standard labor-hours per unit of output 8.5 hours standard labor rate $12.30 per hour the following data pertain to operations concerning the product for the last month: actual hours worked 6,300 hours actual total labor cost $74,970 actual output 800 units

Answer:

Answer A is Linear.  You can see this because each term is equal to the previous term plus a fixed amount (3), making it an arithmetic sequence.

Answer B is not linear.  This is because each term is a multiple of the previous one, making it a geometric sequence.

Answer:

Function A

Step-by-step explanation:

Each time x increases by 1, y increases by 3. Function B is exponential instead of linear, because y increases by a larger number each time rather than increasing by the same amount.

Good luck :)

Answer:

19=13+5

Step-by-step explanation:

The Real Answer For 19=13+5 Is 18.

Answer:

2 units left 1 unit up

Step-by-step explanation:

The following inequalities are correct ,

1. −3 ≤ −1

2. −3<−1

So, Option A & B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The inequalities,

Statement 1:   negative 3 less than or equal to negative 1

−3 ≤ −1

It is correct

Statement 2:  negative 3 less than or equal to negative 1

−3 < −1

It is also correct

Statement 3: negative 3 equals negative 1

−3 = −1

It is Incorrect because -3 is less than -1

Statement 4:  negative 3 greater than or equal to negative

−3 ≥ −1

It is also Incorrect because  -3 is less than -1

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The required line integral is 0.9045 (correct to four decimal places).

The line integral of the function x sin(y z) ds on the curve c, which is defined by the parametric equations x = t², y = t³, z = t⁴, 0 ≤ t ≤ 3, can be calculated as follows:

First, we need to find the derivative of each parameter and the differential length of the curve.

\(ds = √[dx² + dy² + dz²] = √[(2t)² + (3t²)² + (4t³)²] dt = √(29t⁴) dt\)

We have to substitute the given expressions of x, y, z, and ds in the given function as follows:

\(x sin(y z) ds = (t²) sin[(t³)(t⁴)] √(29t⁴) dt = (t²) sin(t⁷) √(29t⁴) dt\)

Finally, we have to integrate this expression over the range 0 ≤ t ≤ 3 to obtain the value of the line integral using a calculator or computer algebra system:

\(∫₀³ (t²) sin(t⁷) √(29t⁴) dt ≈ 0.9045\)(correct to four decimal places).

Hence, the required line integral is 0.9045 (correct to four decimal places).

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Complete Question

The line integral of the vector field given by F(x, y, z) = x sin(yz) over the curve C, parametrized by \(x = t^2, y = t^3, z = t^4\), where 0 ≤ t ≤ 3, can be evaluated to be approximately -0.0439.

The line integral, we need to compute the integral of the vector field F(x, y, z) = x sin(yz) with respect to the curve C parametrized by \(x = t^2, y = t^3, z = t^4\), where 0 ≤ t ≤ 3.

The line integral can be computed using the formula:

\(∫ F(x, y, z) · dr = ∫ F(x(t), y(t), z(t)) · r'(t) dt\)

where F(x, y, z) is the vector field, r(t) is the position vector of the curve, and r'(t) is the derivative of the position vector with respect to t.

Substituting the given parametric equations into the formula, we have:

\(∫ (t^2 sin(t^7)) · (2t, 3t^2, 4t^3) dt\)

Simplifying and integrating the dot product, we can evaluate the line integral using a calculator or CAS. The result is approximately -0.0439.

Therefore, the line integral of the vector field x sin(yz) over the curve C is approximately -0.0439.

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The key approach is to analyze the relationship between the number of solutions to the equation Ax = 0 and the result of Gaussian elimination.

Since the columns of A are linearly dependent, there exist scalars c1, c2, ..., cn (not all zero) such that c1a1 + c2a2 + ... + cnan = 0, where ai represents the columns of A. We can rewrite this equation as a system of linear equations: Ax = 0, where x = [c1, c2, ..., cn]T is a column vector.

The linear dependence of the columns implies that the system Ax = 0 has infinitely many solutions, as we can always find non-trivial combinations of the columns that yield the zero vector.

Now, let's consider applying Gaussian elimination to matrix A. Gaussian elimination transforms the matrix into reduced row echelon form. If the resulting matrix has at least one row of all zeros, it means that there is at least one free variable in the system Ax = 0. This indicates that the system has infinitely many solutions.

Since the system Ax = 0 has infinitely many solutions, and the result of Gaussian elimination with a row of all zeros indicates linear dependence, it follows that the rows of A must also be linearly dependent. Therefore, the linear dependence of the columns implies the linear dependence of the rows.

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Answer:

Domain is... R

Range is... [-2, +unlimited)

If f is defined by a power series that has a positive radius of convergence, then this means that the power series converges to f for all values of x within a certain interval centered at 0. Specifically, the radius of convergence R tells us the size of this interval.

To see why this is the case, let's recall the definition of a power series:
f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4 + ...
This expression tells us that the function f can be written as an infinite sum of terms involving powers of x. The coefficients a0, a1, a2, etc. are constants that determine the size of each term. The important thing to note here is that this series only converges if the limit of its terms as n approaches infinity goes to zero. Now, the radius of convergence R can be calculated using the ratio test:
R = 1/lim sup(|an|^(1/n)) as n approaches infinity
This formula tells us that R is the inverse of the limit superior of the nth root of the absolute value of the coefficients. Intuitively, this means that if the coefficients of the power series grow too quickly, then the series will not converge for any value of x. On the other hand, if the coefficients grow very slowly, then the series will converge for a wide range of values of x. So, if f has a positive radius of convergence, this means that the limit superior of the nth root of the coefficients goes to zero, which implies that the series converges for all values of x within an interval of size 2R centered at 0. In other words, we can plug in any value of x within this interval and get a well-defined value for f(x).

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Answer:

2 t-shirts, 3 cd's, 5 books.

Step-by-step explanation: Johnson wants to spend $105 in total, get 10 items total, and get at least 1 t-shirt, 1 cd, and 1 book. If he did not want to buy 10 items then he could buy 21 books, 10 cd's and 1 book, or 4 t-shirts and 1 book. But because of all the conditions Johnson should buy 2 t-shirts ($50), 3 cd's ($30), and 5 books ($25). $105 total, and as much of each item as possible.

Answer:

Samir would need to invest about $6,644.96, rounded to the nearest ten dollars, for the value of the account to reach $14,000 in 16 years.

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

where:

A = final amount (in this case, $14,000)

P = initial principal (what Samir needs to invest)

r = interest rate (2.5% or 0.025)

n = number of times the interest is compounded per year (365, since it's compounded daily)

t = time (16 years)

Substituting these values into the formula, we get:

14000 = P(1 + 0.025/365)^(365*16)

Simplifying the right side, we get:

14000 = P(1.00006849315)^5840

Dividing both sides by (1.00006849315)^5840, we get:

P = 14000/(1.00006849315)^5840

Using a calculator, we get:

P ≈ 6,644.96

So Samir would need to invest about $6,644.96, rounded to the nearest ten dollars, for the value of the account to reach $14,000 in 16 years.

Answer:

62.208

Step-by-step explanation:

51.84 + 10.368

Answer:

I think if the total amount was $51.84 after tax, then 51.84 x 0.20 = 10.368. $51.84 - 10.368 = $41.472

I think original price was $41.47. I am not sure.

Step-by-step explanation:

The graph-based response to the question is 5/2x + 2/3y = -4. The answer is option (c).

An equation in mathematics is a claim made regarding the equality of two expressions. The equal sign (=) separates it into two portions, left and right. Variables, variables, and operators may be used on the left and right sides of equations.

To find out which equation in the system of linear equations satisfies the second equation, we must insert the values of the supplied solution point (12, -39) into the potential equations.

Let's begin by entering the following values into option (A):

5/3x + 2/3y = 6

5/3(12) + 2/3(-39) = 20

Since this is untrue, equation (A) is not the right answer.

Let's attempt option (B) now.

5/2x + 2/3y = 6

5/2(12) + 2/3(-39) = 30 - 26 = 4

The equation in option (B) is incorrect because this is likewise untrue.

We then test option (C):

5/2x + 2/3y = -4

5/2(12) + 2/3(-39) = -20

Since this is the case, option (C) is the formulation of the linear equations that is correct.

Let's check option (D) last.

5/3x + 2/3y = -6

5/3(12) + 2/3(-39) = -20

Option (D) is the incorrect equation because this is not the case.

The second linear equation for the set of equations whose solution is represented by the point at (12, -39) is as a result:

5/2x + 2/3y = -4, which is option (C).

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Answer:

first

Step-by-step explanation:

(3;0)

y(3) = 2/3 * 3 - 2 = 0

(0;-2)

y(0) = 2/3 * 0 - 2 = -2

Answer:

20

Step-by-step explanation:

Answer: It has 13 sides

Step-by-step explanation:

Answer:

<DHM and <DHR

Step-by-step explanation:

<DHM and <DHR are the angles formed by the dashed rays

Answer:

21 is the answer your welcome

The limit \(\(\lim_{x\rightarrow 2}(f(x)-16h(x))\)\) is calculated using the Theorem on Properties of Limits. By substituting the given limits \(\(\lim_{x\rightarrow 2}f(x)=7\) and \(\lim_{x\rightarrow 2}h(x)=\frac{1}{2}\),\) the final result is \(\(-1\).\)

The limit \(\(\lim_{x\rightarrow 2}(f(x)-16h(x))\)\) can be calculated using the Theorem on Properties of Limits. Given that \(\(\lim_{x\rightarrow 2}f(x)=7\) and \(\lim_{x\rightarrow 2}h(x)=\frac{1}{2}\),\) we can substitute these values into the expression to find the limit.

Using the properties of limits, we can write \(\(\lim_{x\rightarrow 2}(f(x)-16h(x))\) as \(\lim_{x\rightarrow 2}f(x) - 16\lim_{x\rightarrow 2}h(x)\).\) Substituting the given limits, we have \(\(7 - 16\left(\frac{1}{2}\right)\).\)

Simplifying further, we get \(\(\lim_{x\rightarrow 2}(f(x)-16h(x)) = 7 - 8 = -1\).\)

Therefore, the limit of \(\(f(x) - 16h(x)\) as \(x\)\) approaches 2 is -1.

To calculate the limit \(\(\lim_{x\rightarrow 2}(f(x)-16h(x))\),\) we use the Theorem on Properties of Limits, which states that if the limits \(\(\lim_{x\rightarrow a}f(x)\) and \(\lim_{x\rightarrow a}g(x)\)\) exist, then the limits of their sum or difference can be calculated by simply adding or subtracting the individual limits.

In this case, we are given that \(\(\lim_{x\rightarrow 2}f(x) = 7\) and \(\lim_{x\rightarrow 2}h(x) = \frac{1}{2}\).\) By substituting these values into the expression \(\(\lim_{x\rightarrow 2}(f(x)-16h(x))\),\) we obtain \(\(7 - 16\left(\frac{1}{2}\right)\).\)

Simplifying further, we get \(\(\lim_{x\rightarrow 2}(f(x)-16h(x)) = 7 - 8 = -1\).\) This means that as \(\(x\)\) approaches 2, the expression \(\(f(x)-16h(x)\)\) approaches -1.

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The steps in understanding the distribution of the differences in the sample means are-

The sample mean is a measure of the data's center. The sample mean is used to estimate the mean of any population.

Some key features regarding the sample mean are-

The formula for sample mean is-

Sample Mean = (Sum of terms) ÷ (Number of Terms)

\(\frac{\sum x_{i}}{n}\) = \(\frac{\left(x_{1}+x_{2}+x_{3}+\cdots+x_{n}\right)}{n}\)

Where,

\(\sum x_{i}\) = sum of the given data

n  = number of the data

Therefore, the steps in understanding the distribution of the differences in the sample means is given.

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Answer: four

Step-by-step explanation:

Answer:

x=2.33

Step-by-step explanation:

6+3x=12x-15​

-9x=-21

x=21/9

x=2.33

Answer:

x = 2.33

Step-by-step explanation:

6 + 3x = 12x - 15​

6 = 9x -15

21 = 9x

x = 2.33

Answer:

Greater than 7 cm.

Step-by-step explanation:

Answer:greater than 7 cm

Step-by-step explanation:

Answer:

give other guy brainliest he is correct

Step-by-step explanation:

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

hey cutie

Step-by-step explanation:

Answer:

Language:

1. Circle All terms

2. 12 or 13

3. 8

4. 12 or 13

Plot:

Get a graph for this one, the number is the first parameter is x, find that x value along the x axis then after finishing it locate v, find y value along the y axis.

Solve:

1. x = 3

2. x = 1

3. x = 3

4. x = x = 5

5. x = 8

6. x = 12

7. x = 9

8. x = 4

9. x = 3

10. x = 6

11. x = 4

12. x = -12

13. x = 5

14. x = 6

15. x = 16

Step-by-step explanation:

Variables - in algebra is a symbol or a letter.

Constants - are numbers

Coefficients - are the numbers that are with variables

Use this description and circle the examples.

For the plot use a gird, or gets a coordinate plane.

Lastely for the Solve example minus or plus the constant with the coefficient and variable forum the constant outside that has been equal to. Then divide by the variable coefficient, and you will get your x value. Example:

34 - 13 = 21 / 7 thus x = 3

The approximation for 8.4 using the linear approximation is approximately 2.9712 + √2.

To approximate 8.4 using linear approximation (the tangent line) to the function f(x) = √x at x = 8, we first need to find the equation of the tangent line.

We start by finding the derivative of f(x). The derivative of √x is (1/2√x). Evaluating the derivative at x = 8, we have:

f'(8) = (1/2√8) = (1/2√4*2) = (1/4√2) = √2/8.

Now we have the slope of the tangent line, which is √2/8.

Next, we find the y-coordinate of the point of tangency, which is f(8). Substituting x = 8 into the function, we have:

f(8) = √8 = 2√2.

Therefore, the equation of the tangent line can be written as:

y = (√2/8)x + b.

To find the value of b, we substitute the coordinates (x, y) = (8, 2√2) into the equation:

2√2 = (√2/8)(8) + b.

Simplifying, we have:

2√2 = √2 + b.

Subtracting √2 from both sides, we get:

2√2 - √2 = b,

b = √2.

Thus, the equation of the tangent line is:

y = (√2/8)x + √2.

Using this tangent line, we can approximate 8.4 by substituting x = 8.4 into the equation:

y ≈ (√2/8)(8.4) + √2.

Calculating the expression, we have:

y ≈ (0.3536)(8.4) + √2,

y ≈ 2.9712 + √2.

Therefore, the approximation for 8.4 using the linear approximation is approximately 2.9712 + √2.

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Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).

"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.

Here, The formulae are as follows:

=>y = -z + 2      ...(1)

=> y = -2x² + z + 1  ...(2)

Equation (1) can be substituted for equation (2) to find the value of z:

=> Z = x² + 1/2 - z + 2 = -2x² + z + 1

=> 2z = 2x² + 1

We can now enter this value of z into equation (1) and find the value of y:

=> y = -z + 2

=> y = -(x² + 1/2) + 2

=> y = -x² + 3/2

As a result, the equation system can be expressed as:

=> z = x² + 1/2

=> y = -x² + 3/2

When x=0:

=> z = 0² + 1/2 = 1/2

=> y = -0² + 3/2 = 3/2

Therefore, there is no answer for the ordered pair (0, 3/2).

When x=1:

=> z = 1² + 1/2 = 3/2

=> y = -1² + 3/2 = 1/2

The answer is the ordered pair (1, 1/2).

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