I’ll mark you brainliest!!!!! Which situation shows a constant rate of change?

3x - 11 + x + 5 = 180° (Linear pair)

4x - 6° = 180°

4x = 186°

x = 46.5°

The period of the function y = 5sin(6x - π) is π/3, meaning it completes one full cycle every π/3 units. The phase shift is π/6 to the right, indicating that the graph of the function is shifted horizontally by π/6 units to the right compared to the standard sine function.

To determine the period of the function y = 5sin(6x - π), we look at the coefficient of x inside the sine function. In this case, it is 6. The period of a sine function is given by 2π divided by the coefficient of x. Therefore, the period is 2π/6, which simplifies to π/3.

Next, to find the phase shift of the function y = 5sin(6x - π), we look at the constant term inside the sine function. In this case, it is -π. The phase shift of a sine function is the opposite of the constant term inside the parentheses, divided by the coefficient of x. Therefore, the phase shift is (-π)/6, which simplifies to -π/6 or π/6 to the right.

In summary, the function y = 5sin(6x - π) has a period of π/3 and a phase shift of π/6 to the right.

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Answer:

No solution

Step-by-step explanation:

Each side of the equation,once distributed, has 5x.

The 5x's cancel out to x= x-5

Which is incorrect and has no solution.

Explanation:

The dashed line represents the boundary \(y = -\frac{1}{3}x+1\) while the solid boundary line is the graph of \(y = 2x-3\)

We shade the region below both of those boundary lines to form the set of all solution (x,y) points. The reason we shade below is because of the "less than" sign found in both inequalities.

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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Explanation:

Amount = 28.97

coupo

To answer this question, we need to perform a hypothesis test. The null hypothesis is that the proportion of abandoned calls is the same for both shifts, and the alternative hypothesis is that they are different.

We can use a two-sample proportion z-test to test this hypothesis.

First, we need to calculate the pooled proportion of abandoned calls across both shifts:

P = (5 + 7) / (35 + 35) = 0.1714

Next, we can calculate the standard error of the difference between the two proportions:

SE = sqrt(p(1-p)(1/35 + 1/35)) = 0.125

Finally, we can calculate the test statistic:

z = (0.2 - 0.1714) / 0.125 = 2.28

At the 2% significance level, the critical z-value for a two-tailed test is ±2.33. Since our calculated test statistic is less than this value (in absolute terms), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the two shifts differ in terms of proportions of abandoned calls at the 2% significance level.



To perform the hypothesis test, we will follow these steps:

1. Set up the null hypothesis (H0): The proportions of abandoned calls are the same between the two shifts (p1 = p2).
2. Set up the alternative hypothesis (H1): The proportions of abandoned calls are different between the two shifts (p1 ≠ p2).
3. Perform a two-proportion Z-test using the data provided.
4. Compare the resulting p-value to the 2% significance level.

If the p-value is less than 0.02, we reject the null hypothesis, indicating that there is evidence to suggest that the proportions of abandoned calls are different between the two shifts. If the p-value is greater than 0.02, we fail to reject the null hypothesis, suggesting that there is insufficient evidence to conclude that the proportions of abandoned calls are different.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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If the new copier costs $800 per month plus $0.25 for each copy, then the total cost for 6000 copies a month is $2300.

The total cost of leasing a copier from the Shelly group depends on the number of copies made each month.

We have to find the cost for making 6000 copies a month,

The equation to represent the total cost is represented as :

⇒ Total cost = (Monthly lease cost) + (Cost per copy × Number of copies),

⇒ Monthly lease cost = $800

⇒ Cost per copy = $0.25

⇒ Number of copies = 6000,

Substituting the values,

We get,

⇒ Total cost = $800 + ($0.25×6000)

⇒ $800 + $1500

⇒ $2300

Therefore, the total monthly cost is $2300.

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The trigonometric ratios for the angle indicates that the measure of the angle, where tan⁻¹((-√3)/3) = -30°

Trigonometric ratios express the relationship between two sides and an angle of a right triangle.

Let θ represent the angle, we get;

The value of the tangent of the angle is; tan(θ) = -√3/3

Therefore, we get;

The length of the side facing the angle = -√3, and the length of the side adjacent to the angle = 3, from which we get;

The length of the hypotenuse side = √((-√3)² + 3²) = √(12) = 2·√3

The trigonometric ratios indicates that we get;

The sine of the angle is sin(θ) = -√3/2·√3 = -1/2

Therefore, θ = arcsine(-1/2) = -30°

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Answer:

table:

x = -2 , y = 5

x = 0 , y = -3

x = 1 , y = -4

x = 3, y = 0

b

i. line A

ii. y = -1,5

iii. x = -1.25

Step-by-step explanation:

as from the table

Step-by-step explanation:

the last one takes allot of steps but I tried those

Problem:

The point at which a graph hits the x-axis is known as :

Solution:

The zero of the function. This point is characterized by the coordinate

(x, y) = (0, y). Notice that at this point, the coordinate x is always zero.

The minimum amount of paint needed for two coats will be 297 square centimeters.

The shape is a combination of the rectangle and the triangle. Then the area of the shape is calculated as,

A = 1/2 x 18 x 9 + 18 x 12

A = 81 + 216

A = 297 square centimeters

Hence, the minimum amount of paint needed for two coats will be 297 square centimeters.

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The average time in minutes a customer spends waiting in line for service is  5.49 minutes, so the correct answer is D. none of the choices listed.

We can use Little's Law to find the average time a customer spends waiting in line for service:

Average time in line = (Average number of customers in line) / (Service rate)

To find the average number of customers in line, we can use the formula for the M/M/1 queuing system:

Lq = (ρ²) / (1 - ρ)

where

Lq is the average number of customers in the queue

ρ is the utilization of the server, which is equal to the arrival rate divided by the service rate

So, ρ = (Arrival rate) / (Service rate) = 28/35 = 0.8

And, Lq = (0.8^2) / (1 - 0.8) = 0.64 / 0.2 = 3.2

Now we can use Little's Law:

Average time in line = (Average number of customers in line) / (Service rate) = 3.2 / 35

Converting hours to minutes, we get:

Average time in line = (3.2 / 35) * 60 = 5.49 minutes

So the answer is D. none of the choices listed.

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Answer: 5

Step-by-step explanation:

From the question, we are informed that "x varies inversely with v". This means that

x = k/v

where,

k is a constant

We have to find k when x=35 when v=3

x = k/v

35 = k/3

k = 35 × 3

k = 105

Therefore when v = 21, x will be:

x = k/v

x = 105/21

x = 5

Answer: (n + 5)(n - 5)

Explanation: In this problem, we have a binomial that's the difference of two squares because n² and 25 are both perfect squares and we are subtracting or taking the difference of these two squares.

Since the difference of two squares factors as the product of two binomials, we can setup our parenthses and in the first position, we use the factors of n² that are the same which are n · n.

In the second position, we use +5 and -5 as our factors of -25.

So our answer is (n + 5)(n - 5).

I can't make out what the radius of the sphere is, but the equation you're looking for is:

\(V=\frac{4}{3}\pi r^3\)

For example:

If the radius of a sphere is 5 m, it's volume would be,

\(V=\frac{4}{3}\pi (5)^3\)

\(V=\frac{4}{3} (3.14)(5)^3\)

\(V=\frac{4}{3}(3.14)(125)\)

\(V=523.6 m^3\)

Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

Step-by-step explanation:

h(t) = -16t² + 16t + 12

h(t) = -4(4t² - 4t - 3)

h(t) = -4(2t - 3)(2t + 1)

When h(t) = 0, we have t = 1.5 or t = -0.5.

Hence the zeroes are 1.5 and -0.5.

In response to the query, we can state that Therefore, the area of the base of the triangular pyramid is 21 square inches.

A pyramid is a polygon in mathematics, formed by connecting points referred to as bases and polygonal vertices. For each hace and vertex, a triangle called a face is formed. a cone with a polygonal form. A pyramid with a floor and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The vertex, the intersection of a pyramid's flat tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that connect to the top are formed by the edges of the base.

volume of a triangular pyramid

V = (1/3) * Base Area * Height

65 = (1/3) * Base Area * 9.75

Area = 65 / (1/3) / 9.75

Area = 21

Therefore, the area of the base of the triangular pyramid is 21 square inches.

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Answer:

Step-by-step explanation:

The easiest way to explain this is to use slope and then writing equations for lines. The reason for that is because we are told that the production uniformly increases. That "uniform increase" is the rate of change, and since the rate of change is constant, we are talking about the slope of a line, where the rate of change is constant throughout the whole length of the line.

Create coordinates from the info given:

In the third year, 600 units were made. Time is always an x thing, so the coordinate is (3, 600). Likewise for the other bit of info. Time is always an x thing, so the coordinate is (7, 700). Applying the slope formula:

\(m=\frac{700-600}{7-3}=\frac{100}{4}=25\)  which means that 25 units per year are produced. Write the equation to find the number of units produced in any year. I used the point-slope form of a line to do this:

y - 600 = 25(x - 3) and

y - 600 = 25x - 75 so

y = 25x + 525

If we want to know the number of units in the first year, we will replace x with 1 and do the math:

y = 25(1) + 525 so

y = 550 units, choice C.

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

The area of the parallelogram is 0.1875 mile² ⇒ D

Step-by-step explanation:

The formula of the area of a parallelogram is A = b1 × h1 = b2 × h2, where

In the given figure

∵ There is a parallelogram

∵ One of its bases is 0.25 mile

∴ b1 = 0.25 mile

∵ the height of this base is 0.75 mile

∴ h1 = 0.75 mile

→ By using the rule of the area above

∴ The area of the parallelogram = 0.25 × 0.75

∴ The area of the parallelogram = 0.1875 mile²

∴ The area of the parallelogram is 0.1875 mile²

The slope of the line AB in simplest form is 3/2.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We also know that the slope is rise over run, rise represents the y-axis and run represents the x-axis.

From B to C rise is 3 and from B to C run is 2.

Therefore, the slope of the line AB is 3/2.

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Answer:

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.

Graphing is pretty easy. Think of the x and y axis as a number line, you go to the right of 0 you get positive. You go to the left, you get negative. The x axis is just that, the y axis is just like a number line but flipped. You go up for positive and down for negative on the y axis. The middle point is always (0,0). To graph a shape, you just connect the points. To plot positive points you would go right and up. So to plot (8,2), you would go 8 points right on the x axis, then 2 points up on the y axis. Think of Quadrant I as 2 positive points, if both points are positive, plot them there. If you need to plot a negative point then a positive point you would go to Quadrant II. If both of the points are negative, plot them in Quadrant III. If it is a positive point then negative, go to Quadrant IV. Remember, the x axis always comes first. Always go right or left first, then up or down. You determine how many points to go right or left then up or down by the point given. Lets take another example. If you were told to plot (-1,5), that would go in Quadrant II. You would go left 1 and up 5. I explained the concept of the coordinate plane, although, I'm not sure what you mean by coordinate proof. Hope that helped :)

Answer:

SAS, because vertical angles are congruent.

Answer:

The probably. that a person who has been in the hospital for the future of the answers to the questions

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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