Find the third, fourth and fifth moments of an exponential random variable with parameter λ.
Answers
The third, fourth, and fifth moments of an exponential random variable with parameter λ are 12/λ^2, 24/λ^2, and 120/λ^2, respectively.
An exponential random variable with parameter λ has probability density function:
f(x) = λe^(-λx) for x ≥ 0
The nth moment of this distribution is given by:
μn = ∫[0,∞] x^n f(x) dx
We can solve this integral to find the nth moment:
μn = ∫[0,∞] x^n λe^(-λx) dx
To find the third moment:
μ3 = ∫[0,∞] x^3 λe^(-λx) dx
Let u = λx and du = λ dx
Substitute the limits and integrate by parts:
μ3 = [(-x^3 - 3x^2 - 6x - 6)e^(-λx)]0∞ + 6∫[0,∞] x^2 e^(-λx) dx
We can evaluate the first term as zero, since the exponential term goes to zero faster than any polynomial term. Then we use integration by parts again:
Let u = x^2 and dv = e^(-λx) dx, then du = 2x dx and v = (-1/λ)e^(-λx)
Substitute the limits and simplify:
μ3 = 6[(-x^2 - 2x - 2)e^(-λx)]0∞ + 12[(-x - 1/λ)e^(-λx)]0∞ + 12/λ^2
Again, the exponential terms evaluate to zero and we are left with:
μ3 = 12/λ^2
Similarly, the fourth moment can be found as:
μ4 = ∫[0,∞] x^4 λe^(-λx) dx
Using integration by parts twice, we get:
μ4 = 24/λ^2
Finally, the fifth moment can be found as:
μ5 = ∫[0,∞] x^5 λe^(-λx) dx
Using integration by parts three times, we get:
μ5 = 120/λ^2
Therefore, the third, fourth, and fifth moments of an exponential random variable with parameter λ are 12/λ^2, 24/λ^2, and 120/λ^2, respectively.
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Related Questions
A bakery has a sale for 25% off all bread. The sale price of a piece of bread is $16.
Which equation would calculate the original price of the item?
A 0.25y = 16
B 0.75y = 16
C y - 25 = 16
D y + 75 = 16
Answers
Answer:
A
Step-by-step explanation:
what dx gets doxy no matter what age?
Answers
It is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age.
Doxycycline is a broad-spectrum antibiotic that is used to treat a variety of bacterial infections. However, there are certain medical conditions and factors that may contraindicate the use of doxycycline.
Some of the common medical conditions that may prevent the use of doxycycline include:
Allergy or hypersensitivity to doxycycline or other tetracycline antibiotics.
Severe liver disease or impairment.
Pregnancy or breastfeeding.
Children under the age of 8 (because doxycycline can cause permanent discoloration of teeth and affect bone growth).
Kidney disease, because doxycycline is excreted through the kidneys and may accumulate to toxic levels.
In general, the use of doxycycline is based on the patient's medical history, the severity of the infection, and other factors such as age and weight. Therefore, it is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age.
Complete question : It is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age. what dx gets doxy no matter what age?
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factors other than the independent variable may also act on the dependent variable. if these factors vary systematically with the independent variable, they are called:
Answers
Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.
Factor which is other than the independent variable and might produce an effect in the given experiment.Manipulation of independent variable which has an effect on the expressions dependent variable.Other variables which has impact on changing the dependent variables are known as extraneous variable.Extraneous variables are also known as confounding variables.Confounding variables or extraneous variables these are the factors which does not manipulate and are part of the given experiment.Therefore, factors which vary systematically with the given independent variable is called confounds variables or extraneous variable.
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A deck of cards has 5 pink, 2 gray, and 6 black cards. You pick 2 cards from the deck without replacement. What is the probability that the first card is gray and the second card is pink?
Answers
Answer:
\(\frac{5}{78}\)
Step-by-step explanation:
First, find the probability that the first card is gray.
Since there are 13 cards in total, and 2 are gray, the probability will be 2/13
Next, find the probability that the second card is pink.
Since there are now 12 cards in total (since there is no replacement), and 5 are pink, the probability is 5/12.
Now, to find the probability that these are drawn in order, multiply the probabilities together:
\(\frac{2}{13}\) x \(\frac{5}{12}\)
= \(\frac{5}{78}\)
So, the probability is \(\frac{5}{78}\)
A common model for polymer configurational entropy considers each link in the polymer chain backbone to have only three possible values (the three staggered angles, 60,180,300 ) of X, the dihedral angle, all with the same probability and all independent of each other. For a polymer with N monomer units, there are N−1 links. One "configuration" of the polymer means one possible choice for all the N−1 dihedral angles, ×1,×2,…,×N−1. a) Find an equation for the probability of finding the polymer with N monomers in just one of its possible configurations. b) Find an equation for the entropy change in going from a state where only one configuration is allowed to a state where all configurations are allowed. c) If the polymer is stretched by an external force, the effective number of angles available to each link is reduced. Find an equation for the probability of spontaneously observing a polymer in any of the configurations that correspond to a stretched polymer with only two possible angles per link instead of three.
Answers
The equation for the probability of observing a polymer in any of the configurations that correspond to a stretched polymer is:
P = (1/2)^(N-1)
The probability of finding the polymer with N monomers in just one of its possible configurations can be calculated as follows:
Since each link in the polymer chain backbone has three possible values for the dihedral angle (60°, 180°, 300°), and all the angles are independent and have the same probability, the probability of a specific configuration for each link is 1/3.The total number of configurations for the polymer with N monomers is (1/3)^(N-1), since there are N-1 links in the polymer chain backbone.
Therefore, the equation for the probability of finding the polymer in just one configuration is:
P = (1/3)^(N-1)
b) To calculate the entropy change in going from a state where only one configuration is allowed to a state where all configurations are allowed, we need to consider the change in the number of accessible microstates.
In the initial state where only one configuration is allowed, the number of accessible microstates is 1.
In the final state where all configurations are allowed, the number of accessible microstates is (1/3)^(N-1), as mentioned in part a).
The entropy change (ΔS) is given by the equation:
ΔS = kB * ln(Wf / Wi)
Where kB is Boltzmann's constant, Wf is the number of accessible microstates in the final state, and Wi is the number of accessible microstates in the initial state.
Therefore, the equation for the entropy change is:
ΔS = kB * ln((1/3)^(N-1) / 1)
= kB * ln(1/3)^(N-1)
= (N-1) * kB * ln(1/3)
c) If the polymer is stretched by an external force, reducing the effective number of angles available to each link to two, the probability of observing a polymer in any of the configurations that correspond to a stretched polymer can be calculated.
Since each link now has two possible angles per link instead of three, the probability of a specific configuration for each link is 1/2.
The total number of configurations for the stretched polymer with N monomers is (1/2)^(N-1), since there are still N-1 links in the polymer chain backbone.
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Determine the equation of the parabola with focus
(
2
,
5
)
(2,5) and directrix
�
=
18
x=18.
Answers
The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².
A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating
straight line of that surface.
The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.
The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.
The axis of symmetry is the line through the focus and perpendicular to the directrix.
The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens
up" or "opens down.
The directrix is a fixed straight line used in the definition of a
parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the
distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's
the solution to the given problem:
The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)
The vertex is (h,k) = ((18+2)/2,5) = (10,5)
Then we can use the following formula: (x - h)² = 4p(y - k)
Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)
Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)
The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).
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Given the system of equations below. Use the Inverse of the matrix method to solve. x+2y+3z=11
2x+4y+5z=21
3x+5y+6z=27
Answers
The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.
The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.
Here, we will solve this system of equations using inverse of the matrix method as follows:
We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].
The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33] where,
d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,
d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,
d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,
d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,
d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,
d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,
d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,
d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,
d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.
We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]
Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]
Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.
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9. In a combined class of 60 Art and science
Students, the result of their mock examing-
tion showed that 39 of them passed physics
36 Passed Geography and 40 passed History,
of these, 22 passed both physics and History
21 passed both physics and Geography an
23 passed Geography and History. Given
that 10 of them passed all the three subjects
Find:
a. The number of Students who passed only
physics
b. The number of Students who passed
only Geography.
C. The number of student who passed
only History
Answers
The number of students who passed only physics is 6, the number of students who passed only geography is 2, and the number of students who passed only history is 5.
First, let's represent the number of students who passed each subject with the variables P, G, and H. Then, we can represent the number of students who passed multiple subjects with the variables PG, PH, and GH.
We are given the following information:
39 students passed physics (P)
36 students passed geography (G)
40 students passed history (H)
22 students passed both physics and history (PH)
21 students passed both physics and geography (PG)
23 students passed both geography and history (GH)
10 students passed all three subjects (PHG)
We can set up the following equations to represent these relationships:
P = 39
G = 36
H = 40
PH = 22
PG = 21
GH = 23
PHG = 10
We can use these equations to solve for the number of students who passed only physics (P - PH - PG + PHG), only geography (G - GH - PG + PHG), and only history (H - PH - GH + PHG).
So, the number of students who passed only physics is:
P - PH - PG + PHG = 39 - 22 - 21 + 10 = 6
The number of students who passed only geography is:
G - GH - PG + PHG = 36 - 23 - 21 + 10 = 2
The number of students who passed only history is:
H - PH - GH + PHG = 40 - 22 - 23 + 10 = 5
Thus, there are 6 students who passed only physics, 2 students who passed only geography, and 5 students who passed only history.
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A camera has a listed price of 867.98 before tax. If the sales tax rate is 8.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
A camera has a listed price of 867.98 before tax. If the sales tax rate is 8.75%, the total cost of the camera with sales tax included is
$948.08.
To find the total cost of the camera including sales tax, you must use the formula price+(price*tax rate). In this case 867.98 + (867.98 * 0.0875) = 948.08.
To calculate the total cost with sales tax included, you must first determine the tax rate. In this case, the tax rate is 8.75%. To find the total cost, you must first multiply the price of the camera by the tax rate. This number will represent the amount of tax due to the purchase.
Then, you must add the price of the camera to the amount of tax for a total cost of 948.08. finally, to round to the nearest cent it is 948.08.
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If m=3 and b=6 what is the correct slope intercept equation
Answers
Answer:
y = 3x + 6
Step-by-step explanation:
Slope-intercept is written as y = mx + b, in which m = slope and b = y-intercept
Graph -23 +y = 8.
y
8
9
8+
7+
6+
4+
3+
2+
1+
2
-9-8-7 -6 -5 -4 -3 -2.
1 2 3 4 5 6 7 8 9
-2+
-3+
-4+
-5+
-6t
-7+
Answers
Answer:
in the proprety of the number of negs and postive and y the graph -23+y=8 being that the nuber is -15
John has coins in a jar. Five of the coins are pennies, 8 are dimes, and 3 are
quarters. John randomly selects a coin from the jar and without replacing it
randomly selects another coin. What is the probability that he selects a dime and
then a quarter?
Answers
The probability that he selects a dime and then a quarter without replacement is 1/10
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: John has 8 dimes 5 pennies and 3 quarters.
Total number of coins that John has is =8+5+3
=16
Thus the probability of picking a dime is P(dime)= 8/16
=1/2
Therefore the conditional probability that John picks a dime and then a quarter is given by
P(dime/quarter)=1/2×3/15 ( As the dime picked is not replaced)
=1/10
Hence, the probability that he selects a dime and then a quarter without replacement is 1/10
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Two lines, a and b, are parallel. If both of the lines are rotated 90° in the same direction and then translated to the right by the same number of units, which statement about the lines resulting from these transformations is true? They will be parallel. They will be the same line. They will be perpendicular. They will intersect, but they won't be perpendicular.
Answers
Answer:
They will be parallel.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Translation is the movement of a point up, down, left or right. Rotation is the turning of a point about a fixed point.
If two parallel lines a and b are rotated 90° in the same direction, they would still be parallel. If they are then translated to the right by the same number of units, they would still remain parallel to each other.
What are the values of x, y and z in the diagram below? x 107° N z w
Answers
Answer:
73,107,73
Step-by-step explanation:
x=73 ,y=107 ,z=73
Find the coordinates of the centroid of the triangle with the given vertices.
F(1, 5), G(-2, 7), H( – 6, 3)
Answers
The coordinate of the centroid of the given triangle will be at (-2.33,5).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The given triangle with vertices has been drawn.
The midpoint of H( – 6, 3) and F(1, 5) will be as,
x = (-6 + 1)/2 = -2.5
y = (3 + 5)/2 = 4 so D(-2.5,4)
The coordinate of the centroid will intersect 2:1 of the median from the vertex side.
Thus by intercept formula,
x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)
x = -2.33 and y = 5
So the coordinate of vertices will be (-2.33,5).
Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".
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wich mathematical expression represent this statement?the sqaure of a number times 31. 7n2. 3n^2 3.2n + 84. n^3/ 2
Answers
Let the number be represented by "n"
I am a number with 45 tens and 3 ones. What number am I
Answers
Answer:
453
Step-by-step explanation:
Candace is trying to figure out how tall her apple tree is. She is Sft 6in and her shadow is 10ft, while the apple tree's shadow is 32lt, at the same time of day. Using that information, approximately how tall is the apple tree?
Answers
Answer:
b
Step-by-step explanation:
Find the distance between -7, -3 2/3 on a number line.
Answers
Answer:
3 and 1/3 because 7 minus 3 and 1/3 equals 3 2/3 or you could also do 3+3=6 and 2/3+1/3=1 and 1+6=7
The distance between -7 and -3 2/3 on the number line is 3 1/3
How to determine the distance between the numbers?The numbers are given as:
-7 and -3 2/3
Calculate the absolute difference between both numbers
d = |-7 + 3 2/3|
Evaluate the difference
d = | 3 1/3|
Evaluate the absolute value expression
d = 3 1/3
Hence, the distance between -7 and -3 2/3 on the number line is 3 1/3
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please help
the line ABC is tangent to a circle at B centre O with diameter EB the angle DAB = 28
(a) ABE=
(b) EDB=
(c) AOB=
(d) BOD=
(e) OBD=
(f)DBC=
Answers
Answer:
A 90°
B 90°
C 62°
D 118°
Hopefully this helps u
students majoring in psychology surveyed 200 of their fellow students about their dreams. the results of the survey are shown in the venn diagram. let b be the event that the participant dreams in black and white and let c be the event that the participant dreams in color. a venn diagram titled student dreams. one circle is labeled b, 4, the other circle is labeled c, 10, the shared area is labeled 12, and the outside area is labeled 174. what is the probability that a randomly selected participant dreams in black and white or color? 0.06 0.07 0.13 0.26
Answers
The probability that a randomly selected participant dreams in black and white or color is 0.01
The probability that a randomly selected participant dreams in black and white or color is the sum of the probabilities of the individual events (dreaming in black and white or dreaming in color) and the probability of the intersection of the two events (dreaming in both black and white and color).
The probability of dreaming in black and white is the number of participants who dream in black and white divided by the total number of participants surveyed:
P(b) = 4/200
The probability of dreaming in color is the number of participants who dream in color divided by the total number of participants surveyed:
P(c) = 10/200
The probability of dreaming in both black and white and color is the number of participants who dream in both black and white and color divided by the total number of participants surveyed:
P(b ∩ c) = 12/200
The probability of dreaming in black and white or color is the sum of the individual probabilities and the intersection probability:
P(b ∪ c) = P(b) + P(c) - P(b ∩ c) = 4/200 + 10/200 - 12/200 = 2/200 = 1/100
The probability that a randomly selected participant dreams in black and white or color is 1/100.
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Solve inequality 5x+3>48
Answers
Answer:
x>9
Step-by-step explanation:
Answer:
x > 9
Step-by-step explanation:
Simply solve for x.
What we have to do is subtract 3 from both sides, then divide by 5 to both sides.
5x > 45
x > 9
x is greater than 9.
#teamtrees #WAP (Water And Plant)
Need this before thursday.
Answers
The slope of the line will be 1/2 in the given graph.
What is the slope of the line?
The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The graph is given in the question.
According to the given graph, we can take two points (2, 2) and (6, 4).
The line passes through points (2, 2) and (6, 4).
Let
x₁ = 2, y₁ = 2
x₂ = 6, y₂ = 4
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
The slope of line = (4 - 2)/(6-2)
The slope of line = (2)/(4)
The slope of line = 1/2
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Need help with the picture attached, involving derivatives.
Answers
dy/dx = 0 when x = - 2, and x = 2/3 is not possible.
dy/dx = 0 when x = - 1, and x = 5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
y = x³ - 6x² - 15x - 7
Differentiating w.r.t x.
[ d\(x^n\)/dx = n\(x^{n - 1}\) ]
[ dc/dx = 0 ]
dy/dx = dx³/dx - 6dx²/dx - 15dx/dx - d7/dx
dy/dx = 3\(x^{3 - 1}\)dx/dx - 6 x 2\(x^{2-1}\)dx/dx - 15 - 0
dy/dx = 3x² - 12x - 15
Now,
dy/dx = 0
3x² - 12x - 15 = 0
3(x² - 4x - 5) = 0
x² - 4x - 5 = 0
x² - (5 - 1)x - 5 = 0
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x - 5) (x + 1) = 0
x - 5 = 0
x = 5 _____(1)
x + 1 = 0
x = -1 _____(2)
Now,
For x = 2,
dy/dx = 3x² - 12x - 15
dy/dx = 3 x 4 + 24 - 15
dy/dx = 12 - 24 - 15
dy/dx = 12 - 39
dy/dx = -27 _____(3)
For x = 2/3,
dy/dx = 3x² - 12x - 15
dy/dx = 3 x 4/9 + 24 x 2/3 - 15
dy/dx = 4/3 + 16 - 15
dy/dx = 4/3 + 1
dy/dx = 7/3 _____(4)
From (1), (2), (3), and (4)
dy/dx = 0 when x = - 2 and x = 2/3 is not possible.
Thus,
dy/dx = 0 when x = - 1, and x = 5.
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On a test that has a normal distribution, a score of 54 falls two standard deviations
above the mean, and a score of 42 falls one standard deviation below the mean.
Determine the mean of this test.
Answers
Let μ be the mean of the distribution and let σ be its standard deviation.
We know that 54 falls two standard deviations above the mean, this can be express as:
\(\mu+2\sigma=54\)We also know that 42 falls one standard deviation below the mean, this can be express as:
\(\mu-\sigma=42\)Hence, we have the system of equations:
\(\begin{gathered} \mu+2\sigma=54 \\ \mu-\sigma=42 \end{gathered}\)To find the mean we solve the second equation for the standard deviation:
\(\sigma=\mu-42\)Now we plug this value in the first equation:
\(\begin{gathered} \mu+2(\mu-42)=54 \\ \mu+2\mu-84=54 \\ 3\mu=138 \\ \mu=\frac{138}{3} \\ \mu=46 \end{gathered}\)Therefore, the mean of the distribution is 46
y = (3x)2 + 17
when x = 2
Answers
Answer:
y = 29
Step-by-step explanation:
y = (3x)2 + 17
y = (3(2))2 + 17
y = (6)2 + 17
y = 12 + 17
y = 29
continuinty
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a f(x) = x² + 5x 2x + 1 a = 2
Answers
The function is continuous by the property of limits.
Given data ,
To show that the function f(x) = x^2 + 5x / (2x + 1) is continuous at a = 2:
The value of the function at x = 2 is equal to the limit.
Let's proceed step by step:
The function is defined at x = 2:
To check this, substitute x = 2 into the function:
f(2) = (2² + 5(2)) / (2(2) + 1)
= (4 + 10) / (4 + 1)
= 14 / 5
So, f(2)=14/5 and is defined.
The limit of the function as x approaches 2 exists:
We need to evaluate the limit of f(x) as x approaches 2.
lim(x→2) (x² + 5x) / (2x + 1)
We can simplify the expression by directly substituting x = 2 into the function:
lim(x→2) (x² + 5x) / (2x + 1) = (2² + 5(2)) / (2(2) + 1) = 14 / 5
Therefore, the limit of f(x) as x approaches 2 exists and is equal to 14/5.
The value of the function at x = 2 is equal to the limit:
We have already computed f(2) = 14/5, and the limit lim(x→2) f(x) = 14/5.
Since the value of the function at x = 2 (14/5) is equal to the limit as x approaches 2 (14/5), we can conclude that the function is continuous at x = 2.
Hence, satisfying all three conditions, we have shown that the function f(x) is continuous at x = 2.
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The complete question is attached below :
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a f(x) = (x² + 5x) / (2x + 1) a = 2
can you guys help me please as much as you can ^^
Answers
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115
a newspaper boy is trying to perfect his business in order to maximize the money he can save for a new car. daily paper sales are normally distributed, with a mean of 100 and standard deviation of 10. he sells papers for $0.50 and pays $0.30 for them. unsold papers are trashed with no salvage value. how many papers should he order each day? round up.
Answers
To determine how many papers the newspaper boy should order each day, we need to consider his profit margin. His profit is the difference between the revenue earned from selling the papers and the cost of buying them.
The revenue earned is the number of papers sold multiplied by the selling price of $0.50. The cost of buying the papers is the number of papers ordered multiplied by the buying price of $0.30. Let's say he orders x papers each day. The expected value of his revenue can be calculated as x multiplied by the mean of 100 papers,
which is 100x. The expected value of his cost can be calculated as x multiplied by the buying price of $0.30, which is 0.3x. His profit can then be calculated as the difference between his revenue and cost, which is 0.2x (since the selling price of $0.50 minus the buying price of $0.30 is $0.20 profit per paper).
To maximize his profit, he should order the number of papers that gives him the highest expected profit. This occurs at the point where the deviation from the mean is zero. In other words, he should order the number of papers that gives him the highest probability of selling all of them, without having any unsold papers that he needs to throw away.
Using the formula for standard deviation, we can calculate that the probability of selling all 100 papers is 68.3%. The probability of selling 101 papers is slightly lower at 64.2%, while the probability of selling 99 papers is also slightly lower at 64.2%.
Therefore, to maximize his profit, the newspaper boy should order 100 papers each day, since this gives him the highest probability of selling all of them without having any unsold papers. This would give him a daily profit of $10 (100 papers sold x $0.20 profit per paper).
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7a + 5 = 19
What’s the answer
Answers
Answer:
2
Step-by-step explanation:
You have to undo in reverse order- subtraction and addition first, division and multiplication second, then exponents, and finally, parentheses.
Here's the work shown-
7a + 5 (-5) = 19 (-5)
7a/7 = 14/7
a = 2
Answer:
a=2
Step-by-step explanation:
You have to subtract 5 from 19 to get 14.
Then, you get:
7a=14
a=2