1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maksim231197 [3]
3 years ago
5

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a sat

ellite dish and obtained the probability density function f(x) = c(1 - 1/16x^2) for 0 < x < 3, where X is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the value of c that makes f(x) a valid probability density function
Mathematics
1 answer:
ivolga24 [154]3 years ago
4 0

Answer:

c=\frac{16}{39}

Step-by-step explanation:

The probability density function is :

f(x)=c(1-\frac{1}{16}x^{2})

With 0 < x < 3

To be a valid probability density function :

\int\limits^b_a {f(x)} \,dx=1

Where a < x < b

And also

f(x) ≥ 0 for a < x < b

Applying this to the probability density function of the exercise :

\int\limits^3_0 {c(1-\frac{1}{16}x^{2})} \, dx=1

c\int\limits^3_0 {(1-\frac{1}{16}x^{2})} \, dx=1

c(3-\frac{1}{16}\frac{3^{3}}{3})=1

c(\frac{39}{16})=1

c=\frac{16}{39}

We can verify by replacing ''c'' in the original probability density function and integrating :

\int\limits^3_0 {\frac{16}{39}(1-\frac{1}{16}x^{2})} \, dx=

=\frac{16}{39}.(3)-\frac{1}{39}.(\frac{3^{3}}{3})=\frac{16}{13}-\frac{3}{13}=\frac{13}{13}=1

Also, f(x) ≥ 0 for 0 < x < 3

You might be interested in
What is the equation of the line that contains point (6, 4) and is parallel to line m?
9966 [12]

Answer:

d?.............................

3 0
3 years ago
Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B,
oksian1 [2.3K]

The least to greatest slope, the segments are B, C, and A.

We have given that,

The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.

A graph represents the water level to fill the tank on Y-axis per time on X-axis.

The rate of increase of water level is indicated by the slope of the segment. The slope is the ratio of rise to run, and is related to the angle the segment makes with the +x axis.

Segments that have more rise for the same run have greater slope. Segments that make a larger reference angle with the +x axis have a larger slope.

Here, segment B has the least slope, followed by C, then A, which has the largest slope.

In order, the least to greatest slope, the segments are B, C, and A.

To learn more about the slope visit:

brainly.com/question/3493733

#SPJ1

7 0
1 year ago
The momentum of an object, p, is determined by its mass, m, and its velocity, v. The formula for this relationship is shown.
timama [110]

Answer:

b

Step-by-step explanation:

7 0
3 years ago
Can someone give 2 examples of a logarithmic equation with infinite solutions?
Vika [28.1K]

Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.  

\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0

and

\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x

3 0
3 years ago
A worm wriggled forward 4/5 of an inch in 3 minutes. At that rate, how far would the worm go in 1 minute?
Thepotemich [5.8K]

Answer:

4/15 of an inch

Step-by-step explanation:

A worm wriggled forward 4/5 of an inch in 3 minutes.

=> At that rate, the distance the worm would go in 1 minute is:

D = (4/5)/3 = 4/(5x3) = 4/15 of an inch

Hope this helps!

8 0
2 years ago
Other questions:
  • Each of the letters in the word SAMSUNG are seprate cards face down on the table. Determine what the probability is that the car
    6·1 answer
  • Select the graph that would represent the best presentation of the solution set.<br><br> l1-4xl&gt;7
    14·1 answer
  • Math help! asap !! 20 + points and brainlest! ( all problems pls )
    10·1 answer
  • If (x) = 5x -12 what is f(2)?
    8·1 answer
  • If anybody can help me with any of these problems on this paper please do so
    8·1 answer
  • PLEASE ANSWER ASAP !!!!!
    7·1 answer
  • Answer w/ explanation !!<br><br><br> solve for x
    5·1 answer
  • Solve for x please for 10 points
    15·2 answers
  • How do I solve for X?
    6·1 answer
  • Which equation represents a line which is perpendicular to the line 8x + 3y = 3
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!