUV ; (5x+3)+(10x-5)=17x-16 so 15x-2=17x-16 ;14=2x therefore x=7

then substitute x on it.

TUW=5x+3=5(7)+3=35+3=38

WUV=10x-5=10(7)-5=70-5=65

TUV=17x-16=17(7)-16=119-16=103

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3 years ago
Annete is suveyeing people in the city about their interest in a new shopping mall. She found that 180 people, or 37.5% of those
VLD [36.1K]

she surveyed "x" amount, which is the 100%, but we also know that 180 is the 37.5%, so


\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 180&37.5 \end{array}\implies \cfrac{x}{180}=\cfrac{100}{37.5}\implies 37.5x=18000 \\\\\\ x=\cfrac{18000}{37.5}\implies x=480

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3 years ago
Solve each compound inequality (show your work!)
zimovet [89]

Answer:  -1 < x < 8

                x = 3

                x ≠ 2

<u>Step-by-step explanation:</u>

Isolate x in the middle.  Perform operations to all 3 sides.

-6 < 2x - 4 < 12

<u>+4 </u>   <u>      +4</u>   <u>+4 </u>

-2 < 2x       < 16

<u>÷2  </u>  <u>÷2      </u>   <u> ÷2 </u>

-1   <   x       <  8

**************************************************************************

Isolate x.  Solve each inequality separately. Remember to flip the sign when dividing by a negative.

       4x ≤ 12       and       -7x ≤ 21

      <u>÷4  </u>  <u>÷4 </u>                 <u> ÷-7  </u>   <u>÷-7 </u>

        x ≤ 3         and         x ≥  3

Since it is an "and" statement, x is the intersection of both inequalities.

When is x ≤ 3 and ≥ 3?    <em>when x = 3</em>

****************************************************************************

Isolate x.  Solve each inequality separately.

    15x > 30       or           18x < -36

   <u>÷15 </u>  <u> ÷15 </u>                  <u> ÷18  </u>   <u>÷18 </u>

       x > 2          or              x <   2

Since it is an "or" statement, x is the union of both inequalities.

When we combine the inequalities, x is every value except 2.

x ≠ 2

4 0
3 years ago
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