The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.
The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.
When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.
In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.
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Force f acts between a pair of charges, q1 and q2, separated by a distance d. for each of the statements, use the drop-down menus to express the new force in terms of f. q1 is halved, q2 is doubled, but the distance between the charges remains d. q1 and q2 are unchanged. the distance between the charges is doubled to 2d. q1 is doubled and q2 is tripled. the distance between the charges remains d.
The initial force between the two charges is given by:
[tex]F=k\frac{q_{1} q_{2} }{d^2}[/tex]
where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:
1. F
In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.
So, we have:
q'₁=q₁/2
q'₂=2q₂
d'=d
So, the new force is:
[tex]F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F[/tex]
So the force has not changed.
2. F/4
In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.
So, we have:
q'₁=q₁
q'₂=q₂
d'=2d
So, the new force is:
[tex]\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}[/tex]
So the force has decreased by a factor of 4.
3. 6F
In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.
So, we have:
q'₁=2q₁
q'₂=3q₂
d'=d
So, the new force is:
[tex]F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F[/tex]
So the force has increased by a factor of 6.
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Answer:
1. F
2. F/4
3. 6F
give your answer to 1d.p.
Answer: 26.8
Step-by-step explanation:
[tex]\frac{8.2}{m}=\tan 17^{\circ}\\\\\frac{m}{8.2}=\frac{1}{\tan 17^{\circ}}\\\\m=\frac{8.2}{\tan 17^{\circ}}\\\\m \approx 26.8[/tex]
If x and y are in direct proportion and y is 18 when x is 9, find y when x is 5.
Answer:
y=10
Step-by-step explanation:
18/9=1/2
so
x/5=1/2
Answer: The value of y will be 10 when the value of x is 5.
x and y are directly proportional to each other so,we can write the given relation in mathematical form as:
y=kx
k is any constant
We are given: The value of y is 18 when value of x is 9:
x=9 and y=18
Putting the value of x and y in the above equation , we get:
18=9k
k=18/9=2
k=2
So now we have the proportional relation(k) between x and y.
Again,
we have been given the value of x=5 and we are asked the value of y using same proportional relation.
y=k(5)
y=2(5)=10
Hence the value of y the value of x is 10.
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find the area of the parallelogram with vertices a(−3, 0), b(−1, 6), c(8, 5), and d(6, −1).
Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.
The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).
Given information:
A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).
So first we find the adjacent edges as follows:
AB = B - A
= ( (-1-(-3)) , (6-0) )
= (2,6)
AD = D - A
= ((6-(-3)) , (-1-0))
= (9,-1)
We want to find the area of the parallelogram, we do the following step:
[tex]AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right][/tex]
= i(0 - 0) + j(0 - 0) + k(-2 - 54)
= -56k
The area of the parallelogram = | AB x AD |
= √(-56)²
= 56 square unit
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pls help very eassy due tomm!!!
Answer: Hello how are you doing?
Step-by-step explanation: How may I help you?
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
12y would be the answer
Step-by-step explanation:
To simplify, you first need to combine like terms
6y + 6y =12y
-10x+11x=x
x+12y+8 would be the simplified result
Answer:
x+12y+8
Step-by-step explanation:
8+6y-10x+6y+11x
8+6y+6y-10x+11x.......................collecting like term
8+12y+x = x+12y+8
Use the teams data frame from the lahmanrbroom package. fit a multivariate linear regression model to obtain the effects of bb and hr on runs () in 1971. use the tidy() function in the package to obtain the results in a data frame.1) what is the estimate for the effect of bb on runs? what is the estimate for the effect of hr on runs?2) fit a linear model on the results from question to determine the effect of year on the impact of bb. for each additional year, by what value does the impact of bb on runs change?3) what is the p-value for this effect?
1) library(lahmanrbroom)
model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))
tidy(model)
2) model2 <- lm(bb ~ year, data = tidy(model))
3) The p-value for this effect is significantly different from zero.
The teams data frame from the lahmanrbroom package1) To obtain the effects of bb (walks) and hr (homers) on runs in 1971 using the teams data frame from the lahmanrbroom package and the tidy() function, the following code can be used:
library(lahmanrbroom)
model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))
tidy(model)
The estimate for the effect of bb on runs can be found in the 'Estimate' column for the variable 'bb', and the estimate for the effect of hr on runs can be found in the 'Estimate' column for the variable 'hr'.
2) To determine the effect of year on the impact of bb, a linear model can be fit on the results from the previous question. The following code can be used:
model2 <- lm(bb ~ year, data = tidy(model))
The coefficient for the variable 'year' in this model represents the change in the impact of bb on runs for each additional year.
3) The p-value for this effect can be found in the 'p.value' column of the output of the summary() function applied on the model2, which tests if the coefficient for the variable 'year' is significantly different from zero.
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PLEASEE HELPPP!!!!!!Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
At the Bluepoint Ice Cream Parlor, one group of friends ordered 3 small servings of ice cream and 1 large serving of ice cream for $13. Another group of friends ordered 2 small servings of ice cream and 1 large serving of ice cream for $10. How much does the ice cream cost?
The ice cream costs $
for a small serving and $
for a large serving.
The ice cream costs $3 for a small serving and $4 for a large serving.
How to determine the ice cream costs for a small serving and a large serving?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Since 3 small servings of ice cream and 1 large serving of ice cream for $13, and 2 small servings of ice cream and 1 large serving of ice cream for $10. We can set up two equations to represent the situation:
Let S and L represent the cost of small servings and large servings respectively
3S + L = 13 --- (1)
2S + L = 10 --- (2)
From (1):
L = 13 - 3S --- (3)
Put (3) in (2):
2S + L = 10
2S + 13-3S = 10
-S + 13 = 10
S = 13-10
S = $3
Put S = 3 into (3):
L = 13 - 3S
L = 13 - 3(3)
L = 13 - 9
L = $4
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What is the length of segment AB?
50
I attached a pic of my work.
so what I did was find the amount of the other sides of the triangle using their opposite congruent sides. aka, the bottom is 90, which means the top should also be 90. and 90-50 is 40, so the rest of that side (which is one side of the triangle) should be 40.
and then I used the pythagorean theorem, since it is a right triangle (indicated by the squares in the corners).
the theorem states that a^2 + b^2 = c^2
so just plug in the legs (a and b), and you should get the amount of segment AB (which is c)
An archaeologist in turkey discovers a spear head that contains 53% of its original amount of c-14.
find the age of the spear head to the nearest year.
(5250 isn’t right)
The age of the spearhead to the nearest year will be 6,349
When an organism dies, it stops regenerating new carbon, which causes the organism's total carbon-14 concentration to gradually deplete. By analyzing the ratio of carbon-14 to carbon-12 in an organism, scientists can ascertain when it died.
0.53No = Noe^-0.0001t for T.
Divide both sides by No
0.53No = Noe^0.0001t
0.53 = e^-0.0001t
Take the log of both sides
In 0.53 = In e^-0.0001t
Apply In e^x = x.
In 0.53 =-0.0001t
Divide both sides by -0.0001t to solve for t.
t=6,349
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Given the equation d over 13 equals 15, solve for d.
What is the volume of the can of orange juice in cubic centimeters?
Salut/Hello!
Answer: 3120 cubic cm
Step-by-step explanation:
cm - centimeters
=> - results
We know the area is 156 square cm
And the height is 20 cm
We know the area formula is A = L x l
where L - length
and l - latitude
We also know the volume formula is V = L x l x h
where h - height
So we can replace the length and latitude with the area and we have
V = A x h and we know the area and height
So we calculate:
V = 156 x 20 => V = 3120 cubic cm
I hope it was helpful! :]
Suppose that rob and big both raise animals and sell them. Because rob and big have different talents, they have varying abilities to raise these animals. In 1 day, rob can produce either 10 cows or 20 pigs. In 1 day, big can produce either 9 cows or 36 pigs.
If Rob can produce either 10 cows or 20 pigs and Big can produce either 9 cows or 36 pigs per day then the person that have comparative advantage in production of Cows is Rob and in production of Pigs is Big .
For Rob :
in 1 day , the number of cows produced is = 10 cows ,
the number of pigs produced is = 20 pigs ;
For Big :
in 1 day , the number of cows produced is = 9 cows ,
the number of pigs produced is = 36 pigs ;
On comparing ,we get that Rob produces more number of Cows than Big;
and also Big produces more number of Pigs than Rob .
Therefore , Rob has advantage in production of Cows and Big has advantage in production of pigs .
The given question is incomplete , the complete question is
Suppose that Rob and Big both raise animals and sell them. Because Rob and Big have different talents, they have varying abilities to raise these animals. In 1 day, Rob can produce either 10 cows or 20 pigs. In 1 day, Big can produce either 9 cows or 36 pigs.
Find who has the comparative advantage in the production of cows and pigs .
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a committee of 4 is to be selected from a group of 9 women and 7 men. what is the probability that 2 men and 2 women are selected?
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is [tex]$\frac{{7 \choose 2}{9 \choose 2}}{{16 \choose 4}}$[/tex] which simplifies to[tex]$\frac{63}{220}$[/tex] or approximately 28.6%. The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men can be calculated by using the formula for combination, nCr. In this case, we would be selecting 4 people from 16 individuals, so n = 16 and r = 4. The formula is nCr = n!/(r!(n-r)!). This can be simplified to 16C4 = 16!/ (4!(12!)). The answer is 1820/21168, which can be simplified to 86/792, or approximately 11%. Therefore, the probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
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If 16, x, 1, y are in Geometric Progression, find the product of x and y.
The product of x and y is: "1"
Step-by-step Solution:
Given: 16/9, x, 1, y are in Geometric Progression (G.P)
Let the general terms of a Geometric Progression are: a, ar, ar², ar³
So, On comparing we get; a=16/9,
⇒ar² = 1
⇒ 16/9*r² = 1
⇒ r² = 9/16
⇒ r = 3/4
x = ar
⇒ (16/9)(3/4)
⇒x=4/3.
y = ar³
⇒(r)(ar^2) = (3/4)(1)
⇒y=3/4.
Now, to find the product of "x" and "y":
⇒x*y = 4/3 x 3/4
⇒1
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Which of the layer(s) in the diagram below have liquid-like properties? 3 3&4 1,2,3 & 4 2&4 1,2 & 4
The layers in the diagram that have liquid-like properties are layers 1,2,3 and 4. This is determined by the properties of liquids, which are: high viscosity, low compressibility, and the ability to flow.
Viscosity is the measure of a liquid's resistance to flow. It can be calculated using the formula η = (ΔP/l) x (d/Δt), where η is the viscosity, ΔP is the pressure difference, l is the length of the flow, d is the change in distance, and Δt is the time difference.
Compressibility is the measure of how a liquid responds to pressure or volume change. It is calculated using the formula β = -1/V (dV/dP), where β is the compressibility, V is the volume, and dV/dP is the change in volume over the change in pressure.
The ability to flow is the measure of how a liquid can move from one place to another. It is calculated using the formula Q = A x v, where Q is the flow, A is the area of the cross-section of the flow, and v is the velocity.
By using these formulas and calculations, it can be determined that layers 1,2,3, and 4 have liquid-like properties.
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Hey can you help me with this please it’s hard
Answer:
first get one odd No, again more odd number than even, Lastly two or more odd number
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(x)).
2x + 1
2x + 4
X + 4
2x^2 + x - 21
Answer:
2x + 1
Step-by-step explanation:
To find f(g(x)), we need to substitute g(x) for x in the function f(x) = 2x + 7.
so f(g(x)) = 2(x - 3) + 7 = 2x - 6 + 7 = 2x + 1
So the composition of function f(g(x)) is f(g(x)) = 2x + 1.
Find the slope of the ordered pairs below
Answer:
[tex]\boxed{\sf \:Slope(m)=2}[/tex]
Step-by-step explanation:
Let's use the slope formula to find the slope of (2,2) and (3,4):-
Slope formula :- m=(y2-y1)/(x2-x1)
[tex]\sf \left(x_1,\:y_1\right)=\left(2,\:2\right)[/tex]
[tex]\sf \:\left(x_2,\:y_2\right)=\left(3,\:4\right)[/tex]
[tex]\sf m=\cfrac{4-2}{3-2}[/tex]
[tex]\sf m=\cfrac{2}{1}[/tex]
[tex]\sf m=2[/tex]
Therefore, the slope is 2!!
_____________________
Hope this helps!
Have a great day!
Find the area under the standard normal distribution curve to the right of z = 2.12. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.
The area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
What is the Area under the Standard Normal Distribution Curve?The standard normal distribution curve's total area under the curve is 1. We can therefore calculate the likelihood of a value less than or larger than that if we know the Z score, which measures how far a value is above or below the mean. Under the typical normal curve when using the Normal Distribution P(Z>z)=1-P(Z<z) determines the region to the right of z.In this question:
Area right to the right of the z = 2.12
Using a TI-83 Plus/TI-84 Plus calculator,
P(Z> 2.12)
= P(Z<-2.12)
= 0.0170
Therefore the area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
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For her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. How much candy will each of the 15 people get? Choose the correct equation and answer for this situation.
A) 15 ÷ 5 = [tex]\frac{15}{5}[/tex] = 3 pounds
B) 5 ÷ 15 =[tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex] pounds
C) 5 ÷ 15 = 3 pounds
D) 15 ÷ 5 = [tex]\frac{1}{3}[/tex] pounds
If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.
How to find the amount of candy to gives as party treats?Given data:
Candy bought = 5
Number of people invited = 15
Now let find the amount of candy to gives as party treats
Number of candy = Number of people invited / Candy bought
Number of candy = 15/5
Number of candy = 3 pounds
Therefore we can conclude that the correct option is A.
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The regression equation y = 8.6sin(0.24x – 1.88) + 62.8 models the Fahrenheit temperature in a room x hours after midnight. What is the maximum temperature in the room during the first 24 hours?
54.2°F
57.0°F
62.8°F
71.4°F
Answer:
71.4°F
Step-by-step explanation:
The maximum is when [tex]\sin(0.24x-1.88)=1[/tex], yielding a maximum of [tex]8.6+62.8=71.4[/tex].
Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y or vice versa.
For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y.
We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with a unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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Determine if the columns of the matrix A span R2. A = 2 1 0 1 Arlo -3 -1 )-The columns span R2. -The columns do not span R2.
The columns of the matrix A span R2.
In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.
A = [2 1]
[0 1]
[-3 -1]
The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.
For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking
a[2, 0, -3] + b[1, 1]
And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking
a[2,0,-3] + b[1,1,-1].
So the answer would be: The columns of the matrix A span R2.
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Subtract 1/2 and 2/4 using fraction strips
Answer:
0
Step-by-step explanation:
1/2 = 2/4
1/2-2/4 = 0
Mario is cooking dinner for his family recipe he is using calls for 2 3/4 cups of chicken broth and he only has one 1 1/3 cups how much more chicken broth does Mario need for his recipe
Answer:
1 5/12 (One whole number five over twelve)
Step-by-step explanation:
Recipe calls for 2 3/4 cups
No of cups available are 1 1/3 cups
To get the number of cups needed to fulfill the recipe well say:
1 1/3 + X = 2 3/4
X = 2 3/4 - 1 1/3 = 1 5/12
triangle ABC was translated 4 units to the left and 3 units down. write the rule that describes the transition that was applied to the triangle ABC to create triangle A’B’C’
The transition that was applied to the triangle ABC to create triangle A’B’C’ is (x, y) ⇒ (x - 4, y - 3)
What are rigid transformations?Transformation is the movement of a point from its initial location to a new location. Rigid transformations are transformations on the coordinate plane that preserves the shape and size of the figure. Types of rigid transformations are reflection, translation and rotation.
Rigid transformations are translation, reflection and rotation since they preserve the size.
Translation is the movement of a point up, left, right or down in the coordinate plane.
Triangle ABC was translated 4 units to the left and 3 units down using the rule (x, y) ⇒ (x - 4, y - 3)
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1. 3f+10-6f-4
2. 7ab-2a+5ab-9a
3. -2t-8r+3t-4r
4. 2a+9b-5a-10b PLEASE HELP!!
1. 3f + 6
2. 12ab - 11a
3. 1t - 12r
4. 3a -1b
pls pls pls pls mark as brainiliest
pls im literally begging you
Answer:
-3f + 6
12ab - 11a
t - 12
-3a - b
Step-by-step explanation:
3f + 10 -6f -4 Combine like terms
(3f -6f) +( 10-4)
-3f + 6
7ab - 2a + 5ab - 9a
(7ab + 5ab) + (-2a - 9a)
12ab + -11a Adding a negative is the same as subtracting a positive
12ab - 11a
-2t - 8r + 3t - 4r
(-2t + 3t) + (-8r - 4r)
t + -12r
t - 12
2a + 9b - 5a - 10b
(2a - 5a) + ( 9b -10b)
-3a - b
How to solve 3 equations with 3 variables using elimination?
The elimination method is used to solve a system of equations with multiple variables. Repeat this process until all of the variables have been eliminated, then simplify the equations to solve for the remaining variable.
Once a variable has been isolated, it can then be eliminated from the other equations by either adding or subtracting the equations from each other. This process should be repeated until all of the variables have been eliminated from all of the equations.
For example, let's solve the following system of equations with 3 variables a, b, and c:
a + b + c = 8
2a + b + 2c = 12
3a + 2b + 3c = 18
First, isolate the variable c in equation 1 by subtracting b and a from both sides:
c = 8 - a - b
Substitute this expression for c in equation 2 and 3 to eliminate c:
2a + b + 2(8 - a - b) = 12
3a + 2b + 3(8 - a - b) = 18
Then simplify the equations to solve for the remaining variables:
2a + 3b = -4
9a + 6b = 36
Next, isolate the variable a in equation 2 by subtracting 3b from both sides:
a = -4/2 - 3b/2
Substitute this expression for a in equation 1 and 3 to eliminate a:
-4/2 - 3b/2 + b + 8 - b = 8
9(-4/2 - 3b/2) + 6b + 3(8 - b) = 36
Then simplify the equations to solve for the remaining variable:
15b = -12
b = -12/15
Finally, substitute b back into equation 1 or 2 to solve for a:
a + (-12/15) + 8 = 8
a = 8 - (-12/15) - 8
a = 24/15
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in bridge, there are 4 players (a, b, c, d) and each player receives thirteen cards (from a standard shuffled deck of 52 cards). what is the probability that (a) exactly 1 of the 4 players has exactly one ace and one king?
0.168 is the probability that exactly 1 of the 4 players has exactly one ace and one king.
What is probability?The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
a)
Given that,
each player gets 13 cards.
So, n = total no. of ways = ⁵²C₁₃ = 6.350× 10¹¹
As we know, there are 2 black aces and 4 kings in a deck of 52 cards. Since, one black ace out of 2 black aces can be chosen in ²C₁ ways, next one king out of 4 kings in ⁴C₁ ways and the remaining 11 cards from the remaining 46 cards in ⁴⁶C₁₁ ways.
So, m = ²C₁ × ⁴C₁ × ⁴⁶C₁₁
m = 1.067 × 10¹¹
Therefore, Required probability p = m/n
p = (1.067 × 10¹¹) / (6.350× 10¹¹)
p = 0.168
To know more about probability refer to:
brainly.com/question/24756209
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