suppose that x is a normal random variable with mean 5. if p{x > 9} = .2, approximately what is var(x)?

a) The efficiency of the assembly line with 3 workstations = 93.75%

c) To improve the balance to 100%, the tasks should be distributed evenly across the workstations to minimize idle time. However, this might not always be possible due to task dependencies and workstation constraints.

d) The theoretical minimum number of workstations = 3

Let's discuss it further below.

a) To determine the idle time per cycle, use the following formula:

Idle time = (Number of workstations * Actual cycle time) - Σ Time for task i

Idle time = (3 * 9.6) - (4.0 + 1.5 + 3.0 + 3.6 + 3.0 + 2.0 + 3.2 + 3.7 + 2.0 + 2.0)
Idle time = 28.8 - 27.0
Idle time = 1.8 minutes

b) To calculate the efficiency of the assembly line with 3 workstations, use this formula:

Efficiency = Σ Task times / (Number of workstations * Longest assigned activity time)

Efficiency = (27.0) / (3 * 9.6)
Efficiency = 27.0 / 28.8
Efficiency = 0.9375

The efficiency of the assembly line with 3 workstations = 93.75%

c) To improve the balance to 100%, the tasks should be distributed evenly across the workstations to minimize idle time. However, this might not always be possible due to task dependencies and workstation constraints.

d) To find the theoretical minimum number of workstations, use the formula:

Minimum number of workstations = Σ Time for task i / Cycle time

Minimum number of workstations = 27.0 / 11
Minimum number of workstations = 2.45

The theoretical minimum number of workstations = 3 (rounded up to the next whole number).

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The dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

To estimate the true mean April 2023 retail whole milk price with a margin of error of $0.10 and 95% confidence, a dairy farmer can use the sample size formula for estimating population means. The formula is:
n = (Z² × σ²) / E²
where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and E is the margin of error.
For a 95% confidence level, the z-score (Z) is 1.96. The standard deviation (σ) of milk prices is $0.60, and the margin of error (E) is $0.10. Plugging these values into the formula, we get:
n = (1.96² × 0.60²) / 0.10²
n = (3.8416 × 0.36) / 0.01
n ≈ 138.56
Since the sample size must be a whole number, we round up to the nearest whole number to ensure the desired level of accuracy. Therefore, the dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

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This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.

If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula\(R125/(2^t)\) = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula \(R125/(2^t)\) for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.

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Answer:

Step-by-step explanation:

The length of side LJ as shown in the similar shapes is 12.92.

Similar shapes are enlargements of each other using a scale factor.

To calculate the length of side LJ, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1 and solve for KL

Hence, the right option is 12.92.

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9514 1404 393

Answer:

 volume is doubled

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

Then the volume of the modified cylinder is ...

  V = π(2r)²(h/2) = π(4r²)h/2 = 2πr²h . . . . . double the previous volume

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer:

The GCF of 50 and 72 is obviously 2.

a. 6/7, 5/6We need to decide if the given slopes are equivalent (=) or one slope is greater (> or <).Let's compare the given slopes. To compare fractions, we need to find their LCD (Least Common Denominator) and then compare their numerators.

For the given slopes, the LCD is 42. Let's compare the slopes:6/7 = 36/42 and 5/6 = 35/42Now, 36/42 > 35/42Hence, the slope 6/7 is greater than the slope 5/6. Therefore, the answer is 6/7 > 5/6.b. 3/2, 15/10Let's compare the given slopes. To compare fractions, we need to find their LCD (Least Common Denominator) and then compare their numerators.

For the given slopes, the LCD is 10. Let's compare the slopes:3/2 = 15/10 and 15/10 = 15/10Now, 15/10 = 15/10Hence, the slopes 3/2 and 15/10 are equivalent. Therefore, the answer is 3/2 = 15/10.c. 12/10, 7/5We need to decide if the given slopes are equivalent (=) or one slope is greater (> or <).Let's compare the given slopes. To compare fractions, we need to find their LCD (Least Common Denominator) and then compare their numerators.

For the given slopes, the LCD is 10. Let's compare the slopes:12/10 = 6/5 and 7/5 = 7/5Now, 6/5 < 7/5Hence, the slope 7/5 is greater than the slope 12/10. Therefore, the answer is 12/10 < 7/5.

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To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

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To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

when the same person sits on the same board of directors two or more companies ..

The value of the length f is 6. 7

To determine the value, we have to know the different trigonometric identities.

These trigonometric identities are enumerated as;

To determine the length of f

Let us use the tangent identity, we have that;

tan θ = opposite/adjacent

substitute the values, we have;

tan 24 = f/15

Multiply the values, we get;

f = 0. 4452(15)

multiply the values

f = 6. 7

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The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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The scaled values sum up to 1/10.

        k subscript 1 + k subscript 2 = 1

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k  subscript 1 E[theta with hat on top subscript 1] + 10 k subscript 2 E[theta with hat on top subscript 2]

        E[theta with hat on top subscript 1] = theta

        E[theta with hat on top subscript 2] = theta

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k subscript 1 theta + 10 k subscript 2 theta = theta (10 k subscript 1 + 10 k subscript 2) = theta

        k subscript 1 + k subscript 2 = 1

        10 k subscript 1 + 10 k subscript 2 = 10

       k subscript 1 + k subscript 2 = 1

       k subscript 1/10 + k subscript 2/10 = 1/10

Therefore, their sum is equal to 1, and their scaled values sum up to 1/10.

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Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

The area under the curve to the left of the point would be approximately 0.9319 unit square

To indicate the given x value on the curve, we need to plot it on a normal distribution curve with mean (μ) 63.6 and standard deviation (σ) 3.7.

First, we need to calculate the z-score, which is a measure of how many standard deviations away from the mean the given x value is located:

z-score = (x - μ) / σ

Substituting the given values, we get:

z-score = (69.2 - 63.6) / 3.7 ≈ 1.49

Next, we can use a z-score table or a calculator to find the corresponding area under the standard normal distribution curve. The area to the left of a z-score of 1.49 is about 0.9319.

Therefore, the point representing the given x value of 69.2 would be located to the right of the mean (μ) on the normal distribution curve, about 1.49 standard deviations away. The area under the curve to the left of the point would be approximately 0.9319 unit square

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For #1 it's going to be proper because it's pretty specific, and for number two it's going to be all common because it's not citing anything specific.

Answer: 1 6611/12500

Step-by-step explanation: I dunno, not much to explain, just giving you the answer unless you want the explanation.

Answer: 153.47

Step-by-step explanation: I got 153.47 because when you have a whole number with a decimal and another whole number with a decimal you would add how many decimals there is to line up. When you are done with that, you would see how many decimal places behind the decimal and add that to the answer at the end.

Hope this helped!

Told to walk in first week = 5km

Told to walk in second week = 8km

Told to walk in third week = 11km

It is forming a pattern,

5km      8km      11km       ..........

     +3       +3        +3

5km      8km     11km     14km     17km     20km    23km     26km   29km     32km

    +3       +3        +3       +3        +3        +3        +3         +3      +3  

The patient has to walk 32km in the 10th week.

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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the directional derivative of f(x, y) = ln(x² + y) at the point (-1, 1) in the direction of the vector < -2, -1 > is 3/2.

To calculate the directional derivative, we can use the formula:

D_v f(x, y) = ∇f(x, y) · v

where ∇f(x, y) represents the gradient of the function f(x, y) and v represents the direction vector.

First, we find the gradient of f(x, y) by taking its partial derivatives with respect to x and y:

∇f(x, y) = (df/dx, df/dy) = (2x / (x² + y), 1 / (x² + y))

Next, we substitute the values of (-1, 1) into the gradient:

∇f(-1, 1) = (2(-1) / ((-1)² + 1), 1 / ((-1)² + 1)) = (-2/2, 1/2) = (-1, 1/2)

Finally, we take the dot product of the gradient and the direction vector:

D_v f(-1, 1) = ∇f(-1, 1) · < -2, -1 > = (-1)(-2) + (1/2)(-1) = 2 - 1/2 = 3/2

Therefore, the directional derivative of f(x, y) = ln(x² + y) at the point (-1, 1) in the direction of the vector < -2, -1 > is 3/2.

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Answer:

x = 9

Step-by-step explanation:

These are alternate exterior angles and alternate exterior angles are equal if m is parallel to n

6x+5 = 7x-4

Subtract 6x from each side

6x -6x+5 = 7x-6x-4

5 = x -4

Add 4to each side

5+4 =x-4+4

9 =x

Answer:

x = 9°

Step-by-step explanation:

The two angles are alternate exterior angles, so they both are congruent.

The equation is :

6x + 5 = 7x - 4

Add 4 to both sides

6x + 9 = 7x

Subtract 6x from both sides

9 = x

x = 9

Lets check:

6(9) + 5 = 7(9) - 4

54 + 5 = 63 - 4

59 = 59

Correct!

If my answer is incorrect, pls correct me!

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Answer:

Either A or B.

Step-by-step explanation:

Each number in the sequence is being added by 6.

So you can use the equation: x+6

The ninth term in the sequence would be 36 because 30+6=36

Answer:

\(Students = \frac{1}{50}\)

Step-by-step explanation:

Given

\(Track = \frac{1}{30}\)

\(Pizza = \frac{3}{5}\)

Required

The fraction of students in the school that ate Pizza

To do this, we simply multiply the fraction of track students and those among them that ordered pizza.

So, we have:

\(Students = Pizza * Track\)

\(Students = \frac{3}{5} * \frac{1}{30}\)

\(Students = \frac{1}{5} * \frac{1}{10}\)

\(Students = \frac{1}{50}\)

Step-by-step explanation:

it is associative

because in commutative a+b=b+a

but in associates a+(b+c)=(a+b)+c

Answer:

x = 4

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 4 from both sides of the equation:

-6x + 4 (-4) = -20 (-4)

-6x = -20 - 4

-6x = -24

Next, divide -6 from both sides of the equation:

(-6x)/-6 = (-24)/-6

x = (-24)/(-6)

x = 4

x = 4 is your answer.

~

Answer:

-4

Step-by-step explanation:

-6x+4=-20

-6x+24 (add like variables)

-4 (divide by -6)