QUESTION 1 What is Statistical Process Control and Control Charts? O It is a method that uses basic graphics and statistical tools to analyze, control and reduce variability within a process by taking

The equation in integral form by taking the inverse Laplace transform: x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0)), where L^-1 represents the inverse Laplace transform.

To express the given initial value ordinary differential equation (ODE) using convolution notation with *, we can rewrite it as:

(x'' - 8x' + 12x) = f(t)

Taking the Laplace transform of both sides, we have:

s^2X(s) - sx(0) - x'(0) - 8(sX(s) - x(0)) + 12X(s) = F(s)

where X(s) is the Laplace transform of x(t), x'(0) is the initial condition of the derivative of x(t), x(0) is the initial condition of x(t), and F(s) is the Laplace transform of f(t).

Simplifying the equation, we get:

(s^2 - 8s + 12)X(s) - sx(0) - x'(0) + 8x(0) = F(s)

Now, let's express the left-hand side of the equation using convolution notation. Using the property that the Laplace transform of the derivative of a function f(t) is sF(s) - f(0), we can rewrite the equation as:

((s^2 - 8s + 12) - s + 8)X(s) = F(s) + sx(0) + x'(0) - 8x(0)

Simplifying further, we have:

(s^2 - 9s + 20)X(s) = F(s) + sx(0) + x'(0) - 8x(0)

Finally, we can express the equation in integral form by taking the inverse Laplace transform:

x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0))

where L^-1 represents the inverse Laplace transform.

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Answer:

I think 100

Step-by-step explanation:

Based on the normal probability plot constructed for the octane data, it does not appear reasonable to assume that the octane rating is normally distributed. The plot deviates significantly from a straight line, indicating a departure from normality.

A normal probability plot is a graphical tool used to assess whether a dataset follows a normal distribution. In a normal plot, the observed data points are plotted against the corresponding quantiles of a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data can be reasonably modeled as normally distributed.

In this case, when constructing the normal probability plot for the octane data, if the plot deviates significantly from a straight line, it indicates a departure from normality. If the points on the plot show a distinct curvature or exhibit systematic patterns, it suggests that the data does not follow a normal distribution.

By examining the sketch of the normal probability plot for the octane data, if it shows substantial deviations from a straight line, with points deviating from the expected pattern, it implies that the octane rating is not normally distributed. This departure from normality could be due to various factors, such as skewness, outliers, or a different underlying distribution that better fits the data. Therefore, based on the sketch of the plot, it is reasonable to conclude that the octane rating is not normally distributed.

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Answer:

12 months at 6.25%

Step-by-step explanation:

You deposit $1250 into a bank account paying 6.25% simple interest per month. You left the money in for 12 months. Find the interest earned and the amount at the end of those 12 months?

Result:

The interest is $937.5 and the amount is $2187.5.

Explanation:

STEP 1: Convert interest rate of 6.25% per month into rate per year.

STEP 2: Convert 12 months into years.

STEP 3: Find an interest by using the formula , where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this examplee P = $1250, i = 75% and t = 1 years, so

STEP 4: Find an amount by using the formula .

Since P = $1250 and I = $937.5 we have

Answer:

The perimeter to the question is 30.

Step-by-step explanation:

.

[tex]3 + 3 + 3 + 3 + 9 + 9 \\ 6 + 6 + 18 \\ 12 + 18 \\ 30[/tex]

Answer:

This is your answer ☺️☺️

12,351,789

ignore this ------

12346789

+      5000

----------------

12351789

Answer:

288 cm

Step-by-step explanation:

The formula to solve this polygon is: area = 1/2 x perimeter x apothem

To find the perimeter all you have to is find the sum of all sides together: 12+12+6+6+6+6= 48

Then the Apothem is, the "segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side." To find this you find the point from the middle to the edge which is 12cm.

Then you plug in this information into the polygon. 1/2 x 48 x 12= 288!

The polygon is 288 cm!

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Answer:

if you make 4 free throws for every 10 shots taken you would make 20 out of 50 free throws

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

great job mate

The value of variable h is,

⇒ h = 18

We have to given that,

A heptagon with angles are shown in figure.

Here, All the angles are,

⇒ 6h°, 132°, 146°, 146° , (6h + 10)° , (6h + 10)° , 146°, and 132°

We know that,

Sum of all the angles in a heptagon is, 900°

Hence, We get;

⇒ 6h° + 132° + 146° + 146° + (6h + 10)° + (6h + 10)° + 146° + 132° = 900°

Combine like terms,

⇒ 18h + 576 = 900

⇒ 18h = 900 - 576

⇒ 18h = 324

⇒ h = 18

Thus, The value of variable h is,

⇒ h = 18

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a) In Quadrant 2, a sin(20) is equal to -sin(20).

b) In Quadrant 2, cos(2a) is equal to -cos(2a).

c) In Quadrant 2, tan(20) is equal to -tan(20).

In Quadrant 2, the angle 'a' is between 90 degrees and 180 degrees, or π/2 and π radians. Knowing that cos(a) is a negative value, we can determine the exact values for the given trigonometric expressions.

a) a sin(20) = -sin(20):

The sine function (sin) is positive in Quadrant 1 and negative in Quadrant 2. Therefore, the value of a sin(20) in Quadrant 2 is equal to the negative of sin(20). This means that the answer for a sin(20) is -sin(20).

b) cos(2a) = -cos(2a):

The cosine function (cos) is negative in Quadrant 2. Since we are given that a is in Quadrant 2, the angle 2a will also be in Quadrant 2. Therefore, cos(2a) in Quadrant 2 is equal to the negative of cos(2a). Thus, the answer for cos(2a) is -cos(2a).

c) tan(20) = -tan(20):

The tangent function (tan) is negative in Quadrant 2. Hence, the tangent of any angle in Quadrant 2 will be equal to the negative of its positive counterpart. Consequently, the answer for tan(20) in Quadrant 2 is -tan(20).

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Answer:

130⁰. unsure. angle sum, 25+25+x =180, so x=180-25-25

The national average for mathematics on a standardized test in 2011 was 518, with a standard deviation of approximately 48.

In statistics, the bell-shaped distribution is known as the normal distribution or the Gaussian distribution. It is characterized by its symmetry and the majority of the data falling within a certain range.

The national average score of 518 represents the central tendency of the distribution. This means that a large number of students scored around this average score.

The standard deviation of approximately 48 measures the variability or spread of the scores. It indicates how much the scores deviate from the average. In a normal distribution, about 68% of the data falls within one standard deviation of the mean.

By knowing the average score and the standard deviation, we can determine the proportion of students who scored above or below a certain score, as well as calculate percentiles and compare individual scores to the national average.

Understanding the characteristics of the distribution, such as the average and standard deviation, helps in interpreting and analyzing the scores, making meaningful comparisons, and identifying students' performance relative to the national average.

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Answer:

It is plugging it the 36pye

Step-by-step explanation:

h = 36pye

what it wants you to do is plug that into all the numbers

so it be

2 x 36pye (you get it for the next one)

for the fraction ones it would

be divding 36pye by the number on the bottom

Answer: add 3

Step-by-step explanation:

Answer:

slope = 5/3

y-intercept = (0,-3)

Step-by-step explanation:

Make the equation in slope-intercept form:

-5x+3y=-9

add 5x on both sides

3y=5x-9

divide by 3 on both sides

y=5/3x-3

slope = 5/3

y-intercept = (0,-3)

Answer: 17.8% + $1.789.17 + $650 = 2439.348 or 2439

Step-by-step explanation: if you read the word problem it has a key word the key word is total.

Nash uses his credit card with a 17.8% APR, compounded monthly, to pay for a cruise totaling $1,789.17. He can pay $650 per month on the card. What will the total cost of this purchase be?

The mean number of students in the class is 2.4 siblings.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = total sum of siblings / number of students

[(0 x 4) + ( 1 x 4) + ( 2 x 2) + ( 3 x 8) + ( 4 x 4) ] / ( 2 + 4 + 2 + 8 + 4)

= 48 / 20 = 2.4 siblings

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Answer:

Sample standard deviation = 3

Step-by-step explanation:

We can use the following steps to calculate the sample standard deviation for the given data set:

Step 1: First, calculate the mean of the data set by adding all the values and dividing by the total number of values:

(12 + 12 + 12 + 15 + 18 + 18 + 18) / 7 = 15.

Thus, the mean is 15.

Step 2: Next, subtract the mean from each value in the data set to get the deviation of each value from the mean.

(12 - 15) = -3

(15 - 15) = 0

(18 - 15) = 3

Thus, the deviations are -3, -3, -3 0, 3, 3, and 3.

Step 3:   Square each deviation:

(-3)^2 = 9

0^2 = 0

(3)^2 = 9

Thus, the squares of all our deviations are 9, 9, 9, 0, 9, 9, and 9.

Step 4:  Add up all the squared deviations:

9 + 9 + 9 + 0 + 9 + 9 + 9 = 54.

Thus, the sum of the squared deviations is 54.

Step 5:  Find the variance by dividing the sum of squared deviations by one less than the number of values in the data set:

54 / (7 - 1) = 9

54 / 6 = 9

Thus, the variance is 9

Step 6:   Finally, find the sample standard deviation by taking the square root of the variance:

√9 = 3

So, the sample standard deviation for this data set is 3.

Answer:

Relative frequency

Step-by-step explanation:

The real answer is B

Answer:

£6.05

Step-by-step explanation:

Multiply the number of coffees by the cost of coffee:

5 × 65p

325p

Multiply the number of teas by the cost of tea:

2 × £1.40

£2.80

Add the two answers together:

325p + £2.80

Convert p to £

£3.25 + £2.80

£6.05

To determine the normal and shear stresses at point D, which act perpendicular and parallel to the grains, respectively, we require additional information such as the applied forces or loadings at that point.

The given question mentions the need to determine the normal and shear stresses at point D, which act perpendicular and parallel to the grains, respectively. However, to accurately calculate these stresses, we need more information about the system under consideration. Key details include the applied forces or loadings on the system, the material properties, and the specific orientation and arrangement of the grains at point D.

Normal stress, also known as axial stress, refers to the force per unit area acting perpendicular to the surface. Shear stress, on the other hand, represents the force per unit area acting parallel to the surface. The magnitudes and directions of these stresses depend on the applied forces, the geometry of the system, and the material properties.

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The formula for calculating confidence interval is: $\overline{X} \pm Z_{\alpha/2}\frac{σ}{\sqrt{n}}$,

where $\overline{X}$ is the sample mean,

$σ$ is the population standard deviation,

$n$ is the sample size, and $Z_{\alpha/2}$ is the critical value of the standard normal distribution at $\alpha/2$ and $(1-\alpha/2)$ levels of significance respectively. To construct the 90% confidence interval for the given data: n = 240p-hat = 0.55The sample mean is equal to p-hat which is 0.55. Therefore, the margin of error is given by;

ME = Z_{α/2} × √{p-hat(1 - p-hat) / n}α = 0.10, thus α/2 = 0.05, so the area to the right of the critical value is equal to 0.05.

Using the standard normal distribution table, the critical value for α/2 = 0.05 is: Z_{α/2} = 1.64

Therefore, the confidence interval is given by; CI = p-hat ± Z_{α/2} × √{p-hat(1 - p-hat) / n}CI = 0.55 ± 1.64 × √{0.55(1 - 0.55) / 240}CI = 0.55 ± 0.077

Therefore, the confidence interval is (0.473, 0.627) (rounded to three decimal places).

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Answer:

Choice D

Step-by-step explanation:

I believe that it is Choice D. Due to the fact that the moons orbit around Earth is inclined around 5 degrees, not allowing an eclipse to happen every New or Full Moon. Most of the time, the Sun, Earth, and Moon don't line up precisely enough to cause an eclipse.

Answer:

2ft

Step-by-step explanation:

16^3 ft

4 * 2=8

16/8 =2

Answer:

2 ft

Step-by-step explanation:

V = lwh

16 = 4(2)w

16 = 8w

w = 2 ft

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal.

To prove the given equation, we will differentiate both sides with respect to θ and simplify the expression.

Differentiating V cotθ + V^3cosecθ with respect to θ:

d/dθ(V cotθ + V^3cosecθ) = d/dθ(V cotθ) + d/dθ(V^3cosecθ)

Applying the differentiation rules:

= V (-cosec^2θ) + 3V^2cosecθ(-cosecθcotθ)

= -V cosec^2θ - 3V^2cosec^2θcotθ

Now, we need to express the right-hand side of the original equation in terms of dV/dθ:

V cotθ + V^3cosecθ = V(cotθ + V^2cosecθ)

                      = V(cotθ + cotθV^2)

                      = Vcotθ(1 + V^2)

Taking the derivative of the right-hand side with respect to θ:

d/dθ(Vcotθ(1 + V^2)) = V(−cosec^2θ)(1 + V^2) + Vcotθ(0)

                           = -Vcosec^2θ(1 + V^2)

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal. Therefore, we have proved that dV/dθ = V cotθ + V^3cosecθ.

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