Answer:
Step-by-step explanation:
Given that:
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively.
. A sample of four pages is selected without replacement,
Let X and Y denote the number of pages with moderate and high graphics output in the sample
We are meant to determine
a) [tex]f_{XY}(x, y)[/tex] from the given data in the question;
However; the probability mass function can be expressed via the relation:
[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]
We can now have a table shown as :
[tex]X|Y[/tex] 0 1 2 3 4 Total [tex]f_X(x)[/tex]
0 0.1244 0.0873 0.02031 0.0018 0.0001 0.234
1 0.2618 0.13542 0.02066 0.00092 0 0.419
2 0.1964 0.0666 0.00499 0 0 0.268
3 0.0621 0.01035 0 0 0 0.073
4 0.0069 0 0 0 0 0.007
Total [tex]F_Y(y)[/tex] 0.6516 0.2996 0.0460 0.0028 0.0001 1
b) [tex]f_X(x)[/tex]
The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]
[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]
From the table above ; the corresponding values of [tex]f_X(x)[/tex] are :
X 0 1 2 3 4
[tex]f_X(x)[/tex] 0.234 0.419 0.268 0.073 0.007
( since [tex]f_X(x)[/tex] represent the vertical column)
c) E(X)
By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]
we have:
E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]
E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028
E(X) = 1.202
d) fyß(y)
Using the thesis of conditional Probability; we have :
[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]
The conditional probability for the mass function is then:
[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]
where;
[tex]f_X(3) = 0.0725[/tex]
values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)
Therefore; the mass function is:
[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]
e) E(Y | X = 3)
By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]
we have:
⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]
= 0.143
The value of E(Y | X = 3) = 0.143
g) Are X and Y independent?
To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.
From the above previous table :
[tex]f_{(XY)} (0.4) = 0.0001[/tex]
[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001
[tex]f_X (0)[/tex] = 0.234
[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]
We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be non - independent.
A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
Answer:47.1
Step-by-step explanation:6.28/4=x/30
188.4=4x
47.1=x
Answer:
47.1
Step-by-step explanation:
height of 1 book=6.28÷4=1.57
height of 30 books=1.57×30=47.1
A way that landowners took advantage of sharecroppers was by:
A. allowing only whites to farm the land.
B. allowing only African Americans to farm the land.
O c. taking their seeds and tools.
D. paying less for crops raised by African Americans.
SUBMIT
The answer is d . Paying less for crops raised by Africa. Americans
Answer: C. Paying less for crops raised by African-Americans
Step-by-step explanation:
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
[tex]\frac{x-c}{d} > y[/tex]
x - c > dy
x > dy + c
Which flight has the fastest average speed
Answer:
Fastest wind speed ever recorded
That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976
Step-by-step explanation:
Can someone help me with this I don’t know if I’m right so
A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
We have,
Given:
Total number of components (n) = 1000
Number of defective components (d) = 350
a.
P(A) is the probability that the first component drawn is defective:
P(A) = d/n = 350/1000 = 0.35
b.
P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:
Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.
P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349
c.
P(A ∩ B) is the probability that both the first and second components drawn are defective:
P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122
d.
P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:
[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:
[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65
Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.
P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228
e.
P(B) is the probability that the second component drawn is defective:
P(B) = Number of defective components / Total number of components
= 350/1000
= 0.35
f.
P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:
P(A|B) = P(A ∩ B) / P(B)
= (0.35 * 0.349) / 0.35
= 0.349
g.
To determine if A and B are independent, we need to compare
P(A) * P(B) with P(A ∩ B).
P(A) * P(B) = 0.35 * 0.35 = 0.1225
P(A ∩ B) = 0.122
Since P(A) * P(B) = P(A ∩ B), A and B are independent events.
It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.
The occurrence or non-occurrence of A does not impact the probability of B.
Thus,
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
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Write a situation involving sales at an ice cream shop that could be reasonably modeled by the equation
4.50+0.50t=6.
Answer:
4.50 is for two scoops and a normal cone. Upgrades on cone is $0.50 and any additional toppings are also $0.50
Answer:5 × t = 6
Step-by-step explanation:
Step 1: 4.50 + 0.50 = 5
Step 2: We has 5t is 5 × t
Step 3: 5 × t = 6
ABDC is a rhombus with side length 10cm
angle ADC=40degrees
DAC is a sector of a circle with center D
BAC is a sector of a circle with center B
CALCULATE THE SHADED AREA (in cm2)
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
(4,1)
Step-by-step explanation:
(1+7)/2 = 4
(9+(-7))/2 = 1
The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?
Answer:
13.53% probability that no customers arrive in a five-minute period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
They arrive at a rate of two every five minutes
This means that [tex]\mu = 2[/tex]
What is the probability that no customers arrive in a five-minute period?
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
13.53% probability that no customers arrive in a five-minute period
a ford truck enters a highway and travles uniform speed of 50 mph. half an hour later a jaguar enters the highway at the same junction and heads in the same direction at 55 mph. how long after the ford enters the highway does the jaguard catch up
Answer:
5.5 hours
Step-by-step explanation:
We have that the distance is given by:
d = v * t = 50 mph * 1/2 h = 25 miles
The relative speed is given by:
vr = 55 mph - 50 mph = 5 mph
Now the time required to reach
would come being:
t = t '+ d / vr
we know that t '= 1/2 h, replacing:
t = 1/2 h + 25 mi / 5 mph
t = 1/2 h + 5 h
t = 5.5 h
Therefore, the required time is 5.5 hours.
Complete the transformation on the rectangle ABCD shown and choose the resulting vector: Use [ABCD]
edgen.
last option
The previous transformation could be classified as a
✔ reflection across the y–axis
.
Step-by-step explanation:
Answer:
D. [3, -1, -1, 3, 4, 4, 1, 1]
Reflection across the y–axis
Step-by-step explanation:
Please mark as Brainliest!
Which one of the following numbers is an irrational number?
Question 20 options:
A)
134∕675
B)
3.
C)
7.676767…
D)
8.12131415…
Answer:
B
Step-by-step explanation:
rational number means comparison between two numbers
eg: 1:3 or 1/3 or 0.333
irritional number does not
The one of the numbers is an irrational number that is A) 134 / 675
What are rational numbers, and irrational numbers?Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Irrational numbers are those real numbers which are not rational numbers.
Noted that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
For example
: 1:3 or 1/3
or 0.333
But irrational number does not.
The rational number means the comparison between two numbers
A) 134 / 675 = 0.19
B) 3.
C) 7.676767…
D) 8.12131415…
So, A) 134 / 675
This is an irrational number
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Please answer this correctly
Answer:
2 cups more was given to the flower with the most water because 5 cups - 3 cups = 2 cups.
Answer:
2 cups
Step-by-step explanation:
The most water was 5 cups and the least was 3 cups. So:
5-3=2 cups more
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
A door wedge is 5 cm tall. Its has 3.7 cm high triangular bases with 2 congruent 5 cm sides and a 4 cm side. What is its surface area?
Answer:
Surface Area = 84.8 cm²
Step-by-step explanation:
This wedge is simply a triangular prism.
We are given;
Height of door wedge; H = 5 cm
Height of triangular base;h = 3.7 cm
Congruent sides; S2 = S3 = 5cm
base of triangular side;b = S1 = 4 cm
Now, formula for surface area of triangular prism is;
SA = bh + (s1 + s2 + s3)H
Thus, plugging in the relevant values, we have;
SA = (4 x 3.7) + (4 + 5 + 5)5
SA = 14.8 + 70
SA = 84.8 cm²
If x=10 what is (7x -5)
[tex]solution \\ x = 10 \\ now \\ (7x - 5) \\ = (7 \times 10 - 5) \\ = (70 - 5) \\ = 65[/tex]
Hope it helps....
Good luck on your assignment
Answer:
65
Step-by-step explanation:
= 7x-5
Putting x = 10
= 7(10)-5
= 70-5
= 65
Find the area of the circle
Answer:
615.44
Step-by-step explanation:
The area in terms of π is 196π
196 * 3.14 = 615.44
Answer:
615.75
Step-by-step explanation:
Area equals pi times r times 2
A equals 3.14 times 14 times 2
Please help me with this math problem
Answer:
[tex]7x^2-2x-2[/tex]
Step-by-step explanation:
[tex]-3x^2+9+10x^2-11-2x[/tex]
Combine like terms:
[tex]10x^2-3x^2-2x+9-11[/tex]
Simplify:
[tex]7x^2-2x-2[/tex]
Hope this helps!
Answer: 7x^2 - 2x - 2
Step-by-step explanation:
in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.
-3x^2 + 9 + 10x^2 - 11 - 2x rearrange to make easier
-3x^2 + 10x^2 - 2x + 9 - 11 combine like-terms
7x^2 - 2x - 2
A sample consists of 80 separate events that are equally likely what is the probability of each?
Answer:
1/80Step-by-step explanation:
This problem brothers is the probability of mutually exclusive events,
Given the sample space of 80 separate events, the probability of of one event happening is
Pr(each event)= [tex]\frac{1}{80}[/tex]
Solve the system of equations by using substitution
Y=2x+3
Y=x+2
Since our first equation reads y = 2x + 3, we can substitute a 2x + 3
in for y in our second equation and then solve from there.
So we have 2x + 3 = x + 2.
Now subtract x from both sides to get x + 3 = 2.
Now subtract 3 from both sides to get x = -1.
To find y, plug -1 back into either equation.
I have chosen to plug it into the second.
So we have y = (-1) + 2 which simplifies to 1.
So our solution to this system is (-1, 1).
a business owes $8,000 on a loan. every month, the business pays half of the amount remaining on the loan. how much will the business pay in the six-month?
Answer:
$7875
Step-by-step explanation:
1 Month 4000 Paid
2 Months 2000 Paid
3 Months 1000 Paid
4 Months 500 Paid
5 Months 250 Paid
6 Months 125 paid
Total = $7875 Paid
Hope this helped ;)
The population of Boomtown is currently 3000 and expected to grow by 2.3% over the
next year. What will its population be by then?
The population of Dullsville, on the other hand, is currently 13000 and expected to
decrease by 4.1% over the next year. What will its population be by then?
Answer:
a) The Expectation of the Population to grow in the next year
= 3069
b) The Expectation of the Population decrease in the next year
= 12,467
Step-by-step explanation:
Explanation:-
a)
The population of Boom town is currently 3000
Given expected to grow by 2.3 % over the next year
= [tex]3000 X \frac{2.3}{100} = 69[/tex]
= 69
The Expectation of the Population growth in the next year
= 3000 +69 = 3069
b)
The population of town is currently 13000
Given expected to grow by 4.1 % over the next year
= [tex]13000 X \frac{4.1}{100} = 533[/tex]
The Expectation of the Population decrease in the next year
= 13000 - 533 = 12,467
what does a obtuse angle measure between
Answer:
90° and 180°
Step-by-step explanation:
An obtuse angle is any angle larger than 90° and smaller than 180°
Para cubrir un tejado rectangular de 29,7 m de largo ,se gastaron 24 552 locetas de 25cm x19 cm las cuales pierden al colocarse la 1/5 parte de su extensión eficaz . ¿ Qué ancho tenía el tejado ?
Answer:
El tejado tenía un ancho de 31.4 m.
Step-by-step explanation:
Tenemos un techo rectangular, con un largo de 29.7 m y un ancho x, que debemos calcular.
Entonces, la superficie del tejado es:
[tex]S=29.7x\;\,\text{[m}^2\text{]}[/tex]
Las locetas tienen una superficie de 25x19 cm, de las cuales 1/5 se pierde en la colocación. La superficie eficaz que ocupa cada loceta una vez colocada es:
[tex]S_L=(25\cdot19)\cdot(1-1/5)=475\cdot(0.8)=380\;\text{cm}^2[/tex]
Entonces, si se utilizaron 24552 locetas para cubrir todo el techo, podemos expresar la superfice del techo como:
[tex]S=24552\;\text{locetas}\;\cdot380\dfrac{\text{cm2}}{\text{loceta}}\cdot \left(\dfrac{1\text{m}}{100\text{cm}}\right)^2=\dfrac{24552\cdot380}{10000}\;\text{m2}=932.976\;\text{m2}[/tex]
Podemos calcular x igualando este último resultado con la primer ecuación:
[tex]S=29.7x=932.976\\\\x=932.976/29.7=31.413\approx31.4[/tex]
What is the missing number in the pattern? Please Help. Been stuck on this for hours.
Answer:
8
Step-by-step explanation:
The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).
So, 2 x 4 = 8
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice
Answer:
A 16 inches diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let r be the radius and [tex]\theta[/tex] be the angle of a circle.
According with the graph, the area of the sector is given by
[tex]A=\frac{1}{2}r^2\theta[/tex]
The arc length of a circle with radius r and angle [tex]\theta[/tex] is r [tex]\theta[/tex]
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
[tex]2r+r\theta=32 \:in[/tex]
We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]
[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]
Next, we substitute this equation into the area equation
[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]
The domain of the area is
[tex]0<r<12[/tex]
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]
To check if r=8 is a maximum we use the Second Derivative test
if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.
The second derivative is
[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]
Because [tex]A''(r)=-2 <0[/tex] the largest slice is when r = 8 in.
The diameter of the pizza is given by
[tex]D=2r=2\cdot 8=16 \:in[/tex]
A 16 inches diameter will reward you with the largest slice of pizza.
Which inequality is represented by this graph?
Answer:
its probably a. x>-53
my appolgies if it's wrong
What does the “equity” of a tax mean?
Answer:
Equity of taxation means each citizen pays an amount of tax equal to their income and ability to pay the tax.
Answer:
C) The tax is paid equally by everyone
Step-by-step explanation:
Which of the lists of letters all have rotational symmetry?
a. C, H, N, X
b. N, O, S, Z
c. H, J, N, S
d. F, H, X, Z
Answer:
So C doesn't have symmetry so that rules out a
b does though
J doesn't work so that rules out c
F doesn't work so that rules out d
B is answer
Answer:
B. is the rotational symmetry
Step-by-step explanation:
