Effective mean process time = Mean of 60-panel exposure time+Mean repair time=120+240=360 minutes and coefficient of variation (CV)≈0.712
The exposure machine has a mean time of 2 minutes to expose a single panel with a standard deviation of 1 1/2 minutes. The jobs consist of 60 panels, and failures occur between jobs but do not preempt the ongoing job. Repair times remain the same as before.
To compute the effective mean and coefficient of variation (CV) of the process times for the 60-panel jobs, we need to consider the exposure time for each panel and the repair time in case of failures.
Exposure Time:
Since the exposure time for a single panel follows a normal distribution with a mean of 2 minutes and a standard deviation of 1 1/2 minutes, the exposure time for 60 panels can be approximated by the sum of 60 independent normal random variables. According to the properties of normal distribution, the sum of independent normal random variables follows a normal distribution with a mean equal to the sum of the individual means and a standard deviation equal to the square root of the sum of the individual variances.
Mean of 60-panel exposure time = 60 * 2 = 120 minutes
Standard deviation of 60-panel exposure time = √(60 * (1 1/2)²) = √(60 * (3/2)²) = √(270) ≈ 16.43 minutes
Repair Time:
The repair time remains the same as before, which is exponentially distributed with a mean of 4 hours.
Mean repair time = 4 hours = 240 minutes
Effective Mean and CV of Process Times:
The effective mean process time for the 60-panel job is the sum of the exposure time and the repair time:
Effective mean process time = Mean of 60-panel exposure time + Mean repair time = 120 + 240 = 360 minutes
The coefficient of variation (CV) for the 60-panel job can be calculated by dividing the standard deviation by the mean:
CV = (Standard deviation of 60-panel exposure time + Standard deviation of repair time) / Effective mean process time
CV = (16.43 + 240) / 360 ≈ 0.712
Comparing with the results in Problem 3, the effective mean process time for the 60-panel jobs has increased from 270 minutes to 360 minutes. The CV has also increased from 0.60 to 0.712. These changes indicate that the process variability has increased, resulting in longer overall process times for the 60-panel jobs compared to the single-panel exposure.
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Which equation describes how the parent function, y = x3, is vertically stretched by a factor of 4?
Oy=x³ +4
O y=(x+4)³
O. y=4x³
O y=x4
Answer: [tex]y=4x^3[/tex]
Step-by-step explanation:
See attached image.
The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The parent function is,
⇒ y = x³
Now, After vertically stretched by a factor of 4 we get;
The value of function is,
⇒ y = 4x³
Hence, The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
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Helppp please and thank uuu
What transformation is used to create this frieze pattern?
vertical reflection
glide reflection
horizontal reflection
180° rotation
Answer:
Using translation concepts, it is found that the transformation used to create this frieze pattern is a 180º rotation.
Step-by-step explanation:
A new toy comes in the shape of a regular hexagonal pyramid. The base has side lengths of 10 inches and the apothem is 5√3 inches. If the surface area is 420 + 150√3 square inches, what is the slant height?
A. 11 inches
B. 14 inches
C. 7 inches
D. 28 inches
The slant height of the hexagonal pyramid is: B. 14 inches.
What is the Area of a Regular Hexagon?Area of a regular hexagon = 3√3/2(s²)
First, find the area of the regular hexagon:
Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².
Surface area is given as 420 + 150√3 in.².
Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3
Area of the 6 triangles = 420 in.²
Area of 1 triangle = 420/6 = 70 in.²
Use the area of a triangle to find the slant height (h):
70 = 1/2(10)(h)
2(70) = 10(h)
140/20 = h
h = 14 in.
The answer is B. 14 inches.
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Help please!!! Write an equation that represents the line.
Use exact numbers.
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
Using it's concept, there is a 0.1667 = 16.67% probability of tossing a head and drawing a red marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the coin, one out of two outcomes are heads.For the marble, two out of six marbles are red.Hence the probability of tossing a head and drawing a red marble is:
[tex]\frac{1}{2} \times \frac{2}{6} = \frac{1}{6} = 0.1667[/tex]
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ABCD is a rectangle. What is the value of x
A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. which statements about the parabola are true? select two options.
The true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.
What are parabolas?Parabolas are examples of a conic section such that it is formed by the intersection of a cone with a plane parallel to its side.
How to determine the true statements?From the question, the given parameters are:
Vertex = (0,0)
Focus = Negative side of the y-axis
A parabola has quite a number of forms, one of these forms is the general form.
The general form is represented as:
(x - h)^2 = 4p(y - k)
The vertex of the parabola is
(h, k) = (0, 0).
So, we have:
(x - 0)^2 = 4p(y - 0)
Evaluate the difference
x^2 = 4py
Since the focus is on the negative side, the value of p will be negative.
Also, because the vertex is at the origin, the directrix of the parabola will cross through the positive part of the y-axis.
This means that the true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.
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Complete question
A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. Which statements about the parabola are true?
Check all that apply.
The directrix will cross through the positive part of the y-axis.
The equation of the parabola will be in the form y2 = 4px where the value of p is negative.
The equation of the parabola will be in the form x2 = 4py where the value of p is positive.
The equation of the parabola could be y2 = 4x.
The equation of the parabola could be x2 = y.
What is the formula for margin of error?
Z•√√5
√r
OME =
OME =
OME =
z. √s
Z•
77
Z•S
√n
Z S
OME= 77
The margin of error is calculated using the formula, C. ME = z × s / √n.
What is the Formula Used to Determine Margin of Error?The formula for finding the margin of error is given as: ME = z × s / √n, where we have the following:
ME = margin of error
z = z-score
s = population standard deviation
n = sample size
The margin of error is used to determine amount of error in a random sampling.
Thus, the formula is: C. ME = z × s / √n.
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Subtract the matrices. What number fills in ?
The missing number for the subtraction of matrices is 4.
How to subtract the matrices?
The subtraction of two matrices of the same size is really direct. You just need to subtract the elements that are in the same position, then:
[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] \\\\B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]\\\\A - B = \left[\begin{array}{ccc}a_{11} - b_{11}&a_{12}-b_{12}\\a_{21} - b_{21}&a_{22}-b_{22}\end{array}\right][/tex]
Then the missing therm will just be equal to the difference between the last two elements of each matrix:
-2 - (-6) = -2 + 6 = 4
The missing number is 4.
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Can any one help me?
Answer:
64
Step-by-step explanation:
2x-4y=3
x= (3 +4y)/2
substitute into the main equation
y= 0
x= 3/2
16^x /256^y
16^3/2 ÷ 256^0
√16^3 ÷1
= 64
Answer:
64
Step-by-step explanation:
2x - 4y = 3
2x = 4y + 3
x = 2y + 1.5
[tex] \dfrac{16^x}{256^y} = [/tex]
[tex] = \dfrac{16^{2y + 1.5}}{256^y} [/tex]
[tex] = \dfrac{16^{2y + 1.5}}{16^{2y}} [/tex]
[tex] = 16^{2y + 1.5 - 2y} [/tex]
[tex] = 16^\frac{3}{2} [/tex]
[tex] = 4^3 [/tex]
[tex] = 64 [/tex]
A researcher asked 520 randomly selected people of three different age groups (teen, young adult, and adult) about their favorite music genre. the two-way table displays the distribution of the responses. a 4-column table with 3 rows. column 1 has entries country, rock, oldies. column 2 is labeled teen with entries 61, 94, 15. column 3 is labeled young adult with entries 65, 84, 36. column 4 is labeled adult with entries 49, 54, 62. the columns are labeled age and the rows are labeled music. a participant is randomly selected. let c be the event that the participant prefers country music and let t be the event that the participant is a teen. what is the value of p(cc and tc)? 0.12 0.33 0.45 0.55
The value of p(cc and tc) is 0.1173
The distribution of the replies is 0.12, as shown by the two-way table.
We've done that.
520 randomly chosen individuals from the teen, young adult, and adult age groups were asked about their preferred musical genres by the researcher.
The distribution of the answers is shown in the two-way table.
There are 61 teenagers in the country.
seeing as how this is only one of 520,
The probability formula?
P(E) = (Number of favorable outcomes) = Probability of an Event (Sample space).
61/520=0.1173
We calculate 0.1173 by dividing 61 by 520 and rounding to the next hundredth to obtain 0.12.
Thus the value of p(cc and tc) is 0.1173.
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which of the following points could be added to the graph f(x)=-|x+3| to keep the graph a function?
a.(0.3) b.(-3,-6)
c. both a and b d. none of the above
None of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
How to determine the point?The equation of the function is given as:
f(x) = - |x + 3|
The points are given as:
(0, 3) and (-3, -6)
When x = 0, we have:
f(0) = - |0 + 3|
f(0) = -3 --- different y value from (0, 3)
When x = -3, we have:
f(-3) = - |-3 + 3|
f(-3) = 0 --- different y value from (-3, -6)
This means that the x values point to different y values (this does not represent a function)
Hence, none of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
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. A particular airline offers three free snack options to it's passengers: cookies, chips, and crackers. Along with the snack, passengers are offered two free drink options: soda or water. This is a tree diagram that represents the probability of customers choosing the different snack and drink options. Tree Diagram What is the value of Z
The probability that a particular passenger chooses chips and soda as a snack is 0.25 or 25%.
What is probability?In mathematics, probability is considered as the chances a specific situation or event occurs. For example, you can calculate the probability that it rains tomorrow based on general weather patterns.
How to calculate the probability of two events happenning?Calculate or identify the probability of each event happening.Multiply the probabilities of the events involved.What is the probability of Z event happnening?Probability that a person choses soda: 0.5Probability that a person choses chips: 0.5Now, let's multiply these probabilities:
0.5 x 0.5 = 0.25 or 25% (0.25 x 100)This means the probability of a passenger choosing chips and soda as a snack is 0.25 or 25%.
Note: This question is incomplete; here is the missing section:
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It has taken 3 hours to fill a 5 gallon bucket from leaky hose what is the rate in gallons per hour
Answer: 1.7
Step-by-step explanation:
The rate of gallons per hour is the same as the unit rate. You want to find out how many gallons are filled in one hour, so divide 3 down to one, 3 divided by 3 is one. Then, also divide 5 by 3. 5 divided by 3 is 1.6666... and as an hour is out of 60, round it to 1.7.
I hope this helps!
Write the equation of the line that passes through the points (-6,-3) and (-3,1)
Answer:
[tex] y = \frac{4}{3} x + 5[/tex]
Step-by-step explanation:
The slope is
[tex] \frac{ - 3 - 1}{ - 6 - ( - 3)} = \frac{4}{3} [/tex]
Substituting into point-slope form,
[tex]y - 1 = \frac{4}{3} (x + 3) \\ \\ y - 1 = \frac{4}{3} x + 4 \\ \\ y = \frac{4}{3} x + 5[/tex]
What is the probability of rolling a 4, 5, and 6, in that order, on three rolls of a single six-sided die
Answer:
1:216
Step-by-step explanation:
The probability of getting a 4 would be 1/6. The probability of getting a 5 would be 1/6 and the probability of getting a 6 would be 1/6. The bottom number is the total number of outcomes (1,2,3,4,5,6) and the top number is out of that set, how many do I want. In the case of wanting a 4, I want 1 out of those 6 numbers and so on.
Now we multiple these together 1/6 x 1/6 x 1/6 and get 1/216 or another way to write this is 1:216
Select the correct answer. Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -62 -30 -14 -6 -2 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-2, 1]? A. Only function f is increasing, and only function f is negative. B. Only function f is increasing, and both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Both functions are increasing, but function f increases at a faster average rate.
based on the given exponential functions, we can tell that C. Both functions are increasing, but function g increases at a faster average rate.
what function is increasing faster?function g is represented by the model:
g(x) = -18 x (1/3)^x + 2
g(x)=-18(1/3)^x In(1/3)
In1/3 < 0
this means that:
g (x) > 0
for any interval, g(x) > f(x)
this means that g is increasing at a faster rate than f which is increasing as shown by the table given in the question.
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Which function represents a reflection of f(x) = 2(0.35)x over the y-axis?
h(x) = 2(0.35)x
h(x) = –2(0.35)x
h(x) = 2(0.35)–x
h(x) = 2(–0.35)–x
The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
How to determine the reflection?The equation is given as:
f(x) = 2(0.35)^x
The reflection of a function over the y-axis is :
f'(x) = f(-x)
So, we have:
f(-x) = 2(0.35)^(-x)
From the list of options, we have
h(x) = 2(0.35)^(-x)
Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
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Nakeisha read 2 and 3/5 pages in 6 minutes at what rate, in pages per hour, did she read?
The rate at which she reads is 26 pages per hour
How to determine the rate?The given parameters are
Pages = 2 and 3/5
Time = 6 minutes
Convert the time from minutes to hour
Time = 6/60 hour
This gives
Time = 0.1 hour
The rate at which she reads is calculated as:
Rate = Page/Time
This gives
Rate = (2 and 3/5)/0.1 hour
Rewrite as:
Rate = 2.6 pages/0.1 hour
Divide
Rate = 26 pages per hour
Hence, the rate at which she reads is 26 pages per hour
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During the current year mute corporation expected that sell 24,600 telephone switches. fixed cost of the year were expected to be 12,147,000 the unit sales price was budgeted at 3,500 and unit variable costs are budgeted at 1,680. minutes margin of safety in units is
The corporation's margin of safety is 0.73.
What is the margin of safety?Margin of safety is the amount of sales a company makes in excess of the breakeven point.
Margin of safety = (forecasted sales - break-even sales) / forecasted sales
Break even sales = fixed cost / (price per unit - variable cost)
12,147,000 / (3500 - 1680) = 6,674.18
Margin of safety = (24,600 - 6,674.18) / 24,600 = 0.73
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You can fine the run by subtracting the __ coordinate of the lead point from that of the right point
You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point.
The "slope formula" for a straight line connecting any two locations is another name for the rise over run formula. The rise is the difference between the y-coordinates of the two locations. The run is the difference between the x-coordinates of two locations. Divide the rise by the run to find the slope.
The rise over run formula is also known as the slope formula because the fraction consists of a rise, whether the line is moving up or down, divided by the run, which can be either left or right. The slope of the line dictates the direction of the line as well as its steepness.
Thus, "You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point".
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At a sale, dresses were sold for 61% of their original price. If the dresses originally cost $200 each, how much did a dress cost on sale?
The new cost of the dress on sale given the original price is $122
PercentageOriginal cost = $200New cost = 61% of original price
= 61/100 × $200
= 0.61 × 200
New cost = $122
Therefore, the new cost of the dress is $122
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simplify: 2y(y2-4y+1)-2(4y²+5y-2) +5y-8
please tell me fast with full solution
Answer:
look the answer is in the picture and don't forget to like and brainlest
21. A triangle has vertices (1, 5), (2, 7), and (6, 5). After a reflection and a translation, the
coordinates of the image are (5,-2), (6,-4), and (10,-2). Describe the transformation.
22. Find the image of the point at (4, -7) under the translation along the vector (a, b).
Answer:
See below
Step-by-step explanation:
I am not sure about number 22. I think that they are asking you to apply the same rules to the point (4, -7), if that is what they mean, the answer is (8,10)
Of the 30 cars in a parking lot, 12 are blue, 8 are red, 6 are white, and 4 are silver. In simplest form, what are the odds in favor of a red or white car leaving first?
A. 7:8
B. 8:7
C. 1:5
D. 5:1
Answer:
Step-by-step explanation:
8+6=14
14/30 = 7/15
So the final answer is 7/15
pls thank me pls :(
Enacting a modeled response depends on your ability to reproduce the response by converting your stored mental images into overt behavior.
Answer:
??
Step-by-step explanation:
Can someone help me with this?
Need help understanding how to solve
For the two figures to be similar, the missing length must be 30.
What is the missing length?For the two figures to be similar, the dimension of each figures must be proportional to each other.
Let the missing length be x.
Hence,
x/25 = 24/20
We cross multiply
x × 20 = 24 × 25
x × 20 = 600
x = 600/20
x = 30
Therefore, for the two figures to be similar, the missing length must be 30.
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A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes
8/25 is the probability that more than 8 of them are strikes.
Lets simplify the problem,
We are given that a softball pitcher has a 0.507 probability of throwing a strike for each pitch. Also, the softball pitcher throws 15 pitches.
The above situation can be represented through Binomial distribution;
P(X = r) = 0,1,2,3,,.....
where, n = number of trials (samples) taken = 15 pitches
r = number of success = more than 8
p = probability of success which in our question is probability of
Throwing a strike for each pitch = 0.507
LET X = Number of strikes
So, it means X ~ n = 15, p = 0.507
So, Probability that more than 8 of them are strikes = P(X > 8)
P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
After putting the values in it we get,
P = 0.323
P= 8/25 approx
8/25 is the probability that more than 8 of them are strikes.
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Which equation represents a line that passes through the two points in the
table?