Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, a total of 135 items were found to be defective.
What is an estimate of the proportion defective when the process is in control (to 3 decimals)?
What is the standard error of the proportion if samples of size 100 will be used for statistical process control (to 4 decimals)?
Compute the upper control limit and lower control limit for the control chart (to 4 decimals, if necessary)?

The equation that can be used to model the total time y for number of chimes is y = 2x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, it takes Ernest's grandfather clock 2 seconds to chime.

Therefore, the equation that can be used to model the total time y for number of chimes x will be:

y = 2 × x

y = 2x.

The equation is y = 2x.

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The relationship shows a ratio.

What is a relationship?

A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.

How can one tell whether a relationship is a function?

A function is described as having one and only one output for each input value. In this case, the output values are referred to as the range and the input values as the domain.

In the rate the unit of two variables are different. In the ratio the unit of the variable is the same.

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The value of the expression (f * g) by using two ways that is by direct integral and by Laplace transform is equal to (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C.

To compute the convolution of f(t) and g(t) by directly evaluating the integral in the definition of the convolution, we have:

(f * g)(t) = ∫f(w)g(t-w)dw

Substituting in the expressions for f(t) and g(t), we have:

(f * g)(t) = ∫e^w*e^(-6)(t-w)dw

This integral can be evaluated as follows:

(f * g)(t) = ∫e^(-5w)dw

(f * g)(t) = (-1/5)e^(-5w) + C

(f * g)(t) = (-1/5)e^(-5w) + C

To compute the convolution of f(t) and g(t) by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t), we have:

F(s) = L{f(t)} = ∫f(t)e^(-st)dt = ∫e^t*e^(-st)dt = 1/(s-1)

G(s) = L{g(t)} = ∫g(t)e^(-st)dt = ∫e^(-6t)*e^(-st)dt = 1/(s+6)

Therefore,

F(s)G(s) = (1/(s-1))(1/(s+6)) = 1/(s^2-1)

To find the inverse Laplace transform of F(s)G(s), we use the following formula:

L^-1{F(s)G(s)} = ∫F(s)G(s)e^st ds

Substituting in the expression for F(s)G(s), we have:

L^-1{F(s)G(s)} = ∫(1/(s^2-1))e^st ds

This integral can be evaluated as follows:

L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C

L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C

Thus, the convolution of f(t) and g(t) can be computed either by directly evaluating the integral in the definition of the convolution or by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t). In both cases, the result is:

(f * g)(t) = (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C

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Answer:

c. between 4&5 and -1&0

Step-by-step explanation:

Answer:The only rational root of x3−3x2+4x−12=0 is 3.

Step-by-step explanation:

{1,−1,2,−2,3,−3,4,−4,−6,12,−12} , if at least one root is rational.

hope this helps

The issue with this model is that purchases with a cost of $30 appear to be negative, which is impractical in real-world situations.

This is due to the model's linear best fit line's potential for being inaccurate for the end points.

A linear probability model:

Purchasei = 1.7-0.06×pricei

For an increase in $20 in price,

Change in purchase = -0.06 × 20

change in purchase = -1.2

There would be 1.2 less purchase.

Purchase at price of $10 is:

Purchase 10= 1.7 ×0.06 × 10

Purchase 10 = 1.1

Purchase at price of $30 is:

Purchase 30 = 1.7 × 0.06 × 30

Purchase 30 = -0.1

This is the problem with this model that the purchases at price of $30 is coming as negative which is not possible in practical situation.

It is because that the linear best fit line of the model which might not be accurate for the end points.

Hence we get the required estimates here:

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A vertex is a point where two or more curves, lines, or edges meet.

In geometry, vertex generally refers to an intersection point or a corner where lines, curves or edges meet. As a consequence of this definition, the point where two lines meet to form an angle called an included angle are considered vertices. Hence, the corners of triangle, polygons and polyhedral are vertices. For example, the lines of square or rectangle intersect at four corners which are called its vertices (which is the plural of vertex). Similarly, the vertex of curve(s) is where they intersect with each other or with its line of symmetry.

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The flux of the given sphere as calculated from the data is, flux= 5πa³/6.

We can use spherical coordinates for this sphere with radius r=ar =a.

The surface can then be described using the parametric equation as

r(θ,Ф)= acosθsinФi + asinθsinФj + acossθk

The partial derivatives of this parametric function with respect to its parameters are,

r ϕ​=acosθcosϕi+asinθcosϕj−asinϕk

r θ=−asinθsinϕi+acosθsinϕj

​

Therefore,

the cross product will be ,

ndσ=a²[cosθsin²ϕi+sinθsin²ϕj+sinϕcosϕk]dϕd

In these coordinates

F = 5zk = 5acosФk

therefore on integrating we get ,

flux= 5πa³/6

Flux is a physics term that refers to the number of electric or magnetic field lines that pass through a surface in a given amount of time. Field lines provide a visual representation of the magnitude and direction of the field being measured.

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​

Answer:

3

Step-by-step explanation:

Figure A is a dilation of Figure B by a factor of 3

That means that Figure A is 3 times larger than Figure B.

From Figure B to Figure A, the scale factor is 3.

Answer:

The answer is 13.2

Step-by-step explanation:

d = 10

e = 3.2

d + e = 10 + 3.2 = 13.2

Thus, The answer is 13.2

The statement which is true about triangle inequalities is that the sum of the lengths of the 2 sides of a triangle is equal than the third side of the triangle.

In Euclidean geometry, triangle inequalities are a theorem which states that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In shorts, the theorem states that the shortest distance between two points is a straight line.

If the length of a side is equal to the sum of the other two sides, then the vertices have to be colinear, meaning that the three sides form a line segment rather than a triangle. This is called the triangle inequality.

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The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.

Standard deviation

In statistics, standard deviation refers  the square root of variance by determining each data point's deviation relative to the mean.

Given,

Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.

And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80

Here the standard deviation of the sample distribution is calculated as,

=> σₓ = √1.80 = 1.34

Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.

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The probability of getting a tails and a number less than 3 is equal to 1/6.

As given in the question,

Probability of getting heads or tail is:

P (H) = P(T) = 1/2

The probability of getting any number on the die is:

P (1) = P (2) = P(3) = P (4) = P (5) = P (6) = 1/6

The probability of getting a tail on the coin and a number less than 3 on the die is:

P(tails and a number less than 3) = P(tails) x P( a number less than 3)

= 1/2 x [P(1) +P(2)]

= 1/2 x [1/6 +1/6]

= 1/6.

Therefore ,the required probability of getting tails and a number less than 3 is  equal to 1/6.

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From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271  .

6 out of 10 Niceville residents shop at Walmart

So, the probability of shopping at Walmart (p) is = 6/10 = 0.6

The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .

The number of members in the group is(n) = 15 ;

We have to find the probability that, at least thirteen of them shop at Walmart

By the Binomial Probability Distribution,

we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ

So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)

Substituting the values of a , n and p and q ,

We get ;

= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰

= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰

= 0.0219 + 0.0047 + 0.0004

= 0.0271

Therefore, the required probability is 0.0271

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The additional jump in inches that John must make to beat the record is

5 1/4 inches

The problem is solved by converting the given dimensions in ft to  inches

conversion to inches is solved using

12 inches = 1 ft

The record jump is

= 23 feet 1 3/4 in

= 23 * 12 + 1 3/4 in

= 276 + 1 3/4

= 277.75 in

John's best long jump

= 22 ft 8 1/2 in

= 22 * 12 + 8 1/2 in

= 264 + 8 1/2

= 272.5 in

John's additional jump

= record jump - John's best long jump

= 277.75 - 272.5

= 5.25 in

= 5 1/4 in

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The statement of triangle is that it has three corresponding sides and three corresponding angles.

There are at least 3 theorems about triangles, those are: the total of the three interior angles in any triangle is 180 degrees; when a triangle side is constructed, the exterior angle formed is equal to the sum of the interior opposite angles; and, the base angles of an isosceles triangle are equivalent.

Scalene, isosceles and equilateral triangle are the types of triangles which differ from each other based on their side-length. If all the three sides are different in length, then its scalene triangle. If any two sides are equal in length, then it is an isosceles triangle.

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Answer:is c or 3:5

Step-by-step explanation:

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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(Option D. Incentre) The incentre of a triangle is the point equidistant from all three of the triangle's vertices. This means that its distance from each vertex is the same.

The incentre of a triangle is an important point of reference for geometry. It is located at the center of the triangle's inscribed circle, which is the circle that touches each of the triangle's three vertices. This is why the incentre is also known as the triangle's inner center or center of the triangle's inscribed circle. As it is equidistant from all three of the triangle's vertices, the incentre is useful for finding the angles of the triangle and for finding the lengths of the triangle's sides. It can also be used to calculate the area of the triangle.

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The answer is (76.42 ; 78.17)

Given that:

A botanist is attempting to determine how many seeds are typically present in a particular fruit. She collects 65 samples and counts how many seeds are present in each. Using her sample data, the mean is 77.3 and the SD is 5.5.

Sample size, n = 65

Mean, xbar = 77.3

Standard deviation, s = 5.5

Confidence level, Zcritical at 80% = 1.28

Confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.28 * 5.5/sqrt(65)

Margin of Error =0.873

Lower boundary = 77.3 - 0.873 =76.42

Upper boundary = 77.3  + 0.873 = 78.17

Therefore, the answer is (76.42 ; 78.17)

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The table of values represents a quadratic function. And a quadratic function is y = x² / 10.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.

Linear functions have constant first differences.

Here,  if a and b is the first and second term.

Then the first difference is b-a.

Quadratic functions have constant second differences.

Let the first differences are:

b-a = m, c-b = n

Then the second difference is n-m.

Exponential functions have a constant ratio.

The ratio of first term and second term is b/a.

Here, from the table;

y₂-y₁ = 0.4 - 0.9 = -0.5 = m₁

y₃-y₂ = 0.1 - 0.4 = -0.3 = m₂

y₄-y₃ = 0 - 0.1 = -0.1 = m₃

y₅-y₄ = 0.1 - 0 = 0.1 = m₄

y₆-y₅ = 0.4 - 0.1 = 0.3 = m₅

From the first differences, we have no idea about the function property.

So, the second differences:

m₂ -  m₁ = -0.3 + 0.5 = 0.2

m₃ - m₂ = -0.1 + 0.3 = 0.2

m₄ - m₃ = 0.1 + 0.1 = 0.2

m₅ - m₄ = 0.3 - 0.1 = 0.2

Here, the second differences are constant 0.2.

And the common ratio is varying.

So, quadratic functions have constant second differences.

And the quadratic function is y = x² / 10.

Therefore, the given function is a quadratic function.

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The graph of the linear equation y = 9/7x - 9 is attached below

A linear graph is the graphical representation of a straight line. It showcases a linear equation in two variables and shows the linear association between two quantities. A linear function often have a straight line with a slope and y-intercept.

To solve this, we can simply write an equation of the linear equation which is often given as

y = mx + c

Let's substitute the values and find the equation;

y = 9/7x - 9

Kindly find the attached image below;

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The slope-intercept form of a linear equation is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the slope of the line is 1 and it passes through the point (8, –1), we can use the point-slope form of a linear equation to write the equation in slope-intercept form. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Substituting the values given in the problem into the point-slope form, we get:

y - (-1) = 1(x - 8)

Expanding the right side and rearranging the terms, we get:

y + 1 = x - 8

y = x - 9

This is the equation of the line in slope-intercept form. The y-intercept is (-9, 0), which is the point at which the line crosses the y-axis.

According to the provided data, to be one of the top 7% earners a manager needs to earn $48,360.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

The formulas are given below:

[tex]\mu = \frac {\sum x}{N}[/tex]      (Mean)

[tex]\sigma = \sqrt {\frac {\sum (X- \mu ) ^ {2}} {N}[/tex]    (Standard Deviation)

Mean = $48,000

Standard Deviation = $4,000

According to this data, Max Earning made = $48,000 + $4,000

=$52,000

7% of $52,000 = $3,640

To be top 7% earner, A manager must earn = $52,000 - $3,640

=$48,360

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Answer:$53,903

Step-by-step explanation:

Here, the mean, μ, is 48,000 and the standard deviation, σ, is 4,000. Let x be the cutoff salary for teachers in the top 7%. The area to the right of x is 7%=0.07. So, the area to the left of x is 1−0.07=0.93.

Open Excel. Click on an empty cell. Type =NORM.INV(0.93,48000,4000) and press ENTER.

Round the answer to the nearest dollar, is x≈53,903. Therefore, the cutoff salary for managers in the top 7% is $53,903.

The given series diverges.

Given:

aₙ = n²/√n³+7n

using series divergence test

If limₙ→∞ aₙ ≠0, then ∑  aₙ diverges .

limₙ→∞ (n²/√n³+7n) = limₙ→∞ (n²/√n³(1+7/n²)

= limₙ→∞ (n²/n³/²√1+7/n²)

= limₙ→∞ (√n/√1+7/n²)

= (∞/√1+0)

= ∞

Therefore the series diverges.

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The average daily inventory is 253 cases

In this question, we have been given we have been given the number of cases of zippers on inventory t days after the shipment arrives is

N(t) = 630 − 30√18t

We need to find the average daily inventory.

We use the definite integral to compute for the average value over that interval from a to b.

(∫[a_b] f(x) dx )/ (b - a)

Here, a = 1 and b = 18

so, the average daily inventory would be,

∫[18_1] N(t)dt / (18 - 1)

= ∫[18_1] (630 − 30√18t) dt / 17

= 4314.85 / 17

= 253.81

= 253

Therefore,  the average daily inventory = 253 cases

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The complete question is:

the dog days clothing company receives 630 cases of imported zippers every 18 days. the number of cases of zippers on inventory t days after the shipment arrives is  N(t) = 630 − 30√18t. Find the average daily inventory.

The value of x or we can say that the value of side DF will be equal to 5.29.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The sides of the right triangle are,

DE, h = 8

FE, b = 6

DF, p = x

Then, use Pythagoras' theorem,

h² = x² + b²

8² = x² + 6²

x² = 64 - 36

x = √28

x = 5.29  

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Answer:

14/2

Step-by-step explanation:

We can write 7 as 7/1

Multiply the top and bottom by 2/2

7/1 * 2/2 = 14/2

We could multiply by any number over itself

7/1 * 3/3 = 21/3

This is an equivalent fraction

Answer:

See below

Step-by-step explanation:

Examples ( choose one)

14/2

7/1

21/3

98/14

Answer: No, i dont think so.

Step-by-step explanation:

AC = BC is not listed as given.

True, Regardless of the testing point used we arrive at the same answer for the direction of a phase plane.

We were able to sketch the solution, y(t), in the y-t plane for the single differential equation case and observe actual solutions. Due to the fact that our answers are actually vectors, this would be fairly challenging in this situation.

Here, we're going to plot the points that we represent as the system's solutions as points in the x1x2 plane. Our equilibrium solution will line up with the x1x2 plane's origin, which is also known as the phase plane.

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