Answer:601.2
Step-by-step explanation:
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. x=-4,y=6
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.
Given that x varies directly with y, if we introduce a constant of proportionality, k, the expression becomes
x = ky
If x = - 4 when y = 6, then
- 4 = 6k
k = - 4/6 = - 2/3
Therefore, the equation that relates x and y is
x = -2y/3
Answer:
3/2
Step-by-step explanation:
Volume of spheres
Go to I
Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14 for pi and round your final answer to the nearest hundredth.
----
10-
-
-
-
-
-
-
Units 3
For a sphere of radius r the volume V is
V=(4/3)πr³
We have r=10 so
V = (4/3) π 10³ = 4000π/3
Answer: 4000π/3
The volume of a sphere can be calculated using the formula V = 4/3 * π * r³. Assuming the radius is 10 units, the calculated volume is 4186.67 cubic units.
Explanation:The volume V of a sphere can be found using the formula V = 4/3 * π * r³, where π is a constant (approximately 3.14) and r is the radius of the sphere. In your question, it appears there may be missing information as the value for the radius is not provided. Assuming that 10 is the radius of the sphere, we can substitute this value into the formula. So, V = 4/3 * 3.14 * 10³ = 4186.67 cubic units. Therefore, the volume of a sphere with a radius of 10 units is approximately 4186.67 cubic units.
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What is 180 - 15% = ?
Answer:
178.85
Step-by-step explanation:
Answer:
153 !
Step-by-step explanation:
begin by multiplying 180 by .15 then you should get 27. next, subtract 27 from 180 and you're left with 153.
Y= -5x+1
Y=3x-2
Is (3,8) a solution of the system
Final answer:
The point (3,8) does not satisfy either of the two equations y = -5x + 1 and y = 3x - 2, therefore it is not a solution to the system of equations.
Explanation:
To determine whether the point (3,8) is a solution to the system of equations given by y = -5x + 1 and y = 3x - 2, we need to substitute the x and y values of the point into both equations to see if the equations are satisfied.
For the first equation:
y = -5x + 1
8 = -5(3) + 1
8 = -15 + 1
8 ≠ -14
The point (3,8) does not satisfy the first equation because 8 does not equal -14.
For the second equation:
y = 3x - 2
8 = 3(3) - 2
8 = 9 - 2
8 = 7
The point (3,8) does not satisfy the second equation because 8 does not equal 7.
Since the point (3, 8) fails to satisfy both equations, it is not a solution to the system of equations.
Final answer:
The point (3,8) is not a solution to the system of equations y = -5x + 1 and y = 3x - 2, as it does not satisfy either equation when substituting the values of x and y.
Explanation:
The student is asking whether the point (3,8) is a solution to the system of linear equations:
y = -5x + 1
y = 3x - 2
To determine if (3,8) is a solution, we can substitute x with 3 and y with 8 into both equations and see if they hold true.
Substituting into the first equation:
8 = -5(3) + 1
8 = -15 + 1
8 ≠ -14
This does not hold true, so (3,8) is not a solution to the first equation.
Substituting into the second equation:
8 = 3(3) - 2
8 = 9 - 2
8 = 7
This also does not hold true, so (3,8) is not a solution to the second equation either.
Since (3,8) does not satisfy either of the given equations, it is not a solution to the system of equations.
Henry buys 6 circus tickets for himself and five friends for a total of $174. Each friend pays Henry back for his or her ticket. If one of Henry's friends gives him two $20 bills, how much change should Henry return?
Answer:
$11
Step-by-step explanation:
According to the statement, you have that 6 tickets for the price of each ticket is equal to $174 and from that, you can determine the price of each ticket:
6*P=174
P= price of each ticket
P= 174/6= 29
Now, as it says that one of Henry's friends gives him two $20 bills, that means that he gives him $40 and you have to subtract the price of the ticket from that:
40-29= 11
The answer is that if one of Henry's friends gives him two $20 bills, Henry has to return $11.
Final answer:
The cost of one ticket is $29, and if a friend pays with two $20 bills, totaling $40, Henry should return $11 in change.
Explanation:
Henry buys 6 circus tickets for a total of $174. To determine the cost of each ticket, you divide the total cost by the number of tickets:
$174 ÷ 6 tickets = $29 per ticket.
When one of Henry's friends pays him back with two $20 bills, the friend gives Henry $40 in total. To find out how much change Henry should return, you subtract the cost of one ticket from the amount the friend gave:
$40 - $29 = $11.
Therefore, Henry should give his friend $11 in change.
Find the Median
{ 0, 3, 4, 8, 10, 15, 20 }
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
arrange from the smallest to the largest or largest to the smallest and then carry out binary division
Vijay owns a house worth $250,000 with a mortgage of $150,000. He has $3,000 in stock investments and $1,700 in a checking account. He owns a piano worth $1,800. He also owns a car worth $18,000 and owes $6,000 in car loans. Vijay wants to create a net worth statement. What are Vijay’s total assets, liabilities, and net worth? :v
Answer:
Total assets $274,500
Total liabilities $156,000
Net worth $118,500
Step-by-step explanation:
Vijay's assets consist of a house, stock investment , balance in checking account , a piano as well as car owned
Total assets=$250,000+$3,000+$1,700+$1,800+$18,000=$ 274,500.00
Vijay's liabilities are obligations owed to others, which include mortgage loan and car loan
total liabilities=$150,000+$6,000=$156,000
net worth=total assets-total liabilities=$274,500-$156,000=$118,500.00
Yolanda purchased a meal at her favorite restaurant for $5.50. She tipped her waiter 20% of the purchase. Including the tip, what was the total amount of money that she spent at the restaurant? *
Answer: Yolanda spent $6.60 at her favourite restaurant, including the tip.
Step-by-step explanation:
We know that 20% of 5.50 is: 1.10
So, 5.50 + 1.10 = 6.60.
Yolanda spent $6.60 at her favourite restaurant, including the tip.
what is the measure of arc AED
Answer: 194 degrees
Step-by-step explanation:
you are riding a bicycle which has tires with a 25-inch diameter at a steady 15-miles per hour, what is the angular velocity of a point outside the tire in radians per second? give your answer in terms of pi rounding the coefficient to the nearest hundredth.
Answer:
The angular velocity is 6.72 π radians per second
Step-by-step explanation:
The formula of the angular velocity is ω = [tex]\frac{v}{r}[/tex] , where v is the linear velocity and r is the radius of the circle
The unit of the angular velocity is radians per second
∵ The diameter of the tire is 25 inches
∵ The linear velocity is 15 miles per hour
- We must change the mile to inch and the hour to seconds
∵ 1 mile = 63360 inches
∵ 1 hour = 3600 second
∴ 15 miles/hour = 15 × [tex]\frac{63360}{3600}[/tex]
∴ 15 miles/hour = 264 inches per second
Now let us find the angular velocity
∵ ω = [tex]\frac{v}{r}[/tex]
∵ v = 264 in./sec.
∵ d = 25 in.
- The radius is one-half the diameter
∴ r = [tex]\frac{1}{2}[/tex] × 25 = 12.5 in.
- Substitute the values of v and r in the formula above to find ω
∴ ω = [tex]\frac{264}{12.5}[/tex]
∴ ω = 21.12 rad./sec.
- Divide it by π to give the answer in terms of π
∴ ω = 6.72 π radians per second
The angular velocity is 6.72 π radians per second
The result is approximately 21.12 or 6.72 π radians per second.
The question asks for the angular velocity of a point on a bicycle tire with a diameter of 25 inches, traveling at 15 miles per hour.
Convert speed to inches per second:
15 miles per hour = 15 × 5280 feet per hour = 15 × 5280 × 12 inches per hour = 950400 inches per hour
Since there are 3600 seconds in an hour:
950400 inches per hour ÷ 3600 seconds per hour ≈ 264.00 inches per second
Convert diameter to radius in inches:
Diameter = 25 inches, so Radius = 25 ÷ 2 = 12.5 inches
Using the formula:
Linear speed (v) = Angular velocity (ω) × Radius (r)
264.00 = ω × 12.5
ω = 264.00 ÷ 12.5 ≈ 21.12 radians per second
Thus, the angular velocity of a point on the bicycle tire is approximately 21.12 or 6.72 π radians per second in terms of π.
A beverage company wants to determine if people in the United States like their new logo. Which choice BEST represents the population? Every person in the United States. All the people who like their beverages. All the employees of the beverage company. All the people who have tried their beverages.
Answer:
All the people who have tried their beverages will be the representing population.
Step-by-step explanation:
If people in the United States like the new logo of a beverage company that the company wants to determine.
Now, we have to choose from the given options that represent the population.
From my point of view, option fourth option gives the correct answer.
Therefore, all the people who have tried their beverages will be the representing population.
Answer:
Every person in the united states
any help will be greatly received
Answer:
The shop did not meet their goal of selling 65 per month. You can tell this because if you look at the graph you see that January, May, and June are all under the 65 mark.
Hope this helps ;)
The velocity of a particle moving in a straight line is given by v(t) = t2 + 9. (a) Find an expression for the position s after a time t . S(t) = + C (b) Given that s = 3 at time t = 0, find the constant of integration C. C = Find an expression for s in terms of t without any unknown constants.
Answer:
(a)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
Step-by-step explanation:
We know that, the first order derivative of the position of an object is the velocity of the object.
(a)
Given that, the velocity of a particle moving in straight line is
[tex]V(t)=t^2+9[/tex]
[tex]\Rightarrow \frac{dS(t)}{dt}=t^2+9[/tex]
[tex]\Rightarrow {dS(t)}=t^2dt+9\ dt[/tex]
Integrating both sides
[tex]\int {dS(t)}=\int t^2dt+\int9\ dt[/tex]
[tex]\Rightarrow S(t)=\frac{t^3}3+9t+c[/tex] [ c is an arbitrary]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)
Given that S= 3 at time t=0
[tex]\therefore 3=S(t)=\frac{0^3}3+9.0+c[/tex]
[tex]\Rightarrow c=3[/tex]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
The position function is computed by integrating the given velocity function v(t) = t^2 + 9. The constant of integration C was found to be 3 using the given initial condition of s(0) = 3. Thus, the position function without any unknown constants is S(t) = (1/3)t^3 + 9t + 3.
Explanation:The velocity function given for the particle moving in a straight line is v(t) = t2 + 9. This function can be used to find the position function using integral calculus.
hen t=0 the position function S(t) = (1/3)*03 + 9*0 + C = C = 3.
Thus, using the constant of integration we found, we can write the position function without any unknown constants as S(t) = (1/3)t3 + 9t + 3.
(a) Finding the Position Function
To find an expression for the position, we integrate the velocity function. Here, the integral of the given velocity function v(t) = t2 + 9 is S(t) = ∫(t2 + 9)dt = (1/3)t3 + 9t + C, where C is the constant of integration.
(b) Finding the Constant of Integration
Given that s(0) = 3, w
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Simplify to create an equivalent expression 8-4(-x+5)
Answer: 4x _ 12
Cheese
Please help guys :((
Answer:
A) [tex]log_{5}(12)[/tex]
B) [tex]log_{8}(9)[/tex]
C) [tex]log_{9}(25)[/tex]
Step-by-step explanation:
Hello! I am going to walk you through how some simple rules regarding logs!
For A, we will use the 'AM' rule! When adding logs of the same base (in this case 5), you multiply the two answers (3 and 4)!
3 · 4 = 12, giving us [tex]log_{5}(12)[/tex]!
For B, we will use the 'SD' rule! When subtracting logs of the same base (in this case 8), you divide the two answers (9 and 5)!
9/5 = [tex]\frac{x}{5}[/tex] ; simplify! (9/5) x 5 = 9, giving us [tex]log_{8}(9)[/tex]!
For C, we will use the 'MS' rule! When multiplying a number times a logarithm, you can get the same argument by removing the coefficient (2) and squaring the log's answer (5)!
[tex]5^{2} = 25[/tex], giving us [tex]log_{9}(25)[/tex]!
I hope that this helps!
.
Solve for x:
2% of x = 17
a 34
b 8.5
c 85
d 850
Answer:850
Step-by-step explanation:
To find this 2% of x= 17
2/100×x=17
2x/100=17
2x=1700
x=850
the table shows value for the function f, while the graph shows function g.
Which function has the greater slope?
A) f
B) g
C)They are the same.
D)Insufficient information.
Answer:
A
Step-by-step explanation:
A is the right answer
f has the greater slope, 3. The slope of g is 2.
plz mark me Brainliest
Help ASAP Will give Brainllest . Please explain how you got the answer
Answer:
10 yd
Step-by-step explanation:
The length of the top is
6+4 = 10 yd
The bottom must be the same length
To find the length of the bottom side, we can look around the shape to see if there are any similar sides. The sides 6ft and 4ft make up the same length as the bottom side, so, we can add.
6 + 4 = 10ft.
Best of Luck!
A lumber mill needs one more tree cut down that is at least 41 feet long. The person cutting down the tree is 5 feet 3 inches tall. Using shadows to determine whether a tree is tall enough, the person stands next to the tree and measures the length of his shadow as 36 inches. What is the length (to the nearest tenth of a foot) of the tree's shadow that will allow the tree to be cut down?
Answer:
23.4 feet
Step-by-step explanation:
Please refer to the attached image for explanations
Using similar triangles and a proportion, the length of the tree's shadow that will allow it to be cut down needs to be 448 inches, or 37.3 feet to the nearest tenth of a foot.
To find the length of the tree's shadow that would allow for the tree to be tall enough (41 feet or more) to be cut down, we need to use similar triangles. The person cutting the tree is 5 feet 3 inches tall, which is 63 inches, and their shadow is 36 inches long. Using this information, we can set up a proportion since the tree and the person form similar triangles with their respective shadows. The proportion is 63 inches / 36 inches = 492 inches (41 feet) / length of tree's shadow. To find the tree's shadow length, we cross multiply and solve for the tree's shadow length as follows:
63 * length of tree's shadow = 36 * 492
Length of tree's shadow = (36 * 492) / 63
Length of tree's shadow = 28224 / 63
Length of tree's shadow = 448 inches
Therefore, the length of the tree's shadow needs to be 448 inches, or to the nearest tenth of a foot, 37.3 feet.
The area of a triangular sail is given by the expression 1 2 bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 8 inches and h = 5 inches? The area of a triangular sail in a sail model is in2.
Answer:
The area of the triangular sail is 20 square inches.
Step-by-step explanation:
We are given the following in the question:
Dimensions of triangular sail:
Base, b = 8 inches
Height, h = 5 inches
Area of triangular sail =
= Area of triangle
[tex]=\dfrac{1}{2}\times b\times h[/tex]
Putting values, we get,
[tex]A = \dfrac{1}{2}\times 8\times 5\\\\A = 20\text{ square inches}[/tex]
Thus, the area of the triangular sail is 20 square inches.
I need to know what is the un given side by using Soh Coa Toa
Answer:
1.68 km
Step-by-step explanation:
You want the horizontal distance (on the ground) from beneath the helicopter to the vertex of the 37 degree angle. The hypotenuse is given and is 2.1 km.
We want to find the horizontal distance when we already know the angle and the hypotenuse.
That horizontal distance could be called 'x.' Then:
x/r = adj/hyp = cos 37 degrees, which becomes adj = (2.1 km)cos 37 degrees, which is found using a calculator: adj = (2.1 km)(0.7987) = 1.68 km
It took 4 balloons to make the duck float. The duck
weighs 56 grams.
With 1 balloon, how many grams could you make float?
Submit
Answer: 14 grams
Step-by-step explanation:
It took 4 balloons to make a duck that weighs 56 grams to float. With one balloon, the number of grams that will float will be 56 grams divided by 4. This will be:
= 56 grams ÷ 4
= 14 grams
Weight carry by 1 balloon is 14 gram
Given that;Weight of duck = 56 grams
Number of balloon need to float duck = 4
Find:Weight carry by 1 balloon
Computation:Weight carry by 1 balloon = Weight of duck / Number of balloon need to float duck
Weight carry by 1 balloon = 56 / 4
Weight carry by 1 balloon = 14 gram
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A park planner is designing a dog park. He wants to use a metal fence to enclose a kennel at the dog park. The vertices of the fence are shown below. The units on the coordinate plane are yards.
Point A (4,-4)
Point B (-4,-4)
Point C (-4,3)
Point D (1,3)
Point E (1,-1)
Point F (4,-1)
The park planner wants to add a gate between points A and F. He will not put metal fencing on that side. What is the total number of yards of metal fencing that will be needed for the kennel at the dog park?
The total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.
The fence segments are determined by the vertices A, B, C, D, E, and F. The distances between consecutive vertices can be calculated using the distance formula:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's calculate the lengths of the segments:
1. Length of AB: [tex]\(\sqrt{(-4 - 4)^2 + (-4 - (-4))^2} = \sqrt{64 + 0} = 8\) yards[/tex]
2. Length of BC: [tex]\(\sqrt{(-4 - (-4))^2 + (3 - (-4))^2} = \sqrt{0 + 49} = 7\) yards[/tex]
3. Length of CD: [tex]\(\sqrt{(1 - (-4))^2 + (3 - 3)^2} = \sqrt{25 + 0} = 5\) yards[/tex]
4. Length of DE:[tex]\(\sqrt{(1 - 1)^2 + (-1 - 3)^2} = \sqrt{0 + 16} = 4\) yards[/tex]
5. Length of EF: [tex]\(\sqrt{(4 - 1)^2 + (-1 - (-1))^2} = \sqrt{9 + 0} = 3\) yards[/tex]
Now, sum up these lengths:
[tex]\[ 8 + 7 + 5 + 4 + 3 = 27 \][/tex]
So, the total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.
Question 4: Please help. What are the coordinates of the point that partitions BA⎯⎯⎯⎯⎯⎯⎯ according to the part-to-part ratio 2:4?
Enter your answer as an ordered pair, formatted like this: (42, 53)
Answer:
(9,-4)? I'm not sure.
Leora had some money in her wallet. She spent $18.62 buying groceries and had $43.55 left. How much money did she have in her wallet before she bought the groceries?
Answer:
$62.17
Step-by-step explanation:
Answer:
The answer is 62.17.Because you would add 18.62 + 43.55 to get your answer of 62.17
if i can get brainliest that would be great :)
Use technology or a z-score table to answer the question.
The nightly cost of hotels in a certain city is normally distributed with a mean of $180.45 and a standard deviation of $24.02.
Approximately what percent of hotels in the city have a nightly cost of more than $200?
Answer: The percentage of hotels in the city have a nightly cost of more than $200 is 21%
Step-by-step explanation:
Since the nightly cost of hotels in a certain city is normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the nightly cost of hotels.
µ = mean cost
σ = standard deviation
From the information given,
µ = $180.45
σ = $24.02
The probability that a hotel in the city has a nightly cost of more than $200 is expressed as
P(x > 200) = 1 - P(x ≤ 200)
For x = 200,
z = (200 - 180.45)/24.02 = 0.81
Looking at the normal distribution table, the probability corresponding to the z score is 0.79
Therefore,
P(x > 200) = 1 - 0.79 = 0.21
The percentage of hotels in the city have a nightly cost of more than $200 is
0.21 × 100 = 21%
The ministry of health was interested in the relationship between office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire.
The study investigates the connection between office habits and health outcomes. Key considerations include factors such as stress, job status, personal hygiene, and historical trends in workforce health. The goal is to improve policies to promote healthier workplaces.
Explanation:The ministry of health study you're referring to is looking into how habits within the office workplace can impact employees' health. Various factors such as stress levels, personal hygiene habits, the status of the job, and societal impacts can influence the health outcomes of individuals in workplaces.
Stress is a critical factor, as studies have suggested those in high stress or low status jobs, such as the mentioned British civil servants, are more prone to health issues like heart disease. This emphasizes the necessity of stress management in the workplace.
Another element of consideration is personal hygiene, which relates to individuals' private habits in maintaining their physical appearance, not strictly health-related. Various habits could reflect differently on personal health outcomes.
Historical context also plays a role in understanding workforce health trends, such as the transformation during and after World War II. Anthropologists worked intensively on public and private health initiatives, focusing on improving health outcomes both in warfare and post-war times, which influenced the health perspectives in today's workplaces.
This is a multidimensional investigation that potentially will reveal valuable insights that could inform policies on how to better protect workers' health and productivity. Overall, a healthy workforce translates to a more robust and vibrant society.
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7. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal
Answer:
After 49 months the total cost of the two systems will be equal.
Step-by-step explanation:
To Find: We need to find the number of months will the total cost of the two systems be equal
Solution:
For Satellite receiver:
Satellite receiver cost = $298.90
Monthly charge = $68.70
Let the Number of months be denoted by 'x'.
Now we can say that;
Total cost using Satellite receiver is equal to sum of Satellite receiver cost and Monthly charge multiplied by number of months.
framing in equation form we get;
Total cost using Satellite receiver = [tex]298.90+68.70x[/tex]
For Using Cable:
Monthly charge = $74.80
So we can say that;
Total cost using cable is equal to Monthly charge multiplied by number of months.
framing in equation form we get;
Total cost using cable = [tex]74.80x[/tex]
Now to find the number of months when both the cost will be the same so we will make both the equation equal we get;
[tex]298.90+68.70x=74.80x[/tex]
Combining the like terms we get;
[tex]74.80x-68.70x=298.90\\\\6.1x=298.90[/tex]
Dividing both side by 6.1 we get;
[tex]\frac{6.1x}{6.1}=\frac{298.90}{6.1}\\\\x=49[/tex]
Hence After 49 months the total cost of the two systems will be equal.
A garden table and a bench cost $840 combined. The garden table costs $60 less than the bench. What is the cost of the bench?
Answer:
450 $
Step-by-step explanation:
1). Bench = x
Garden Table = x - 60
2). x + x - 60 = 840
2x = 900
x = 450 $ - the cost of the bench.
Hope this Helps)))
The cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A garden table and a bench cost $840 combined.
The garden table costs $60 less than the bench.
Let the cost of the bench is x
Cost of the Garden Table = x - 60
x + x - 60 = 840
2x = 900
x = 450 $ - the cost of the bench.
Thus, the cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.
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If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting four queens and two kings.
Answer:
The probability is 0.000000207176
Step-by-step explanation:
In this question, we are asked to calculate the probability that if 6 cards are selected from a deck of cards, we will be having 4 kings and 2 queens.
Before we answer, we should understand that in a deck of cards, there are 4 queens and 4 kings. The probability of selecting a king is the same as the probability of selecting a queen which is 4/52 = 1/13
Okay now we want to find the probability of the six cards being 4 kings and 2 queens. Since the probabilities are equal, we proceed to calculate at the same time.
That would be (1/13)^6 = 0.000000207176
The probability of selecting 4 kings and 2 queens is 0.000000207176
Final answer:
The probability of getting four queens and two kings out of six cards from a standard deck of 52 cards is calculated by dividing the product of the combinations of getting those particular cards by the total number of six-card combinations available from the deck.
Explanation:
To calculate the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards, we can follow these steps:
Identify the total number of ways to choose 6 cards from 52: This can be calculated using combinations, as the order the cards are drawn doesn't matter. The formula for combinations is:
C(n, k) = n! / (k! × (n-k)!)
In this case, n = 52 (total cards) and k = 6 (cards chosen). Therefore, the total number of ways to choose 6 cards is:
C(52, 6) = 52! / (6! × (52-6)!) ≈ 270,735,576
Identify the number of ways to get four queens and two kings: We need to choose 4 queens out of 4 and 2 kings out of 4. Again, using combinations:
C(4, 4) × C(4, 2) = 1 × 6 = 6
There are only 6 ways to get this specific combination (4 queens and 2 kings) within the 6 cards chosen.
Calculate the probability: Finally, divide the number of successful outcomes (6) by the total number of possibilities (270,735,576) to get the probability:
Probability = 6 / 270,735,576 ≈ 0.000002217 ≈ 0.0002%
Therefore, the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards is incredibly low, at approximately 0.0002%.