kiran has a sock drawer that has $7$ different pairs of matching socks. every day for a week, he pulls out two socks at random (without replacement). what is the expected number of days that kiran wears matching socks?

The sampling technique used in this scenario is stratified random sampling. Stratified random sampling is a useful technique for obtaining a representative sample from a population with identifiable subgroups, and can improve the validity and generalizability of survey results.

Stratified random sampling involves dividing the population into homogeneous groups, or strata, based on a specific characteristic, and then taking a random sample from each stratum. In this case, the population of gym members was divided into men and women, which are two distinct and easily identifiable strata. A simple random sample was then taken from each stratum to obtain a representative sample of both genders.

The use of stratified random sampling can increase the precision and accuracy of the sample by ensuring that each stratum is represented proportionally in the sample. This technique is commonly used when the population of interest exhibits a significant characteristic that may impact the outcome of the survey. For example, if the survey was investigating the effectiveness of a new exercise program, it would be important to ensure that both men and women were represented equally in the sample, as their physiological differences may impact their response to the program.

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The probability that a randomly chosen student is taking tech given that they are taking art is 50%.

To find the probability that a randomly chosen student is taking tech given that they are taking art, we need to use conditional probability. We can use the formula:

P(Tech | Art) = P(Tech and Art) / P(Art)

We know that 62 students are taking both tech and art, so P(Tech and Art) = 62. To find P(Art), we need to subtract the number of students who are only taking tech or only taking art from the total number of students:

P(Art) = (74 - 62) + (112 - 62) + 62 = 124

Therefore, we have:

P(Tech | Art) = 62 / 124 = 0.5

So the probability that a randomly chosen student is taking tech given that they are taking art is 50%.

In summary, we can use conditional probability to find the probability that a randomly chosen student is taking tech given that they are taking art. We need to find the number of students who are taking both tech and art and the total number of students taking art, and then divide the two numbers to get the probability.

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Answer:

See below

Step-by-step explanation:

Slope-intercept form of an equation of line:

[tex]y = mx + c[/tex]  —— eq(i)

Where:

c = y-intercept

  = y-value for which the corresponding x-value is 0

  = [tex]-1[/tex] (From the provided table)

m = slope
   = [tex]\frac{rise}{run}[/tex]

   = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex] —- eq(ii)

Choose any two sets of coordinates and then substitute in eq(ii). I chose:

[tex](3, 8)[/tex] as [tex](x_{1}, y_{1})[/tex]

[tex](4, 11)[/tex] as [tex](x_{2}, y_{2})[/tex]

   = [tex]\frac{11 - 8}{4 - 3}[/tex]

   = [tex]\frac{3}{1}[/tex]

∴ m = [tex]3[/tex]

Substituting the values of c and m in eq(i):

[tex]y = (3)x + (-1)[/tex]

∴ Equation for the function

[tex]y = 3x - 1[/tex]

The determinant of matrix A matrix equation when k1 = -4 and k2 = 0, we have x1 = -12/23 and x2 = 4/23.

The given system of equations can be written as a matrix equation as follows:

A * X = K

where

A = [[7, 3], [-2, -1]]

X = [x1, x2]

K = [k1, k2]

To solve for X, we can use the inverse of matrix A as follows:

X = A^-1 * K

To find the inverse of matrix A, we can use the formula:

A^-1 = (1/det(A)) * [[-1, -3], [2, 7]]

where det(A) is the determinant of matrix A.

Plugging in the values of A^-1 and K, we get:

X = (1/det(A)) * [[-1, -3], [2, 7]] * [-4, 0]

X = [-12/23, 4/23]

Therefore, when k1 = -4 and k2 = 0, we have x1 = -12/23 and x2 = 4/23.

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To find vectors w1 and w2 so that s will be the transition matrix from [w1, w2] to [v1, v2], you need to follow these steps:

1. First, arrange the given vectors v1 and v2 in matrix form, let's call this matrix V:
  V = |v1 v2|

2. Next, arrange the unknown vectors w1 and w2 in matrix form, let's call this matrix W:
  W = |w1 w2|

3. Your goal is to find the transition matrix S, which when multiplied with matrix W will give you matrix V:
  S * W = V

4. To find the transition matrix S, you need to multiply both sides of the equation with the inverse of matrix W:
  S = V * W⁻¹

5. Now, calculate the inverse of matrix W (W⁻¹), and multiply it with matrix V to obtain the transition matrix S.

Keep in mind that we cannot provide specific numerical values for w1 and w2 without knowing the values of v1 and v2. However, by following these steps, you can find the vectors w1 and w2 that correspond to the given transition matrix S from [w1, w2] to [v1, v2].  

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Part A:

Best graphical representation to display data will be line graph.

Given,

Scores of basketball team during the first 13 games of the season

{85, 94, 101, 118, 107, 110, 114, 96, 117, 105, 121, 88, 125}.

Now,

Part B:

We can create line graph with a very simple technique.

Firstly,

On x - axis take the number of season the team has played. In our case the number is 13 so take 13 distinct points on the x - axis.

Secondly,

On y -axis take the scores of the team in each of the 13 seasons corresponding to their values at x - axis.

Then,

Plot the points on the graph for all 13 seasons .

Last step,

Join all the points in the graph with the help of ruler. This will form the required line graph of the question.

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The next row of Pascal's triangle for the given row 1 7 21 35 35 21 7 1 is equal to  1 8 28 56 70 56 28 1.

Row of Pascal's triangle is equal to,

1 7 21 35 35 21 7 1

To find the next row of Pascal's triangle given the row 1 7 21 35 35 21 7 1,

Use the property that each element in Pascal's triangle is the sum of the two elements directly above it.

Let us calculate the next row,

Row  =       1 7 21 35 35 21 7 1

Next row =  1 _ _ _ _ _ _ 1

To fill in the missing values,

Start by writing down the first and last elements, which are always 1,

Row = 1 7 21 35 35 21 7 1

Next row= 1 _ _ _ _ _ _ 1

Next, we can calculate the remaining elements by adding the two elements directly above each empty space,

Row =  1 7 21 35 35 21 7 1

Next row = 1 8 _ _ _ _ 8 1

Continuing the process,

Row = 1 7 21 35 35 21 7 1

Next row = 1 8 28 _ _ 28 8 1

Row = 1 7 21 35 35 21 7 1

Next row = 1 8 28 56 _ 56 28 1

Row = 1 7 21 35 35 21 7 1

Next row = 1 8 28 56 70 56 28 1

Therefore, the next row of Pascal's triangle is 1 8 28 56 70 56 28 1.

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A value of r greater than 0.40 indicates a stronger correlation than 0.40.

The correlation coefficient, denoted as "r," measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to 1. When the absolute value of r is closer to 1, it indicates a stronger correlation. In this case, a value of r greater than 0.40 suggests a stronger positive correlation than 0.40.

This means that as one variable increases, the other variable tends to increase as well, and the relationship between the variables is more pronounced. For example, if the correlation coefficient is 0.60, it indicates a stronger positive correlation than 0.40. Similarly, if the correlation coefficient is 0.90, it indicates an even stronger positive correlation. On the other hand, if the correlation coefficient is negative, such as -0.60 or -0.90, it indicates a stronger negative correlation.

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(a) Event "X and Y": F

(b) Event "X or Y": A, B, C, D, F

(c) The complement of the event X: E, F, G

(a) Event "X and Y": F

The letter "F" satisfies both conditions: it comes before "E" (Event X) and it is found in the word "FACE" (Event Y).

(b) Event "X or Y": A, B, C, D, F

The letters A, B, C, D, and F satisfy either condition: they come before "E" (Event X) or they are found in the word "FACE" (Event Y).

(c) The complement of the event X: E, F, G

The complement of Event X includes all the letters that do not come before "E". In this case, the letters E, F, and G do not satisfy the condition of coming before "E".

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We start by using the chain rule to find the derivative of w with respect to t: dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

dw/dt = 320 when t = 1.

To find ∂w/∂x, we treat y and t as constants and differentiate w = x^2 y^2 t with respect to x:

∂w/∂x = 2xy^2 t

To find ∂w/∂y, we treat x and t as constants and differentiate w = x^2 y^2 t with respect to y

∂w/∂y = 2x^2 yt

To find ∂w/∂t, we treat x and y as constants and differentiate w = x^2 y^2 t with respect to t:

∂w/∂t = x^2 y^2

Substituting the given values x = 4t and y = 2t, we get:

∂w/∂x = 2(4t)(2t)^2 t = 32t^4

∂w/∂y = 2(4t)^2 (2t) t = 64t^4

∂w/∂t = (4t)^2 (2t)^2 = 64t^4

Using these values, we can write:

dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

= (32t^4)(4) + (64t^4)(2) + (64t^4)

= 320t^4

Finally, substituting t = 1, we get:

dw/dt = 320(1)^4 = 320

Therefore, dw/dt = 320 when t = 1.

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Answer:

5%

Step-by-step explanation:

100 - 95 = 5

The radius of convergence of the power series 12"x" n! n=1 is infinity.To determine the radius of convergence, we use the ratio test.

Let a_n be the nth term of the series, then a_n = 12"x" n! / n. Applying the ratio test, we have:

lim as n approaches infinity of |a_{n+1}/a_n| = lim as n approaches infinity of |12"x" (n+1)! / (n+1)| / |12"x" n! / n|

= lim as n approaches infinity of |12"x"| * (n+1) / n

= |12"x"| * lim as n approaches infinity of (n+1) / n

Since lim as n approaches infinity of (n+1) / n = 1, the limit simplifies to |12"x"|. The ratio test tells us that the series is convergent when |12"x"| < 1 and divergent when |12"x"| > 1. Since |12"x"| is always positive, the series is convergent for all values of x, which means the radius of convergence is infinity.

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The appropriate growth model for the given scenario would be a logistic growth model where the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach.

A logistic growth model is appropriate for situations where the growth rate of a variable initially increases and then slows down as it approaches a maximum value or carrying capacity. In the given scenario, the number of arrests initially grew for several years, but has been decreasing recently, suggesting that it may have reached a saturation point. Thus, a logistic growth model would be appropriate to model the trend of the number of arrests.

In a logistic growth model, the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach. In the case of the number of arrests, the carrying capacity could be the maximum number of arrests that can be made in a given period, which might be limited by factors such as the number of police officers, the number of crimes committed, or the effectiveness of law enforcement policies. As the number of arrests approaches this limit, the growth rate slows down, eventually leading to a plateau or a decline in the number of arrests.

Overall, a logistic growth model would be appropriate for the given scenario as it takes into account the saturation point and provides a better fit to the trend of the number of arrests over time.

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The travel time for a college student travelling between her home and her college is uniformly distributed between 40 and 70 minutes. The probability that the college student will finish her trip in 60 minutes or less is c. 0.6667.

To calculate the probability, we'll use the information about the travel time uniformly distributed between 40 and 70 minutes.
Step 1: Identify the range of possible travel times.
The range is from 40 to 70 minutes, so the total range is 70 - 40 = 30 minutes.
Step 2: Identify the desired range (60 minutes or less).
Since we want to find the probability that the trip takes 60 minutes or less, the desired range is 60 - 40 = 20 minutes.
Step 3: Calculate the probability.
Since the distribution is uniform, the probability is simply the ratio of the desired range to the total range. Therefore, the probability is 20/30 = 2/3 = 0.6667.

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The multiplier is 5. To find the multiplier, we use the formula: Multiplier = 1 / (1 - MPC), where MPC is the marginal propensity to consume.

In this case, the consumption function is c = 75 + 0.80yd, which implies that MPC = 0.80. Therefore, the multiplier is 1 / (1 - 0.80) = 5. This means that an initial change in investment spending of $50 will lead to a total change in output (GDP) of $250, assuming no other changes in the economy.

The multiplier effect occurs because the initial injection of spending leads to an increase in income, which in turn leads to an increase in consumption, and so on, in a multiplier process.

It is important to note that the multiplier effect assumes that there are no leakages (such as taxes or imports) in the economy, which can reduce the size of the multiplier.

Additionally, the multiplier effect assumes that the economy is operating below full capacity, so that there is room for output to expand.

If the economy is already operating at full capacity, the multiplier effect may be limited, as additional spending may lead to inflationary pressures rather than an increase in output.

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Answer:Usually you should just use these two rules:

T(x)+T(y) = T(x+y)

cT(x) = T(cx)

Where T is your transformation (in this case, the scaling matrix), x and y are two abstract column vectors, and c is a constant.

If these two rules work, then you have a linear transformation :)

Step-by-step explanation:

The probability that a person will be able to complete a 5000 mile trip without having to replace the car battery can be calculated using the cumulative distribution function (CDF) of the exponential distribution. The answer is approximately 60.7%.

To explain further, we know that the average value of the exponential distribution is 10000 miles. This means that the expected value of the number of miles a car can run before its battery wears out is 10000 miles. The probability that the car's battery will last for at least 5000 miles can be calculated using the CDF of the exponential distribution. The CDF of the exponential distribution is given by F(x) = 1 - e^(-x/μ), where x is the number of miles and μ is the average value of the distribution.

Substituting x = 5000 and μ = 10000, we get F(5000) = 1 - e^(-0.5) ≈ 0.607. Therefore, the probability that a person will be able to complete a 5000 mile trip without having to replace the car battery is approximately 60.7%. This means that there is a 60.7% chance that the car's battery will last for at least 5000 miles, and the person will not have to replace it during the trip.

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The equation of the tangent to the curve x = 5 sin(t), y = t^2 + t at the point (0,0) is y = 5x.

To find the equation of the tangent line, we need to find the derivative of y with respect to x. Using the chain rule, we get:

dy/dx = dy/dt * dt/dx

To find dt/dx, we can take the reciprocal of dx/dt, which is:

dt/dx = 1/(dx/dt)

dx/dt = 5 cos(t), so:

dt/dx = 1/(5 cos(t))

Now, to find dy/dt, we take the derivative of y with respect to t:

dy/dt = 2t + 1

So, putting it all together, we get:

dy/dx = dy/dt * dt/dx = (2t + 1)/(5 cos(t))

At the point (0,0), t = 0, so:

dy/dx = 1/5

So the equation of the tangent line is:

y = (1/5)x + b

To find the value of b, we plug in the coordinates of the point (0,0):

0 = (1/5)(0) + b

b = 0

Therefore, the equation of the tangent line is: y = (1/5)x

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A hamburger has 350 calories. So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.

To solve the problem, you can use algebraic equations. Let x be the number of calories in an order of fries. Then, the number of calories in a hamburger is 50 + x. The problem tells us that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:

2(50 + x) + 3x = 1700

Simplifying and solving for x, we get:

100 + 2x + 3x = 1700

5x = 1600

x = 320

So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.

Explanation:

To solve the problem, we need to set up an equation that relates the number of hamburgers and fries to the total number of calories. We can use algebraic variables to represent the unknown quantities. Let x be the number of calories in an order of fries, and let y be the number of calories in a hamburger.

The problem tells us that each hamburger has 50 + x more calories than each order of fries. This means that the number of calories in a hamburger is equal to the number of calories in an order of fries plus 50:

y = x + 50

We also know that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:

2y + 3x = 1700

Now we can substitute the first equation into the second equation to eliminate y:

2(x + 50) + 3x = 1700

Simplifying and solving for x, we get:

2x + 100 + 3x = 1700

5x = 1600

x = 320

So an order of fries has 320 calories. We can substitute this value back into the first equation to find the number of calories in a hamburger:

y = x + 50

y = 320 + 50

y = 370

Therefore, a hamburger has 370 calories.

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Angles a and 139 are corresponding angles thus a = 139°

Angles a and b are supplementary hence b = 41°

When a transversal connects two parallel lines, it creates corresponding angles, which are two angles in a pair. A transversal produces a total of eight angles when it crosses two parallel lines. Pairs of these angles that are at the same relative position at each intersection are said to be corresponding angles.

Angles that correspond to one another have the same measure and are therefore congruent. The characteristics of parallel lines and the angles that the transversal forms lead to this congruence.

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Susan most likely used angle facts related to the sum of angles in a triangle to calculate angle a and then used triangle angle-sum property to find angle b.

To answer your questions:

Susan likely used angles facts related to the sum of angles in a triangle to find the calculation of angle a. This principle states that the sum of all angles in a triangle is always equal to 180 degrees.

For angle b, she then used triangle angle-sum property, which states that the measure of an angle of a triangle is equal to the sum of the measures of the other two angles subtracted from 180 degrees.

For instance, if angle a was 41 degrees, and the third angle was known to be 100 degrees, she would subtract these two angles from 180, resulting in angle b being 39 degrees.

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Answer:

6

Step-by-step explanation:

8+9+1 is 18, and since there are 3 numbers, we must divide 18 by 3, 2 which is 6

Answer: 6

Step-by-step explanation:

8+9+1 = 18
3 numbers
18/3 = 6

The complementary error function is a function commonly used in communications and signal processing to compute the tail probabilities of Gaussian random variables. It is defined as:

Q(x) = 1/√(2π) ∫x to ∞ e^(-t^2/2) dt

where x is a real number. Geometrically, Q(x) represents the area under the standard normal probability density function to the right of x. This means that Q(x) gives the probability that a standard normal random variable takes on a value greater than x.

The complementary error function is related to the error function, erf(x), which is defined as:

erf(x) = 2/√(π) ∫0 to x e^(-t^2) dt

In fact, Q(x) can be expressed in terms of erf(x):

Q(x) = 1/2 erfc(x/√2)

where erfc(x) is the complementary error function.

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Jack ate 1/10 cup more strawberries than Leo

The problem states that Leo ate 3/5 cup of strawberries, and Jack ate 7/10 cup of strawberries. We need to find out how much more Jack ate than Leo.

To solve this problem, we first need to find a common denominator for the two fractions. The denominator is the bottom number of a fraction, which represents the total number of equal parts that make up a whole.

The smallest common denominator for 5 and 10 is 10. We can convert the fraction 3/5 into an equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 6/10.

Now, we have two fractions with the same denominator: 6/10 and 7/10. To find out how much more Jack ate than Leo, we can subtract the fraction representing what Leo ate from the fraction representing what Jack ate:

7/10 - 6/10 = 1/10

Therefore, Jack ate 1/10 cup more strawberries than Leo did.

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Let's start by defining some variables:

P0 = 151000      // initial population in 2013

r = 0.05         // constant annual growth rate

t = 7            // number of years from 2013 to 2020

The exponential model for the population can be written as follows:

y = P0 * (1 + r)^t

Substituting in the values we get:

y = 151000 * (1 + 0.05)^7

y ≈ 209749

Therefore, the exponential model that represents the population of the city t years after 2013 is y = 151000 * (1 + 0.05)^t, and the estimated population in 2020 is about 209,749.

Note that the result is an estimation, and can be affected by various factors, such as migration and mortality rates, that are not accounted for in the model.

Function g(r) = -(I + 8)³ has a restricted domain, since the cube of any real number can be either positive or negative, but not both. Specifically, in this case, the domain of g(r) is restricted to the set of real numbers where (I + 8)³ is non-negative.

The given statement is "In determining the size of hail stones, weather spotters should report the longest dimension of the largest hail stone"

This statement is False because meteorologists ought to report the hail stones' diameter in millimeters rather than their longest dimension.

The longest dimension is the longest line member between the two points of the hailstone, while the periphery is the longest distance between the two points. The standard measurement utilized by meteorologists is the periphery, which is a more accurate measurement of the size of the hail gravestone.

This is because the hailstone size could be used as an indicator of the wind speed and the height of the storm where it formed. The National Weather Service uses size criteria to issue various hail size warnings.

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The answer to your question would be 1530 because the whole number is 1800 and then the 85% would be 153.

The solution to the given expression 3(1/4 - 2) + |-7| is 7/4.

The expression is given as follows:

3(1/4 - 2) + |-7|

To solve the given expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we need to simplify the expression inside the parentheses:

1/4 - 2 = -7/4

Next, we can simplify the expression by multiplying 3 by -7/4:

3(-7/4) = -21/4

Finally, we need to evaluate the absolute value of -7:

|-7| = 7

Substituting the values into the original expression, we get:

3(1/4 - 2) + |-7| = -21/4 + 7

Combining like terms, we get:

3(1/4 - 2) + |-7| = -21/4 + 28/4

Simplifying, we get:

3(1/4 - 2) + |-7| = 7/4

Therefore, the solution to the expression 3(1/4 - 2) + |-7| is 7/4.

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The complete question is as follows:

Solve the below expression

3(1/4 - 2) + |-7|

The solution of the inequality is,

⇒ q = 11

We have to given that;

The inequality is,

⇒ 56 ≤ 3 + 6q

Now, We can simplify as;

⇒ 56 ≤ 3 + 6q

⇒ 56 - 3 ≤ 6q

⇒ 53 ≤ 6q

⇒ 8.33 ≤ q

Hence, By options, The solution of the inequality is,

⇒ q = 11

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