Suppose you have 20 pairs of socks, with each pair being a different color. You put them all in the washing machine. The washing machine eats four socks at random. What is the expected value for the number of complete pairs that make it out alive

According to the question the 90th percentile of the average wingspan is approximately 15.1419.

To determine if we can use the normal distribution to model the sample mean  \((\( \bar{x} \))\) , we need to check if the sample size is large enough and if the population distribution is approximately normal.

In this case, the sample size is 20, which is considered large enough. Additionally, the population distribution of wing spans is given as normally distributed. Therefore, we can use the normal distribution to model the sample mean.

The mean of \(\( \bar{x} \) (sample mean)\) is the same as the mean of the population, which is 15mm.

The standard deviation of \(\( \bar{x} \) (sample mean)\) is given by the formula:

\(\[ \text{Standard deviation of } \bar{x} = \frac{\text{Standard deviation of population}}{\sqrt{\text{Sample size}}} \]\)

Plugging in the values, we have:

\(\[ \text{Standard deviation of } \bar{x} = \frac{0.5}{\sqrt{20}} \approx 0.111 \text{ mm} \]\)

To calculate the probability that the average wingspan is higher than 15.15 mm, we need to calculate the z-score for 15.15 mm using the formula:

\(\[ z = \frac{\text{Value} - \text{Mean}}{\text{Standard deviation}} \]\)

Plugging in the values, we have:

\(\[ z = \frac{15.15 - 15}{0.111} \approx 1.35 \]\)

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of 1.35. Let's denote this probability as \(\( P(Z > 1.35) \).\)

To find the 90th percentile of the average sample wingspan, we need to find the z-score associated with a cumulative probability of 0.90. Let's denote this z-score as \(\( Z_{0.90} \).\)

The calculator function we would use to compute the 90th percentile would be \(\( \text{invNorm}(0.90) \) or \( \text{invNorm}(0.90, \text{mean}, \text{standard deviation}) \).\)

Using the calculator function, we can find the 90th percentile of the average wingspan:

\(\[ \text{90th percentile of the average wingspan} = \text{invNorm}(0.90, 15, 0.111) \]\)

To find the 90th percentile of the average wingspan, we can use the formula:

\(\[ \text{90th percentile of the average wingspan} = 15 + 0.111 \cdot \text{invNorm}(0.90) \]\)

Using this formula, we can calculate the value. By evaluating the inverse normal function at a cumulative probability of 0.90, we find that

\(\(\text{invNorm}(0.90) \approx 1.2816\)\).  

Plugging this value into the formula, we have:

\(\[ \text{90th percentile of the average wingspan} = 15 + 0.111 \cdot 1.2816 \]\)

Evaluating the expression, we get:

\(\[ \text{90th percentile of the average wingspan} \approx 15.1419 \]\)

Therefore, the 90th percentile of the average wingspan is approximately 15.1419.

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Answer:

plot between 1/3 and 2/3 or 1/2.

The variable "monthly rainfall in Vancouver" is a quantitative variable. It represents a measurable quantity (amount of rainfall) and can be expressed as numerical values. Therefore, the correct answer is B. quantitative.

Let's further elaborate on why "monthly rainfall in Vancouver" is considered a quantitative variable.

Measurability: Rainfall can be measured using specific units, such as millimeters or inches. It represents a numerical value that quantifies the amount of precipitation during a given month.

Numerical Values: Rainfall data consists of numerical values that can be added, subtracted, averaged, and compared. These values provide quantitative information about the amount of rainfall received in Vancouver each month.

Continuous Range: The variable "monthly rainfall" can take on a wide range of values, including decimals and fractions, allowing for precise measurement. This continuous range of values supports its classification as a quantitative variable.

Statistical Analysis: The variable lends itself to various statistical analyses, such as calculating averages, measures of dispersion, and correlation. These analyses are typically performed on quantitative variables to derive meaningful insights.

In summary, "monthly rainfall in Vancouver" satisfies the characteristics of a quantitative variable as it involves measurable quantities, numerical values, a continuous range, and lends itself to statistical analysis.

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To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

Dependent

Step-by-step explanation:

Two events are said to be dependent when the outcome of the first event is  related to the other.

When two events, A and B are dependent, the probability of occurrence of A and B is:

P(A and B) = P(A) · P(B|A)

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Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.

If two events A and B depend on each other, then the probability  of A and B occurring is

P(A and B) = P(A)  P(B|A)

Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.

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Based on the given dataset and information that the last digit of the CUNY ID is 5, the following steps are taken to analyze the data. The OLS estimates of coefficients B and β are calculated, and the predicted values of Y for each observation are determined. Residuals are calculated, along with the explained sum of squares (ESS), total sum of squares (TSS), and residual sum of squares (RSS). The coefficient of determination (R²) is calculated to assess the goodness of fit. Finally, the predicted value of Y is determined when X is equal to the last digit of the CUNY ID + 1.

a) To regress Y on X, we use ordinary least squares (OLS) estimation. The OLS estimates of coefficients B and β represent the intercept and slope, respectively, of the regression line. The coefficients are determined by minimizing the sum of squared residuals.

b) The predicted value of Y for each observation is obtained by plugging the corresponding X values into the regression equation. In this case, since the last digit of the CUNY ID is 5, the predicted value of Y would be calculated for X = 5.

c) Residuals are the differences between the observed Y values and the predicted Y values obtained from the regression equation. To calculate the residual for each observation, we subtract the predicted Y value from the corresponding observed Y value.

d) The explained sum of squares (ESS) measures the variability in Y explained by the regression model, which is calculated as the sum of squared differences between the predicted Y values and the mean of Y. The total sum of squares (TSS) represents the total variability in Y, calculated as the sum of squared differences between the observed Y values and the mean of Y. The residual sum of squares (RSS) captures the unexplained variability in Y, calculated as the sum of squared residuals.

e) The coefficient of determination, denoted as R², is a measure of the proportion of variability in Y that can be explained by the regression model. It is calculated as the ratio of the explained sum of squares (ESS) to the total sum of squares (TSS).

f) To predict the value of Y when X equals the last digit of the CUNY ID + 1, we can substitute this value into the regression equation and calculate the corresponding predicted Y value.

g) The coefficient B represents the intercept of the regression line, indicating the expected value of Y when X is equal to zero. The coefficient β represents the slope of the regression line, indicating the change in Y associated with a one-unit increase in X. The interpretation of β depends on the context of the data and the units in which X and Y are measured.

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The value of A(final amount) is $550.

Simple Interest for the principal "P" , rate "R%" , and time period "T" , is calculated using the formula

SI = (P*R*T)/100

In the question ,

it is given that

the principal(P) is $500        ...(i)

interest rate(R) is 5%             ...(ii)

time period(T) is 2 years       ...(iii)

the interest will be

= (P*R*T)/100

Substituting the values from equation (i) , (ii) and (iii) , we get

Interest = (500*5*2)/100

= (500*10)/100

= 5000/100

= 50                      ....(iv)

So the interest is $50 .

the final amount(A) = Principal + Interest

Substituting the values from equation (i) and (iv)

we get ,

final amount(A) = 500 + 50

= 550

Therefore , the value of A(final amount) is $550 , the correct option is (A)$550 .

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Conditions (a) and (c) are necessary for n to be divisible by 6, but neither is sufficient. Condition (d) is both necessary and sufficient for n to be divisible by 6.

(a) and (c) are necessary conditions because 6 is a multiple of 3 and 12, so any number that is divisible by 6 must also be divisible by 3 and 12. However, being divisible by 3 or 12 does not guarantee divisibility by 6. For example, 9 is divisible by 3 but not by 6, and 12 is divisible by 12 but not by 6.

Condition (d) is both necessary and sufficient for divisibility by 6 because 6 is the product of 2 and 3, and 24 is the product of 2, 3, and 4. Any number that is divisible by 2, 3, and 4 is also divisible by 6.

Conditions (e) and (f) are not necessary or sufficient for divisibility by 6. For example, 9^2 is divisible by 3 but 9 is not divisible by 6, and 6 is even and divisible by 3 but not all even numbers divisible by 3 are also divisible by 6.

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The numerical value of AB is 24

The given parameters are:

BD = BC

BD = 5x - 26

BC = 2x + 1

AC = 43

BD = BC implies that:

5x - 26 = 2x + 1

Evaluate the like terms

3x = 27

Divide by 3

x= 9

To calculate the length AB, we use the following equation

AB = AC - BC

So, we have:

AB = 43 - 2x - 1

Substitute 9 for x in AB = 43 - 2x - 1

AB = 43 - 2 * 9 - 1

Evaluate the product

AB = 43 - 18 - 1

Evaluate the difference

AB = 24

Hence, the numerical value of AB is 24

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If the probability of having a defect is 20%, then the probability that there is no defect is 0.8 or 80%.

The probability that there is no defect can be calculated by subtracting the probability of having a defect from 1. Since the probability of having a defect is 20%, the probability of no defect is:

1 - 0.20 = 0.80

Therefore, the probability that there is no defect is 80%.

In probability theory, the complement rule states that the probability of an event occurring is equal to 1 minus the probability of its complement. In this case, the event of interest is having no defect, and its complement is having a defect.

If the probability of having a defect is 20%, it means that out of every 100 cases, 20 cases would have a defect. Hence, the remaining 80 cases would not have a defect. This means that the probability of no defect is 80% or 0.80.

By subtracting the probability of having a defect (20%) from 1, we obtain the probability of no defect (80%). This is because the sum of the probabilities of mutually exclusive events must be equal to 1. Therefore, the probability that there is no defect is 80%.

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Answer:diameter = 20m, sidewalk =2m

a

Step-by-step explanation:area of the flower bed = pie r square . 3.14 x 10 x 10

= 314.00m SQ

area of flower bed = pie r square

=3.14 x 8 x 8

= 200.96 m sq

side walk = incl area - excl area= 314 - 200.96 = 113.4m sq

Answer:

Step-by-step explanation:Cake Price = Labor (hours of estimated work x your hourly rate) + Cost of Ingredients + Overhead It comes down to basic cost accounting, factoring in your direct and indirect costs. And of course, valuing your time!

The number of ways to roll a total of 24 with four 10-sided dice is 2925.

To solve this problem using inclusion-exclusion, we need to consider all possible ways to roll a total of 24 with the four 10-sided dice, and then subtract the number of cases where at least one die rolls a number greater than 10.

However, we also need to add back the number of cases where at least two dice roll a number greater than 10, since they were subtracted twice.

Let A be the event that at least one die rolls a number greater than 10, and let B be the event that at least two dice roll a number greater than 10. Then we can use the inclusion-exclusion principle:

N(A) = total number of ways to roll 24 with four 10-sided dice = (number of solutions to x1 + x2 + x3 + x4 = 24) = C(24 + 4 - 1, 4 - 1) = C(27, 3) = 2925

N(B) = total number of ways to roll 24 with at least two dice greater than 10

If two dice are greater than 10, then their sum can be 11, 12, ..., 18, for a total of 8 possibilities. For each of these cases, we need to find the number of ways to distribute the remaining 16 points among the four dice, where each die can have any value from 1 to 10. This can be done using stars and bars:

For 11, the remaining 16 points can be distributed among 4 dice in C(16 + 4 - 1, 4 - 1) = C(19, 3) = 969 ways.

For 12, the remaining 16 points can be distributed among 4 dice in C(14 + 4 - 1, 4 - 1) = C(17, 3) = 680 ways.

For 13, the remaining 16 points can be distributed among 4 dice in C(12 + 4 - 1, 4 - 1) = C(15, 3) = 455 ways.

For 14, the remaining 16 points can be distributed among 4 dice in C(10 + 4 - 1, 4 - 1) = C(13, 3) = 286 ways.

For 15, the remaining 16 points can be distributed among 4 dice in C(8 + 4 - 1, 4 - 1) = C(11, 3) = 165 ways.

For 16, the remaining 16 points can be distributed among 4 dice in C(6 + 4 - 1, 4 - 1) = C(9, 3) = 84 ways.

For 17, the remaining 16 points can be distributed among 4 dice in C(4 + 4 - 1, 4 - 1) = C(7, 3) = 35 ways.

For 18, the remaining 16 points can be distributed among 4 dice in C(2 + 4 - 1, 4 - 1) = C(5, 3) = 10 ways.

So, the total number of ways to roll 24 with at least two dice greater than 10 is:

N(B) = 8*(969 + 680 + 455 + 286 + 165 + 84 + 35 + 10) = 38304

By the inclusion-exclusion principle, the number of ways to roll a total of 24 with four 10-sided dice is:

N = N(A) - N(B)

N = 2925

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Answer:

top one

Step-by-step explanation:

brainliest

Answer:

the top one is bigger. always check the digit placing and exponents!

a) To determine the exact value of sin0, we can use the unit circle. Since 0 is between 0 and 2, it lies in the first quadrant where both the sine and cosine values are positive.

We know that sin0 = opposite/hypotenuse, so we need to find the opposite and hypotenuse of a right triangle with angle 0 on the unit circle. Since the radius of the unit circle is 1, the hypotenuse is 1.

To find the opposite, we draw a line from the point (1,0) (which corresponds to 0 on the unit circle) to the y-axis. This forms a right triangle with angle 0, where the opposite side is the length of this line. By using the Pythagorean theorem, we get:

opposite² + adjacent² = hypotenuse²

opposite² + 1² = 1²

opposite² = 0

Therefore, the opposite side has length 0 and sin0 = 0.

b) To determine the exact value of sec0, we use the fact that sec0 = 1/cos0. Since 0 is between 0 and 2, it still lies in the first quadrant where cosine is positive.

Using the Pythagorean theorem again, we can find the adjacent side of the same right triangle we used earlier:

opposite² + adjacent² = hypotenuse²

adjacent² + 1² = 1²

adjacent² = -1

Since the adjacent side of a triangle cannot have a negative length, we know that sec0 is undefined.

c) To determine the exact value of csc0, we use the fact that csc0 = 1/sin0. Since we already found that sin0 = 0, we know that csc0 is undefined.

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The constant of proportionality is 1 point for every 10 minutes of play.

The equation that represents the relationship is:

Points = (Time played in minutes) / 10

The number of points awarded for 12 minutes of play is 1.2 points.

Part A: Scenario 1: For every 2 minutes of play, the game awards 1/2 point.

Scenario 2: For every 15 minutes of play, the game awards 1 1/4 points.

Scenario 1: 2 minutes → 1/2 point

Scenario 2: 15 minutes → 1 1/4 points (which is equal to 5/4 points)

2 minutes / 1/2 point = 15 minutes / 5/4 points

(2 minutes / 2) / (1/2 point) = (15 minutes / 2) / (5/4 points)

1 minute / (1/2 point) = 7.5 minutes / (5/4 points)

1 minute * (2/1 point) = 7.5 minutes * (4/5 points)

2 minutes / point = 30 minutes / 5 points

Finally, let's simplify the equation by multiplying both sides by 5:

10 minutes / point = 30 minutes / 1 point

From this equation, we can see that the constant of proportionality is 1 point for every 10 minutes of play.

Part B: The equation that represents the relationship is:

Points = (Time played in minutes) / 10

Part C: To graph the relationship, we'll plot points on the y-axis and time played in minutes on the x-axis. The points awarded increase linearly with time, and for every 10 minutes played, the player receives 1 point. Therefore, the graph will be a straight line with a positive slope of 1/10. The y-intercept will be at (0, 0) since no points are awarded for 0 minutes played.

Part D: To find the number of points awarded for 12 minutes of play, we'll use the equation from Part B:

Points = (Time played in minutes) / 10

Substituting the value of 12 minutes:

Points = 12 / 10 = 1.2 points

So, 1.2 points are awarded for 12 minutes of play.

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Step-by-step explanation:

8 ¾ = 35/4

\( \frac{134}{ \frac{35}{4} } = \frac{134 \times 4}{35} = \frac{536}{35} \)

The z-score of a car that is 6 years old is  -0.625.

To find the z-score of a car that is 6 years old, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).

Plugging in the values, we get:

z = (6 - 8) / 3.2 = -0.625

Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.

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Answer:

0

Step-by-step explanation:Velocity at t= 0s is 20m/s and the velocity at t= 10s is 20m/s.

a= 20-20/ 10s

a=0m/s

Answer: answer is 0

Step-by-step explanation:

Answer:

Thanks for letting me know I might try that later today

Step-by-step explanation:

:)

The complete function for the given graph is: y = - |x - 1| + 3.

Two linear functions combine to form the piecewise-defined function known as the absolute value function.

This absolute value function is frequently used to calculate the separation on the number line between two values. No matter which of two numbers, a and b, is larger, |ab| will provide the distance between them as a positive number.

The corner point in a graph is where the direction of the graph shifts. This point is highly useful for computing the horizontal and vertical shifts in the equation for a transformed absolute value function.

From the given graph of the function:

y = - |x - 1| + 3, is the complete solution, such that.

when x = 0

y = - |0 - 1| + 3,

y = - 1 + 3 = 2

(0, 2) is the point which satisfy the graph.

Thus, the complete function for the given graph is: y = - |x - 1| + 3.

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Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

(3, 8)

Step-by-step explanation:

Coordinate (-3, -8)

Reflect across the y-axis. The x will change to the opposite, and the y will remain the same. So, the coordinate is (3, -8)

Then reflect the result across the x-axis. The y will change to the opposite, and the x will remain the same. So, the coordinate is (3, 8)

So, the coordinate of the final point is (3, 8)

Given:

The point is A(-1,3).

To find:

The coordinates of the final image. If the given point reflected in

(a) x-axis

(b) line y=4.

Solution:

(a)

If a figure reflected across the x-axis, then

\((x,y)\to (x,-y)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3)\)

Therefore, the coordinates of the final image are A'(-1,-3).

(b)

If a figure reflected across the line y=4, then

\((x,y)\to (x,-(y-4)+4)\)

\((x,y)\to (x,-y+4+4)\)

\((x,y)\to (x,-y+8)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3+8)\)

\(A(-1,3)\to A'(-1,5)\)

Therefore, the coordinates of the final image are A'(-1,5).