how do find a missing term

Answer:

(-8, 6)

Step-by-step explanation:

The formula for reflecting a point across the y-axis is (x, y) → (-x, y).

Substitute: (8, 6) → (-8,6)

I hope this helped! :)

The corresponding defect rate is 1 - 0.7699 = 0.2301.

The corresponding defect rate for a production process with capability indices Cp = 0.5 and Cpk = 0.4 can be calculated by using the Z value associated with the Cpk value. The Z value is the number of standard deviations from the mean that corresponds to the Cpk value. The Z value can be found using the formula Z = Cpk * 3. In this case, Z = 0.4 * 3 = 1.2.
Once the Z value is known, the corresponding defect rate can be found by using the normal distribution curve. The area under the curve between -Z and Z represents the proportion of items that are within the specification limits. The area outside of this range represents the defect rate. The area under the normal distribution curve between -1.2 and 1.2 is approximately 0.7699. Therefore, the corresponding defect rate is 1 - 0.7699 = 0.2301.
So, the corresponding defect rate for a production process with capability indices Cp = 0.5 and Cpk = 0.4 is 0.2301.

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Answer: 118728

Step-by-step explanation:

You can just simply find this answer using a calculator.

The principal value of integral  ∫ x sin x/ X^4 + 4 dx can be evaluated as PV ∫ x sin x/ X^4 + 4 dx = (1/4) [2(π/2) - π] = π/4

To evaluate the principal value of the integral ∫ x sin x/ X^4 + 4 dx, we can use the substitution u = x^2, du = 2x dx. Then, we have:
∫ x sin x/ X^4 + 4 dx = (1/2) ∫ sin(u)/ (u^2 + 4) du
Next, we can use partial fractions to simplify the integrand:
sin(u)/ (u^2 + 4) = A/(u + 2) + B/(u - 2)
Multiplying both sides by (u + 2)(u - 2) and setting u = -2 and u = 2, we get:
A = -1/4, B = 1/4
Therefore, we have:
(1/2) ∫ sin(u)/ (u^2 + 4) du = (1/2)(-1/4) ∫ sin(u)/ (u + 2) du + (1/2)(1/4) ∫ sin(u)/ (u - 2) du
Using integration by parts on each integral, we get:
(1/2)(-1/4) ∫ sin(u)/ (u + 2) du = (-1/8) cos(u) - (1/8) ∫ cos(u)/ (u + 2) du
(1/2)(1/4) ∫ sin(u)/ (u - 2) du = (1/8) cos(u) + (1/8) ∫ cos(u)/ (u - 2) du
Substituting back u = x^2, we have:
∫ x sin x/ X^4 + 4 dx = (-1/8) cos(x^2)/(x^2 + 2) - (1/8) ∫ cos(x^2)/ (x^2 + 2) dx + (1/8) cos(x^2)/(x^2 - 2) + (1/8) ∫ cos(x^2)/ (x^2 - 2) dx
Note that since the integrand has poles at x = ±√2, we need to take the principal value of the integral. This means we split the integral into two parts, from -∞ to -ε and from ε to +∞, take the limit ε → 0, and add the two limits together. However, since the integrand is even, we can just compute the integral from 0 to +∞ and multiply by 2:
PV ∫ x sin x/ X^4 + 4 dx = 2 lim ε→0 ∫ ε^2 to ∞ [(-1/8) cos(x^2)/(x^2 + 2) + (1/8) cos(x^2)/(x^2 - 2)] dx
Using integration by parts on each integral, we get:
2 lim ε→0 [(1/8) sin(ε^2)/(ε^2 + 2) + (1/8) sin(ε^2)/(ε^2 - 2) + ∫ ε^2 to ∞ [(-1/4x) sin(x^2)/(x^2 + 2) + (1/4x) sin(x^2)/(x^2 - 2)] dx]
The first two terms tend to 0 as ε → 0. To evaluate the integral, we can use the substitution u = x^2 + 2 and u = x^2 - 2, respectively. Then, we have:
PV ∫ x sin x/ X^4 + 4 dx = ∫ 0 to ∞ [(-1/4(u - 2)) sin(u)/ u + (1/4(u + 2)) sin(u)/ u] du
= (1/4) ∫ 0 to ∞ [(2/u - 1/(u - 2)) sin(u)] du
Using the fact that sin(u)/u approaches 0 as u approaches infinity, we can apply the Dirichlet test to show that the integral converges. Therefore, we can evaluate it as:
PV ∫ x sin x/ X^4 + 4 dx = (1/4) [2(π/2) - π] = π/4

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Total charge for 1,920 squares feet is $160.

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.

Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.

City carpet can install 1,200 square feet of carpet in 2.5 hours

In 1 hour they can install \(\frac{1200}{2.5} =480 squares feet\)

In 4 hour they can install 1920 squares feet carpet

They charge $40 per hour

So total charges for 1920 square feet will be 4 ×40

= $160

Total charge for 1,920 squares feet is $160.

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Answer:7

Step-by-step explanation:

To find the median you need to first put the number in order from least to greatest this would be 2, 4 ,5, 7, 7, 7, 8

next you have to find the number in the middle

That is your median, 7 is your median.

Answer:

V ≈ 258 ft³

Step-by-step explanation:

I given the diameter d= 7.9 ft so the radius is r = d/2 = 7.9/2  ft

Volume of a sphere is

V = (4/3) π·r³ = (4/3) · π · (7.9/2)³ = 258.1546167 ft³

Answer:C. f(x)=7+5x

Step-by-step explanation:

12=5(1)+n

12=5+b

-b+12=5

-b=5-12

5-12=7

-b=7

f(x)=7+5x

I know this because I just answered this question and got it right

The equation of the function is f(x) = 7 + 5x option (C) f(x) = 7 + 5x is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The table is given,

From the data given in the table:

12 = 5(1)+n

12 = 5+b

b = 7

The function would be:

f(x) = 7 + 5x

Thus, the equation of the function is f(x) = 7 + 5x option (C) f(x) = 7 + 5x is correct.

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To estimate the difference between proportions, sample around 3355 stalks from each section of the field.

In order to estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, we need to determine the sample size required to achieve a desired level of precision and confidence.

To estimate the required sample size, we can use the formula for sample size determination for estimating the difference between two proportions. This formula is based on the assumption of a normal distribution and requires the proportions from each section.

Let's denote the proportion of stalks damaged in the middle section as p1 and the proportion of stalks damaged in the outer perimeter as p2. We want to estimate the difference between these proportions to within 0.02 (±0.02) with 90% confidence.

To calculate the required sample size, we need to make an assumption about the value of p1 and p2. If we don't have any prior knowledge or estimate, we can use a conservative estimate of p1 = p2 = 0.5, which maximizes the required sample size.

Using this conservative estimate, we can apply the formula for sample size determination:

n = (Z * sqrt(p1 * (1 - p1) +\(p2 * (1 - p2)))^2 / d^2\)

where:

Plugging in the values, we get:

n = (1.645 * sqrt(0.5 * (1 - 0.5) + 0.5 *\((1 - 0.5)))^2 / 0.02^2\)

n = (1.645 * sqrt\((0.25 + 0.25))^2\)/ 0.0004

n = (1.645 * sqrt\((0.5))^2\) / 0.0004

n =\((1.645 * 0.707)^2\) / 0.0004

n =\(1.158^2\) / 0.0004

n = 1.342 / 0.0004

n ≈ 3355

Therefore, the required sample size from each section of the field would be approximately 3355 stalks, in order to estimate the true difference between proportions of stalks damaged in the two sections to within 0.02 with 90% confidence.

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To estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, approximately 665 stalks from each section should be sampled.

In order to estimate the true difference between proportions of stalks damaged in the middle and outer perimeter sections of the sugarcane field, a representative sample needs to be taken from each section. The goal is to estimate this difference within a certain level of precision and confidence.

To determine the sample size needed, we consider the desired precision and confidence level. The requirement is to estimate the true difference between proportions of stalks damaged within 0.02 (i.e., within 2%) with 90% confidence.

To calculate the sample size, we use the formula for estimating the sample size needed for comparing proportions in two independent groups. Since an equal number of stalks will be sampled from each section, the total sample size required will be twice the sample size needed for a single section.

The formula to estimate the sample size is given by:

n = [(Z * sqrt(p * (1 - p)) / d)^2] * 2

Where:

n is the required sample size per section

Z is the Z-value corresponding to the desired confidence level (for 90% confidence, Z = 1.645)

p is the estimated proportion of stalks damaged in the section (unknown, but assumed to be around 0.5 for a conservative estimate)

d is the desired precision (0.02)

Plugging in the values, we can calculate the sample size needed for each section.

n = [(1.645 * sqrt(0.5 * (1 - 0.5)) / 0.02)^2] * 2

n ≈ 664.86

Rounding up, we arrive at approximately 665 stalks that should be sampled from each section.

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Answer:

finding how many inches he goes in an hour (multiply by 3600)

Step-by-step explanation:

The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.

To find the average rate, follow these steps:

Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\)  is 24.

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To find a basis for the eigenspace corresponding to each listed eigenvalue of matrix A, we need to determine the null space of the matrix A - λI, where λ is the eigenvalue and I is the identity matrix.

Given a matrix A and its eigenvalues, we can find the eigenvectors associated with each eigenvalue by solving the equation (A - λI)v = 0, where λ is an eigenvalue and v is an eigenvector.

To find the basis for the eigenspace, we need to determine the null space of the matrix A - λI. The null space contains all the vectors v that satisfy the equation (A - λI)v = 0. These vectors form a subspace called the eigenspace corresponding to the eigenvalue λ.

To find a basis for the eigenspace, we can perform Gaussian elimination on the augmented matrix [A - λI | 0] and obtain the reduced row-echelon form. The columns corresponding to the free variables in the reduced row-echelon form will give us the basis vectors for the eigenspace.

For each listed eigenvalue, we repeat this process to find the basis vectors for the corresponding eigenspace. The number of basis vectors will depend on the dimension of the eigenspace, which is determined by the number of free variables in the reduced row-echelon form.

By finding a basis for each eigenspace, we can fully characterize the eigenvectors associated with the given eigenvalues of matrix A.

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Answer:

1st and 4th are the right triangles

Answer:

x>1

Step-by-step explanation:

In order to do this, we can take the inequality:

3+2x>5

now there are constants on both sides meaning we can combine them like the following:

3+2x>5

-3      -3

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

2x>2

Now we can simplify

2x/2>2/2

therefore, the answer is x>1

In order to graph this on a line you would need to put in a circle which is not filled in because x isn't equal to and greater than 1 so we put in a blank circle and since x is always going to be greater than 1, we would put a line that keeps going on.

You would put this line to the right of 1

o----------->

1 2 3 4 5 6

that is how the line would look like

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Answer:

d= -1/8

Step-by-step explanation:

8d+d+3d+2+4d= 16d+2

16d= -2

d= -1/8

To calculate the value of Mike's car in 2017, we need to consider the 30% decrease in value each year from 2014 to 2017.

Let's break down the calculations year by year:

Year 2014: The car is worth £12,000 (given).

Year 2015: To calculate the value in 2015, we need to decrease the value by 30%:

Value in 2015 = £12,000 - (30/100) * £12,000

= £12,000 - £3,600

= £8,400

Year 2016: To calculate the value in 2016, we need to decrease the value by 30% again:

Value in 2016 = £8,400 - (30/100) * £8,400

= £8,400 - £2,520

= £5,880

Year 2017: Once again, we decrease the value by 30%:

Value in 2017 = £5,880 - (30/100) * £5,880

= £5,880 - £1,764

= £4,116

Therefore, the value of Mike's car in 2017 is £4,116.

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To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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The seasonal problem may be predicted using the difference between actual sales and the trend portion of the sales as given by the equation: \(Ft 40-6.5t+2t².\)

Solving the given equation: \(Ft = 40 - 6.5t + 2t²\)Hence, the trend portion of quarterly sales of condominiums over a long cycle is given by the equation\(Ft = 40 - 6.5t + 2t²\) where t is time in quarters (Q1 1981 is t=1, Q2 1981 is t=2, Q3 1981 is t=3, etc.)

Given that sales exhibit seasonal variations, the seasonal problem may be predicted using the difference between actual sales and the trend portion of the sales as given by the equation Ft = 40 - 6.5t + 2t².

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Answer:

56 in

Step-by-step explanation:

Square ....so each side is = x

x * x = area = 196

x^2 = 196

x = sqrt (196) = 14 in

perimeter = x  + x + x + x = 56 in

Answer:

56 inches

Step-by-step explanation:

Given,

Area of square = 196 square inches

To find : Perimeter of the square = ?

Formula : -

Area of square = side²

side² = 196

         = 14 x 14

side² = 14²

side = 14 inches

Formula : -

Perimeter of the square = 4 x side

perimeter of the square

= 4 x 14

= 56 inches

Answer:

no photo

Step-by-step explanation:

we need a photo to decide if answer is correct or not

Answer:

47.5

Step-by-step explanation:

19÷2=9.5x5=47.5

The range of feasible values for the multiple coefficients of correlation is from -1 to 1.

The multiple coefficients of correlation, also known as the multiple R or R-squared, measures the strength and direction of the linear relationship between a dependent variable and multiple independent variables in a regression model. It quantifies the proportion of the variance in the dependent variable that is explained by the independent variables.

The multiple coefficients of correlation can take values between -1 and 1.

A value of 1 indicates a perfect positive linear relationship, meaning that all the data points fall exactly on a straight line with a positive slope.

A value of -1 indicates a perfect negative linear relationship, meaning that all the data points fall exactly on a straight line with a negative slope.

A value of 0 indicates no linear relationship between the variables.

Values between -1 and 1 indicate varying degrees of linear relationship, with values closer to -1 or 1 indicating a stronger relationship. The sign of the multiple coefficients of correlation indicates the direction of the relationship (positive or negative), while the absolute value represents the strength.

The range from -1 to 1 ensures that the multiple coefficients of correlation remain bounded and interpretable as a measure of linear relationship strength.

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The relation y = 2^x represents y as a function of x. Therefore, the correct answer is d) Yes, because each value of x corresponds to exactly one value of y.

The relation y = 2^x represents an exponential function, where y is defined in terms of x. For any given value of x, there is a unique corresponding value of y. Each value of x serves as the input to the function, and it produces a single output y based on the exponential operation of raising 2 to the power of x.

This means that for every value of x, there exists exactly one value of y. Hence, the relation y = 2^x satisfies the definition of a function, making the correct answer d) Yes, because each value of x corresponds to exactly one value of y.

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Matthew is 4 years old.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here Matthew is younger than Kadeem. their ages are consecutive even integers. Let Matthew's age be M and Kadeem's age be K then according to the question we have

M+2K = 28

now since 28 is an even number both the numbers in the LHS must be even thus the possibilities are

M+2K = 28

4    12

8    10  but if 2K= 10 then K=5 but 5<8 and 5 is not even thus this case is not possible

So, we can say that M=4 and 2K = 12 then K=6

Hence Matthew is 4 years old

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Answer:divideing by the whole number

Step-by-step explanation:

Answer:

96 ways

Step-by-step explanation:

Given

\(Day = 86400\ seconds\)

Required

Ways to divide it into period of seconds

What this question implies is to determine the total number of factors of 86400

To start with, we determine the prime factorization of 86400

To do this, we continually divide 86400 by 2; when it can not be further divided, we divide by 3, then 7, then 11...

\(86400/2 = 43200\)

\(43200/2=21600\)

\(21600/2=10800\)

\(10800/2=5400\)

\(5400/2= 2700\)

\(2700/2 = 1350\)

\(1350/2=675\)

\(675/3=225\)

\(225/3=75\)

\(75/3=25\)

\(25/5=5\)

\(5/5 = 1\)

This implies that:

\(86400 = 2^7 * 3^3 * 5^2\)

The number of factors d is the solved by:

\(d = (a+1)*(b+1) *(c+1)\)

Where

\(n = 2^a * 3^b * 5^c\)

By comparison:

\(a = 7\)

\(b = 3\)

\(c=2\)

So:

\(d = (7+1)*(3+1) *(2+1)\)

\(d = 8*4 *3\)

\(d = 96\)

Hence, there are 96 total ways

The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. We can apply this principle to prove the following statements:

(a) Given any seven integers, there will be two that have a difference divisible by 6.

We can divide the integers into six pigeonholes based on their remainders when divided by 6: {0}, {1}, {2}, {3}, {4}, and {5}. Since there are seven integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their difference will be divisible by 6.

(b) Given any five integers, there will be two that have a sum or difference divisible by 7.

We can divide the integers into six pigeonholes based on their remainders when divided by 7: {0}, {1}, {2}, {3}, {4}, {5}, and {6}. Since there are five integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their sum or difference will be divisible by 7.

Note that if the two integers have the same remainder when divided by 7, then their difference will be divisible by 7. If they have different remainders, then their sum will be divisible by 7.

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