Complete question :
For a continuous random variable X, P(23 ≤ X ≤ 66) = 0.25 and P(X > 66) = 0.14. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
a. P(X < 66)
b. P(X < 23)
c. P(X = 66)
Answer:
P(X < 66) = 0.86
P(X < 23) = 0.61
P(X = 66) = 0
Step-by-step explanation:
Given that:
X, P(23 ≤ X ≤ 66) = 0.25 and
P(X > 66) = 0.14 ;
Recall:
P(x ≤ a) + p(x ≥ a) = 1
Then ; P(X < 0.66) = 1 - 0.14 = 0.86
Hence,
P(X < 0.66) = 0.86
P(23 ≤ X ≤ 66) = 0.25
P(X < 66) = 0.86
Hence,
P(X < 23) = 0.86 - 0.25 = 0.61
Probability that a continuous random variable is exactly equal to a particular number equals 0
Hence,
P(X = 66) = 0
The random variables X and Y are jointly continuous, with a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,otherwise, where c is a normalizing constant. For x∈[0,0.5] , the conditional PDF fX|Y(x|0.5) is of the form axb . Find a and b .
Answer:
The value of a and b are 8 and 1 respectively
Step-by-step explanation:
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 , \text{otherwise}\end{matrix}\right.[/tex]
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1\\\\c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1\\\\\frac{c}{2}\int_{0}^{1}x\left ( 1-y^2\right )\text{dx}=1\\\\\frac{c}{2}\int_{0}^{1}(x-x^3)\text{dx}=1\\\\\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1\\\\\frac{c}{2}\left [ \frac{1}{2}-\frac{1}{4} \right ]=1\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1\\\\c=8[/tex]
Conditional pdf of [tex]f_{x,y}(x|0.5)[/tex]
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
Normalizing pdf of 1
[tex]f_{y}y=\int_{0}^{y} 8yx \text{dx}[/tex]
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\\f_{y}y=4y(y^2)\\f_{y}y=4y^3\\f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}=\frac{2x}{0.25}=8x[/tex]
We are given that PDF [tex]f_{x|y}(x|0.5)[/tex] is of the form [tex]ax^b[/tex]
So, on comparing 8x with [tex]ax^b[/tex]
So, a = 8 , b = 1
So, the value of a and b are 8 and 1 respectively
The resulting value of a and b given the conditional PDF of fX|Y(x|0.5) is mathematically given as
a = 8 , b = 1 .
What are the values of a and b?Question Parameters:
a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,
For x∈[0,0.5]
the conditional PDF fX|Y(x|0.5)
Generally, the equation for the function of (x,y) is mathematically given as
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 ,\end{matrix}\right.[/tex]
Therefore
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1[/tex]
[tex]c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1[/tex]
[tex]\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1[/tex]
[tex]\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1[/tex]
C=8
Where, the conditional PDF fX|Y(x|0.5)
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
We have
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\[/tex]
[tex]f_{y}y=4y^3[/tex]
[tex]f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}[/tex]
f_{x|y}(x|0.5)=8x
In conclusion. with the pdf in the form of ax^2
8x comparing ax^b
The value of a = 8 , b = 1 .
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Write an equation of a line in slope-intercept form that passes through the point (-2, 4) and has a slope of -3. (no spaces in your answer)
Answer:
y = - 3x - 2
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
y = - 3x + b Input Slope
Step 3:
4 = - 3 ( - 2 ) + b Input x and y
Step 4:
4 = 6 + b Multiply
Step 5:
- 2 = b Subtract 6 on both sides
Answer:
y = - 3x - 2
Hope This Helps :)
The ratio of boys to girls is 4:6 in Mrs. Franklin's class. If there are 36 girls, how many boys are there?
Answer:
24
Step-by-step explanation:
Lets say 4 boys to 6 girls if there are 36 girls do 4x6 to figure out the ratio of boys would be 24 boys and 36 girls if the other way around it would be 24 girls and 36 boys
A triangular prism has a base area of 15 square meters. If the volume of the prism is 135 cubic meters, what is the height of the prism? SHOW YOUR WORK. (5 points)
a
3 meters
b
45 meters
c
9 meters
d
27 meters
need done quick
the abbreviation for the constant change in a graph or table?
Answer:
ROC
Step-by-step explanation:
ROC. rate of change
On a table or graph, the constant change is same as the unit rate, rate of change or slope, which can be denoted as m.
Constant change on a graph or table simply refers to the rate of change of the output (y) over the change in input (x).
Constant change in a graph or table is the same as the unit rate or the slope value which is dented by the letter m.
Constant rate of change, unite rate, and slope can be denoted as m of a graph or table.
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After how many years will $1,500 you invested now will be worth $3000 if it is compounded monthly at 4% interest?
consider the figure below. which of the following lines are parallel? justify your answer.
Answer:
1. r1 || r2 because of the same side or consecutive interior theorem
2. l1 || l2 because they are corresponding angles
The angle formed between two parallel lines having a common transversal have several common properties
The correct responses are;
1. Lines r₁ and r₂ are parallel
2. Lines, l₁ and l₂ are parallel
lines r₁ and r₂, are parallel
The reason why the given lines are parallel are as follows:
1. The given figures are presented as shown in the attached diagram
From the diagram, we have that the same side interior angles formed by the common transversal l₂ the lines r₁ and r₂ are 63° and 117°, which are supplementary angles (63° + 117° = 180°)
Therefore, lines r₁ and r₂ are parallel given that same side interior angles formed by two parallel lines having the same transversal are supplementary
2. From the attached diagram, we have;
The alternate exterior angles formed between the lines, l₁ and l₂ that have the common transversal r₁ are equal, therefore;
Lines, l₁ and l₂ are parallel, given that the alternate exterior angles formed by two parallel lines having a common transversal are equal
From the diagram, we also have that the other angle of the linear pair angle with the 63° angle is 117°, and the second angle of the linear pair angle is both either corresponding angle and alternate interior angle with the given 117°
Therefore, lines r₁ and r₂, are parallel given that corresponding angles and the alternate interior angles formed between parallel lines having a common transversal are equal
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Please help what Is 4/5 divided by 2
Answer:
2/5
Step-by-step explanation:
Answer:
2.25 is your answer
Step-by-step explanation:
Which of the following is NOT true about Nebuchadnezzar?
He created a code of laws that were very strict.
He created the Hanging Gardens for his wife.
He went insane at the end of his life.
He decorated the city with colored bricks and animal statues.
Your answer would be C.
He did not go insane
An electrician charges a base fee of $65 plus $50 for each hour of work. The minimum the electrician charges is $165. Create a table that shows the amount the electrician charges for 1, 2, 3, and 4 hours of work. Determine the domain and range of the relation in context and explain whether or not this represents a function.
P.S The range values are repeated. So it's a total of 3 range values, and 1 is repeated.
Is there more information so that I solve?
Domain: hours worked
Domain Values: 1,2,3,4
Range: dollars charged
Range Values: 165, 215, 265
The relation is a function. Each domain value is paired with exactly one range value.
Ali"s dog weighs 8 times more than her cat. Together the animals weigh 54 lbs. How much does Ali's dog weigh?
Answer:
48 lbs
Step-by-step explanation:
say that the cat weighs x pounds. then the dog weighs 8x pounds. together they weigh 54 pounds. So our equation is x+8x=54. solve for x to get the cat's weight, and you get x=6. The cat weighs 6 lbs. all I need to do now is multiply 6 by 8 so this the dog weighs 8 times as much as the cat. 8•6=48. the dog weighs 48 pounds.
what is the 12
th term rule of the linear sequence 13 7 1 -5 -11
Answer:
-53, f(n) = -6(n-1) + 13
Step-by-step explanation:
given the equation to this linear/arithmetic sequence for the nth term: f(n) = -6(n-1) + 13
f(12) = -6(12-1) + 13
f(12) = -6(11) + 13
f(12) = -66 + 13
f(12) = -53
*substitute and simplify*
______________
f(n) = f(1) + d(n-1)
given f(1) = 13, f(2) = 7, and f(3) = 1
7-13 = 1-7 = -6 = d
= f(1) + d(n-1)
f(1) = 13 so
the equation must be f(n) = 13 - 6(n-1) or -6(n-1) + 13
Systems of equations. Will give brainlest!
Answer:
Step-by-step explanation:
which is a endpoint of a ray
Answer:
A is the endpoint ray
Step-by-step explanation:
Point A is the ray's endpoint. One way to think of a ray is a line with one end. A ray starts at a given point and goes off in a certain direction forever, to infinity. The point where the ray starts is called (confusingly) the endpoint.
If u answer this i will give your answer a like and help with anything u need!
Answer:
0 . 4 = 2 / 5
Step-by-step explanation:
Help out
It is due at 7:00
Answer:
I want the free points. Sorry :)
A proportional relationship is shown in the table below:
xxx 000 1.31.31, point, 3 2.62.62, point, 6 3.93.93, point, 9 5.25.25, point, 2
yyy 000 111 222 333 444
What is the slope of the line that represents this relationship?
\qquad
1.3
Graph the line that represents this relationship.
m= 46
I know this becuase i just did this on khan :)))))
(9, - 4) and (5, 3) In simplest radical form
Answer: 33
Step-by-step explanation:
(9,-4) and (5,3)
=9*5+(-4)*3
=33
Graph the line of the slope of 1/4 and includes the point (0,2)
Answer:
I'm on Edulastic.com taking a 100 Q test and this question is on it!
Step-by-step explanation:
Imao im fgging confused
The graph of the required line [tex]\bold{y=\frac{x}{4}+2}[/tex] is given below.
Slope point form of equation of line: -An equation of line with slope m and passing through point (p, q) is:
(y - q) = m × (x - p)
We have been given the slope of the line m = 1/4,
and a point (p, q) = (0, 2)
Using the slope-point form equation of line would be,
⇒ (y - 2) = 1/4 × (x - 0)
⇒ (y - 2) = 1/4(x)
⇒ y = x/4 + 2 ...............................(1)
So, the equation of the line is [tex]y=\frac{x}{4} +2[/tex].
To plot the line we need at least two coordinate points.
We have been given a point (0, 2).
We need to find another point.
Substitute x = -4 in equation (1),
⇒ y = (-4)/4 + 2
⇒ y = -1 + 2
⇒ y = 1
So, another point on the line would be (-4, 1).
Now, we plot points (0, 2) and (-4, 1) on coordinates plane.
Then the graph of the line [tex]\bold{y=\frac{x}{4}+2 }[/tex] is as shown in figure.
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13. Which type of flower is the better buy?
Type of
Number of
Cost ($)
Flower
Flowers
Roses
2.
$7
Lilies
3
$9
Tulips
4
$11
Answer:
Tulips
Step-by-step explanation:
7÷2 is 3.50$ Each Rose costs 3.50$
9÷3 is 3$ Each Liliy costs 3$
11÷4 is 2.75$ Each Tulip costs 2.75$
Terrell had a chain of 56 paper clips. Some of the paper clips fell off. Now there are 38 paper clips in the chain. How many fell off?
Answer:
56 - 38 = 18
Step-by-step explanation:
Answer:
18 paper clips
Step-by-step explanation:
56 paperclips originally - x paperclips = 38 paperclips
56 - x = 38
+ x + x
56 = 38 + x
- 38 - 38
18 = x
x = 18
Is 8(3x+2) and 4(6x÷4) equivalent?
Answer:
x= - 8/9
Step-by-step explanation:
TEST
1) ERROR ANALYSIS: Identify and correct the error in describing the transformation of the parent
function.
Sadly the question is incomplete, so we can not see the described transformation of the parent function, thus we can't see the error in that description.
What we can do is describe the transformation shown here.
Here we can see the parent function:
f(x) = x^2
This function opens upwards, so what we see in the graph is this function reflected across the horizontal axis (the x-axis). So the transformation is just a reflection across the x-axis.
(notice that it passes through (-1, -1) and (1, -1), so there is no dilation nor contraction)
For a general function f(x), a reflection across the x-axis is just:
g(x) = -f(x)
So here the transformed function is:
g(x) = - x^2
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write an equation in slope-intercept form that meets the criteria described slope =3,through (5,2)
Answer:
y = 3x - 13
Step-by-step explanation:
Which statement about -8 and
-12 is true?
Answer:they are both neagtive numbers.
Step-by-step explanation:
they say it right in front of you.
Please Help ASAP PLEASE !!!!!!!
Which mathematical property is demonstrated?
If y=−7 and −7=z, then y = z.
A. symmetric property of equality
B. closure property of multiplication
C. closure property of addition
D. transitive property of equality
Answer:
transitive property of equality
Step-by-step explanation:
I know cus i took the test also sorry it took so long dude
Cameron has 75% as many shirts as her brother. How many shirts does her brother have if Cameron has 9 shirts?
Answer:
12 t-shirts
Step-by-step explanation:
12 x 75% = 9 = 9 t-shirts
Michael is renting a bicycle for $12 per hour. How many cents per minute?
Answer:
0.20
Step-by-step explanation:
Find all values of k the value of the fraction 11k−15/3 is greater than the value of the fraction 5−2k/4 .
Answer:
k>3/2
Step-by-step explanation:
To solve this, you need to do fraction cross-multiplying.
So, If a/b=c/d, then a*d=c*b
After you cross-multiply, you get this: (11k-15)*4>3(5-2k)
If you simplify 3(5-2k), you get 15-6k
Then, simplify the next side as well
The full simplified expression should be: 44k-60>15-6k
If you add 60 to both sides, you get 44k>-6k+75
Then add 6k to both sides 50k>75
Then all you have to do is divide both sides by 50 and you get:
K>3/2 OR k>1.5
Helpppppppppppppppppppppppppppppppppppp