In the wafer fabrication process, one step is the implantation of boron ions. After a wafer is implanted, a diffusion process drives the boron deeper in the wafer. In the diffusion cycle, a ‘boat’ holding 20 wafers is put in a furnace and baked. A pilot (or test) wafer is also included. After ‘baking’, the pilot wafer is stripped and tested for resistance in 5 places.
(a) What components of variability can be estimated?
(b) and R control charts with a sample size of 5 were constructed. The control charts exhibited a definite lack of control with many OOC points on the chart. What is a better charting strategy?
(c) Why were there so many OOC points on the chart?
Answers
The components of variability that can be estimated include within-sample variability, between-sample variability, and process variability while using an Individuals (I) chart or an X-chart is a better charting strategy to address the lack of control with many OOC points on the control charts.
(a) In the given scenario, the following components of variability can be estimated:
Within-sample variability: This represents the variability within each sample of 5 resistance measurements on the pilot wafer. It provides an estimate of the measurement error or random variability associated with the testing process itself.Between-sample variability reflects the variability between different samples of 5 resistance measurements. It captures the inherent variation in the resistance measurements among other groups or batches of wafers.Process variability: This refers to the variability introduced by the diffusion process itself, including the boron ion implantation and subsequent baking in the furnace. It represents the variation in resistance measurements due to differences in the actual diffusion process.(b) and (c) Given that the control charts constructed with a sample size of 5 exhibited a definite lack of control with many out-of-control (OOC) points, it suggests that the process is not in a state of statistical control. In such cases, an alternative charting strategy should be considered. One possible strategy is to use an Individual (I) chart or an X-chart instead of an R-control chart.
An Individuals (I) chart or an X-chart plots the individual resistance measurements rather than the range of measurements (as in the R chart). This charting strategy helps detect shifts or trends in individual data points, allowing for better monitoring of process stability.
To construct an Individuals chart, follow these steps:
Collect resistance measurements from the pilot wafer for each sample of 5 measurements.Calculate the average resistance value for each sample of 5 measurements.Plot the individual resistance measurements on the chart against the sample number (or time order) to observe any patterns or shifts.Establish control limits on the chart, typically using ±3 standard deviations from the overall average or using control limits based on statistical process control (SPC) principles.Using an Individuals chart, you can better identify specific points or trends that may indicate the cause of the lack of control and take appropriate corrective actions to improve the process.
Regarding the reason for the many OOC points on the chart, it could be due to various factors, such as:
Changes in the diffusion process: If there were variations in the boron ion implantation or baking process during different cycles, it could lead to inconsistent resistance measurements and result in out-of-control points on the chart.Equipment or measurement issues: If there were problems with the furnace or the resistance testing equipment, it could introduce measurement errors and contribute to the lack of control on the chart.Environmental factors: Factors like temperature or humidity fluctuations in the manufacturing environment could impact the diffusion process and lead to inconsistent resistance measurements.Learn more about the components of variability at
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Related Questions
which of the following examples are vague questions? select all that apply. 1 point how much time did you spend waiting in line? do you generally prefer hot or cold?
Answers
How much time did you spend in line, question 1? is a direct response to the second question, "Do you like hot or cold?" is a vague query.
An inquiry that lacks focus on a particular subject area and is wide, ambiguous, unclear, and nebulous in nature. You won't be able to adequately analyze the data acquired at the end of the day if your survey has ambiguous questions.
You should use specific language in your survey questions, so make sure to do so. Additionally, make sure to refrain from using technical jargon and terminology that few people can normally grasp in your surveys.
Questions that are excessively general or insufficiently specified are ambiguous or vague. Generic responses that aren't pertinent to your research are frequently the outcome. Make sure your survey questions are written simply and in a way that respondents will find them simple to understand in an effort to avoid vague survey questions.
Typical Vague Questions
Do you believe our clients would advocate for us?
Are we superior to other ed-tech businesses?
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Which of the following statements are FALSE？
need your kind help
Answers
Find the degree of polynomial 2x⁵-10x⁴-5x²+12x⁸-6
help
Answers
Intercept is (0,-6)
Find the exact value of x.
Answers
Answer:
x =9 ,6
Step-by-step explanation:
Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
1. how many cups of water should he use with 6 scoops of fruit mix?
2. Rate needed?
3. Unit rate?
4. Interpretation of unit rate?
Answers
For per unit scoops of powdered 2 cups of Water is Needed.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given, Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
We have to find how many cups of water should he use with 6 scoops of fruit mix
Let "n" be the number of cups required for 6 scoops of fruit mix
3 cups of water ⇒ 1.5 scoops of fruit mix.
Then, n cups of water ⇒ 6 scoops of fruit mi
So, by cross multiplication,
6 * 3 = n *1.5
n = 12
Ryan has to use 12 cups of water for 6 scoops.
thus,
For per unit scoops of powdered 2 cups of Water is Needed.
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a rectangular pen is built with one side against a barn. if 2500 m of fencing are used for the oterh three sides of the pen, what dimensions maximizze the area of the pen
Answers
The dimensions that maximize the area of the pen are 1250 meters parallel to the barn and 625 meters perpendicular to the barn on both sides.
To maximize the area of a rectangular pen built with one side against a barn, you must determine the optimal dimensions for the other three sides, given a fixed amount of fencing (2500 meters). Let's denote the length of the pen parallel to the barn as "x" meters and the length of the two other sides perpendicular to the barn as "y" meters each. Since we have 2500 meters of fencing, we can express this constraint as:
x + 2y = 2500
We need to maximize the area (A) of the pen, which is given by the product of its dimensions:
A = xy
To solve this problem, we can express "y" in terms of "x" using the constraint equation:
y = (2500 - x) / 2
Now, substitute this expression for "y" into the area formula:
A = x * (2500 - x) / 2
Simplifying the equation, we get:
A = -x^2 / 2 + 2500x / 2
To find the maximum area, we must determine the value of "x" that maximizes the function A(x). To do this, we take the derivative of A(x) with respect to x and set it equal to zero:
dA/dx = -x + 2500/2 = 0
Solving for "x," we find that x = 1250 meters. Using the constraint equation, we can calculate "y" as:
y = (2500 - 1250) / 2 = 625 meters
Thus, the dimensions are 1250 meters parallel to the barn and 625 meters perpendicular to the barn on both sides.
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Solve by eliminating the fraction:
9+3/4x=7/8-10
Answers
Answer:
Exact form: \(\frac{-145}{6}\)
Decimal form: -26.16
Mixed-number form: -24 \(\frac{1}{6}\)
Step-by-step explanation:
hope this helps :)
Answer:
sxdcgfvhnjk
Step-by-step explanation:
Write the system first as a vector equation and then as a matrix equation. 5x1 + x2 - 3x3 = 8 2x2 + 4x3 = 0
Answers
The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].
To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.
To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].
We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.
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How many different ways can you arrange the letters in the word
sandworm?
O 16,777,216
O 40,320
O 64
O 36,122
hurry pls!!!
Answers
Answer: B (40,320)
Step-by-step explanation:
I am learning the same stuff.
But you take 8 to the factorial (!) and you end up getting 40,320
create a variable to hold the length of the side of the
square and assign it to 4. define
another variable to hold the area of
sqaure using the first variable, calculate the area of the sqaure
and out
Answers
The final code looks like this:var side = 4;var area;area = side * side;console.log("The area of the square is " + area);
To create a variable to hold the length of the side of the square and assign it to 4 and define another variable to hold the area of the square, using the first variable, to calculate the area of the square and output it; the code is as follows:
To define the variables and calculate the area of a square, the following steps can be followed:
Step 1: Define a variable to hold the length of the side of the square and assign it to 4. This can be done using the following code:var side = 4;
Step 2: Define another variable to hold the area of the square. This can be done using the following code:var area;
Step 3: Calculate the area of the square using the first variable. This can be done using the following code:area = side * side;
Step 4: Output the area of the square.
This can be done using the following code:console.log("The area of the square is " + area);
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what is the probability that the person selected drives a truck exercises four or more times per week?
Answers
The probability that the person selected drives a truck exercises four or more times per week is 0.633.
Define probability.The probability of an event occurring is known as probability. This might range from an occurrence being impossible to have a chance to happen to be certain for sure. Probability is measured mathematically on a scale from 0 to 1.
Given,
The person selected who drives a truck exercises four or more times per week.
P(The person selected drives a truck and exercises four or more times per week)
= 36/120 + 52/120 - 12/120
= 76/120
Simplifying,
= 19/30
= 0.633(approximately)
The probability that the person selected drives a truck exercises four or more times per week is 0.633.
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What is the answer to this?
Answers
The y-intercept of the given function is (0,-7) and the horizontal asymptote is y=−3.
The given function is f(x)=-(2)ˣ⁺²-3.
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞),{x|x∈R}
Range: (-∞,-3),{y|y<-3}
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): None
y-intercept(s): (0,-7)
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=−3.
Therefore, the y-intercept of the given function is (0,-7) and the horizontal asymptote is y=−3.
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fA= 2.3, B = 8.7 and C = 2.2, find the percentage error in evaluating A+B/C
Answers
Answer:
8.8
Step-by-step explanation:
You need to at A and B so 2.3+8.7=11. Then you take your 11 and - by C 2.2.
Hope this helps.
How do you calculate greater than less than carculator ?
Answers
In order to calculate greater than and less than values involves using logical operations to compare two values and determine if they are equal, greater than, or less than.
In mathematics, logical operations are used to compare two values and determine if they are equal, greater than, or less than. The most common logical operations used in greater than less than calculations are the "greater than" symbol (>) and the "less than" symbol (<).
When comparing two values, we can use the following logical operations:
Greater than: If the first value is greater than the second value, we write the "greater than" symbol (>). For example, 5 > 3 means that 5 is greater than 3.
Less than: If the first value is less than the second value, we write the "less than" symbol (<). For example, 3 < 5 means that 3 is less than 5.
Equal to: If the first value is equal to the second value, we write the "equal to" symbol (=). For example, 5 = 5 means that 5 is equal to 5.
To use a greater than less than calculator, you simply input two values, and the calculator will perform the logical operation to determine if the first value is greater than, less than, or equal to the second value.
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The price p of a pizza is $6. 95 plus $0. 95 per topping t on the pizza, write a function rule
Answers
Answer:
p = 6.95 + (0.95 × t)
Step-by-step explanation:
What is a function rule?A function rule explains how to convert an input value (x) into an output value (y) for any given function.
p = 6.95 + (0.95 × t)Why do we do this?To get the total price (p) we need to add the cost of the pizza itself, and add each topping. The part of the equation (0.95 × t) can solve for the price of each topping, so we add that on.
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
Answers
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
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Time left 2:09:2 Cabury's produces 5000 chocolates bars in day with 4 staff, a day is considered 8 hours( total payroll is $200/day). It's daily overhead expense is $400. What is the multi-factor productivity Select one: O a. 625 bars/hr O b. 25 bars/$ O c. 8.3 bars/$ O d. 700 bars/hr O e. 12.5 bars/$
Answers
The multi-factor productivity of Cadbury's can be calculated by dividing the output (number of chocolate bars produced) by combined input factors (labor and overhead expenses). Correct answer is (c) 8.3 bars/$.
Multi-factor productivity measures the efficiency with which multiple inputs are used to produce a certain output. In this case, we need to calculate the productivity of Cadbury's by considering the number of chocolate bars produced and the combined input factors of labor and overhead expenses.
The number of chocolate bars produced in a day is given as 5000. Since a day is considered 8 hours, we can calculate the production rate per hour by dividing the total number of bars by the total hours:
5000 bars / 8 hours = 625 bars/hr. Therefore, option (a) 625 bars/hr is incorrect.
The combined input factors include the labor cost and the overhead expense. The labor cost per day is $200, and since there are 4 staff members, each staff member's cost would be $200 / 4 = $50. The overhead expense is given as $400 per day. Therefore, the total input cost is $400 (overhead) + $200 (labor) = $600.
To calculate the multi-factor productivity, we divide the output (number of bars) by the input cost: 5000 bars / $600 = 8.3 bars/$. Hence, the correct answer is (c) 8.3 bars/$, representing the multi-factor productivity of Cadbury's.
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Why do you think wars cause periods of high inflation
Answers
Answer:
because countrys are printing money because they dont have a lot
Step-by-step explanation:
due to the smoke
Step-by-step explanation:
by so much gun fire from canons and bombs so much smoke and destruction in the air will cause high inflation
Tommy thought of a number. He multiplied the number 4, then added six. The result was fifty. What was Tommy's starting number?
Answers
Answer:
Was number 11
Step-by-step explanation:
50 - 6 = 44
44 dividid 4 is 11
The bridge to cross the Neches River between Evadale and Silsbee is a toll bridge. It cost cars $3 to cross and trucks $5 to cross. Last Saturday a total of 76 cars and trucks crossed the bridge and the total tolls charged was $276. How many trucks crossed the bridge?
Answers
Answer:
48? because you take 76 times 3 showing how many cars there are which is 228 then subtract 276 from 228 and boom there's your answer
solve this equation
i am having a hard time doing so
k(t) = 10t - 19
Answers
Answer: k = \(\frac{10 - 19}{t}\)
Step-by-step explanation:
k(t) = 10t - 19
\(\frac{k(t)}{t}\) = \(\frac{10t - 19}{t}\)
k = \(\frac{10 - 19}{t}\)
hope this is correct/helps!
an automobile speedometer with circular scales reading both miles per hour and kilometers per hour is shown. what speed is indicated in kilometers per hour?
Answers
The
speed
indicated in kilometers per hour is 85 km/h, as shown on the circular scale of the automobile
speedometer
.
The automobile
speedometer
is an instrument that measures the speed of a vehicle. It has a circular
scale
that reads both miles per hour (mph) and kilometers per hour (km/h). To determine the
speed
in kilometers per hour, the user must first locate the needle on the scale. The needle should be pointing to a specific number that corresponds to both mph and km/h. For example, if the needle is pointing to 85, then the speed indicated in kilometers per hour is 85 km/h. It is important to note that if the needle is located between two
numbers
, the user should determine the approximate speed by interpolating the two numbers. To find the speed in miles per hour, the user can simply look at the number that corresponds to the needle on the scale. In this case, the speed indicated in miles per hour is 53 mph.
The complete question: An automobile speedometer with circular scales reading both miles per hour and kilometers por hour is shown. What speed is indicated in miles per hour? 100 120 140 80 160 *60 180 200 40 20 220 Own 240 Express your answer in miles per hour v.2 mph
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speedometer
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i don't understand the second part (see photo)
Answers
Answer:
Step-by-step explanation:
Prime numbers has only two factor 1 and the number itself
Here, 2 , 3 prime factors
36 = 2 * 2 * 3 * 3
which points of concurrency are always inside the triangle?
Answers
Answer: The centroid is the point of concurrency of the three medians in a triangle. It is the center of mass (center of gravity) and therefore is always located within the triangle.
Perpendicular bisectors: acute/right/obtuse …… ...
Construction: Location of Point of Concurrency
Explanation: The point of concurrency is the point where three or more lines, segments, or rays intersect forming a point. Out of the four namely the Centroid, Incenter, Circumcenter, and Orthocenter, only the Centroid and Incenter is always located inside the triangle.
Centroid: where the medians intersect.
Incenter: where the angle bisectors intersect.
Step-by-step explanation. Hope this helps lol!
Select two ratios that are equivalent to 2:92:92, colon, 9.
Answers
Answer:
The only options equivalent to 2:9 are B and C. A ratio is a comparison between two or more numbers
Step-by-step explanation:
Answer:
B and C
Step-by-step explanation:
what is the difference between the mean and median of 3,8,10,15
Answers
Answer:
Ok, so. You can think of the mean being acually mean because you have to do more work. When solving for the mean you add all the answers together then divide by the amount of numbers you have. For example, you have the numers (1, 2, 3) add them together (1+2+3) to get 6 then divide by 3 (6/3) to get a mean of two. The median is also fairly easy to remember. You line your numbers up least to greatest, left to right. and mark one off of each side at a time. If you have a even amount of numbers and reach the center, you add the two centers together then divide by to to get the median. If you have an odd amount of numbers, there should be one in the exact center left over.
Step-by-step explanation:
Mean) 3+8+10+15=36, 36/4=9 ANSWER=9
Median) 8+10=18, 18/2=9 ANSWER=9
In the case, the mean and median are the same and depending on context you could choose either method. It also helps that there is no outlyer. If there were on I would recomend finding the median.
R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of R when A = 5.
b) Work out the value of A when R = 9
Answers
The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.
What is the value of R when A equal 5 and value of A when R equal 9?Proportional relationships are relationships between two variables where their ratios are equivalent.
If R is inversely proportional to A.
R ∝ 1/A, then
R = k/A
Where k is the proportionality constant.
Given that;
R = 12 A = 1.5Proportionality constant k = ?First, we determine the proportionality constant.
R = k/A
Plug in R = 12 and A = 1.5 and solve for k
k = R × A
k = 12 × 1.5
k = 18
a) The value of R when A = 5 will be;
R = k/A
R = 18 / 5
R = 3.6
b) The value of A when R = 9
R = k/A
R × A = k
A = k/R
A = 18 / 9
A = 2
Therefore, the value of A when R equal 9 is 2.
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The population of a country has been increasing for several decades. In 1990, the population was about 233 million people. In 2014, the population was about 291 million people. Determine the percent increase in the country's population during this time period.
Answers
Answer:
the answer for this question is increase 24.89%
Step-by-step explanation:
100%= 233 million
? = 291 million
100%/(233×10^6) : x/(291×10^6)
x=[100%×(291×10^6)]/(233×10^6)
x=124.8927039
x=124.89
124.89%-100%=24.89%
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)^2= 19
Answers
The solutions to the equation (3x - 5)²= 19 are: - \(\frac{\sqrt{19} + 5}{3}\) and \(\frac{\sqrt{19} + 5}{3}\) .
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
In this question we have been given an equation that is (3x - 5)²= 19
Now taking square root both sides
(3x - 5)² = 19
3x - 5 = ± \(\sqrt{19}\)
Add 5 to both sides to make equation simpler
3x = ± \(\sqrt{19}\)+ 5
Divide both sides by 3
x = ±\(\frac{\sqrt{19} + 5}{3}\)
Now separating the solutions we get
x = \(\frac{\sqrt{19} + 5}{3}\) .
x = - \(\frac{\sqrt{19} + 5}{3}\) .
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The manager of a snack bar buys bottled water in packs of 35 and candy bars in packs of 20. Then, she sells the items individually. Yesterday, she bought the same number of water bottles as candy bars to sell at the snack bar. If she bought the lowest number of items possible, how many packs of each item did she buy? 5 packs of bottled water and 5 packs of candy bars 4 packs of bottled water and 7 packs of candy bars 8 packs of bottled water and 14 packs of candy bars 20 packs of bottled water and 35 packs of candy bars
Answers
Answer:
8 packs of bottled water and 14 packs of candy bars
Step-by-step explanation:
Provided,
Each pack of water bottles = 35 bottles
Each pack of candy = 20 candy
Since quantity of candy in each pack is small than quantity of water bottle in each pack, in order to have same quantity in numbers of both bottles and candies,
Purchase quantity of candy packs shall be more than the pack of water bottles.
Further, with this option 1 and 2 are not valid as candy packs are same or less than packs of water bottle.
In option 3 and 4, option 3 have smaller quantities as provided manager bought the least possible quantity.
Accordingly
Option 3
8 packs of water bottle = \(8 \times 35 = 280 \ water\ bottles\)
14 packs of candy = \(14 \times 20 = 280 \ candies\)
Since the quantities of water bottles and candies are same this is an opt answer.
C. 8 packs
Step-by-step explanation: