Answer:
they are positively correlated.
Step-by-step explanation:
We can calculate the individal expectations first. FIrst player will win if that player's roll is greater than the bank's roll. There are (6 possible rolls of player 1 * 6 possible rolls of bank =) 36 total possible rolls, out of which player 1 will win in 15 cases.
[tex]\therefore E(I_i) = 1\cdot \frac{15}{36} + 0 \cdot \frac{21}{36} = \frac{5}{12} \approx 0.4167[/tex]
For the joint expectation, there are (6 possible rolls of player 1 * 6 possible rolls of player 2 * 6 possible rolls of bank =) 216 total possible rolls.
Cases where both players win: Expectation = $2.
If bank rolls 1, both players will win in 5*5 = 25 cases. P1 is one of {2,3,4,5,6}, P2 is one of {2,3,4,5,6}
If bank rolls 2, both players will win in 4*4 = 16 cases.
If bank rolls 3, both players will win in 3*3 = 9 cases.
If bank rolls 4, both players will win in 2*2 = 4 cases.
If bank rolls 5, both players will win in 1*1 = 1 cases.
If bank rolls 6, both players will win in 0*0 = 0 cases.
Total cases = 25+16+9+4+1+0 = 55 cases.
Cases where player 1 wins $1 and player 2 loses: Expectation = $1.
If bank rolls 1, player 1 will win and player 2 will lose in 5*1 = 5 cases. P1 is one of {2,3,4,5,6}, P2 is {1}
If bank rolls 2, player 1 will win and player 2 will lose in 4*2 = 8 cases.
If bank rolls 3, player 1 will win and player 2 will lose in 3*3 = 9 cases.
If bank rolls 4, player 1 will win and player 2 will lose in 2*4 = 8 cases.
If bank rolls 5, player 1 will win and player 2 will lose in 1*5 = 5 cases.
If bank rolls 6, player 1 will win and player 2 will lose in 0*6 = 0 cases.
Total cases = 5+8+9+8+5+0 = 35
Cases where player 2 wins $1 and player 1 loses: Expectation = $1.
This is the same as above with player 1 and 2 exchanged.
Total cases = 35
Cases where both players lose: Expectation = $0.
If bank rolls 1, both players will lose in 1*1 = 1 cases. P1 is {1}, P2 is {1}
If bank rolls 2, both players will lose in 2*2 = 4 cases.
If bank rolls 3, both players will lose in 3*3 = 9 cases.
If bank rolls 4, both players will lose in 4*4 = 16 cases.
If bank rolls 5, both players will lose in 5*5 = 25 cases.
If bank rolls 6, both players will lose in 6*6 = 36 cases.
Total cases = 1+4+9+16+25+36 = 91 cases.
Total of all cases (we expect this to be 216 as mentioned above) = 55+35+35+91=216
So, joint expectation is:
[tex]E(I_1I_2) = \frac{2\cdot 55 +1\cdot 35+1\cdot 35+0\cdot 91}{216} = \frac{180}{216}= \frac{5}{6} \approx 0.8333[/tex]
So, the covariance is given by:
[tex]\texttt{Cov}(I_1I_2) =E(I_1I_2) -E(I_1)\cdot E(I_2)= \frac{5}{6}-\frac{5}{12}\cdot\frac{5}{12}=\frac{95}{144} \approx 0.6597[/tex]
As this is greater than 0 and closer to 1, they are positively correlated.
The reason why this result is expected is because the same bank roll is being used for both players. So, it is very likely that both players will win if the bank roll is 1 or even 2. Also, it is very likely that both players will lose if the bank roll is 6, 5, or even 4. This shows positive correlation between the events.
Which pairs of non-overlapping angles share a ray to make a right angle?
Answer:
JGH and JGF
Step-by-step explanation:
Both adjacent and make a right angle
∠KGJ and ∠FGH are the pairs of non-overlapping angles that share a ray to make a right angle.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
In the given figure, we need to find the pairs of non-overlapping angles that share a ray to make a right angle.
We can see that ∠EGF and ∠HGF make a right angle but line FG is overlapping or common in both the angles.
∠KGJ and ∠FGH make a right angle and pairs of non-overlapping angles.
So, this is the correct pair for the condition.
Learn more about a right angle;
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What is the slope of the line given by the equation below?
y-20 = 5(x-2)
Answer:
5
Step-by-step explanation:
first you need to simplify this equation and put it in slope intercept form which is y = mx + b
after simplifying you will get y = 5x + 10
since the slope is m , the answer will be 5
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
What are the next two numbers in the pattern of numbers; 45, 15, 44, 17, 40, 20, 31, 25, ...
Answer:
15, 33
(if I'm not wrong, it should work this way)
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
ASAP
What is the sum of 16.87 + (–98.35)?
–115.22
–81.48
81.48
115.22
Solution,
16.87+(-98.35)
=16.87-98.35
= -81.48
Hope it helps
Good luck on your assignment
Answer:-81.48
Step-by-step explanation:
16.87 + (–98.35)
-81.48
If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps
Does this graph represent a function? Why or why not?
A
B
C
D
Answer:
B
Step-by-step explanation:
As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.
This particular function is f(x)=x^2.
Hope that helped,
-sirswagger21
Answer:
Yes is passes the vertical line test
Step-by-step explanation:
This parabola is a function. it has a one to one correspondence and passes the vertical line test
Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of the second fourth and fifth
Answer:
see below
Step-by-step explanation:
We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.
x + 5x + 10 = 3(3x + 8) - 41
6x + 10 = 9x + 24 - 41
6x + 10 = 9x - 17
3x = 27
x = 9
The numbers are 9, 10, 11, 12, 13.
Charlotte is creating a triangular pennant with geometry software.
The base measure of the pennant on screen is 550 pixels. The height
is 275 pixels. Charlotte resizes the pennant, keeping the aspect ratio
constant, so the height is 165 pixels. What is the scale factor of the
dilation? What is the base of the pennant?
~~~~~~~~~~~~~~
pls help T-T
Answer:
Base of the Pennant = 330 pixels
Scale Factor =0.6
Step-by-step explanation:
The base measure of the pennant on screen is 550 pixels.
The height is 275 pixels.
[tex]A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1[/tex]
If Charlotte resizes the pennant, keeping the aspect ratio constant.
Height = 165 pixels
Therefore:
[tex]\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330[/tex]
Therefore, the scale factor of the dilation [tex]=\dfrac{330}{550}= \dfrac{165}{275}=0.6[/tex]
Base of the Pennant = 330 pixels
Scale Factor =0.6
Find the value of x:
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
Determine whether the given value is a statistic or a parameter.A homeowner measured the voltage supplied to his home on 42 random days, and the average (mean) value is 127.1 volts.A) The given value is a statistic for the year because the data collected represented a population.
B) The given value is a parameter for the year because the data collected represent a sample.
C) The given value is a parameter for the year because the data collected represent a population.
D) The given value is a statistic for the year because the data collected represent a sample.
Answer:
[tex] \bar X = \frac{\sum_{i=1}^{42} X_i}{n}[/tex]
And for this case the sample mean is
[tex]\bar X = 127.1[/tex]
And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since [tex] E(\bar X) =\mu[/tex], and the best option would be:
D) The given value is a statistic for the year because the data collected represent a sample.
Step-by-step explanation:
For this case we know that a homeowner take a random sample of 42 voltage values ina year and he calculate the sample mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^{42} X_i}{n}[/tex]
And for this case the sample mean is
[tex]\bar X = 127.1[/tex]
And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since [tex] E(\bar X) =\mu[/tex], and the best option would be:
D) The given value is a statistic for the year because the data collected represent a sample.
Write the point slope form of an equation of the line through the points (-2,6) and (3,-3)
Answer:
A.
Step-by-step explanation:
So first you need to find the slope:
[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]
Since it's point slope, you have to use a point:
It's either:
[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]
or
[tex](y+2)=-\frac{8}{5}(x-3)[/tex]
Check which answer has those:
A.
The solution is Option A.
The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -2 , 6 )
Let the second point be Q ( 3 , -2 )
The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )
On simplifying the equation , we get
Slope m = ( 8 / -5 ) = -8/5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 6 = ( -8/5 ) ( x - ( -2 ) )
On simplifying the equation , we get
y - 6 = ( -8/5 ) ( x + 2 )
Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )
To learn more about equation of line click :
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Please help meee
Which number line model represents the expression -2/5 + 4/5:
The number line model that represents the expression -2/5 + 4/5 is: Option B
How to solve Inequality on number line?
To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.
Now, in this case, the operation to solve is:
-2/5 + 4/5
Solving this gives 2/5
Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem
Read more about Inequality on number line at: https://brainly.com/question/24372553
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Solve: 4x^-2 – 3x^-1– 1 = 0
Answer:
1, -4
Step-by-step explanation:
4x^-2 – 3x^-1– 1 = 0Let x^-1 = 1/x = y
4y^2 - 3y - 1 = 04y^2 - 4y + y - 1 = 0(y - 1) (4y + 1) = 01. Root 1
y - 1 = 0 y = 11/x= 1x = 12. Root 2
4y + 1 = 04y = -1y = -1/41/x = - 1/4x = -4If the nurse to patient ratio in a long term care unit is 3:15, how many nurses would you expect to see in a unit with 25 patients?
Answer:
5
Step-by-step explanation:
Divide both sides by 3 to get
1:5
Multiply by 5
To get 5:25
5 nurses for 25 patients
Answer:
5
Step-by-step explanation:
3 x 5 = 15
n x 5 = 25
n = 5
A farmer knows that every 50 eggs his chickens lay, only 45 will be marketable. If his
chickens lay 1000 eggs in a week, how many of them will be marketable?
Answer:
900 eggs
Step-by-step explanation:
45/50 are marketable
divide the top and bottom by 5
9/10
Multiply this fraction by the 1000 eggs laid
9/10 *1000
900 eggs will be marketable
Answer:
900
Step-by-step explanation:
A line intersects the point (-11, 4) and has
a slope of -2. What are the inputs to the
point-slope formula?
y - [?] = [ ](x-[])
Answer: Point slope form is y-y1=m(x-x1)
Step-by-step explanation:
Here y1=4
x1=-11
m i.e slope=-2
And there you go.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
-1, 1
13, 15
Step-by-step explanation:
x and x+2 are the integers
x*(x+2)= 7(x+x+2) -1x²+2x= 14x+14-1x² - 12x -13= 0Roots of the quadratic equation are: -1 and 13.
So the integers pairs are: -1, 1 and 13, 15
The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it is reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?
Answer:
0.699
Step-by-step explanation:
got it on khan academy, should get brainliest thanks
At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37.5 grams.
What is the half-life of the goo in minutes?
________
Find a formula for
G(t),
the amount of goo remaining at time T.
G= _________
How many grams of goo will remain after 32 minutes?
Answer:
Half-life of the goo is 49.5 minutes
[tex]G(t)= 300e^{-0.014t}[/tex]
191.7 grams of goo will remain after 32 minutes
Step-by-step explanation:
Let [tex]M_0\,,\,M_f[/tex] denotes initial and final mass.
[tex]M_0=300\,\,grams\,,\,M_f=37.5\,\,grams[/tex]
According to exponential decay,
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt[/tex]
Here, t denotes time and k denotes decay constant.
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014[/tex]
So, half-life of the goo in minutes is calculated as follows:
[tex]\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes[/tex]
Half-life of the goo is 49.5 minutes
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}[/tex]
So,
[tex]G(t)= M_f=M_0e^{-kt}[/tex]
Put [tex]M_0=300\,\,grams\,,\,k=0.014[/tex]
[tex]G(t)= 300e^{-0.014t}[/tex]
Put t = 32 minutes
[tex]G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams[/tex]
determine the slope of a line with the equation 6x+2y-4=0
If f(x)=7+4c and g(x) = 1/2x what is the value of (f/g)(5)
Answer: 270
Step-by-step explanation:
The notation [tex](\frac{f}{g})(5)[/tex] means to divide [tex]\frac{f(5)}{g(5)}[/tex]. Now that we know we have to divide, we can plug them into this equation.
[tex]\frac{7+4(5)}{\frac{1}{2(5)} }=\frac{27}{\frac{1}{10} }[/tex]. We know that dividing by a fraction means to multiply by its reciprocal, so we'll do that.
[tex]27*10=270[/tex]
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is this distance?
Answer:
150
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 90. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
90^2 + 120^2 = c^2
c=150
Solve for a.
ab +c= d.
Answer:
a = (d -c)/b
Step-by-step explanation:
Undo the addition of c, by subtracting c.
ab +c -c = d -c
ab = d - c
Undo the multiplication by b, by dividing by b.
ab/b = (d -c)/b
a = (d -c)/b
what is the value sin(?)= cos 28
Answer: 62
Step-by-step explanation:
Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.
Hope that helped,
-sirswagger21
Which of the following shows the extraneous solution to the logarithmic equation log Subscript 7 Baseline (3 x cubed + x) minus log Subscript 7 Baseline (x) = 2 x = negative 16 x = negative 4 x = 4 x = 16
Answer:
x = -4Step-by-step explanation:
A graphing calculator shows there is one solution to ...
[tex]\log_7{(3x^2+x)}-\log_7{(x)}=2[/tex]
However, the usual solution method would be to combine the logarithms and take the antilog to get ...
[tex]\log_7{\left(\dfrac{3x^3+x}{x}\right)}=2\\\\\log_7{(3x^2 +1)}=2\\\\3x^2+1=7^2\\\\x^2=\dfrac{49-1}{3}=16\\\\x=\pm 4\qquad\text{take the square root}[/tex]
This gives two solutions. the "solution" x = -4 is extraneous, as it doesn't work in the original equation. "x" must be positive in the log expressions.
Answer:
x = - 4
Step-by-step explanation:
Got it right :)
Sandy is tiling her floor woth square tiles.The kength one of the sides of each tiles is3/4 foot.Her floor is 9 feet by 10 feet .What is the area of the tile she using to tile her floor
Hey there! I'm happy to help!
Since the tiles are square, all of their sides are the same. We see that one of the side lengths is 3/4. So, to find the area of the square, we square 3/4 (multiply it by itself)
3/4 × 3/4= 9/16
Therefore, the area of Sandy's tile is 9/16 square feet.
BONUS
We can also find the area of our floor, which is 9 feet by 10 feet, so it is 90. We can then divide by 9/16 to figure out how many tiles we need.
90/9/16=160
So, you would need 160 of these tiles to fill the floor.
I hope that this helps!
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
It would be a cone with a radius of 4 units rotating around y-axis.
Which set of ordered pairs does NOT represent a function ?
Answer:
The answer is C.
Step-by-step explanation:
For a function, we do a vertical line test. If there is more than one point in one single x-position, it is not a function. Example, the ordered pairs (1, 1) and (1, 2) do NOT describe a function because there are more than one point on x=1.
