(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1
(b) The expectation of the product of the two points will be 1/6
(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2
We have, X=(0,1)
Y | X=X=(0, X)
a) Let f(x,y) be the joint probability distribution of the two points will be:
f(X)=1
f(Y|X)=1/x
[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]
b) Let E(XY) be the expectation of the product of the two points.
[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]
c) Let f(y) be the marginal distribution of the point your friend picks.
So, the value of f(y) will be:
[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]
d)for 0<y<1
[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]
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Add the equations.
3x - y = -5
7x + y=15
A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20
Answer:
its c
Step-by-step explanation:
Determine the value of x.
Options:
03√2
03√3
3
6
Answer:
x=
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
because tan30⁰=
[tex] \frac{ \sqrt{3} }{3 } \\ \[/tex]
3/x=root 3 over3
[tex]3 \sqrt{3} [/tex]
33 points! Help please! Simplify 8 - (4)(3)/cube root 8 + 5
A. 12/7
B. -12/7
C. 4/7
D. -4/7
The given expression is simplified as -4/7. So, the correct option is D.
What is simplify?To simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Given that, (8-(4)(3))/(∛8 +5).
The given expression can be simplified as follows
Numerator of fraction simplified as 8-(4)(3)
= 8-12
= -4
Numerator of fraction simplified as (∛8 +5)
We know that, cube root of 8 (∛8) is 2
=(2 +5)
= 7
Thus, the fraction is -4/7
So, the expression (8-(4)(3))/(∛8 +5) is reduced to -4/7.
The simplified form of expression is -4/7. Therefore, option D is the correct answer.
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Please help me with this!
Answer:
The regualar hippo massed 4.45 times as much as the pygmy hippo. (Not sure what I should round to)
Step-by-step explanation:
First, convert each of the fractions to a whole number. To do this get the whole number to the left of the fraction multiply it by the denominator and add the numerator. Once you have found both masses. Get the mass of the regular hippo and divide by the pygmy hippos mass.
Reguar Hippo Mass Calcualtion:
24*2=48
48+1=49kg
Pygmy Hippo Mass Calcualtion:
5*2=10
10+1-11kg
Final Calcuation:
49/11=4.45kg
Answer: 4.45 times as much
Let me know if this helped!
What is the next term in the following sequence: 0, 5, 11, 18, … 24 26 23 25
Answer: i think the next number should be 26
Step-by-step explanation:
Find value of K for which
Y=2x+K is tangent to
y=x²-4x+4
To find the value of K, we need to find the point at which the line Y=2x+K is tangent to the parabola Y=x^2-4x+4. This means that the line and the parabola will have the same y-value at this point, and the line will be tangent to the parabola (meaning it will just touch the parabola at this point, without intersecting it).
To find the point at which the line and parabola are tangent, we can set Y=2x+K equal to Y=x^2-4x+4 and solve for x:
2x + K = x^2 - 4x + 4
x^2 - 4x + 4 - 2x - K = 0
(x-2)^2 = K
x = 2 +/- sqrt(K)
Since the line is tangent to the parabola, it will just touch the parabola at this point, which means that the parabola will have a minimum value at this point. This means that the value of K must be nonnegative, because the square root of a negative number is not a real number. Therefore, K must be equal to or greater than 0.
So, the value of K for which Y=2x+K is tangent to Y=x^2-4x+4 is K >= 0.
Which equation is equivalent to the formula d = rt? r equals d over t r = dt t equals r over d t = dr
The equation is equivalent to the r = d/t.
There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
We have to find which equation is equivalent to the formula d = rt.
Formula given: d = rt
Divide both sides by t
d/t = rt / t
d/t = r
Thus, the equation is equivalent to the r = d/t.
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the area of the triangle formed by the x and y intercepts of the parabola y=0.5(x-3)(x+k) is equal to 1.5 square units. find all possible values of k.
The possible values of k are -0.56, -3.56, -2 and -1.
Find all possible values of k ?We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)
Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
As, area of a triangle = 1/2 * (base )* (height )
Substituting the values, we get,
1.5=1/2 *(3+k)*(1.5k)
i.e.3= 4.5 k + 1.5k ²
i.e. k = -0.56 and k = -3.56
or
1.5=1/2* (-3-k )*(1.5k)
i.e.
3 = -4.5 k - 1.5²
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
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For the function: y = startroot x minus 7 endroot minus 1 the domain is : x ≥ the range is: y ≥
The function's range is in the interval (1, ∞).
What is function's range ?Members of a set can congregate in mathematics.
These sets' constituents are referred to as elements. The correspondence between the two groups is known as a relation when the elements of each group are paired up together.
So, between two sets, a relation is a collection of ordered pairs of elements.
The term "function" refers to a particular type of relation where each element in the first group, referred to as the domain, corresponds to exactly one element in the second group, referred to as the range.
The elements in the domain couple with exactly one element in the range, and this is how a function is a pairing between two sets.
According to our question-
[7, ] is the interval notation.
The function's range falls between the numbers (1, ).
provided function
Determine the function's domain:
You do not want to use a counterargument to the square root in this situation (you cannot find the solution of a negative square root, at least as a real number).
What you actually do is "impose" that the argument always ends in a yes or a no (you know the square root of a positive number or zero).
You then solve for x to determine the variable's ALLOWED values by setting the argument greater than or equal to zero:
Consequently, the function is in the domain.
Find the function's range:
The set of all y values in the function's range is when,
range of the function is in the interval (1, ∞).
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Answer: first 7,1 second 7, -1
Step-by-step explanation: edge 2023
Suppose sine (x) = four-fifths and cos(x) < 0. What is the value of cos(2x)? negative startfraction 14 over 25 endfraction negative startfraction 7 over 25 endfraction startfraction 7 over 25 endfraction startfraction 14 over 25 endfraction.
Because the value of x is 126° and the value of cos 2x is -0.301, which is fractionally identical to -7/25, the value of cos 2x will be -7/25.
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.
Here,
sin x=4/5
x=126°
Cos 126°=-0.588
cos (2*126)=-0.310
The value of cos 2x will be -7/25 because value of x is 126° and that of cos 2x is -0.301 that is fractionally equal to -7/25.
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Answer:
B
Step-by-step explanation:
on edge
A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second.
Write an equation that shows the relationship between the elevation of the feather, y, and the number of seconds it has been falling, x.
the equation of the function is y=-2x+10
Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast and $0.90 for one egg and one piece of toast. Write a system of equations that can be used to
determine how much she charges for each egg and each piece of toast.
Enter your answer in the space below.
√x
Answer:
Each egg costs $0.60
Each piece of toast costs $0.30
Step-by-step explanation:
Let's assume that the cost of a single egg is E
And the price of a toast as T
Kendra charges $1.50 for one toast and two eggs
The equation above will be
2E + T = $1.50
And the other equation is
E + T = $0.90
For the second equation, we make E the subject of the formula
E = 0.90 - T
Now substitute for this in equation 1
2E + T = 1.50
It will now be 2(0.90 - T) + T = 1.50
1.80 - 2T + T = 1.50
T= $0.30
price of one toast is $0.30
And now, for the price of an egg, we substitute T = 0.30 in the equation
E= $0.60
there are two formulas that can be used to find the volume of a rectangle prism. Find the volume using both formulas
Step-by-step explanation:
Formula 1: V = lwh
V = 10 x 8 x 6
V = 480
Formula 2: V = 2lw + 2lh + 2wh
V = 2(10 x 8) + 2(10 x 6) + 2(8 x 6)
V = 480
The volume of water in a tank is modeled by the function y = 1.15x3 – 0.1x2 + 2 where x is the number of minutes after the faucet filling the tank is turned on. . How long will it take for the tank to fill to 247 feet.
Answer:
2
Step-by-step explanation:
: in this context, the y-intercept represents the volume of water already in the tank
Evaluate the expression for x = 3, y = 3, and z = 5.
12z-3y
4z-z
Enter your answer in the box.
To answer this question, simply plug in the values that represent the variables into the respective equations.
If z=5 and y =3, then 12z - 3y can be written as:
(12 × 5) - (3 × 3)
(60) - (9)
= 51
If z = 5, then the expression 4z -z can be written as:
(4 × 5) - 5
20-5
= 15
51 and 15 are your answers
There are four people in Haydens family. Each person always eats 3/4 of a cheese pizza. How many whole pizzas should they order?
In linear equation,3 whole pizzas should they order .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
total people = 4
Each person always eats 3/4 of a cheese pizza.
3/4 + 3/4 + 3/4 + 3/4
= 3 + 3 + 3 + 3 /4
= 12/4
= 3
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Anais goes to the store to get granola bars 1 pack of 100 granola bars is $8.67.
Another pack of granola bars is 50 granola bars for $5.48. Which is the better buy?
The better option is to buy the Granola bar.
What is a unit value?
When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities.
To determine which is the better buy, you need to compare the price per granola bar for each option. To do this, you can divide the price of each pack by the number of granola bars it contains.
For the first pack of 100 granola bars, the price per granola bar is $8.67 / 100 granola bars = $0.09 per granola bar.
For the second pack of 50 granola bars, the price per granola bar is $5.48 / 50 granola bars = $0.11 per granola bar.
Since the price per granola bar is lower for the first pack, it is the better buy. You would save money by purchasing the first pack of 100 granola bars instead of the second pack of 50 granola bars.
Hence, the better option is to buy the Granola bar.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the
blanks.
Tony is starting a business selling handmade necklaces. He has decided to invest an initial amount of
$381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for
$9 per necklace. Once he makes and sells a certain number of necklaces, he will break even, with
identical expenses and sales. How many necklaces would that take? What would the total expenses and
sales be then?
After selling
necklaces, Tony would have total expenses and sales of $
It will take the sales of 381 necklaces to reach break-even.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that Tony invest an initial amount of $381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for $9 per necklace.
Let the number of necklace be x then;
8x + 381 = 9x
Solving;
9x - 8x = 381
x = 381
Therefore, Total expenses = 8x + 381
8(381) + 381
= 3429
Thus, Total sale = 9x = 3429
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rewrite the equation x^2+26x+164.5=0 in the form (x-p)^2=q
We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:
(x + 13)^2 = 4.5
How to rewrite the quadratic equation?Here we want to rewrite the quadratic equation:
x^2 + 26x + 164.5 = 0
To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:
(a + b) = a^2 + 2ab + b^2
We can rewrite the given quadratic as:
x^2 + 26x + 164.5 = 0
x^2 + 2*13*x + 164.5 = 0
The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:
x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0
x^2 + 2*13*x + 169 - 4.5 = 0
(x + 13)^2 = 4.5
That is the equation we wanted to get.
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Good points please answer
The values of given functions are Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119.
What are trigonometric equation?Trigonometric equation is a condition including at least one trigonometric ratios of obscure points. It is communicated as proportions of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) points. For instance, cos2 x + 5 sin x = 0 is a mathematical condition.
According to question:We have,
Cosx = 12/13
Use sin^2(x) + Cos^2(x) = 1
sinx = [tex]\sqrt{1-cos^{2}x}[/tex] = 5/13
We know that
Sin2x = 2sinxcosx
Sin2x = 2(5/13)(12/13)
Sin2x = 120/169
Using cos2x = 2cos^2x - 1
cos2x = 2(12/13)^2 - 1
Cos2x = 119/169
Then, using tanx = sinx/cosx
tan2x = sin2x/cos2x
tan2x = [tex]\frac{\frac{120}{169} }{\frac{119}{169} }[/tex] = 120/119
Thus, required values Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119
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Required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
What is trigonometric ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
[tex]cos2x=cos^2x-sin^2x[/tex]
[tex]sin2x=2sinxcosx\\\\tan2x=(2tanx)/(1-tan2x)[/tex]
..
[tex]sinx= -\frac{12}{13}[/tex]
you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0
[tex]sinx=-\frac{12}{13} (given)\\\\\cosx=\frac{5}{13} \\\\tanx=-\frac{12}{5}[/tex]
..
[tex]cos2x=cos^2x-sin^2x=\frac{25}{169-144} \times \frac{1}{69} =-\frac{119}{169} \\\\\\sin2x=2sinxcosx=2\times(-\frac{12}{13}) \times (\frac{5}{13} )=-\frac{120}{169} \\\\\\tan2x=\frac{2tanx}{1-tan^{2}x } \\\\\\=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=\frac{120}{119}[/tex]
required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
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Find an equation of the line that goes through the points (-3,-11) and (8,55). Write your answer in the form
y=mx+b.
y =
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{55}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{55}-\stackrel{y1}{(-11)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{55 +11}{8 +3} \implies \cfrac{ 66 }{ 11 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 6 ( x +3) \\\\\\ y+11=6x+18\implies {\Large \begin{array}{llll} y=6x+7 \end{array}}[/tex]
The measures of two vertical angles are given by the expressions (x+16)° and (2x - 3).
Find the value of x . What is the measure of each angle?
Answer:
see explanation
Step-by-step explanation:
vertical angles are congruent , then
2x - 3 = x + 16 ( subtract x from both sides )
x - 3 = 16 ( add 3 to both sides )
x = 19
Then
x + 16 = 19 + 16 = 35°
since the angles are congruent , then
the measure of each angle is 35°
What is the Median? The student council sells candy bars to raise money for a dance.
Use the bar graph shown to answer the questions below.
A bar graph titled Candy Bars Sold. The vertical axis shows Number of Candy Bars with values ranging from 0 to 100. The horizontal axis shows Student Council Members with names as Dave, Jenny, John, Sarah, Alex. Points are (Dave, 90), (Jenny, 50), (John, 60), (Sarah, 70), and (Alex, 50).
What is the mode for this data set?
Mode =
50
candy bars
What is the median for this data set?
Median =
candy bars
What is the mean for this data set?
Mean =
64
candy bars
Answer:
50
Step-by-step explanation:
ezpz
Original Equation: y = 2x + 7
Which equation will shift the graph of the original equation up 2 units?
Responses
A y = 2x + 9y = 2x + 9
B y = 2x + 5y = 2x + 5
C y = 2x + 2y = 2x + 2
D y = 2x - 2y = 2x - 2
E y = 4x + 7
Therefore the solution to the given question equation will shift the graph of the original equation up 2 units in y=2x + 9
What is equation?equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.
Here,
It follows a linear function. y=mx + b
If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.
In order to move the graph up by 2 units, you must add 2 units to b.
In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.
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What is the slope of this line?
Answer:
m = 2/5
:)))))))))))))))))))))))))))
Pens are sold in a pack of 10 for 95 krona ( Swedish money ). If the price is reduced by 30%, what is new cost per pen
The new cost per pen based on the information is $6.650.
What is the cost per pen?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this case, the pens are sold in a pack of 10 for 95 krona and the price is reduced by 30%, the new price will be:
= 95 - (30% × 95).
= 95 - 28.5
= $66.50
The new cost for every pen will be:
= $66.50 / 10
= $6.650
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1. If a rubber ball is dropped from a height of 10 feet, the function
f(x) = 20 (0.6)* gives the height in feet of each bounce, where
x is the bounce number. What will be the height of the 5th bounce?
Round to the nearest tenth of a foot.
2. A population of pigs is expected to increase at a rate of 4% each
year. If the original population is 1000, the function f(x) = 1000 (1.04)*
gives the population in x years. What will be the population in 12 years?
Please help
If a rubber ball is dropped from a height of 10 feet, The height of the 5th bounce and the population in 12 years
2.4 feet1700 pigs What will be the height of the 5th bounce?Generally, For the first problem, the height of the 5th bounce can be calculated by plugging in 5 for x in the function
f(x) = 20 (0.6)^x:
f(5) = 20 (0.6)^5
= 20 (0.12)
= 2.4 feet
What will be the population in 12 years?For the second problem, the population in 12 years can be calculated by plugging in 12 for x in the function f(x) = 1000 (1.04)^x:
f(12) = 1000 (1.04)^12
= 1000 (1.70)
= 1700 pigs
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On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts
remaining alive in this population decreases rapidly due to the lack of flowers for them to eat.
The relationship between the elapsed time, t, in days, since the beginning of winter, and the
total number of locusts, N(t), is modeled by the following function:
N(t) 8950 (0.49)^t/2
Complete the following sentence about the daily rate of change in the locust population.
Round your answer to two decimal places.
Every day, the locust population is multiplied by a factor of ____.
Answer:
0.7
Step-by-step explanation:
Sandpiper Company ha 25,000 hare of cumulative preferred 1% tock, $150 par and 50,000 hare of $5 par common tock. The following amount were ditributed a dividend:
20Y1 $75,000
20Y2 15,000
20Y3 112,500
Determine the dividend per hare for preferred and common tock for each year. Round all anwer to two decimal place
$22500 is interest rate of common tock for each year.
What is an explanation of the interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off.
Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.
Amount distributed as dividends = $15000
Total Preferred dividend to be paid = $37500
But Total Preferred dividend paid/avaiable = $15000
dividend per share(P.S) = $0.60 **(15000 / 25000shares)
Since the preferred stock cumulative dividend to be paid in Next year due to less payment in current year would be = $22500 or $0.90 per share
Remaining dividend = 0
Equity dividend per share = 0
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An angle meaure 48° le than the meaure of it upplementary angle. What i the meaure of each angle?
Answer:
132
Step-by-step explanation: Supplementary=180 So all you have to do is subtract 48 from 180 and should give you 132.
Hope that helps!