what is the probability of a defect when the lower and upper specification limits are 3 standard deviations away from the mean?

Answer:

2⁵ / ( 2²)⁵

2⁵ / (2×2)⁵

2⁵ / ( 4 )⁵

2⁵ / 4⁵

32 / 1024

4 / 128

1 / 32

0.03125

Median is the appropriate measure of centre to identify which coffee shop normally sells the most coffee per hour, and the findings reveal that Wide Awake is the coffee shop that typically sells the most coffee per hour.

We must contrast the central tendency measures of the two datasets to identify which coffee shop normally sells the most coffee per hour. The mean and the median are our two available measurements of central tendency.

By adding up all the values and dividing by the total number of values, the mean—the average value of the data—is determined. When values are ordered in order, the median is the middle value in the dataset.

When we compute the mean and median for both coffee shops, we obtain:

Mean = (1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5 + 9.5 + 3 + 5) / 12 = 6.125 gallons of coffee ground

Average: 5 gallons

Mean = (2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 15 + 5 + 2.5) / 10 = 6.5 gallons while wide awake.

4.5 gallons is the median.

We can see from the figures above that the mean values for both coffee shops are nearly equal, with Coffee Ground's mean being slightly lower at approximately 5 gallons compared to Wide Awake's mean at about 6.5 gallons. Yet, the median value for Wide Awake is 4.5 gallons as opposed to 5 gallons for Coffee Ground.

When there are outliers in the data or when the distribution is skewed, the median is a better indicator of central tendency to utilize. Given that the datasets are tiny and contain outliers, the median is a more appropriate measurement in this situation. We can infer from the median numbers that Wide Awake normally sells the most coffee each hour.

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Answer:

Whichever equation has a slope of 5/7.

Step-by-step explanation:

Parallel lines will always share the same slope. The slope is found by denoting where the variable m is at. It is noteworthy of the placement of m in the given slope equation:

y = mx + b

Therefore, whichever choice(s) have 5/7 as a slope would be your answer.

~

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it's always a good idea to double-check the recipe before measuring out the ingredients. Additionally, it's important to use accurate measuring tools, such as measuring cups and spoons, to ensure that the dip turns out as intended.

How to calculate the problem?

Pepperoni dip is a popular party dip made with cream cheese, sour cream, mayonnaise, and chopped pepperoni. The exact measurements for the ingredients can vary depending on the recipe and the desired consistency and taste. However, a typical recipe might call for:

8 oz cream cheese, softened

1/2 cup sour cream

1/2 cup mayonnaise

1 cup chopped pepperoni

To convert these measurements to improper fractions, we can use the fact that 1 cup is equivalent to 8 fluid ounces. Therefore, the measurements in improper fractions are:

8/1 (or simply 8) ounces of cream cheese

1/2 cup = 4 fluid ounces of sour cream

1/2 cup = 4 fluid ounces of mayonnaise

1 cup = 8 fluid ounces of chopped pepperoni

It's worth noting that some recipes may use different measurements or units, such as teaspoons or tablespoons, so it's always a good idea to double-check the recipe before measuring out the ingredients. Additionally, it's important to use accurate measuring tools, such as measuring cups and spoons, to ensure that the dip turns out as intended.

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Your complete question is :-What are the measurements for the ingredients in pepperoni dip? Use improper fractions when needed.

We are given the system of equations:

p = d + 3 ----(1)

p + 2d = 10.50 ----(2)

We can use substitution to solve for the variables. From equation (1), we can see that p = d + 3. We can substitute this expression for p in equation (2) to get:

(d + 3) + 2d = 10.50

Simplifying this equation, we get:

3d + 3 = 10.50

Subtracting 3 from both sides, we get:

3d = 7.50

Dividing both sides by 3, we get:

d = 2.50

Now that we know the value of d, we can substitute this back into equation (1) to solve for p:

p = d + 3

p = 2.50 + 3

p = 5.50

Therefore, the solution to the system is p = 5.50 and d = 2.50.

In order to be certain that the probability of at least one occurrence of each of the six faces of the die is greater than 0.99, you would need to toss the die a minimum of[tex]6 x 5 x 4 x 3 x 2 = 720[/tex] times.

For example, if you tossed the die 6 times, the probability of at least one occurrence of each of the six faces is 0.54. This probability increases with each additional toss, reaching 0.99 after 720 tosses.

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Answer:

80

Step-by-step explanation:

edge 2023

The probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes, assuming a population standard deviation of 1.5 minutes and using the Central Limit Theorem, is approximately 0.881 or 88.1%.

Since we have a sample size of 50, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean. We know that the population standard deviation is 1.5 minutes. Therefore, the standard error of the mean is:

SE = σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212

To find the probability that the mean time spent reading is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean (which is not given, but we can assume is equal to the sample mean of 25), and SE is the standard error of the mean calculated above.

So, for the lower bound of 24.7 minutes:

z = (24.7 - 25) / 0.212 ≈ -1.42

And for the upper bound of 25.5 minutes:

z = (25.5 - 25) / 0.212 ≈ 2.36

We can then use a standard normal distribution table or calculator to find the probability that z is between -1.42 and 2.36, which represents the probability that the sample mean is between 24.7 and 25.5 minutes:

P(-1.42 < z < 2.36) ≈ 0.881

Therefore, the probability is 0.881 or 88.1%.

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Answer:

.............

Step-by-step explanation:

.............

Answer:

perimeter = 96.8 m

Step-by-step explanation:

the sides of a square are congruent , then perimeter (P) is calculated as

P = 4s ( s is the side length )

the area (A ) of a square is calculated as

A = s²

given A = 585.64 , then

s² = 585.64 ( take square root of both sides )

s = [tex]\sqrt{585.64}[/tex] = 24.2

Then

P = 4 × 24.2 = 96.8 m

Answer:

= 96.8 m

Step-by-step explanation:

Area of a square = side²

Perimter of a square = 4*side

Then:

585.64 = side²

√585,64 = √side²

it is a geometric figure, therefore, only the positive value will be obtained

24.2m = side

Perimeter = 4*side

Perimeter = 4*24.2

The constant percent rate of change in the exponential function [tex]f(x) = 2(3)^x[/tex] is 200%, indicating a doubling of the output value for each unit increase in the input value.

The equation [tex]f(x) = 2(3)^x[/tex] represents an exponential function. Exponential functions have a constant percent rate of change, which means that the percent change between any two points on the graph of the function is the same.

In this case, we can find the percent rate of change by calculating the ratio of the output values for any two input values that differ by 1. For example, if we compare the output value when x=1 to the output value when x=0, we get:

[tex]f(1) = 2(3)^1 = 6[/tex]

[tex]f(0) = 2(3)^0 = 2[/tex]

The percent change from x=0 to x=1 is:

percent change = (f(1) - f(0)) / f(0) x 100%

= (6 - 2) / 2 x 100%

= 200%

This means that the output value increased by 200% when the input value increased by 1. We can also express this as a constant percent rate of change by dividing the percent change by the change in input value:

constant percent rate of change = percent change / change in input value

= 200% / 1

= 200%

Therefore, the equation [tex]f(x) = 2(3)^x[/tex] has a constant percent rate of change of 200%.

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Answer:

10 inches

Step-by-step explanation:

If the original figure has a height of 25 inches and it was photocopied at a scale of 40%, we can find the new height of the figure by multiplying the original height by the scale factor:

new height = 25 inches x 0.4

new height = 10 inches

Therefore, the new height of the figure is 10 inches.

Answer:

Wassup

Step-by-step explanation:

By multiplying the initial height by the scale factor, which is 40% or 0.4 in decimal notation, the new height of the image can be calculated.

New height: 25 inches times 0.4 to equal 10 inches.

The figure's revised height is 10 inches as a result.

Answer: C

Step-by-step explanation:

Area of Square = [tex]l^2[/tex]
Area of Rectangle = [tex]lw[/tex]

Square A = [tex]l^2[/tex]

6 = [tex]l^2[/tex]

[tex]l[/tex] = 2.449

Rectangle B = [tex]lw[/tex]

5 = 2.449 x [tex]w[/tex]

[tex]w[/tex] = 2.0008

For Square C, [tex]l[/tex] = [tex]w[/tex]

Square C = [tex]l^2[/tex]

Square C = 2.0008²

Square C = [tex]\frac{25}{6}[/tex] OR 4.166

The new coordinates for the function g(x) at the point (1,6) are (1,5).

What is coordinates ?

Coordinates are a set of values that specify the position of a point or an object in space. They are used to locate points in a plane or in three-dimensional space. In the plane, a point can be located using two coordinates, called the x-coordinate and the y-coordinate. In three-dimensional space, a point can be located using three coordinates, called the x-coordinate, y-coordinate, and z-coordinate.

The coordinates of a point are typically written as an ordered pair (x, y) in the plane, or as an ordered triplet (x, y, z) in three-dimensional space. The x-coordinate represents the position of the point along the horizontal axis, the y-coordinate represents the position of the point along the vertical axis, and the z-coordinate represents the position of the point along the third axis, which is usually perpendicular to the x- and y-axes.

To find the new coordinates for the function g(x) given that the point (1,6) is on the graph of y = f(x), we can substitute x = 1 and y = 6 into the equation for g(x) and simplify:

g(x) = 2f(1/3(x-1)) + 5

g(1) = 2f(1/3(1-1)) + 5

g(1) = 2f(0) + 5

g(1) = 2f(0) + 5(1)

g(1) = 2f(0) + 5

Since the point (1,6) is on the graph of y = f(x), we know that f(1) = 6. To find f(0), we can use the fact that the function passes through the origin (0,0) because:

g(1) = 2f(0) + 5

g(0) = 2f(-1/3) + 5

Since the point (1,6) is on the graph of y = f(x), we can use it to find the value of f(1/3) as follows:

(1,6) is on the graph of y = f(x)

so f(1) = 6

and 1/3(1-1) = 0

This means that the point (1/3, f(1/3)) is on the graph of y = f(x). Therefore, we can use the transformation in g(x) to find the new y-coordinate for g(1) as follows:

g(1) = 2f(1/3(1-1)) + 5

g(1) = 2f(0) + 5

g(1) = 2(0) + 5

g(1) = 5

Therefore, the new coordinates for the function g(x) at the point (1,6) are (1,5).

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The data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

The mean is a measure of central tendency that represents the average value of a set of numbers. There are different types of means, including the arithmetic mean , the geometric mean , and the harmonic mean.

The spread of data refers to the variability or dispersion of a set of values. It provides information about how spread out or clustered the data is. A set of data can have a high or low spread, depending on the range of values and how they are distributed.

In the given question,

The spread of a data set refers to how much the individual data points in the set vary from each other. There are several measures of spread that are commonly used, including the range, variance, and standard deviation.

To find the spread of the data set {4, 2, 6, 10, 8, 0}, we can calculate the range, which is the difference between the maximum and minimum values in the set. The maximum value in the set is 10, and the minimum value is 0, so the range is:

Range = maximum value - minimum value = 10 - 0 = 10

Therefore, the spread of the data set is 10.

In other words, the data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

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Answer:

Its 6

Step-by-step explanation:

Did the test

58 degrees at m24 as angles are congruent since they are vertical angles visible in the diagram.

In geometric, an angle is a figure made up of two rays that share a vertex and are referred to as the side of the angle. An angle's measurement is the degree of rotation required to turn a single rays around the vertex till it crosses the other ray. Angles are commonly expressed as degrees or radians.

given

Angles 24 and 25, which are congruent since they are vertical angles, are visible in the diagram. We know that: since angle 25 is marked as 58 degrees

m24=m25=58 degrees

The measurement of 24 is thus:

58 degrees at m24 as angles are congruent since they are vertical angles visible in the diagram.

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Since the outputs of -5 and 1, and -1 and 7, are not equal, we can conclude that f is injective.

In mathematics, a function is a rule that assigns a unique output value to each input value in a given set. The input values are also known as the domain of the function, while the output values are known as the range. A function can be thought of as a machine that takes an input and produces an output. For example, a simple function could be doubling a number. In this case, the input is the number to be doubled, and the output is the result of doubling that number.

Here,

To determine if a function is injective, we need to check whether different inputs produce different outputs. In other words, if for any two distinct inputs x and y, f(x) is not equal to f(y), then the function is injective.

Let's examine the table of values for the function f:

× -5 -3 -1 0 3 5

f(×) 1 3 7 3 2 4

We can see that f(-5) = 1, f(-3) = 3, f(-1) = 7, f(0) = 3, f(3) = 2, and f(5) = 4.

Since the outputs of -5 and 1, and -1 and 7, are not equal, we can conclude that f is injective. Therefore, for this function, no two distinct inputs produce the same output.

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Complete question:

A function f is expressed through a table of values. Determine if f is injective:

× -5 -3 -1 0 3 5

f(×) 1 3 7 3 2 4

Answer:

true

Step-by-step explanation:

3.5*2.5-6=2.75

2+0.75= 2.75

It is proven true.

Using division, we can find that he must sell 2123 pairs to get a profit of $69840.

One of the four fundamental operations in mathematics is division, along with addition, subtraction, and multiplication. The splitting of a large group into smaller groups so that each group contains an equal number of items is a straightforward definition of division. It is a mathematical process used for equitable grouping and distribution.

Here,

Profit by selling one pair of shoes = $80.

Now, expenses = $100,000

Total profit he wants = $69,840.

So, total revenue to be generated = 100000 + 69840

= $169840.

Let x be the total pairs sold.

So, x = 169840/80

= 2123.

Therefore, he must sell 2123 pairs to get a profit of $69840.

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The measure of angle P = 67.38, calculated the trigonometric function value, we get the same answer.

We have all sides of the triangle, so we can calculate the trigonometric function value of angle P :

sin P = 12/13 ≈ 0.9231

Since △PQR is a right-angled triangle, we can use the cosine or sine or tan rule to find the ∠P

1) Sine

sin ∠P = opposite/ hypotenuse = 12/13

∠P = sin −1 (12/13) = 67.38

(2) Cosine

cos ∠P = adjacent/ hypotenuse = 5/13

∠P = cos−1 (5/13) = 67.38

(3) tan

tan ∠P = opposite/ adjacent = 12/5

∠P = tan−1 (12/5) = 67.38

Hence, as you can see that whichever rule is being used, the answer will always be the exact same.

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The new number that was added to the set is 74 by using mean formula for some numbers.

Let's begin by determining the mean of a set of numbers using the following formula:

average = (sum of numbers) / (number of numbers)

We can write: since we know that the mean of 21 numbers is 30.

/ 21 = 30 = (sum of 21 numbers)

Multiply LHS and RHS by woth 10:

sum of 21 digits equals 630

The new mean will now be determined by adding a new number to the set. Let's call the new number x since we don't yet know its value. We can write: 32 = (sum of 21 numbers + x) / 22 since we also know the new mean is 32.

The result of adding the two sides together is: total of the 21 numbers plus x = 704

We may change the equation to read 630 + x = 704 as we already know the sum of the original 21 values is 630.

630 is subtracted from both sides, giving us:

x = 74

74 is the new number that was so added to the collection.

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(a) The standard error of the mean is 129. (b) The probability that the sample mean will be more than $27,175 is 0.50 (c) The probability that the sample mean will be within $1,000 of the population mean is 0.955. (d) The probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100 is 0.999.

(a) The standard error of the mean is the square root of the population standard deviation divided by the sample size, which in this case is 7,400/57 = 129.12. The value of the standard error of the mean is therefore 129 (rounded to the nearest whole number).

(b) To find the probability that the sample mean will be more than $27,175, you can use the Z-score formula. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175)/129 = 0. The probability that the sample mean will be more than $27,175 is 50%, since the probability of any Z-score of 0 is 0.50.

(c) To find the probability that the sample mean will be within $1,000 of the population mean, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/129 = ±7.8. The probability that the sample mean will be within $1,000 of the population mean is 95.5%, since the probability of any Z-score of ±7.8 is 0.955.

(d) To find the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/74 = ±13.5. The probability that the sample mean will be within $1,000 of the population mean is 99.9%, since the probability of any Z-score of ±13.5 is 0.999.

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The two pieces of information which are needed to determine the critical f-value are "degrees of freedom" and "alpha level".

The critical f-value is defined as the threshold or cutoff value used to determine whether an obtained F-value is statistically significant or not.

To determine the critical f-value, we need two pieces of information:

(i) The degrees-of-freedom for numerator and denominator of the F-distribution.

These are denoted as df₁ and df₂, respectively. The degrees of freedom depend on the sample sizes and the number of groups being compared.

(ii) The alpha-level : This is the probability of making a "Type I" error, or rejecting the null hypothesis when it is actually true.

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The solution to the given inequality expression is: x ≥ -8 and it is shown on the number line attached

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle. An open circle shows it does not include the value. A closed circle shows it does include the value.

We are given the inequality expression as:

8x - 4 ≥ -68

Add 4 to both sides to get:

8x ≥ -64

Divide both sides by 8 to get:

x ≥ -8

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Answer:

1) car speed = 1.05km/minute

2) 5.25 km in 5 minutes

Step-by-step explanation:

1) [tex]\frac{63km}{60minutes}=1.05km/minute\\[/tex]

2) 1.05 km × 5 minutes = 5.25 km

Answer:

Step-by-step explanation:

process =63/60=1.05m/min

Consider concert tickets as a long-term savings objective.Therefore, the answer is A.

Savings refers to anything that existing at any given moment, a stock variable, whereas saving refers to an action occurring over period, a flow variable. Even seasoned economists and financial experts frequently refer to "saving" for "savings" due to the widespread misunderstanding of this distinction.\

Saving for a concert is not a long-term savings goal because it is a short-term financial goal. Long-term savings goals typically involve saving money for events or expenses that will occur several years or even decades in the future, such as college, a down payment on a house, or retirement. Saving for a concert is unlikely to take more than a few months or a year, so it is not a long-term goal.

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Answer:

length = 10 in

width = 8 in

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Then:

36 = 2(h + w)          Eq. 1

h = 2 + w                 Eq. 2

h = length

w = width

From Eq. 1

36/2 = h + w

18 = h + w              Eq. 3

Replacing Eq. 2 in Eq. 3

18 = (2+w) + w

18 = 2 + 2w

18 - 2 = 2w

16 = 2w

16/2 = w

w = 8

From Eq. 2

h = 2 + w

h = 2 + 8

h = 10

Check:

from Eq. 1:

36 = 2(h + w)

36 = 2(10 + 8)

36 = 2*18

Answer:

its A) true

Step-by-step explanation:

they are adjacent because they are next to each other

The value of the function f at t = 7, will be 11.

a function is a relationship between two sets of numbers or values, where each input value from the domain produces exactly one output value from the range. This relationship can be represented by a graph, an equation, or a table.

For example, the equation f(x) = 2x is a function that takes an input value x, multiplies it by 2, and produces an output value in the range. If we input x = 3 into this function, we get f(3) = 2

The function is given as,

f = 2t – 3

At t = 7, the value of the function f will be.

f = 2 x 7 – 3

f = 14 – 3

f = 11

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The complete question is;

Find the output, f, when the input, t, is 7. f = 2t - 3