X 1 A probability density function of a random variable is given by f(x) = on the interval [2, 8]. Find the expected value, the variance, 18 9 and the standard deviation. The expected value is u (Roun
Answers
The expected value is `10X/3`, the variance is `20X/27`, and the standard deviation is `[2 sqrt(5X/27)]/3`.
Given: A probability density function of a random variable is given by `f(x) = X/18` on the interval `[2, 8]`.
We have to find the expected value, the variance, and the standard deviation.
So, `f(x) = X/18` on the interval `[2, 8]`.
To find the expected value, we have to use the formula:
`u = int(x*f(x)) dx`.
Here, `int` means the integration of `x*f(x)` over the interval `[2, 8]`.
So, `u = int(x*f(x)) dx
= int(x*X/18) dx` over the interval `[2, 8]`
=`X/18 int(x) dx` over the interval `[2, 8]`
=`X/18 [(x^2)/2]` over the interval `[2, 8]`
=`X/18 [(8^2 - 2^2)/2]`=`X/18 [60]`
=`10X/3`.
Therefore, the expected value is `10X/3`.
To find the variance, we have to use the formula:
`sigma^2 = int((x-u)^2 * f(x)) dx`.
Here, `int` means the integration of `(x-u)^2 * f(x)` over the interval `[2, 8]`.
So, `sigma^2 = int((x-u)^2 * f(x)) dx
= int((x-(10X/3))^2 * X/18) dx` over the interval `[2, 8]`
=`X/18 int((x-(10X/3))^2) dx` over the interval `[2, 8]`
=`X/18 int(x^2 - (20/3) x + (100/9)) dx` over the interval `[2, 8]`
=`X/18 [(x^3/3) - (10/3) (x^2/2) + (100/9) x]` over the interval `[2, 8]`
=`X/54 [(8^3 - 2^3) - (10/3) (8^2 - 2^2) + (100/9) (8 - 2)]`
=`X/54 [1240]`
=`20X/27`.
Therefore, the variance is `20X/27`.
To find the standard deviation, we have to use the formula: `sigma = sqrt(sigma^2)`.
So, `sigma = sqrt(sigma^2) = sqrt(20X/27) = sqrt[4*5X/27] = [2 sqrt(5X/27)]/3`.
Therefore, the standard deviation is `[2 sqrt(5X/27)]/3`.
Hence, the expected value is `10X/3`, the variance is `20X/27`, and the standard deviation is `[2 sqrt(5X/27)]/3`.
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Related Questions
Leila wants to rent a boat and spend at most $93. The boat costs $8 per hour, and Leila has a discount coupon for $3 off. What are the possible numbers of
hours Leila could rent the boat?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
Answer:
0 ≤ t ≤ 18
Step-by-step explanation:
The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.
Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.
According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:
5t ≤ 93
This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.
Simplifying the inequality:
5t ≤ 93
Dividing both sides by 5 (since the coefficient of t is 5):
t ≤ 93/5
t ≤ 18.6
Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:
t ≤ 18
0 ≤ t ≤ 18
Answer: 0≤t≤12
Step-by-step explanation:
(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)
If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.
Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.
Derive u(c,n)=ln(c)+0.4×ln(1−n) w.r.t. n which stands for labor. 1/c 1/n 0.4/(1−n) 0.4 ∗
1/(1−n) ∗
(−1) QUESTION 18 Derive the following function u(c,n,h)=(5×ln(c)×2×ln(1−n))+ 1−γ
h 1−γ
where γ=2.5 w.r.t. h. The evaluate the numeric value of this derivative at the point c=1, n=0.5, and h=2
Answers
To derive the function u(c, n, h) = \((5 * ln(c) * 2 * ln(1 - n)) + (1 - γ) / h\)with respect to h, we can follow the standard rules of differentiation. the numeric value of the derivative at the given point is -0.375.
Step 1: Take the derivative of each term separately.
The derivative of 5 * ln(c) * 2 * ln(1 - n) with respect to h is 0 since h does not appear in this term.
The derivative of (1 - γ) / h with respect to h can be found using the quotient rule:
\(d/dh [(1 - γ) / h] = [(h * 0 - (1 - γ) * 1) / h^2] = -(1 - γ) / h^2\)
Step 2: Simplify the derivative.
The derivative of u(c, n, h) with respect to h is -(1 - γ) / h^2.
Now, we can evaluate the numeric value of this derivative at the point c = 1, n = 0.5, and h = 2.
γ = 2.5
c = 1
n = 0.5
h = 2
Substituting these values into the derivative expression:
\(d/dh [(5 * ln(c) * 2 * ln(1 - n)) + (1 - γ) / h]\)
= -(1 - γ) / h^2
= -(1 - 2.5) / 2^2
= -1.5 / 4
= -0.375
Therefore, the numeric value of the derivative at the given point is -0.375.
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Triangle GHJ with coordinates
G (2, -9), H (3, 8), and/(1,6) is
rotated 270° counterclockwise
about the origin.
Answers
When Triangle GHJ is rotated 270° counterclockwise about the origin the points would be:
G' = (-9, -2) H' = (8, -3) J' = (6, -1)What are the coordinates after 270° counterclockwise rotation?When a figure is rotated 270° counterclockwise about the origin, the vertices go from (x, y) to (y, -x).
This means that the vertices of the GHJ prime will be:
G = (2, -9)
G' = (-9, -2)
H = (3, 8)
H' = (8, -3)
J = (1, 6)
J' = (6, -1)
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do these ordered pairs satisfy a linear function? explain (1,-5),(1,0)(1,5)(1,10)
Answers
Answer:
Yes, because the x-coordinate does not change. It would be a vertical, linear solution.
Two times x is 8 more than y. The sum of x and two times y is 14. Write two equations and graph to find the value of y.
y = -6
y = 4
y = -4
Answers
Answer:
y = 4
Step-by-step explanation:
2x = y+ 8
x + 2y = 14
x = 14 - 2y
2 * (14 - 2y) = y + 8
28 - 4y = y + 8
y + 4y = 28 - 8
5y = 20
y = 4
x = 14 - 2*4 = 6
Answer:
y=4
Step-by-step explanation:
I took the test.
Identify which of the following factoring pattern each of the following polynomials fit
Answers
EXPLANATION
Given the polynomials in the problem, we can assevere that:
Formula of Perfect Square Trinomial:
(a+b)^2 = a^2 + 2ab + b^2
Difference of Squares formula:
(a^2 - b^2)
Now, we need to find what formula match better.
y^2 + 12y - 36 -----> Neither
Help me ASAP please!!!
Answers
Answer:
85 inches²
Step-by-step explanation:
Each triangle equals 15 inches
15(4)=60
Square= 5×5=25
60+25=85 inches²
Use the solution method from this example to find a basis for the given subspace. S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]} Give the dimension of the basis. v
Answers
Answer:
Step-by-step explanation:
The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.
To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:
[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]
R2 - 3R1 -> R2
R3 -> R3 + 2R1
[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]
-1/2R2 -> R2
[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]
R3 - R2 -> R3
[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]
We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:
[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]
Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.
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Fill in the blanks to explain the meaning of "fragments."
Selma had been arranging some flowers in her favorite vase when she
accidentally knocked it over. The vase had shattered. So Selma collected
the fragments and put them in a pile, pushing aside the scissors she had
used to cut the tough stems. Next, she looked online for some tips on how
to fix the vase, and then she began gluing the vase back together.
Selma picked through the
the vase.
on the table. Then she decided to
Answers
The meaning of fragments as used in the passage above is pieces. This means that Selma had arranged to collect the pieces of the broken vase.
What is the meaning of fragments?The meaning of fragments as used in the passage above is pieces. To determine the meaning of a word, we can look at the dictionary meaning as well as the contextual meaning.
The contextual meaning of the word fragments can be seen from what happened earlier which was the breakage of the vase. So, after the vase broke, Selma picked its pieces.
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Answer:
Selma picked through the (broken bits) on the table. The she decided to (repair) the vase.
The sail of a boat is in the shape of a right triangle. which expression shows the length, in meters, of the sail? the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long. 7(tan 50°) 7(sin 50°) tangent 50 degrees over 7 sine 50 degrees over 7
Answers
The expression for the length of the sail is x = 7( tan 50° ).
According to the given question.
The sail of a boat is in the shape of a right triangle.
And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.
Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side
And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.
So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.
Let the length of the sail be x meters.
Now, in the given right angled triangle
We can say that
tan A = Opposite side/Adjacent side
⇒ tan 50° = x/7
⇒ x = 7( tan 50° )
Hence, the expression for the length of the sail is x = 7( tan 50° ).
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4/8y=3/8. Solve for y. (The numbers are fractions)
Answers
if the area of a triangle is 30 . 2 in. 2 and the base is 5 in., what is the height?
Answers
If the area of a triangle is 30.2 in² and the base is 5 in, the height of the triangle is 12.08 in.
To find the height of the triangle, follow these steps:
The given information is that the area of a triangle = 30.2 in² and the base = 5 in. We need to calculate the height of the triangle which can be found using the formula for the area of a triangle. Area of a triangle = 1/2 × base × height.\(\\\)⇒ 30.2 = 1/2 × 5 × height\(\\\)⇒ 30.2 = 2.5×heightSo, we have found that height = 30.2 / 2.5 = 12.08Therefore, the height of the triangle is 12.08 inches.
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I need help with this, if anyone can I appreciate it. ✨
Answers
Answer:
85, -91
Step-by-step explanation:
The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -4, 0, and 2.
Which graph could be the graph of f(x)?
Answers
the function will be f(x) = x³ + 2 x² - 8x.
We are given that:
The degree of the polynomial function f(x) is = 3
Roots of the function for f(x) = 0 are:
-4, 0 and 2
That is
x = -4, x = 0 and x = 2
Which can also be written as:
x + 4 = 0, x = 0 and x - 2 = 0
So, the function will be:
f(x) = (x + 4) (x) (x - 2)
f(x) = x (x² - 2 x + 4 x - 8)
f(x) = x (x² + 2 x - 8)
f(x) = x³ + 2 x² - 8x
Graph of the function is shown in the image.
Therefore, the function will be f(x) = x³ + 2 x² - 8x.
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Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answers
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
carla believed that her teammates on the track team were faster than she was, so she began putting in extra practices in order to become just as fast as them. this is an example of . a. compensation b. rationalization c. regression d. displacement please select the best answer from the choices provided a b c d
Answers
Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
Carla began putting in extra practices in order to become just as fast as them. This is an example of: Option A. CompensationCarla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.
Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.
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Suppose that during one period of extreme cold, the average daily temperature decreased 11 F each day.
How many days did it take for the temperature to decrease by 9 OF? (Examples 1 and 3)
STEP 1
Write an equation. Let x represent
X=
STEP 2 Solve the equation. Show your work.
It took
days for the
temperature to decrease by 9 °F.
Answers
Answer:
The temperature decreased by 9 °F in 0.82 days.
Step-by-step explanation:
Let the number of days it takes for the temperature to decrease by 9 °F be \(x\).
Given:
Average daily temperature decreases by \(11\) °F.
Decrease of temperature in 1 day = \(11\) °F.
∴ Decrease in temperature in x days is \(11x\).
Now, as per question, decrease in temperature in 'x' days is 9 °F.
Therefore, \(11x=9\)
\(x=\frac{9}{11}\)
\(x=0.82\)
Therefore, the temperature decreased by 9 °F in 0.82 days.
The probability that a hockey team will win a match is 0.4. The probability that the team will draw is 0.3. Work out the probability that the team will not win. (1 Point)
Answers
Answer:
P(team will win)=0.4
P(team will draw)=0.3
P(t want will not win) = 1 - 0.4+0.3
=1-0.7=0.3
Please someone help solve:
2/2t√3≡4-2√3
Answers
Answer:
i'm assuming you want to solve for t?
t=(2√3+3)/6
how to find the measure of the obtuse angle
Answers
23x+68x-2=180
X=2
Justify: Same side interior angles
Answer:
Measure of obtuse angle is 134 degrees
Step-by-step explanation:
these two angles are supplementary so they add up to 180
68x-2 +23x=180
91x-2=180
91x = 182
x = 2
plug in x
68 (2) -2 = 134
23 (x) = 46
HELPPP PLEASEE SMART PEOPLE ON HERE
Answers
Answer: C
Step-by-step explanation:
Answer:
the answer is C I swear to yo mama
How do you tell if a pair of equations are parallel perpendicular or neither?
Answers
Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.
Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.
Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.
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The following question has two parts. First, answer part A. Then, answer part B. Part A:Gabriel's father has a garden in the back yard. The dimensions of the garden are shown here. The width is labeled as 2 2/3 feet. The length is labeled as 7 3/4 feet. Part A Calculate the area of the garden. Show at least one step before you show your solution. Part B:You found the area of the garden in Part A. Explain briefly, without doing any calculations, how you would find 5/6 of this area
Answers
The area of a rectangular garden with a width of 2 2/3 feet and a length of 7 3/4 feet is 22 and 5/6 square feet (22 5/6 sq.ft).
1) Solution to part A: Gabriel's father has a rectangular garden that is 2 2/3 feet wide and 7 3/4 feet long. First, convert the mixed number to an improper fraction: 2 2/3 = 8/3.2 2/3 is 8/3 when simplified.
Let's find the length of the garden. First, convert the mixed number to an improper fraction:
7 3/4 = 31/4.3 3/4 is 31/4 when simplified.
Now we have the dimensions of the garden let's find the area of the garden.
The area formula for a rectangle is length * width. Length = 31/4 ft. and width = 8/3 ft.
Area = (31/4) * (8/3) sq.ft
= 62/3 sq.ft
= 20 2/3 sq.ft.
Approximate area of the garden is 20.67 square feet (rounded to hundredth).
Therefore, the area of the garden is 20 2/3 square feet (20.67 sq.ft).
2) Solution to part B: In order to find 5/6 of the area of the garden, we multiply the garden's area by 5/6.5/6 of the area of the garden = (5/6) * 20 2/3 sq.ft
= (5/6) * (62/3) sq.ft
= (5*62)/(6*3) sq.ft
= 310/18 sq.ft
= 155/9 sq.ft
= 17.22 sq.ft (rounded to hundredth).
Therefore, without performing any computations, 5/6 of the area of the garden can be obtained by multiplying the area of the garden by 5/6.
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What is the formula for the sum of exterior angles in a polygon?
Answers
The sum of a regular polygon's exterior angles will always equal 360 degrees.
What is exterior angles?Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).
Here,
The sum of the exterior angles of a regular polygon will always equal 360 degrees.
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a consumer group is investigating the number of flights at a certain airline that are overbooked. they conducted a simulation to estimate the probability of overbooked flights in the next 5 flights. the results of 1,000 trials are shown in the following histogram. based on the histogram, what is the probability that at least 4 of the next 5 flights at the airline will be overbooked?
Answers
The probability of at least 4 of the next 5 flights being overbooked is 1.0%.
The probability of an event occurring is determined by analyzing the data from a sample.
A histogram is often used to visualize the distribution of data, which can be used to calculate the probability of an event occurring.
By examining the histogram, you can determine the probability of a certain event occurring based on the height of the corresponding bar in the graph.
From the histogram, it is clear that the probability of at least 4 of the next 5 flights being overbooked is 1.0%.
This is because there is only one bar in the histogram that corresponds to the probability of 4 out of 5 flights being overbooked.
This bar has a height of 1.0%, which indicates a 1.0% probability of at least 4 out of 5 flights being overbooked.
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Geometry Application. The perimeter of a square is 36 inches. Write and solve an equation to find the length of each side of the square. (Hint: Remember that the perimeter is the distance around a figure.)
Answers
Answer:
144
Step-by-step explanation: simple do 36x4 which equals 144. the for comes from all sides of the shape
Brainliest answer to the quickest and most accurate response
Answers
(7x+14)+(4x-22)=180
11x-18=180
11x=198
x=18
(4)(18)-22
50
the small angles are 50
(3y+11)+10y=180
13y+11=180
13y=169
y=13
(10)(13)
130
the large angles are 130
proof:
(130(2))=(50(2))= 360
message
A kitchen was remodeled and granite counter tops were installed. A rectangular island in the kitchen now has a granite top measuring 8 ft. By 6. 2 ft. By 5. 3 inches. The density of granite is 2. 7 kg/cm3.
How much does the counter top weigh in pounds?
1 kg = 2. 2 pounds
Answers
The weight of the countertop in pounds is 3693121.08 pounds.
Given that :
A kitchen was remodelled and granite countertops were installed.
The granite top is rectangular.
Dimensions are 8 ft. by 6. 2 ft. by 5.3 inches.
Convert the measurements into centimetres.
1 feet = 30.48 cm
So,
8 feet = 243.84 cm
6.2 feet = 188.976 cm
5.3 feet = 13.462 cm
The volume of the rectangular container is the product of the length, width and height.
Volume of the granite top = 243.84 × 188.976 × 13.462
= 620327.719342 cm³
Density of the granite = 2. 7 kg/cm³.
Mass = Density × Volume
= 2. 7 × 620327.719342
= 1674884.84222 kg
= 1674884.84222 × 2.2 pounds
= 3693121.08 pounds
Hence the mass of the countertop is 3693121.08 pounds.
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Some objects, like the wrecking ball, have energy as a result of their motion.
4. How does the wrecking ball have the potential to exert force on another object?
Answers
The energy transferred to any object by wrecking ball is proportional to force exerted on the object.
What is law of conservation of energy?
The law of conservation of energy states that energy can never be created nor destroyed but can be converted from one form to another.
The wrecking ball, have energy as a result of their motion and this energy is known as kinetic energy.
K.E = ¹/₂mv
where;
v is the velocity of the wrecking ball in motion.Based on the law of conservation of energy, when a wrecking ball hits another object, some of its kinetic energy will be transferred to the object while some of the kinetic energy will be converted into thermal energy.
The energy transferred to any object by wrecking ball is proportional to force exerted on the object.
K.E = force x displacement
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how do i factorize x2+14x+49
Answers
Answer:
(x + 7) (x + 7)
Step-by-step explanation:
What's the square root of x^2?
That's x
What's the square root of 49
That's 7
And what makes 14?
7 + 7 = 14
So therefore the answer is (x + 7) (x + 7)
Easy Kevin Durant is so smart!
Answer:
The middle number is 14 and the last number is 49.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 14
Multiply together to get 49
Can you think of the two numbers?
Try 7 and 7:
7+7 = 14
7*7 = 49
Fill in the blanks in
(x+_)(x+_)
with 7 and 7 to get...
(x+7)(x+7)
Answer:
(x+7)(x+7)