Solution :
From the given equation :
E[ E (X|Y) ] = E (X)
a). Then,
E[ E [ X|Y,Z] | Z] = E [ X|Z ]
---- True
E [ E [ X|Y ] | Z ] = E [ X|Z ]
---- False
E [E [X | Y,Z ]] = E [X|Y ]
---- False
b). Th quantity E [ g (X,Y) | Y,Z ] is ,
A random variable ----- TrueA number ----- FalseA function of (X,Y) ----- FalseA function of (Y,Z) ----- TrueA function of Z only ------- FalseThe low of iteration tell the following statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)
From the given equation the law of iterated expectations
[tex]E[ E (X|Y) ] = E (X)[/tex]
Therefore We have to find a)
What is the definition of iteration?Iteration is the repetition of a process in order to generate a sequence of outcomes.
So by using the low of iteration we can say that,
E[ E [ X|Y,Z] | Z] = E [ X|Z ] ---- True
E [ E [ X|Y ] | Z ] = E [ X|Z ] ---- False
E [E [X | Y,Z ]] = E [X|Y ] ---- False
b). Th quantity E [ g (X,Y) | Y,Z ] is ,
For a random variable y this is ----- True
For a number ----- False
For a function of (X,Y) ----- False
For a function of (Y,Z) ----- True
For function of Z only ------- False
Therefore,The low of iteration tell the following statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)
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Solve.
x^2 - 9x + 3 = 0
x= or x=
Answer:
Step-by-step explanation:
x^2 - 9x + 3 = 0 is a quadratic whose coefficients are a = 1, b = -9 and c = 3.
Use the quadratic formula to solve it.
The discriminant, b^2 - 4ac, is 81 - 4(1)(3), or 81 - 12, or 69.
The roots are:
-b ± √(discriminant)
x = -------------------------------
2a
And these roots in this particular problem are:
-(-9) ± √69 9 ± √69
= ------------------------------- = ----------------
2(1) 2
Evaluate f(g(3)) if f(x)=6x−4 and g(x)=x2.
(Please Explain! Thank you)
Answer: 50
Step-by-step explanation:
f(x) = 6x-4 and g(x) = x^2
f(g(3)) means what is the value of the function f when it is evaluated at the value of g(3).
So g(x) is x^2 so g(3) is 3^2 = 9
Therefore we put 9 in for f(g(3))= f(9) = 6(9) - 4 = 54 - 4 = 50
Suppose you have 3 bags. Two of them contain a single $10 bill, and the third contains a single $5 bill. Suppose you pick one of these bags uniformly at random. You then add a $5 bill to the bag, so it now contains two bills. The bag is shaken, and you randomly draw a bill from the bag without looking into the bag. Suppose it turns out to be a $5 bill. If a you draw the remaining bill from the bag, what is the probability that it, too, is a $5 bill
Answer:
1/2
Step-by-step explanation:
Number of bags = 3
number of bags with $10 bill initially = 2
number of bags with $5 bill initially = 1
assume :
event you pick a $5 bill at first draw = A
event you pick a $5 bill at second draw = B
hence : P ( A n B ) = 1/3 * 1 = 1/3
P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 ) = 2/3
therefore P( that the second drawn bill is $5 )
P( B | A ) = P(A n B ) / P ( A )
= (1/3) / (2/3) = 1/2
The probability that it, too, is a $ 5 bill is 33.33%.
Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:
3 bags = 2 with a 10 bill and 1 with a 5 bill 1/3 = 0.3333 0.3333 x 100 = 33.33
Therefore, the probability that it, too, is a $ 5 bill is 33.33%.
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If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+ g)(x).
Answer:
5x+6
Step-by-step explanation:
f(x) = 3x + 10
g(x) = 2x - 4
(f+ g)(x)= 3x + 10 + 2x - 4
Combine like terms
= 5x+6
Which box holds more popcorn?
Answer:
Amanda's popcorn container holds more popcorn
Step-by-step explanation:
First we'll have to find the volume.
The Volume helps us determine which is bigger.
Step 1
We'll find Amanda's popcorn container
10cm*10cm*13.5cm=1350cm
Step 2
We'll find Mary's popcorn container
8cm*8cm*20cm=320cm
Step 3
Since Amanda's popcorn container has 1350cm (volume) and Mary's popcorn container has 320cm (volume) we'll have this. 1350cm>320cm. We can determine the Amanda's popcorn container has holds more,
Final Answer
Amanda's popcorn container holds more popcorn
A wedge of cheese is shaped like a triangular prism. The wedge of cheese is 7 inches tall. The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches. If you ate this whole block of cheese, about how many cubic inches would you have eaten (ignoring the holes)?
420 in
193 in
385 in
210 in
Answer:
193 in
Step-by-step explanation:
Volume of a triangular prism:
The volume of a triangular prism is the base area multiplied by the wedge, that is:
[tex]V = A_bw[/tex]
The base area is one half times the triangle base times it's height, so:
[tex]V = 0.5*b*h*w[/tex]
The wedge of cheese is 7 inches tall.
This means that [tex]w = 7[/tex]
The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.
This means that [tex]b = 11, h = 5[/tex]
Volume:
[tex]V = 0.5*b*h*w = 0.5*11*5*7 = 192.5[/tex]
Rounding, approximately 193 in.
Belinda wants to invest in an option that would help to increase your investment value by the greatest amount in 20 years. Will there be any significant can difference in the value of Belinda‘s investment after 20 years if she uses option two over option one? Explain your answer, and show the investment value after 20 years for each option.
Step-by-step explanation:
Part A, Option 1 is a exponential function while option is a linear equation.
Part B, Let y=b*a^(x) be the function for option 1. At x=1, y=1100 and at x=2, y=1210. 1100=b*a and 1210=b*a^2. Dividing them both we get, b=1.1 and a=1000. y=1000*(1.1)^(x). For option 2, it's a linear equation with a function y(x)=1000+100x.
The 20 year difference would be immense. With option 1, Belinda will get $6727.5 whereas with option 2, they will end up with $3000
find the hcf of 100,24
Answer:
4
Step-by-step explanation:
24 = 2^3 x 3
100 = 2^2 x 5^2
HCF = 2^2 = 4
Find the area of the shaded regions.
Answer:
around 22, or 21.98
Step-by-step explanation:
[tex]s1 = {r}^{2} \times \pi = 9 \times 3.14 = 28.26[/tex]
[tex]s2 = 1 \times 3.14 = 3.14[/tex]
[tex]s3 = 28.26 - (3.14 \times 2) = 28.26 - 6.28 = 21.98[/tex]
University Trailer Sales Company sold 356 utility trailers during a recent year. If the gross annual sales for the company was $328128, what was the average selling price for each trailer?
The average selling price of each trailer was nearly $
(Round to the nearest whole number.)
Answer:
The Answer is 2000$..........
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 6y = -42
Answer:
y = -1/2x -7
Step-by-step explanation:
3x + 6y = -42
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x+6y = -3x-42
6y = -3x-42
Divide each side by 6
6y/6 = -3x/6 - 42/6
y = -1/2x -7
There is a sales tax of S6 on an item that costs 888 before tax. The sales tax on a second item is $21. How much does the second item cost before tax?
Step-by-step explanation:
before Tax
Coast = 888
in 2ND Item = $21
• 888/21
= $42.28
Find the probability that a randomly
selected point within the circle falls
in the white area.
r = 4 cm
2.5 cm
3 cm
3 cm
[?]%
Round to the nearest tenth of a percent.
Answer:
61.2%
Step-by-step explanation:
Area of the circle π(4²) = 50.265... cm²
Area of the triangle = ½(6)(6.5) = 19.5 cm²
probability of landing is white is
1 - (19.5 / 50.265) = 0.612059...
The probability that a randomly selected point within the circle falls in the white area is 61.22%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
As we know the circle is a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
The total outcomes = The area of a circle
The area of the circle = πr²
The area of the circle = π(4)²
Because r = 4 cm
The area of the circle = 50.285 square cm
The area of the triangle = (1/2)(3+3)(4+2.5)
The area of the triangle = 19.5 square cm
The area of the white region = 50.285 - 19.5 = 30.785 square cm
Probability = 30.785/50.285
Probability = 0.6122 or
Probability = 61.22%
Thus, the probability that a randomly selected point within the circle falls in the white area is 61.22%.
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Are 3(3x - y) and 12 ( x - 4y ) equivalent expression?
Answer:
No, they are not.
Step-by-step explanation:
If you distributed 12(x - 4y), you would get 12x - 48y. If you distributed 3(3x-y), you would get 9x- 3y. 12x - 48y and 9x - 3y are not equivalent. Hope this helped!
find inverse of f(x)=- 1/2 x+11
Answer:
-2x + 22
Step-by-step explanation:
We have the function f(x) = -1/2x + 11 and are asked to find the inverse of it.
To find the inverse, we will follow the according steps :
Replacing x with ySolving for yLet's do as followed:
Replacing x with y :
Since f(x) can be also written as y, we can do y = -1/2x + 11, thus making the switch alot easier.
y = -1/2x + 11
x = -1/2y + 11
Solve for y :
We have to get y alone to find the inverse, to do so, get rid of the outlier by subtracting 11 from both sides :
x - 11 = -1/2y
Now divide both sides by -1/2 to get y alone and retrieve our inverse :
-2(x - 11)
Distribute to get the inverse :
-2x + 22
How many unit cubes are on each layer of the cube?
6
3
12
9
Answer:
6
Step-by-step explanation:
Remember: Each layer has 6 cubes. Step 3 Count the cubes. cubes Multiply the base and the height to check your answer. So, the volume of Jorge's rectangular prism is cubic centimeters. if wrong very sorry
Answer:
9
Step-by-step explanation:
took the test
Complete the equation: x2 + 8x + __ = (__)^2
Answer:
B
Step-by-step explanation:
16,x+4
by completing square formula
Terry got 27 out of 50 for his Maths test. What is his mark as a percentage?
Answer:
54%
Step-by-step explanation:
Concepts:
A percent is a value indicating hundredth parts of any number. 1%/one percent would be equal to a hundredth part, and 100% would be the entire quantity.Solving:
Let's solve this problem by going through the steps to find the percentage.
1. Find out the entire amount
Since Terry got 27/50 on his math test, we can assume he got 27 questions right out of 50 questions. This means, in total, there was 50 questions.2. Divide the number you want expressed as a percent by the total quantity
The number we want in this question to be expressed as a percent is 27, and the total quantity is 50.27 ÷ 50 = 0.543. Multiply the resulting value by 100
The result we got when we divided 27 by 50 is 0.540.54 · 100 = 544. Add the percent symbol (%) at the end of the value
The value we got was the number 5454%Therefore, Terry's marks as a percentage is 54%.
A concern of Major League Baseball is that games last too long. Some executives in the league's headquarters believe that the mean length of games this past year exceeded 3 hours (180 minutes). To test this, the league selected a random sample of 80 games and found the following results: = 193 minutes and s = 16 minutes.
Based on these results, if the null hypothesis is tested using an alpha level equal to 0.10, which of the following is true?
a. The null hypothesis should be rejected if xbar > 182.31.
b. The test statistic is t = 1.2924.
c. Based on the sample data, the null hypothesis cannot be rejected.
d. It is possible that when the hypothesis test is completed, a Type II statistical error has been made.
Answer:
it is possible that when the hypothesis test is completed,a type ll statistical error has been made
given the circle find the arc measure
9514 1404 393
Answer:
87°
Step-by-step explanation:
Call the circle center point X. The measure of arc FG is the measure of central angle FXG, which is the supplement of central angle GXH.
arc FG = 180° -93° = 87°
Which improper fraction is equivalent to 17.8?
89/10
93/10
89/5
Answer:
17.8.
Step-by-step explanation:
89/5
= 17 4/5
= 17.8.
The correct improper fraction which is equivalent to 17.8 is,
⇒ 17.8 = 89 / 5
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
We have to given that;
The number is,
⇒ 17.8
Now,
We can simplify the number as;
⇒ 17.8
⇒ 178 /10
⇒ 89 / 5
Therefore, The correct improper fraction which is equivalent to 17.8 is,
⇒ 17.8 = 89 / 5
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Evaluate the variable expression x y for the given values of x and y. (If an answer is undefined, enter UNDEFINED.) x = 0; y = 21
Please if anyone can help me
Meena's father's present age is six times Meena's age. Five years from now she will be one-third of her father's present age. What are their present ages?
Answer:
Meena's age is 5 and her fathers age is 30 years old.
Step-by-step explanation:
Let's assume Meena's age to be x years old.
Meena's dads present age is 6x.
5 years from now Meena's age will be (1/3)rd of her dads age
x+5= 1/3 * 6x
x+5=2x
x=5.
Meenas present age is 5 years and her dads age is 30 years
ixl area of sectors. I am struggling on this question
Answer:
español :/
Step-by-step explanation:
Answer:
256/5 pi
Step-by-step explanation:
= angle/360 × pi×r^2
= 72/360 × pi × 16^2
= 51.2 pi
= 256/5 pi
What is the value of X
A 15
B 21
C 26
D 105
Answer:
B)21
Step-by-step explanation:
∠KN=∠ML
∠KN=90°+15°
=105°
∠ML=105°
5x°=105°
x°=105÷5
x°=21°
Answer:
[tex]5x=90+15[/tex]
Add, 90 + 15 = 105
[tex]5x=105[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}=\frac{105}{5}[/tex]
[tex]x=21[/tex]°
[tex]\textbf{OAmalOHopeO}[/tex]
Complete the table. Round your entries to the
nearest thousandth.
a
b
C
dz
ex
ASAP
a=2,5937
b=2,7048
c=2,7181
d=2,7183
e=2,7183
What is the Square root of 30 ,12,36
Answer:
the square root of:
30: 5.477225575
12: 3.464101615
36: 6 <-- explanation of square root: any number that when multiplied by itself equals your wanted number (in this case 36) will be the square root of your wanted number.
Graph: y – 3 = 1/2 (x + 2)
Answer:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Step-by-step explanation:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Answer: See below
Concept:
There are different forms of linear equations:
Slope-intercept form: y = mx + bPoint-slope form: y - y₁ = m (x - x₁)Standard form: Ax + By = CIntercept form: x / x₁ + y / y₁ = 1Solve:
Given: y - 3 = 1/2 (x + 2)
Here, we can see the linear equation is in the form of point-slope form.
x₁ = -2
y₁ = 3
m = 1/2
Point included in the graph = (-2, 3)
Slope of the graph = 1/2
Hope this helps!! :)
Please let me know if you have any questions
Please help explanation if possible
Answer:
10% gain
Step-by-step explanation:
[P2-P1]/P1
(33-30)/30=3/30=.1 or 10% gain.
Answer:
10%
Step-by-step explanation:
→ Minus the new share from the old one
33 - 30 = 3
→ Divide the answer by the original price
3 ÷ 30 = 0.1
→ Multiply the answer by 100
0.1 × 100 = 10%
