a) The cumulative distribution function F of X is: F(x) = P(X ≤ x) = 1
b) The mean E(X) is: E(X) = 0.5 hours.
c) The variance Var(X) is: the variance of X is approximately 0.0833 hours².
To find the cumulative distribution function (CDF) of X, we need to consider two cases: when the boy comes back inside before 45 minutes and when the boy is brought inside by his mother after 45 minutes.
(a) Cumulative Distribution Function (CDF) F of X:
For 0 ≤ x < 0.75 (when the boy comes back inside before 45 minutes):
Since the boy comes back inside uniformly distributed on the interval [0, 1], the CDF is simply the probability that the boy comes back inside before time x.
The probability of the boy coming back inside before x is equal to x, as it is a uniform distribution.
F(x) = P(X ≤ x) = x
For 0.75 ≤ x ≤ 1 (when the mother brings the boy inside after 45 minutes):
If the boy is not back inside at 45 minutes (0.75 hours), his mother brings him inside.
Therefore, the probability of the boy coming back inside before x in this case is 1.
F(x) = P(X ≤ x) = 1
(b) Mean (Expected Value) E(X):
The expected value of X, denoted by E(X), is the average time the boy spends outside before coming back inside.
For a uniform distribution on the interval [0, 1], the expected value is the midpoint of the interval.
Therefore, E(X) = (1 + 0) / 2 = 0.5 hours.
(c) Variance Var(X):
The variance of X, denoted by Var(X), measures the spread or variability of the random variable X around its mean.
For a uniform distribution on the interval [0, 1], the variance is given by:
Var(X) = (1² - 0²) / 12 = 1 / 12 ≈ 0.0833 hours²
So, the variance of X is approximately 0.0833 hours².
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A particle moves along a horizontal line so that its position at time t, t ≥ 0, is given by
s(t) = 40 + te^−t/20.
Find the minimum velocity of the particle for 0 ≤ t ≤ 100.
Answer:
The minimum velocity of the particle = [tex]-e^{-2 }[/tex] units
Step-by-step explanation:
Given - A particle moves along a horizontal line so that its position at time t,
t ≥ 0, is given by s(t) = 40 + te^−t/20.
To find - Find the minimum velocity of the particle for 0 ≤ t ≤ 100.
Proof -
Velocity, v(t) = [tex]\frac{d}{dt}(40 + te^{-\frac{t}{20} } )[/tex]
Now,
[tex]\frac{d}{dt}(40 + te^{-\frac{t}{20} } )[/tex] = [tex]\frac{d}{dt}(40 ) + \frac{d}{dt}(te^{-\frac{t}{20} } )[/tex]
= 0 + [tex]t\frac{d}{dt}(e^{-\frac{t}{20} } ) + e^{-\frac{t}{20} }\frac{d}{dt}(t )[/tex]
= [tex]t(-\frac{1}{20} )e^{-\frac{t}{20} } + e^{-\frac{t}{20} }[/tex]
⇒v(t) = [tex]-\frac{t}{20}e^{-\frac{t}{20} } + e^{-\frac{t}{20} }[/tex]
Now,
For minimum velocity, Put [tex]\frac{d}{dt}(v(t)) = 0[/tex]
Now,
[tex]\frac{d}{dt}[v(t)] = \frac{d}{dt} [ -\frac{t}{20}e^{-\frac{t}{20} } + e^{-\frac{t}{20} } ][/tex]
= [tex]-\frac{2}{20} e^{-\frac{t}{20} } + \frac{t}{400} e^{-\frac{t}{20} }[/tex]
Now,
Put [tex]\frac{d}{dt}(v(t)) = 0[/tex], we get
[tex]-\frac{2}{20} = - \frac{t}{400}[/tex]
⇒t = 40
Now,
Check that the point is minimum or maximum
Calculate [tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex]
Now,
[tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex] = [tex]\frac{d}{dt} [ -\frac{2}{20} e^{-\frac{t}{20} } + \frac{t}{400} e^{-\frac{t}{20} }][/tex]
= [tex]\frac{1}{400}e^{- \frac{t}{20} } [ 3 - \frac{t}{20}][/tex]
⇒[tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex] = [tex]\frac{1}{400}e^{- \frac{t}{20} } [ 3 - \frac{t}{20}][/tex] > 0
∴ we get
t = 40 is point of minimum
So,
The minimum velocity be
v(40) = [tex]-\frac{40}{20}e^{-\frac{40}{20} } + e^{-\frac{40}{20} }[/tex]
= [tex]-2e^{-2 } + e^{-2 }[/tex]
= [tex]-e^{-2 }[/tex]
⇒v(40) = [tex]-e^{-2 }[/tex] units
∴ we get
The minimum velocity of the particle = [tex]-e^{-2 }[/tex] units
down the additive inverse of 4 by 7
Answer:
[tex] \color{magenta} \huge{ \boxed{answer}}[/tex]
The additive inverse of 4/7 is -4/7.hopefully help:)
Step-by-step explanation:
#CarryOnLearningWhich transformation could NOT be used to prove that two circles are congruent to one another?
a dilation with a scale factor of 2
a dilation with a scale factor of 1
a reflection
a rotation
Answer:
the congruent the congruent???
Step-by-step explanation:a dilation a dilation with two factors???
The transformation which could not be used to prove that two circles are congruent to one another is dilation with a scale factor of 2.
Option A is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Dilation:
It changes the size of the figure so, the transformed figure is not congruent with the original figure.
Scale factor = 1 will not change the size of the figure.
Scale factor = 2 will change the size of the figure.
Reflection:
It does not change the size or the shape.
Rotation:
It does not change the size or the shape.
Thus,
The transformation of dilation with a scale factor of 2 could not be used to prove that two circles are congruent to one another.
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Felicia and gabriella are on the hamilton middle school basketball team. The box plots show the number of points they scored in 8 basketball games.
Answer:
I
Step-by-step explanation:
I need the box plot to do the problem
Melinda and Davy are making postcards to announce their new address. The table shows the number of postcards they can make together during each hour they are working. If they continue to make postcards at this rate, what is the total number they will make in 6 hours? Postcards
Number of Hours Number of Postcards
1 7
2 14
3 21
Answer:
3
Step-by-step explanation:
The sides of the figure below measure 11, 22, and 27 meters. Find the perimeter. Do not include units in your answer
Answer:
27
Step-by-step explanation:
try that it should work for their
The perimeter of the figure is 60
How to determine the perimeter?The side lengths are given as:
11, 22, and 27 meters
The perimeter of the triangle is the sum of its side length.
So, we have:
Perimeter = 11 + 22 + 27
Evaluate the sum
Perimeter = 60
Hence, the perimeter of the figure is 60
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What would you call the expression 2x -5y - 7?
Answer:
Trinomial
Step-by-step explanation:
Its called a Trinomial since it has 3 terms in it
Hope its helps!
Can someone please help!!!
Answer:
its the 3rd one
Step-by-step explanation:
anime recommendations
Answer:
what genre babe♀️
Answer:
It depends on a lot what kind you like and if u have watched a lot
the promised Neverland
Black Clover
Aot
HxH
Monster
Code grass
The classroom of the elite
Psycho pass season 1 only
COMEDY
The disastrous life of saiki k
Kaguya sama love is war
I need help and I don’t know how to check it
Answer:
y=2x+3
Step-by-step explanation:
cuánto es 567 + 678 es igual
Answer: 1245 :)
Step-by-step explanation:
Answer:
la respuesta es 1245
567+678=1245
Use a double number line to answer Problem 1-5.
Tanner collected 360 cans and bottle while fundraising for his baseball team. This eas 40% of what Reggie collected. How many cans and bottles dif Reggie collect?
Answer:
900 cans and bottles.
Hope that helps!
Step-by-step explanation:
360 / 4 = 90
90 x 100 = 900
Hope that helps!
HELPPPPP PLSSSSSS !!!!!!!
Charmaine is having a party. She'll have 4 tables for every 8 guests. Complete the table below showing the number of tables and the number of guests
Answer:
Top is 18, Bottom goes 6 for 12, then 7 for 14, then 10 for 20
Step-by-step explanation:
2 guests = 1 table
What is the number?
Help me
The shorter leg of a right triangle is 10 meters. the hypotenuse is 2 meters longer than the longer leg. Find all three sides
Answer:
the shorter leg is 10 meters, longer leg is 24 meters and the hypotenuse is 26 meters
5. Can two fractions point to the same location on the number line? Explain.
Answer:
1 2 = 2 4 = 3 6 = 4 8 = etc. All of these fractions are located at the same point on the number line. Therefore, they represent the same number. From the paper folding exercises, we see that increasing both numerator and denominator of a fraction by the same factor gives an equivalent or equal fraction.
Hope this helps :) Just know I tried.
Please help!!! I'm very confused! Im giving points for it but if please tell the truth <3
Answer:
A
Step-by-step explanation:
It actually trying to trick you with a double negative
Answer:
A
Step-by-step explanation:
Squares do have right angles, if they did not have to then all other ssquares with no right angles would be considered rhombuses.
The question is sking which does not apply, a does not apply but thats what theyre asking so its a
Function lis defined by the equation r
R=5/8t - 9
Function 2 is defined by the following table,
I
Which function has a greater y-intercept?
Answer:
Both have the same y-intercept (-9)
Step-by-step explanation:
✔️Function 1, r = ⅝t - 9, is given in the slope-intercept form, y = mx + b.
b = y-intercept = -9
y-intercept for Function 1 = -9
✔️Function 2, using the table given, the y-intercept is the value of r when t = 0.
Thus, r = -9 when t = 0.
y-intercept for Function 2 = -9
✔️Both functions has the same y-intercept. None is greater than the other.
Determine the slope of the line whose equation is 2x-3y=5
Can someone help quick please
Answer:
PC = 4 cm
Step-by-step explanation:
AP = 4 cm
Because AB = BC, PB = PB, and we know that angle PBA = 90 degrees: triangle PBA is congruent to triangle PBC by the Side-Angle-Side theorem.
PC = AP because corresponding parts of congruent triangles are congruent.
Which table of ordered pairs represents a proportional relationship? I’m a timer please hurry thank you so much
х
-3
-4
-5
у
3
2
1
x
-1
-3
-5
у
1
3
5
-2.
-4
-6
y
1-5
1-7
-9
х
--2
-3
-4
у
0
-1
1-2
I
Answer:
I'd say the second one. the others are all showing a linear relatiknship
Someone please help me
HELP FAST FAST FAST
IM GIVING BRAINLIEST!!!!
A trapezoid has an area of 13.5 inches. The bases are 3 inches and 6 inches. Determine the height of the trapezoid.
EXPLAIN THE PROCESS AND THE STEPS PLEASEEE
Answer:
h=3in
Step-by-step explanation:
A=a+b
2h
Solving forh
h=2A
a+b=2·13.5
3+6=3in
Janet is writing a book. She writes 3 pages every 2 days. If she continues at the same
pace, how long will it take her to write a 400-page book?
Which proportion could be used to solve this problem?
HELP ASAP!! In a right triangle, the longer leg is twice the shorter leg and the hypotenuse is 8 more than the shorter leg. Find the length of the shorter leg.
Answer:
We can't find an exact number, but the answer is x.
plz help right now plz
Find cos (P)
Q
74
70
P
24
R
A.
37
12
В.
35
37
C.
12
Answer:
cos P = 71.09
Step-by-step explanation:
cos = [tex]\frac{adajcent}{hypotenuse}[/tex]
cos P = [tex]\frac{24}{74}[/tex]
cos P = 0.324
cos-1 of 0.324 is 71.09
cos P = 71.09
Need it now. I'll give you another 100 when done if all i right.
This it the test please do as fast as posible and show work. thank you and sorry
Need answers for 1 and 2. Please
Answer:soultion
Step-by-step explanation: solution
Answer this correctly I’ll give brainalist + 10 points
Answer:
x = 43
Step-by-step explanation:
Since these angles are inside a right angle, we know their sums are complementary (they add up to 90°.)
x + x + 4 = 90
2x + 4 = 90 | Combine x's
2x = 86 | Subtract 4 from both sides
x = 43 | Divide both sides by 2