Consider two continuous random variables X and Y with joint pdf f(x,y)= k(2y- x 4 ) for 1
Answers
Answer:
The answer is "1.6 and \(\frac{11}{12}\)".
Step-by-step explanation:
The joint pdf by x and y
\(1< x<2\\ 0< x< 1\)
In point a:
\(\to K \int^1_{y=0} \int^2_{x=1} (2y - \frac{x}{4}) dx, dy =1\\\\ \to k \int^{1}_{y=0} 2y - \frac{x^2}{8} \int^{2}_{1} dy=1\\\\\to k \ \ y^2 \int^1_{0} - \frac{1}{8} (3) =1 \\\\ \to k \ (1-\frac{3}{8}) =1\\\\\to k= \frac{8}{5}\\\\\)
\(= 1.6\)
In point b:
In the original pdf of x
\(\to fx(x)= k \int^{1}_{y=0} (2y-\frac{x}{4}) dy =k\)
\(= k \int^{2}_{1} (x-\frac{x^2}{4}) dx =k\\\\= k \frac{x^2}{2} - \frac{x^3}{12})^2_{1} =k\\\\= k \frac{1}{2} \times 3 - \frac{1}{12} \times 7 =k \\\\ =\frac{3}{2} - \frac{7}{12}\\\\= \frac{11}{12}\)
Related Questions
PLEASE HELP DUE IN 1 HOUR
Answers
The 3rd and 4th expressions cannot be simplified using the quotient rule for exponents
How to determine expressions that cannot be simplified using the quotient rule for exponents?The quotient rule for exponents states that if you have two exponents, and you want to divide them, you can do so by subtracting the exponent of the denominator from the exponent of the numerator.
The general form of the quotient rule:
xᵃ / xᵇ = xᵃ⁻ᵇ
Given:
(3²9⁻¹2³)/(8⁵7⁻²)
(3²9⁻¹2³)/(8⁵7⁻²) = (3² × 3²⁽⁻¹⁾ × 2³)/(8⁵×7⁻²)
= (3² × 3⁻² × 2³)/(2³⁽⁵⁾ ×7⁻²)
= (3²⁺⁽⁻²⁾ × 2³)/(2¹⁵ × 7⁻²)
= (3⁰ × 2³)/(2¹⁵ × 7⁻²)
= (1 × 2³)/(2¹⁵ × 7⁻²)
= (2³)/(2¹⁵ × 7⁻²)
= 2³⁻¹⁵ × 7² ( quotient rule is used here)
= (2⁻¹²) (7²)
(4⁻²x⁻¹)/(4⁻¹x⁻²)
(4⁻²x⁻¹)/(4⁻¹x⁻²) = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾ ( quotient rule is used here)
= 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾
= (4⁻¹) (x¹)
(6x⁻⁸z²)(6⁵x⁻¹z²)
(quotient rule cannot be used to simplify this expression because the two expressions are multiplying each other)
(q⁻⁵r¹¹)/(s⁶t⁻¹⁵)
(quotient rule cannot be used here because there are no like bases)
Learn more about quotient rule on:
https://brainly.com/question/29125865
#SPJ1
13. Ticket sales at the First Run Theater total at least $7,600 per week. An adult's ticket costs $7.50 and a child's ticket costs $4.00. If a represents the number of adult tickets sold in a week and c represents the number of child tickets, which algebraic sentence represents the money received each week from ticket sales?
a) 7.50 a + 4.00 c= 7,600
b) 7.50 a + 4.00 c > 7,600
c) 7.50 a + 4.50 c > 7,800
d) 7.50 a + 4.00 c < 7,600
Answers
Answer:
b) 7.50 a + 4.00 c > 7,600
Step-by-step explanation:
In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answers
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?
Please help me with this question
Answers
Answer:
y=720.622*(1.039)^t
1057 individuals
Step-by-step explanation:
use desmos to make a table and use the equation
y1~a*b^x1
that will give you an equation and you plug in 10 for x since x is the number of days
Review the graph.
On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answers
Answer:
36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²
Step-by-step explanation:
This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.
Black & Decker Manufacturing sold a set of saws to True Value Hardware. The list price was $3,800. Black & Decker offered a chain discount of 8/3/1. The net price of the saws is:
Answers
The net price of the saws that Black & Decker Manufacturing sold to True Value Hardware on a chain discount of 8/3/1 is $3,357.21.
What is a chain discount?A chain discount refers to a type of discount offered to customers, which is sequentially applied to the list price to arrive at the net price.
Chain discounts involve a series of trade discounts applied in sequence.
Data and Calculations:List price = $3,800
Chain discount = 8/3/1
First net price = $3,496 ($3,800 x 1 - 8%)
Second net price = $3,391.12 ($3,496 x 1 - 3%)
Third net price = $3,357.21 ($3,391.12 x 1 - 1%)
Thus, the net price based on a chain discount of 8/3/1 is $3,357.21.
Learn more about chain discounts at https://brainly.com/question/1515915
#SPJ1
Help I don’t know how to solve these it’s about functions pls give me an answer with an explanation. f(x)=-x+2;Solve for x when f(x)=1
Answers
For the function f(x) = x + 2, the value of x when f(x) = 1, gives x = -1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Given that:
f(x) = x + 2
When f(x) = 1, substituting:
1 = x + 2
x = -1
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
In a survey of employees at a fast food restaurant, it was determined that 13 cooked food, 16 washed dishes, 20 operated the cash register,
7 cooked food and washed dishes, 6 cooked food and operated the cash register, 8 washed dishes and operated the cash register, 3 did all
three jobs, and 5 did none of these jobs. Complete parts a) through f) below.
how many employees took the survey?
Answers
Answer:1
Step-by-step explanation:
What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
Answers
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
\(\sf V = \dfrac{(l)(b)(h) }{3}\)
\(\sf V = \dfrac{(8.4)(8.6)(6) }{3}\)
\(\sf V = \dfrac{433.44 }{3}\)
\(\sf V = 144.48 \ cubic \ feet\).
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
Learn more about volume here:
brainly.com/question/1578538
ILL GIVE BRAINLEST, find the value of x
Answers
Answer:
73
Answer:
Answer:
Answer:
Triangle ABC is similar to triangle EFD. Whatscale factor is required to dllate triangle ABCso that its image, A' B'C', is congruent totriangle EFD?
Answers
Since triangles ABC and EFD are similar, their correponding sides are proportional.
We can see from the picture that side AB is equivalent to side EF. We can also see that side AC is equivalent to unknown side ED.
Since the triangles are similiar we can set the following ratio:
AB / EF = AC / ED
12 / 5 = 15 / ED
12 . ED = 5 . 15
12 . ED = 75
ED = 75 / 12
ED = 25 / 4
Let's check the scaling factor k must be:
AB / EF = 12 / 5
AC / ED = 15 / 25/4
AC / ED = 15 . 4 / 25
AC / ED = 60 / 25
AC / ED = 12 / 5
Since A'B'C' is congruent to EFD, then ABC must have the same scaling factor as above which is 12 / 5.
Answer: scaling factor = 12 / 5
please help me with this question
Answers
Answer:
\( {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }\)
Explanation-
As,
\(a^{\frac{1}{n} } = \sqrt[n]{a} \)
and
\(a^{-n}=1/a^n\)
If an exponential model has a 9% decay rate,
what multiplier would be used in the function
model?
0.9 1.09
1.9 0.91
Answers
=====================================================
Explanation:
If you lose 9% of a substance, then you keep the remaining 91% because 100% - 9% = 91%. Or you can think of it as 91% + 9% = 100%
Then we convert 91% to decimal form to get 0.91
-----------
Or you can do the steps like this:
9% = 0.09
1 - 0.09 = 0.91
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(1.08)^x
Answers
Answer:
It represents growth, and the percentage rate of increase is of 8%
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
\(A(t) = A(0)(1 + r)^t\)
In which A(0) is the initial amount and r is the rate of change, as a decimal. If positive, it is growth, if negative, it is decay.
In this question:
\(y = 21(1.08)^x\)
So
\(1 + r = 1.08\)
\(r = 0.08\)
Since r is positive, it represents growth, and the percentage rate of increase is of 0.08*100% = 8%
determine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number 1-11=?
Answers
Given: A clock arithmetic
To Determine: The difference from 1 - 11 counterclockwise
Solution
Draw the 1'O clock time as shown below
Let us move 11 counterclockwise
This is as shown below
From the above, it can be seen that we started from 1 and moved 11 times counterclockwise to land at 2
Hence, the answer 2
Rotation 90° clockwise about the origin
Answers
At a sale, a desk is being sold for 29% of the regular price. The sale price is $272.60.
What is the regular price?
Answers
Answer:$940
Step-by-step explanation:
29%=$272.60
100%=
100%*$272.60/29%=$940
$940
What is the answer....................................................
Answers
Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.
Step-by-step explanation:
A certain virus infects one in every 300 people. A Test used to detect the virus in a person is positive 85% of the time if that prerson has the virus and 5% of the time if the person does not have the virus. This 5% result is called a false positive. Let "A" be the event the person is infected and "B" the event the person tests positive. Find the probability that a person has the virus given that they have tested positive find the P(A/B)= Round to nearest tenth of a % Don't include % sign.
Answers
The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045
We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:
P(A | B) = P(B | A) * P(A) / P(B)
where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.
To find P(B), we can use the law of total probability, which states that:
P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)
where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.
Substituting the values, we get:
P(B) = 0.85 * 1/300 + 0.05 * 299/300
= 0.059
Now we can plug in the values into Bayes' theorem:
P(A | B) = 0.85 * 1/300 / 0.059
= 0.0045 or 0.45%
Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).
To learn more about probability here:
https://brainly.com/question/30034780
#SPJ1
The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3. Its daily sales goal is $720. Write and graph the linear equation that describes the problem. Use the graph to find how many baskets of blueberries it must sell to reach its goal if 60 baskets of cherries are sold.
Answers
Answer:
a. SOLVED
b. \(4c+3b=720\)
c. (Below)
d. 160
Step-by-step explanation:
1 cherry = $4
1 blueberry = $3
60 cherry basket:
60 × 4
= 240
Goal amount = $720
Bw day selling blueberry basket
Money:
= 720 - 240
= 480
Blueberry basket = 480 ÷ 3
\(\frac{480}{3}\)
\(=160\)
Cherry = 60
Blueberry = 160
Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The
total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?
Answers
Answer:
$47.48
Step-by-step explanation:
Let x = the amount owed Sept.
x + x - 2.23 = 292.43 Combine like terms
2x -2.23 = 292.43 Add 2.23 to both sides
2x - 2.23 + 2.23 = 292.43 + 2.23
2x = 294.66 Divide both sides by 2
\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)
x = 147.33 this is the bill for September
Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.
Total:
147.33 + 145.10 = 292.43
292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.
A circular pizza that is 14 inches in diameter is cut into 4 equal slices. What is the area of one of the slices
Answers
Answer:
I think its should be 4
Step-by-step explanation:
14.95/65 what is the quotient
Answers
Answer:
0
Step-by-step explanation:
Hope this helps!
(Brainliest is appreciated)
3 4 7 11 next two terms are
Answers
Answer:
18 and 29 are the following terms in the series pattern as a result.
Step-by-step explanation:
The series pattern 1, 3, 4, 7, and 11 is given, and the two next numbers in the series is to be found
Let's find the logic behind the series pattern arrangement
Term one is one, and term two is three.
The third term appears to be the sum of the first and second terms
= 3+4 = 7
The fourth term appears to be the sum of previous two terms
= 4+7 = 11
Accordingly, the following term should be equal to the sum of the two terms before it, which is 7+11 = 18 , using the same pattern.
Similarly Next term is = 11+18 = 29 , using the same pattern.
18 and 29 are the following terms in the series pattern as a result.
To know more about Terms
https://brainly.in/question/25728179
#SPJ4
Use the context of a 24-pack of soda to explain why 3/8 is NOT equivalent to 4/12.
Answers
Answer:
Step-by-step explanation:
if we're going by a 24 pack of soda, 3/8 would be 9 sodas while 4/12 is a third, which would be 8 sodas
Match the following. Match the items in the left column to the items in the right column. 1. domain the first element of a relation or function; also known as the input value. 2. output a relation in which every input value has exactly one output value. 3. input the x-value of a function. 4. relation any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane. 5. function the y-value of a function. 6. range the second element of a relation or function; also known as the output value.
Answers
The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.
What is the appropriate matching of the following items?1. Domain - the first element of a relation or function; also known as the input value.
3. Input - the x-value of a function.
6. Range - the second element of a relation or function; also known as the output value.
4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. Output - a relation in which every input value has exactly one output value.
5. Function - the y-value of a function.
learn more about domain of a function: https://brainly.com/question/1369616
#SPJ9
The biology teacher has 59 tests to grade.
She grades 40 of the tests. Let t equal the number of tests she has left to grade. Choose the equation that will solve the problem.
OPTIONS-
t/40 = 59
40t = 59
t-40 = 59
t + 40 = 59
Answers
Answer:
t + 40 = 59
Step-by-step explanation:
We know
She has 59 tests to grade. So, it will be the total of the equation.
She already grades 40 on the tests.
t is the number of tests she has left to grade.
So, the equation is
t + 40 = 59
An environmental study was conducted. It reported that houses with more inhabitants do not necessarily produce more or less trash. What can be determined?
A. There is no correlation between number of inhabitants and amount of trash produced.
B. There is a correlation between number of inhabitants and amount of trash produced. However, there is no causation. This is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
C. There is a correlation between number of inhabitants and amount of trash produced. There may or may not be causation. Further studies would have to be done to determine this.
Answers
Answer:
C.
Step-by-step explanation:
There's no problem for now but it still needs to be monitored in case something might happen.
What is B^2+8b+7??
Can someone explain it step by step please?
Answers
Step-by-step explanation:
B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).
To factor a quadratic expression, you can use the following steps:
1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).
2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.
In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:
(b+7)(b+1)
This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).
Here is a step-by-step explanation of how to factor B^2+8b+7:
1. The coefficient of the middle term is 8.
2. The constant term is 7.
3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.
4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).
To solve it, you can use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 8, and c = 7.
So, substituting the values, we get:
x = (-8 ± √(8^2 - 4(1)(7))) / 2(1)
x = (-8 ± √(64 - 28)) / 2
x = (-8 ± √36) / 2
x = (-8 ± 6) / 2
x = -1 or -7
Therefore, B^2+8b+7 is equal to -1 or -7.
Una clase tiene 42 alumnos. Se puede determinar que 3/9 son niños y 4 6 son niñas, ¿Cuántos niños y cuantas niñas hay en la clase?
Answers
The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
Read more on fractions here: brainly.com/question/2194108
#SPJ1
Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?