What are the equations for the asymptotes of this hyperbola?
Y^2/36 - x^2/121=1
Answers
Answer:
\(\huge{\mathfrak{Solution}}\)
\(\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}\)
\(\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}\)
\(\huge\boxed{\mathfrak{We \: get,}}\)
\((h,k) = (0,0),a = 6,b = 11\)
\(For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k\)
\(Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0\)
\(\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}\)
If y²/36 - x²/121 = 1, the asymptotes are y = (36/121) x and y = -(36/121) x.
To find the equations for the asymptotes of the hyperbola represented by the equation y²/36 - x²/121 = 1, we can compare it with the standard form of a hyperbola:
(y - k)² / a² - (x - h)² / b² = 1
where (h, k) represents the center of the hyperbola.
In the given equation, we have y²/36 - x²/121 = 1. To put it in standard form, we need to divide both sides by 1 (which is essentially dividing by 1 on the right side):
y²/36 - x²/121 = 1 / 1
Now, we can see that a² = 36 and b² = 121.
To find the equations of the asymptotes, we use the center (h, k) and the values of a and b. The asymptotes of a hyperbola have equations of the form:
y = k ± (a/b)(x - h)
In this case, the center (h, k) is (0, 0), a² = 36, and b² = 121:
The equations for the asymptotes are:
y = 0 ± (36/121) x
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Related Questions
different types of polygons?
Answers
The types of polygons are different based on the number of sides they have and the sum of their interior angles.
What are the different types of polygons ?The characteristics of different polygons are defined by the number of sides they have and the measure of their angles. Some polygons include:
Triangles: A polygon with three sides. They can be classified as equilateral, isosceles, or scalene based on the measure of their angles.Quadrilaterals: A polygon with four sides. They can be classified as square, rectangle, rhombus, or parallelogram based on the measure of their angles.Pentagons: A polygon with five sides. They can be regular or irregular, based on the measure of their angles.Hexagons: A polygon with six sides. Heptagons: A polygon with seven sides. Octagons: A polygon with eight sides. Nonagons: A polygon with nine sides.Decagons: A polygon with ten sides.There are other polygons and they change based on the number of sides they have.
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Put the equation in
slope-intercept form.
y - 4x = 17
y = 4x + [?]
Enter
Answers
Answer: To put the equation y - 4x = 17 in slope-intercept form, we need to isolate the y variable on one side of the equation and have the coefficient of x be the slope of the line and the constant term be the y-intercept.
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation y - 4x = 17, we can isolate y by adding 4x to both sides:
y - 4x + 4x = 17 + 4x
y = 4x + 17
So, the equation in slope-intercept form is y = 4x + 17, where the slope (m) is 4 and the y-intercept (b) is 17.
Step-by-step explanation:
y-4x = 17
slope intercept= y= 4x + 17
Use the property of logarithm to expand and simplify the expression ?
Answers
Simplify expression
\(\begin{gathered} \log _{12}\sqrt[3]{\frac{12+x}{144x}}= \\ =\log _{12}(\frac{12+x}{144x})^{\frac{1}{3}}= \\ =\frac{1}{3}\log _{12}(\frac{12+x}{144x})= \\ =\frac{1}{3}(\log _{12}(12+x)-\log _{12}(144x))= \\ =\frac{1}{3}(\log _{12}(12+x)-(\log _{12}(144)+\log _{12}(x)))= \\ =\frac{1}{3}(\log _{12}(12+x)-2+\log _{12}(x))= \\ =\frac{1}{3}\log _{12}(12+x)-\frac{2}{3}+\frac{1}{3}\log _{12}x \end{gathered}\)So our final answer will be:
\(\frac{1}{3}\log _{12}(12+x)-\frac{2}{3}+\frac{1}{3}\log _{12}x\)8.2 Pythagorean Theorem Practice
3.
8 in.
15 in.
INCLUDE UNITS!!!
Answer:
Answers
64 + 225= c^2
289=c^2
take the square root of 289 and you get 17
Answer: 17 inches
Can someone help me answer this?
Answers
Answer: i believe it’s 12ft
Step-by-step explanation:
Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding
Answers
The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.
Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.
The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.
To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.
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5. The price of a new gym bag is $37.00 plus 8% sales tax. What is the sales tax on this gym
bag in dollars and cents?
Answers
Answer:
$25.00 which is $24.50
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): Dot was discarded near "x.s".
(2): "37." was replaced by "(37/1)".
Unauthorized use of the imaginary unit "i" or syntax error in complex arithmetic expression
Henry and David have played 35 tennis matches.
Henry has won 20 times.
David won the rest.
a) Estimate the probability that Henry wins.
b) Estimate the probability that David wins.
Answers
Answer:
A. Henry wins the tennis matches
Which do you think is easier to understand and why do you think so, multiplying radicals or multiplying polynomials?
Answers
I believe that its easier to understand the multiplication of a radical than that of a polynomial.
How to illustrate the information?In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.
A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:
= 3✓2 × 4✓2
= 12✓4
= 12 × 2
= 24
The multiplication of a radical is easier.
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Which equation represents the line that passes through the points (–2, 4) and (4, 6)?
Answers
Answer:
maybe take off the ( and then add the numbers then see tht from there and maybe subtract
Step-by-step explanation:
g(x) = 3x2 – 2x +5
Find f(2)
Answers
find the local and absolute minima and maxima for the function over (−[infinity], [infinity]). (order your answers from smallest to largest x.) y = x^3 - 12x
(x, y) =
(x, y) =
Answers
The function y = x^3 - 12x has a local minimum at x = 2 with a corresponding y-value of -16. There are no local or absolute maxima for this function over the entire range of (-∞, ∞).
The local and absolute minima and maxima of the function y = x^3 - 12x over the entire range (-∞, ∞) are as follows:
Local minimum: There is no local minimum for this function.
Local maximum: There is no local maximum for this function.
Absolute minimum: The absolute minimum occurs at x = 2, where y = -16.
Absolute maximum: There is no absolute maximum for this function.
To determine the local and absolute minima and maxima, we need to find the critical points of the function. These occur where the derivative is equal to zero or does not exist. Taking the derivative of the function, we get y' = 3x^2 - 12. Setting y' = 0 and solving for x, we find x = ±2.
By analyzing the sign of the derivative around these critical points, we can determine the nature of the extrema. However, since we are considering the entire range of (-∞, ∞), there are no local maxima or minima. The function simply increases or decreases without bound.
The absolute minimum occurs at x = 2, where y = -16. However, there is no absolute maximum as the function has no upper bound.
In conclusion, the function y = x^3 - 12x has a local minimum at x = 2 with a corresponding y-value of -16, but no local maximum, absolute minimum, or absolute maximum over the entire range (-∞, ∞).
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ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
Answers
The most appropriate choice for profit and loss will be given by
Uncle Ben will feed his cows 2 pounds of grain supplement.
What is profit and loss?
If the selling price is more than the cost price, then the difference between the selling price and the cost price will give the profit.
If the selling price is less than the cost price, then the difference between the selling price and the cost price will give the loss.
Here,
For 1 pound
Cost price of grain supplement = \(0.70 \times 1\)
= $\($0.70\)
Selling price of milk = \(0.20 \times 5\)
= $\(1\)
Profit = $(\(1 - 0.70\))
= $0.30
For 2 pounds
Cost price of grain supplement = \(0.70 \times 2\)
= $\($1.40\)
Selling price of milk = \(0.20 \times 9\)
= $\(1.80\)
Profit = $(\(1.80 - 1.40\))
= $0.40
For 3 pounds
Cost price of grain supplement = \(0.70 \times 3\)
= $\($2.10\)
Selling price of milk = \(0.20 \times 12.3\)
= $2.46
Profit = $(\(2.46 - 2.10\))
= $0.36
For 4 pounds
Cost price of grain supplement = \(0.70 \times 4\)
= $\($2.80\)
Selling price of milk = \(0.20 \times 15.5\)
= $3.1
Profit = $(\(3.1 - 2.80\))
= $0.30
For 5 pounds
Cost price of grain supplement = \(0.70 \times 5\)
= $\($3.50\)
Selling price of milk = \(0.20 \times 18\)
= $3.60
Profit = $(\(3.60 - 3.50\))
= $0.10
For 6 pounds
Cost price of grain supplement = \(0.70 \times 6\)
= $\($4.20\)
Selling price of milk = \(0.20 \times 20\)
= $4
Loss = $(\(4.20 - 4\))
= $0.20
For 7 pounds
Cost price of grain supplement = \(0.70 \times 7\)
= $\(4.90\)
Selling price of milk = \(0.20 \times 21.5\)
= $\(4.30\)
Loss = $(\(4.90 - 4.30\))
= $0.60
For 8 pound
Cost price of grain supplement = \(0.70 \times 8\)
= $\($5.60\)
Selling price of milk = \(0.20 \times 22.5\)
= $\(4.50\)
Loss = $(\(5.60 - 4.50\))
= $1.10
For 9 pounds
Cost price of grain supplement = \(0.70 * 9\)
= $\(6.30\)
Selling price of milk = \(0.20 * 23\)
= $\(4.60\)
Loss = $(\(6.30 - 4.60\))
= $1.70
Since profit from 2 pounds of grain supplement is the most, Uncle Ben will feed his cows 2 pounds of grain supplement.
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Complete Question
Farmer Ben knows that feeding a grain supplement to his cows will produce more milkaccording to the following schedule:
ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
The table has been attached here
if I divide a number by 12 the answer is 60 and the remeinder is 9 what is the number
Answers
Answer:
729
Step-by-step explanation:
let n be the number , then
\(\frac{n}{12}\) = 60 + \(\frac{9}{12}\) ( multiply through by 12 to clear the fractions )
n = 720 + 9 = 729
Find the coordinates of the point after a 180∘ rotation about the origin.
(2,-3)
Answers
Answer: (-2,3)
Step-by-step explanation:
The formula for 180 degrees rotation is (-x,-y).
(2,-3). Plug the formula in, when plugging a positive and a negative, it's negative. When plugging a negative and a negative, it makes a positive.
So (-2, 3)
Let J={1,2,3,4,...} in the Universe U={0,1,2,3,4,...}. Which set is the complement of J?
A) Ø
B) {0}
C) {1,2,3,4...}
D) {0,1,2,3,4...}
Answers
Answer:
c
Step-by-step explanation:
i know
A farmer has 220 bushels of apples for sale at his route stop side stand. He sells an average of 15 1/8 bushels each day represent the total change in number of bushels he has for sale after seven days.
Answers
After \(7\) days, there has been a total increase of sale \(116.2\)bushels in his available inventory.
What do the words "sell" and "sell" mean?Sale, which appears in the expressions for sale as well as on sale, refers to a trade at a discounted price. As used as a verb, sell means to provide something in return for money.
Which of the two available meanings?The act or selling products or services is the definition of sale at its most fundamental level. It may also be used to describe a quantity sold or a certain period during which prices are lowered. These explanations are all nouns. Use the word sale in any writing if you're discussing the exchange of products or services for cash in the noun form.
A farmer sells an average of \(15 \frac{1}{8}\) bushels each day.
We write above improper fraction \(15 \frac{1}{8}\) in proper fraction as \(\frac{121}{5}\)
And the decimal form of given fraction 121/5 is:
\(\frac{121}{5} = 24.2\)
After \(7\) days, he would sold \((15 \frac{1}{8} ) * 7\) bushels.
We simplify an expression \((15 \frac{1}{8} ) * 7\)
\((15 \frac{1}{8} ) * 7 = 24.2 * 7\)
\(=169.4\)
As a result, the farmer would have only \(220-169.4 = 50.6\) bushels for sale.
Therefore, the total change in the number of bushels he has for sale after \(7\) days \(= 169.4\)
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the first quartile of a data set is 2.5. Which statement about the data values is true?
Answers
The statement that can be considered true ,Data set represents the number of hours spent studying per week, it means that 25% of the individuals surveyed studied for 2.5 hours or less per week. Option C) is the correct answer.
The first quartile of a data set is 2.5, the statement that can be considered true about the data values is that 25% of the values in the data set are less than or equal to 2.5.
The first quartile, denoted as Q1, is a measure of central tendency that divides a data set into four equal parts. It represents the value below which the first 25% of the data lies. In this case, since the first quartile is 2.5, it implies that 25% of the data values in the set are less than or equal to 2.5.
This information provides insights into the distribution and spread of the data set. For example, if the data set represents the number of hours spent studying per week, it means that 25% of the individuals surveyed studied for 2.5 hours or less per week.
It's important to note that without further information about the data set, we cannot make any specific conclusions about the maximum or minimum values, the distribution shape, or the values within the other quartiles. Additional statistical measures and analysis would be needed to determine those aspects.
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The full question will be :
What statistical measure represents the value below which the first 25% of the data lies in a data set?
Options:
a) Median
b) Mean
c) First quartile (Q1)
d) Third quartile (Q3)
\(3q + 2p + 7\)
Answers
5q+7
Explanation
3q+2q+7
Collect like terms by adding their coefficients
(3+2)q+7
Add the numbers
5x+7
what dose this equal 2(6x-4)=3(6x+2)
Answers
Answer:
-7/3
Step-by-step explanation:
2(6−4)=3(6+2)
2(6x-4)=3(6x+2)
Solve
1
Distribute
2(6−4)=3(6+2)
{\color{#c92786}{2(6x-4)}}=3(6x+2)
12−8=3(6+2)
{\color{#c92786}{12x-8}}=3(6x+2)
2
Distribute
12−8=3(6+2)
12x-8={\color{#c92786}{3(6x+2)}}
12−8=18+6
12x-8={\color{#c92786}{18x+6}}
3
Add
8
8
to both sides of the equation
12−8=18+6
12x-8=18x+6
12−8+8=18+6+8
12x-8+{\color{#c92786}{8}}=18x+6+{\color{#c92786}{8}}
5 more steps
Solution
=−7/3
Use distributive property and PEMDAS
2(6x-4)=3(6x+2)
12x-8=18x+6
now add like variables....
-12x on both sides..
6x-8=6
+8 on both
6x=14
divide 6 on both sides
14/6 is
2.33
-7a + 5a = -25 + 21 Solve for a
If you can't figure it out its ok!
Answers
Answer: a = 2
Step-by-step explanation: combine both sides. Remove variable by dividing, answer is 2
-7a + 5a = -25 + 21
-7a + 5a = -4
-2a = -4
a = 2
How to find the possibility?
Answers
Answer:
Step-by-step explanation:
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Probability of event to happen P (E) = Number of favourable outcomes/Total Number of outcomes
Determine whether the statement is true or false. Explain your reasoning. If itis false, provide a counterexample.Statement: Two triangles that have congruent angles are congruent.
Answers
Answer:
The statement is False
Explanation:
Statement: Two triangles that have congruent angles are congruent.
The statement is False.
As a counterexample, consider the two triangles below:
The two triangles above have congruent angles 45°-45°-90.°
However, the side lengths are not the same, thus, the triangles are not congruent, hence supporting our claim that the given statement is False.
let c be the point on the line segment ab that is twice as far from b as it is from a. if a − oa l, b − ob l, and c − oc l, show that c − 2 3 a 1 1 3 b.
Answers
The vector c = (2/3)a + (1/3)b, where c represents the position vector of point C on the line segment AB.
Let's consider the line segment AB, where point C is located. We can express the position vectors as a = OA, b = OB, and c = OC. According to the given information, C is twice as far from B as it is from A. This implies that the ratio of the distances AC and BC is 1:2.
To prove that c = (2/3)a + (1/3)b, we can use the concept of a linear combination of vectors. Since C is two-thirds of the distance from A, and the remaining one-third of the distance from B, we assign the weights (coefficients) of 2/3 to vector a and 1/3 to vector b. Thus, the position vector of C, c, can be expressed as the sum of these weighted vectors: (2/3)a + (1/3)b.
By distributing the weights and combining the terms, we can simplify the expression: (2/3)a + (1/3)b = (2/3)(OA) + (1/3)(OB) = (2/3)OA + (1/3)OB = OC.
Therefore, we have proven that c = (2/3)a + (1/3)b, confirming that point C lies two-thirds of the way from A and one-third of the way from B on the line segment AB.
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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H0: μ = 74 and Ha: μ < 74 are to be tested using a random sample of n = 25 observations.
If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.)
Answers
The probability of a Type I error when μ = 76, using a level 0.01 test with n = 100, is approximately 0.0099.
To determine the probability of a Type I error when μ = 76, we need to calculate the probability of rejecting the null hypothesis (H0: μ = 74) when it is actually true.
In this case, we are given that the standard deviation (σ) is 9, the sample size (n) is 100, and the significance level (α) is 0.01.
Since the test is conducted using a level 0.01 significance level, the critical region is determined by the lower tail of the distribution. We reject the null hypothesis if the test statistic falls in the critical region.
Since the sample size is large (n = 100), we can use the normal distribution to approximate the sampling distribution of the sample mean.
The test statistic follows a standard normal distribution under the null hypothesis, with a mean of 74 and a standard deviation of σ/√n = 9/√100 = 0.9.
To find the critical value that corresponds to a significance level of 0.01, we can use a standard normal distribution table or a calculator. The critical value is approximately -2.33.
Now, we can calculate the probability of a Type I error:
P(Type I error) = P(reject H0 | H0 is true)
P(Type I error) = P(sample mean < critical value | μ = 74)
Since μ = 74, the sample mean is normally distributed with a mean of 74 and a standard deviation of 0.9 (σ/√n).
P(Type I error) = P(sample mean < -2.33 | μ = 74)
Using a standard normal distribution table or a calculator, we can find the probability associated with the z-value -2.33, which is approximately 0.0099.
Therefore, the probability of a Type I error when μ = 76, using a level 0.01 test with n = 100, is approximately 0.0099.
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3.) What is the constant of proportionality (c.o.p.) in the table below?* number of days food in grams 7 4 30
Answers
According to the given table.
Days Grams
7 4 1/5
30 18
The constant of proportionality is found with the following formula.
\(m=\frac{y_2-y_1}{x_2-x_1}\)First, we transform the mixed number 4 1/5 into a fraction.
\(4\frac{1}{5}=\frac{4\cdot5+1}{5}=\frac{20+1}{5}=\frac{21}{5}\)So, we use the following
\(\begin{gathered} x_1=7 \\ x_2=30 \\ y_1=\frac{21}{5} \\ y_2=18 \end{gathered}\)Replacing these values in the formula, we have
\(m=\frac{18-\frac{21}{5}}{30-7}=\frac{\frac{90-21}{5}}{23}=\frac{\frac{69}{5}}{23}=\frac{69}{23\cdot5}=\frac{69}{115}=\frac{3}{5}\)Therefore, the constant of proportionality is 3/5.Draw a sketch of y = x2 - x - 3for values of x in the domain -3 <=x<= 3. Write down the coordinates of the turning point in your solution. Hence, from your sketch, find approximate solutions to:x2 – X – 3 = 0.
Answers
The sketch of the function y = \(x^{2}\) - x - 3 for -3 <= x <= 3 reveals a parabolic curve that opens upwards. The turning point of the parabola, also known as the vertex, can be identified as (-0.5, -3.25).
To sketch the graph of y = \(x^{2}\) - x - 3, we consider the given domain of -3 <= x <= 3. The function represents a parabola that opens upwards. By calculating the coordinates of the turning point, we can locate the vertex of the parabola.
To find the x-coordinate of the turning point, we use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1. Substituting these values, we have x = -(-1)/2(1) = -0.5.
To find the y-coordinate of the turning point, we substitute the x-coordinate (-0.5) into the equation y = \(x^{2}\) - x - 3. Evaluating this expression, we get y = \(-0.5^{2}\) - (-0.5) - 3 = -3.25.
Therefore, the turning point of the parabola is approximately (-0.5, -3.25).
From the sketch, we can estimate the approximate solutions to the equation \(x^{2}\)- x - 3 = 0 by identifying the x-values where the graph intersects the x-axis. These solutions are approximately x ≈ -2.5 and x ≈ 1.5.
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Solve the following equation for b be sure to take into account whether a letter is capitalized or not f = ad
Answers
Answer:
Step-by-step explanation:
J
Pls help me and thank youuu
Answers
Answer: 0.6 or 60 cents.
Step-by-step explanation:
Answer:
I believe it is $1.7.
Step-by-step explanation:
I rounded it from 1.666666667. Something like that.
Two socks are selected at random from a draw of loose socks- there are 4 green socks and 6 yellow socks
What is the probability that two of the socks will both be green if the socks are drawn without replacement
Answers
Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
What is the hypergeometric distribution formula?The formula is:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, we have that the values of the parameters are:
N = 10, k = 4, n = 2.
The probability that both are green is P(X = 2), hence:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333\)
0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
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