The expected value of X is 8.
a) Here is a sketch of the density function p(x) with respect to the detection area:
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_____________|_____________
1 1.5 3 6 10
b) The formula for the expected value (or mean) of a continuous random variable X with density function p(x) is:
E(X) = ∫xp(x)dx
To find the expected value of X for the given density function, we need to split the integral into several parts based on the different intervals where p(x) takes different forms:
E(X) = ∫_(-∞)^1 xp(x)dx + ∫_1^2 xp(x)dx + ∫_2^3 xp(x)dx + ∫_3^6 xp(x)dx + ∫_6^10 xp(x)dx + ∫_10^∞ xp(x)dx
Note that the first and last integrals are both zero, since p(x) = 0 for x < 1 and x > 10. The other integrals can be evaluated as follows:
∫_1^2 xp(x)dx = ∫_1^2 (x-1)dx = [x^2/2 - x]_1^2 = 1/2
∫_2^3 xp(x)dx = ∫_2^3 (x-1)dx = [x^2/2 - x]_2^3 = 3/2
∫_3^6 xp(x)dx = ∫_3^6 (1/3)dx = 1
∫_6^10 xp(x)dx = ∫_6^10 (x/12)dx = [x^2/24]_6^10 = 5/2
Therefore, we have
E(X) = 0 + 1/2 + 3/2 + 1 + 5/2 + 0 = 8
So the expected value of X is 8.
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Quadrilateral DEFG is a rectangle, DH=4w+20, and GH=6w. What is GH?
The value of GH in the rectangle is 60 units.
How to find the side of a rectangle?A rectangle is quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
Therefore, the diagonal of the rectangle divides the rectangle into congruent triangles.
Therefore,
DH = GH
4w + 20 = 6w
subtract 4w from both sides of the equation
4w - 4w + 20 = 6w - 4w
20 = 2w
divide both sides of the equation by 2
w =20 / 2
w = 10
Therefore,
GH = 6(10)
GH = 60 units
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It costs $1.12 to buy 7 gift tags. If the tags all cost the same amount, what is the price of each tag?
Each gift tag costs $0.16.
We have,
To solve this problem, we need to determine the price of each gift tag given that it costs $1.12 to buy 7 tags.
Let "x" be the price of each gift tag in dollars.
Then, if we buy 7 tags, the total cost would be 7 times the price of each tag:
7x
We know that this total cost is $1.12, so we can set up a proportion:
7x / 1 = 1.12 / 1
Simplifying, we get:
7x = 1.12
Now we can solve for "x" by dividing both sides by 7:
x = 1.12 / 7
Simplifying, we get:
x = 0.16
Therefore,
Each gift tag costs $0.16.
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Find the zeros of the quadratic function f(x) = –3x2 + 12x – 9 from the graph.
A −9
B−3 and −9
C1 and 3
D 2
Check the picture below.
What is the mean absolute deviation of the data set?
{12, 10, 10, 8, 6, 7, 7, 12}
01
02
06
09
Answer:
(b) 2
Step-by-step explanation:
You want the mean absolute deviation of the data ...
{12, 10, 10, 8, 6, 7, 7, 12}
MADThe mean absolute deviation (MAD) is the mean of the absolute values of the differences between the data values and their mean. The calculation of this is shown in the attachment.
The mean absolute deviation is 2.
<95141404393>
Mike measured the height of an art frame as 6. 33 feet, but the actual height was 7 feet. What is the percent of error in Mike's measurement?
Mike's measurement therefore had a percent error of 9.57% .
Finding the discrepancy between Milk's measurement and the real height of the art frame, dividing it by the actual height, and multiplying the result by 100 will get the percent inaccuracy.
Mike's measurement and the real height differ in the following ways:
6 feet - 7 feet = 0.67 feet.
We divide this difference by the actual height to determine the percent error:
7 feet / 0.67 feet is 0.0957
The percentage is finally calculated by multiplying by 100:
0.0957 x 100 = 9.57%
Mike's measurement therefore had a percent error of 9.57%. This indicates that the difference between his measurement and the actual height of the art frame was roughly 9.57%.
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What is the length of line segment EB? 42 units 50 units 65 units 73 units
The length of line segment EB is Option C- 65 units .
In a parallelogram, opposite sides are equal. Therefore, AE = CB = p-8 and CE = AB = 2p-58. Also, AD and BE are diagonals of the parallelogram, and they bisect each other. Thus, we can say that DE = EB. So, we have DE = p+15 and EB = p+15.
AE + EB + CE + DE = perimeter of parallelogram
(p-8) + (p+15) + (2p-58) + (p+15) = 4p - 56
4p - 56 = 4(p - 14)
Therefore, the perimeter of the parallelogram is 4(p-14). Since opposite sides are equal in a parallelogram, we can say that:
2(p-8) + 2(2p-58) = 4(p-14)
p = 50
Substituting the value of p in the equation EB = p+15, we get:
EB = 50 + 15 = 65.
However, we need to remember that DE = EB. Therefore, the length of line segment EB is 65 units (Option C).
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the complete question is:
AE = p 8, CE = 2p 58, and DE = p + 15 in the parallelogram illustrated. How long is the line segment EB?
A - 40units
B.50 units
C.65 units
D.73 units
Answer:
c) 65 units
Step-by-step explanation:
2023 on edge
Find the area and perimeter of rectangle DEFG whose
endpoints are D(-3, 1), E(1, 3), F(2, 1), and G(-2, -1)
The area of rectangle DEFG is 16 square units and its perimeter is 12 units.
To find the area, we can use the formula: Area = length x width We can find the length and width by calculating the distance between the coordinates of opposite sides of the rectangle.
Length = EF =
[tex] \sqrt{} ((2-1)^2 + (1-3)^2)[/tex]
=
[tex] \sqrt{} (2 + 4) = \sqrt{} (6)[/tex]
Width = DG =
[tex] \sqrt{} ((-3+2)^2 + (1+1)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)[/tex]
The area of rectangle DEFG = length x width =
[tex] \sqrt{} (6) x \sqrt{} (6)[/tex]
= 6 x 2 = 16 square units.
To find the perimeter, we can add up the lengths of all four sides: Perimeter = DE + EF + FG + GD
DE =
[tex] \sqrt{} ((1+3)^2 + (-3+(-1))^2) = \sqrt{} (16 + 4) = \sqrt{} (20)[/tex]
EF =
[tex] \sqrt{} ((2-1)^2 + (1-3)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)[/tex]
FG =
[tex] \sqrt{} ((2+2)^2 + (1+1)^2) = \sqrt{} (16 + 4) = \sqrt{} (20)[/tex]
GD =
[tex] \sqrt{} ((-2+3)^2 + (-1-1)^2) = \sqrt{} (1 + 4) = \sqrt{} (5)[/tex]
The perimeter of rectangle DEFG =
[tex] \sqrt{} (20) + \sqrt{} (6) + \sqrt{} (20) + \sqrt{} (5) [/tex]= 12 units.
Hence, The area of the rectangle is 16 square units and the perimeter is 12 units.
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Sheri took out a $396,000, 15-year mortgage with an APR of 3.65%.
Her monthly payment is $2,820.59. What was her ending balance at the
end of that first month?
Answer:
Her balance would be $ 90,931.84.
Step-by-step explanation:
trust me
Please help!
Need help fast.
A) The corresponding unit rate for each package is,
For Cannie cakes;
⇒ $1.85
Bark bits;
⇒ $2.25
Woofy Waffles;
⇒ $1.9
B) The best buy by the units rates is, Cannie cakes.
We have to given that;
Jeremiah needed dog food for his new pippy.
Now, We get;
A) The corresponding unit rate for each package is,
For Cannie cakes;
⇒ 74/40
⇒ $1.85
Bark bits;
⇒ 27/12
⇒ $2.25
Woofy Waffles;
⇒ 76 / 40
⇒ $1.9
Hence, We get;
B) The best buy by the units rates is, Cannie cakes.
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Someone help please
The question is in the attachment.
From the provided data, it can be deduced that "Butterflies and Ladybugs" is seemingly preferred over the other option in question.
How to explain the dataConfirmation of this determination is available because sample 2 received a greater number of votes for "Butterflies and Ladybugs" than sample 1 did. Additionally, the total amount of votes awarded to "Butterflies and Ladybugs" was more pronounced compared to the two remaining choices within sample 2.
One should not make assertions from this dataset stating that "Butterflies and Ladybugs" are the most favored choice overall or universally.
This claim cannot be verified due to the small size of the research survey as solely two samples were utilized; therefore, we may infer that these findings could potentially vary if an alternative method or larger experiment was adopted.
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6. Find the image of (3, 6) reflected across the y-axis.
(6,3)
(3,-6)
(-3,-6)
(-3,6)
The image of the point after the reflection over the y-axis is (-3, 6)
How to find the image after the reflection?For any point of the form (x, y), a reflection across the y-axis just changes the sign of the x-value.
Then the reflection gives:
(x, y) ---> (-x, y)
Here we apply this reflection to the point (3, 6), then we will get:
(3, 6) ---> (-3, 6)
That is the image after the reflection over the y-axis, then the correct option is the fourth one.
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Whether at home, at school, where you work, or where you play, you see marketing in almost everything you do. Yet there is much more to marketing. Behind it all is a massive network of people and activities competing for your attention and purchases. What does "it" refer to? O a massive network O everything you do O attention O marketing
"it" refers to marketing.
The statement emphasizes that marketing is present in various aspects of our lives and is supported by a massive network of people and activities that compete for our attention and purchases.
Marketing refers to any actions a company takes to attract an audience to the company's product or services through high-quality messaging. Marketing aims to deliver standalone value for prospects and consumers through content, with the long-term goal of demonstrating product value, strengthening brand loyalty, and ultimately increasing sales.
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what is the lcm of 2 4 6 9 10
Answer:
We can find the LCM (Least Common Multiple) of these numbers by finding the prime factorization of each number and then multiplying the highest power of each prime factor together.
Prime factorization of 2: 2
Prime factorization of 4: 2^2
Prime factorization of 6: 2 * 3
Prime factorization of 9: 3^2
Prime factorization of 10: 2 * 5
The highest power of 2 is 2^2.
The highest power of 3 is 3^2.
The highest power of 5 is 5^1.
Multiplying these numbers together gives us:
2^2 * 3^2 * 5^1 = 180
Therefore, the LCM of 2, 4, 6, 9, and 10 is 180.
Step-by-step explanation:
When a sphere is moved about its center it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position. Prove using something related to orthogonal properties.
To prove that when a sphere is moved about its center, it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position using orthogonal properties, follow these steps:
1. Consider a sphere with center O and any diameter AB.
2. When the sphere is moved about its center, the center O remains fixed.
3. Rotate the sphere such that diameter AB is now in a new position A'B'.
4. Since the sphere has been rotated about its center, the orthogonal properties are preserved. This means that the planes that are perpendicular to the diameter at the center O remain unchanged.
5. The orthogonal planes to diameter AB intersect at the center O and form a fixed line in space.
6. Now, rotate the sphere again, such that diameter A'B' returns to its initial position as AB. This rotation is possible because the orthogonal planes and their intersection (the fixed line) are preserved.
7. Since diameter A'B' has returned to the initial position of AB, it proves that it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position.
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Determine the interval(s) on which the given function is decreasing.
A. (–[infinity], –1) ∪ (0,[infinity])
B. (1, [infinity])
C. (–[infinity], –1) ∪ (1, [infinity])
D. (–1, 0)
The given function is decreasing on the interval (-1, 3/2).
To determine the intervals on which a function is decreasing, we need to find the values of x for which the function's derivative is negative. If the derivative is negative, then the function is decreasing.
Let's consider each option:
A. (–[infinity], –1) ∪ (0,[infinity])
To find the derivative of the function, we first need to find the function itself. Without knowing the function, we cannot determine the derivative or the intervals on which it is decreasing.
B. (1, [infinity])
Again, we need to know the function to determine its derivative and the intervals on which it is decreasing.
C. (–[infinity], –1) ∪ (1, [infinity])
Similarly, we need to know the function to determine its derivative and the intervals on which it is decreasing.
D. (–1, 0)
Let's assume the function is f(x). To find its derivative, we can use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1).
If the given function is decreasing on the interval (-1, 0), then its derivative, f'(x), must be negative on that interval. Therefore, we can set up the inequality f'(x) < 0 and solve for x.
Let's first find the derivative of the function:
f(x) = x^2 - 3x + 2
f'(x) = 2x - 3
Now we can set up the inequality:
2x - 3 < 0
Solving for x, we get:
x < 3/2
So the function is decreasing on the interval (-1, 3/2).
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Pythagorean theorem HELP PLEASE
Answer:
9.22
Step-by-step explanation:
pythagorean theorem is C squared= A squared +B squared. because C is 11 and if you square 11 its 121 and 6 squared is 36 so if u do 121-36 its 85
and if u root 85 it comes out as 9.22
Sylvia owns a bookstore called The Happy Cat, currently valued at $175, 000. Determine the value of the business in 3 years if
Sylvia predicts 13% growth.
$285, 332.88
$252,506.98
$268,418.60
$223,457.50
Answer:
To calculate the value of the business in 3 years, we use the formula for compound interest:
A = P * (1 + r/100)^(t)
where A is the final amount, P is the initial amount, r is the annual interest rate as a decimal, t is the number of years.
A = $175,000 * (1 + 0.13/1)^(1*3) = $268,418.60
Therefore, the value of the business in 3 years is $268,418.60. Option C is the correct answer.
Solve the first equation (a)
The simplified value of the expression is 12km³.
We have,
[tex]12k^2m^8 \div 4km^5[/tex]
This can be written as:
[tex]\frac{12k^2m^8}{ 4km^5}[/tex]
Canceling common expression.
= 12km³
Thus,
The simplified value of the expression is 12km³.
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What is the outlier for the data set?
A. 5
B. 9
C. 10
D. there is none
Answer:
The answer to your problem is, A. 5
Step-by-step explanation:
What is an outlier?
What just like it says an outlier it something “ away “ or “ out of civilization of its fellow numbers “
You can see that the hours of 8 - 10 they are all bunched up together
But you can see hour 5 seems a bit lonely
Which then we call he outlier
Thus the answer to your problem is, A. 5
Consider the inner product (f, g) = integral -1 to 1, f(x)g(x) dx on P2, the vector space of all polynomials of degree 2 or less. Find the projection of f = x^2 + 5x onto the subspace W of P2 spanned by the orthonormal basis (g1, g2), where g1=1/√2 and g2 =√ (3/2).
Proj w(f) = _____
The projection of f onto the subspace W, we need to take the inner product of f with each of the basis vectors in W and multiply by the basis vectors. Then we add the results together. Therefore, the projection of f onto W is 2/3 + √2.
So, first we need to find the inner products of f with g1 and g2:
(f, g1) = integral -1 to 1, f(x)g1(x) dx
= integral -1 to 1, ([tex]x^2[/tex] + 5x)(1/√2) dx
= (1/√2) integral -1 to 1, [tex]x^2[/tex] dx + (5/√2) integral -1 to 1, x dx
= (1/√2) (2/3) + (5/√2) (0)
= √2/3
(f, g2) = integral -1 to 1, f(x)g2(x) dx
= integral -1 to 1, ([tex]x^2[/tex] + 5x)√(3/2) dx
= √(3/2) integral -1 to 1, [tex]x^2[/tex] dx + √(3/2) integral -1 to 1, 5x dx
= √(3/2) (2/3) + √(3/2) (0)
= √(2/3)
Now we can find the projection of f onto W:
projW(f) = (f, g1) g1 + (f, g2) g2
= (√2/3) (1/√2) + (√(2/3)) (√(3/2))
= 2/3 + √2
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Arc/Angle measures I need help with this
Step-by-step explanation: One way to measure an arc is with degrees. The measure of an arc is equal to the measure of its corresponding central angle. Below, m D C ^ = 70 ∘ and m G H ^ = 70 ∘ . When you measure an arc in degrees, it tells you the relative size of the arc compared to the whole circle.
Posterior probabilities are _____.
a. simple probabilities
b. conditional probabilities
c. joint probabilities
d. marginal probabilities
83. The numbers from 0 to 24 are to be placed in the boxes to form a magic square. Some
of the numbers are already filled in. What number goes in the box marked A?
19 7
A
2
16
24 12
234
1 27 19
22
18
21
17
Solve the equation dX(t) = rX(t)(1 - X(t)dt + oX(t)dW, XO) = Xo, where r and o are constants. Find X(t), E(X(t)) and V(X(t)).
X(t) = Xo/[1 + (1 - Xo)/Xo exp(-[r - o^2/2]t - oW(t))]
E[X(t)] = Xo/(1 + (1 - Xo)/Xo exp(-r t)),
V[X(t)] = Xo^2 exp(rt)/(1 + (1 - Xo)/Xo exp(rt))^2 - Xo^2/(1 + (1 - Xo)/Xo exp(-r t))^2.
The given equation is a stochastic differential equation (SDE) of the form dX(t) = a(X(t))dt + b(X(t))dW(t), where W(t) is a Wiener process (Brownian motion), a(X(t)) = rX(t)(1 - X(t)), b(X(t)) = oX(t), and Xo is the initial condition.
To solve this SDE, we use Itô's lemma, which states that for a function f(X(t)) of a stochastic process X(t), the SDE for f(X(t)) is given by df(X(t)) = (∂f/∂t)dt + (∂f/∂X)dX(t) + 1/2(∂^2f/∂X^2)(dX(t))^2.
Applying Itô's lemma to the function f(X(t)) = ln(X(t)/(1 - X(t))), we get df(X(t)) = [1/X(t) + 1/(1 - X(t))]dX(t) - 1/2[X(t)^(-2) + (1 - X(t))^(-2)](dX(t))^2.
Substituting a(X(t)) and b(X(t)) in the above expression, we get d[f(X(t))] = [r(1 - 2X(t))dt + o(1 - 2X(t))dW(t)] - 1/2[r^2X(t)(1 - X(t))^2 + o^2X(t)^2]dt.
Integrating both sides of the above expression from time 0 to t and using the initial condition X(0) = Xo, we get ln[X(t)/(1 - X(t))] = ln[Xo/(1 - Xo)] + [r - o^2/2]t + oW(t).
Solving for X(t), we get X(t) = Xo/[1 + (1 - Xo)/Xo exp(-[r - o^2/2]t - oW(t))].
Taking the expectation and variance of X(t), we get:
E[X(t)] = Xo/(1 + (1 - Xo)/Xo exp(-r t)),
V[X(t)] = Xo^2 exp(rt)/(1 + (1 - Xo)/Xo exp(rt))^2 - Xo^2/(1 + (1 - Xo)/Xo exp(-r t))^2.
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To determine how attractive a particular market is using the BCG portfolio analysis, ________ is(are) established as the vertical axis.
a. Competitive intensity
b. Sales dollars
c. Market size
d. Market growth rate
e. Market profit potential
To determine how attractive a particular market is using the BCG portfolio analysis, Market profit potential is(are) established as the vertical axis.
Market profit potential is established as the vertical axis in the BCG portfolio analysis to determine how attractive a particular market is.
The BCG (Boston Consulting Group) portfolio analysis is a framework used to analyze a company's business units or product lines based on their market growth rate and relative market share. The relative market share is established as the horizontal axis, and the market growth rate is established as the vertical axis. The resulting four quadrants are named: "Stars," "Cash Cows," "Question Marks," and "Dogs."
However, in some modified versions of the BCG matrix, such as the GE-McKinsey Matrix, the vertical axis may be replaced with other factors such as market attractiveness, industry strength, or competitive position. Nevertheless, in the original BCG matrix, the vertical axis represents the market growth rate, which is a measure of the market's potential for growth and profitability.
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How do I find the period of a sine/cosine function??
For Example:
Answer: use 2 π | b | , where is the frequency.
Step-by-step explanation:
To find the period of any sine or cosine function, use 2 π | b | , where is the frequency. Using the first graph above, this is a valid formula: 2 π 1 2 = 2 π ⋅ 2 = 4 π .
Hope that helps
0.75 + 0.006x > 0.81
Answer:
x > 10
Step-by-step explanation:
Subtract 0.75 from 0.81.
This gives you 0.06
Then divide, by the coefficient of x, 0.006
x > 10
Answer:
x > 10
Step-by-step explanation:
0.75 + 0.006x > 0.81
-.75 -.75
0.006x > 0.06
---------- -------
0.006 0.006
x > 10
Emily recorded the test scores of the students in her class
in the dot plot below. Which measure of center would be best
to use for this distribution?
The measure of center that would be best to use for this distribution is the median
How to explain the measure of centerIf the distribution is generally symmetric, the mean is the appropriate measure of center to use. This is because the mean considers every value in the distribution and is affected equally by each value.
As a result, if the dot plot has a skewed distribution, the median is the best measure of center to employ, whereas the mean is the best measure of center to use if the distribution is nearly symmetric.
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Bob has a bag of jelly beans. There are 5 red jelly beans and 6 blue jelly beans in the bag. Write a ratio that compares the number of red jelly beans to the number of blue jelly beans.
Group of answer choices
A. 6:5
B. 5:6
C. 5:11
Answer: B
Step-by-step explanation: red to blue
Answer: B
Step-by-step explanation:
Because it asks for you to create a ratio comparing red to blue, you need to order it that way. Since there are 5 reds and 6 blues, you list the 5 in the ratio before you list the 6. It would end up looking like this:
5:6
Is there a rigid transformation that would map ΔABC to ΔDEC?
Answer:
Step-by-step explanation:
Yes, there is a rigid transformation that can map triangle ΔABC to triangle ΔDEC.
A rigid transformation is a transformation that preserves the size, shape, and orientation of a figure. It includes translations, rotations, and reflections. In order for triangle ΔABC to be mapped to triangle ΔDEC, the two triangles must have the same size, shape, and orientation. This can be achieved through a combination of translation, rotation, and/or reflection. For example, if triangle ΔABC is translated by a certain vector and then rotated or reflected, it can be mapped onto triangle ΔDEC.
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