If the coordinates of A are (-4,2) and the coordinates of B are (1,-4). What are the coordinates of the midpoint of AB?

-2, -1/2

-3/2, -1

-1, -3/2

-1/2, -2


The answer is -3/2, -1. Got it right on edge.

Answer:

Step-by-step explanation:

The value of Domain should appear once.

Relation 1 is a function

Domain: t, j, v, s

Relation 2 is a function

Domain: -2, 4, 3 - 9, - 1

Relation 3 is not a function

Domain: 5, -2, -2, 5

Relation 4 is not a function

Domain: b, v, m, m

the complete set of trig ratios for this triangle is: sinθ = 8/10, cosθ = 3/5, tanθ = 4/3

To draw the triangle, let's label one of the acute angles as θ and the side opposite that angle as 8 (since sinθ = opposite/hypotenuse and sinθ = 8/10). We can then label the hypotenuse as 10 (since it is given in the ratio) and use the Pythagorean theorem to find the adjacent side:

a² + b² = c²

a² + 8² = 10²

a² + 64 = 100

a² = 36

a = 6

Now we can find the other two trig ratios:

cosθ = adjacent/hypotenuse = 6/10 = 3/5

tanθ = opposite/adjacent = 8/6 = 4/3

Therefore, the complete set of trig ratios for this triangle is:

sinθ = 8/10

cosθ = 3/5

tanθ = 4/3

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The company will make a net profit of $11,000 and will also receive a higher return on investment (57.89%) compared to the return on investment of 4.8% that they will receive if they choose to scrap the inventory.

Cost is the total expenditure incurred in the production or acquisition of goods and services. It includes labour, material, and other related expenses. Cost is an important factor in any business decision as it determines the price of a product or service and provides a guide to how much can be produced and how much profit will be generated. Cost also helps in setting budgeting and pricing strategies and helps businesses manage their resources efficiently.

George should process the inventory further at a cost of $19,000. This decision is the most profitable one for Truck Accessories. This is because the company will incur a net profit of $11,000 (34,000 - 19,000) from the sale of the inventory if he decides to process it further. If he chooses to scrap the inventory, the company will incur a net loss of $76,500 (80,500 - 4,000). Thus, the processing option is the more profitable one in this case.

In terms of return on investment, the processing option will yield a return of 57.89% (11,000/19,000), which is significantly higher than the return of 4.8% that the company will get from scrapping the inventory. This shows that processing the inventory further is the wiser decision for Truck Accessories.

In conclusion, the processing option is the better choice for Truck Accessories. The company will make a net profit of $11,000 and will also receive a higher return on investment (57.89%) compared to the return on investment of 4.8% that they will receive if they choose to scrap the inventory.

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The correct graph would be best to display the data is,

Steven can easily see which genres received the most responses and which genres received the least responses.

Now, we get;

For display the data on different genres and compare the percentage of responses, a pie chart would be the best option.

A pie chart can easily show the distribution of responses across different genres, and the size of each slice will correspond to the percentage of responses for that genre.

By comparing the sizes of the slices, Steven can easily see which genres received the most responses and which genres received the least responses.

Thus, The correct graph would be best to display the data is,

Steven can easily see which genres received the most responses and which genres received the least responses.

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Answer: C

Step-by-step explanation:

The 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33.

Number is a mathematical concept used to quantify a particular quantity or amount, or to name a specific object or entity. It is used in a variety of ways such as counting, measuring, comparing, estimating, and expressing mathematical relationships. Numbers are used for counting, measuring, and many other operations. Numbers can be expressed in numeric form, such as 1, 2, 3; in algebraic form, such as x^2-3x+2; or in symbolic form, such as √2. Numbers can also be used to represent functions or variables.

A 99.7% confidence interval for the true proportion of teachers who provide extra credit can be calculated as:

p′ ± 3σp′ = 0.27 ± (3 × 0.03) = 0.21 to 0.33

This confidence interval indicates that the true proportion of teachers who provide extra credit is between 0.21 and 0.33 with a 99.7% confidence level. That is, there is a 99.7% probability that the true proportion of teachers who provide extra credit is between 0.21 and 0.33.

The confidence interval for the true proportion of teachers who provide extra credit is determined by calculating the sample proportion (p′), sampling standard deviation (σp′), and the critical value of the normal distribution (Zc), which is the number of standard deviations from the mean that the sample proportion is likely to be. In this case, the critical value of the normal distribution is 3, because a 99.7% confidence level corresponds to a Z-score of 3. The confidence interval is calculated by adding and subtracting the critical value multiplied by the standard deviation from the sample proportion.

This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion. For example, a school administrator may use the confidence interval to determine the likely proportion of teachers who provide extra credit and make decisions about how to allocate resources.

In conclusion, the 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33. This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion.

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The 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33.

What is number?

Number is a mathematical concept used to quantify a particular quantity or amount, or to name a specific object or entity. It is used in a variety of ways such as counting, measuring. comparing, estimating, and expressing mathematical relationships. Numbers are used for counting, measuring, and many other operations. Numbers can be expressed in numeric form, such as 1, 2, 3; in algebraic form, such as x^2-3x+2; or in symbolic form, such as √2. Numbers can also be used to represent functions or variables.

A 99.7% confidence interval for the true proportion of teachers who provide extra credit can be calculated as:

p' ± 3op' = 0.27 ±(3 x 0.03) 0.21 to 0.33

This confidence interval indicates that the true proportion of teachers who provide extra credit is between 0.21 and 0.33 with a 99.7% confidence level. That is, there is a 99.7% probability that the true proportion of teachers who provide extra credit is between 0.21 and 0.33.

The confidence interval for the true proportion of teachers who provide extra credit is determined by calculating the sample proportion (p'), sampling standard deviation (op'), and the critical value of the normal distribution (Zc), which is the number of standard deviations from the mean that the sample proportion is likely to be. In this case, the critical value of the normal distribution is 3, because a 99.7% confidence level corresponds to a Z-score of 3. The confidence interval is calculated by adding and subtracting the critical value multiplied by the standard deviation from. the sample proportion.

This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion. For example, a school administrator may use the confidence interval to determine the likely proportion of teachers who provide extra credit and make decisions about how to allocate resources.

In conclusion, the 99.7% confidence interval for the true proportion of teachers who provide extra credit is 0.21 to 0.33. This confidence interval is an estimate of the true proportion of teachers who provide extra credit, and it can be used to make decisions or predictions about the population proportion.

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Answer:

47 is before B, 49 is after B, 51 is the second to last number before C, 55 is before D, and 57 is after D.

Step-by-step explanation:

hope this helps

Therefore, the solutions of the given equation in the interval [0, 21) are 0, 2π, and 3π/2. We write the answer in terms radians of π and separate the solutions with commas:

0, 2π, 3π/2.

Trigonometric identities are equations that relate different trigonometric functions to each other. These identities are true for all values of the variables involved in the equation. There are several different types of trigonometric identities, including:

Pythagorean identities: These are equations that relate the squares of the three basic trigonometric functions: sine, cosine, and tangent. The most common Pythagorean identity is:

[tex]sin^2 \alpha + cos^2 \alpha = 1[/tex]

This identity is true for all values of [tex]\alpha[/tex].

We start by using the trigonometric identity:

sin²θ + cos²θ = 1

Rearranging it, we get:

sin²θ = 1 - cos²θ

So, we can rewrite the given equation as:

sin²0 = sin²0 + cos²0 - cos0

Simplifying further, we get:

cos0 = cos²0

This gives us two cases:

Case 1: cos0 = 0

This occurs when 0 is an odd multiple of π/2. In the given interval [0, 21), the only solution in this case is 3π/2.

Case 2: cos0 = 1

This occurs when 0 is an even multiple of π. In the given interval [0, 21), the solutions in this case are 0 and 2π.

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The pattern of association for the scatter plot is a strong, negative nonlinear association.

Since, We know that;

A scatter plot is a type of graph used to display the relationship between two variables.

In a scatter plot, each observation consists of a pair of values, one for each variable, and is represented by a single point on the graph.

Now,

Looking at the scatter plot, we can observe that the points do not form a straight line, indicating that there is a nonlinear association between the number of cupcakes and the cost per cupcake.

We can also see that as the number of cupcakes ordered increases, the cost per cupcake generally decreases until it reaches a minimum value, after which it remains relatively constant.

Therefore, the pattern of association for the scatter plot is a strong, negative nonlinear association.

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Answer:

  (c)  There is a strong, negative linear association

Step-by-step explanation:

You want to know the pattern of association for the attached scatter plot.

The attachment shows a line of best fit drawn through the given data. The correlation coefficient is computed as -0.97, considered to be a strong negative association. The match between the line and the data suggests the association might be linear.

We can describe the pattern as ...

  There is a strong, negative linear association, choice C.

__

Additional comment

The match is slightly better to an exponential curve, so we might say there is a strong negative nonlinear association. (r²=0.9738 vs 0.9489 for a linear model.)

We note that the total cost for 8 or 9 cupcakes is less than the total cost for some lesser numbers.

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The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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The expression that are equivalent to 10x are 5 * 2x, 2 * 5x, 15x - 5x, 2(5x) and 2 * 5 * x

From the question, we have the following parameters that can be used in our computation:

10x

The expression 10x can be rewritten in any of the following ways

5 * 2x

2 * 5x

15x - 5x

2(5x)

2 * 5 * x

There are several other expressions that are equivalent to 10x

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The value of the given expression is 0.3667.

The given expression is (-5+5√3)/3.

The given expression can be solved as follows

5(-1+√3)/3

= 5(-1+1.22)/3

= (5×0.22)/3

= 1.1/3

= 0.3667

Therefore, the value of the given expression is 0.3667.

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Answer: We can evaluate this triple integral using spherical coordinates, since the region of integration is a ball. In spherical coordinates, the region of integration is defined by:

4 ≤ ρ ≤ 8

0 ≤ θ ≤ 2π

0 ≤ φ ≤ arccos(1/√3)

The integrand is:

f(ρ, θ, φ) = ρ^3 cos^2(φ) (ρ^2 sin^2(φ) - 3)^(-1/2)

Therefore, the triple integral can be written as:

∫∫∫W f(ρ, θ, φ) dV

= ∫0^2π ∫0^arccos(1/√3) ∫4^8 ρ^3 cos^2(φ) (ρ^2 sin^2(φ) - 3)^(-1/2) ρ^2 sin(φ) dρ dφ dθ

This integral is difficult to solve analytically, but we can use numerical integration to approximate the value. Using a numerical integration tool, the value of the triple integral is approximately equal to 28.863. Therefore:

∫∫∫W f(x,y,z) dV ≈ 28.863

Step-by-step explanation:

The vertices of the rectangular garden is plotted on the graph

Given data .

Let the rectangular garden be represented as ABCD

Now , the vertices of the garden is

A ( 4 , 3 ) , B ( 6 , 3 ) , C ( 6 , 9 ) and D ( 4 , 9 )

On plotting the coordinates on the graphical plane , we get

So , the perimeter of the garden is P = 2 ( 2 + 6 )

P = 16 units

And , area of garden is A = 12 units²

Hence , the vertices of the garden is plotted

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Answer:

b) ∠x and ∠z
e) ∠b and ∠d

Step-by-step explanation:

Vertical angles are angles that are opposite of each other. They are also congruent. In the two figures shown, these are the only vertical angles that are part of the answers.

Rounding to the nearest hundredth, we get:

[tex]f (4) \approx3859.69.[/tex]

Let's start by using the given information to find the base of the exponential function.

We know that. [tex]f (2) = 9[/tex], so, we can write:

[tex]f(2) = a*b^2 = 9[/tex]

where a is a constant and b is the base of the exponential function.

We also know that f (2.5) = 94, so we can write:

[tex]f(2.5) = a*b^2.5 = 94[/tex]

Now we can divide the second equation by the first to eliminate a:

[tex]f(2.5) / f(2) = (ab^2.5) / (ab^2) = b^(2.5-2) = b^0.5[/tex]

So, we have:

[tex]b^0.5 = 94/9[/tex]

Taking the square of both sides, we get:

[tex]b = (94/9)^2[/tex]

Now we can use this base to find f (4):

[tex]f(4) = a*b^4[/tex]

To find a, we can use the first equation:

[tex]a = f(2) / b^2 = 9 / (94/9)^2[/tex]

Plugging in the values, we get:

[tex]a = 0.00086189[/tex]

So,

[tex]f(4) = ab^4 = 0.00086189(94/9)^4[/tex]

Rounding to the nearest hundredth, we get:

[tex]f(4) \approx3859.69[/tex]

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Answer:

Perimeter= approximately 43.2

Area=88

Answer:

mark me brilliant

Step-by-step explanation:

We can find the perimeter of the polygon by adding up the lengths of its sides, which can be found using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

where d is the distance between the two points with coordinates (x1, y1) and (x2, y2).

The sides of the polygon are:

- SV, with endpoints (-11,-8) and (0,-8)

- UT, with endpoints (0,0) and (-11,0)

- TS, with endpoints (-11,0) and (-11,-8)

- UV, with endpoints (0,0) and (0,-8)

Using the distance formula for each side, we get:

- SV = √[(-11 - 0)^2 + (-8 - (-8))^2] = 11 units

- UT = √[(0 - (-11))^2 + (0 - 0)^2] = 11 units

- TS = √[(-11 - (-11))^2 + (0 - (-8))^2] = 8 units

- UV = √[(0 - 0)^2 + (-8 - 0)^2] = 8 units

Therefore, the perimeter of the polygon is:

Perimeter = SV + UT + TS + UV = 11 + 11 + 8 + 8 = 38 units

To find the area of the polygon, we can divide it into two triangles: STU and SVU. The base of both triangles is 11 units (the distance between points S and T, and the distance between points U and V). The height of triangle STU is 8 units (the distance between points T and U), and the height of triangle SVU is also 8 units (the distance between points S and V).

The area of each triangle can be found using the formula:

Area = (1/2) x base x height

For triangle STU:

Area(STU) = (1/2) x 11 units x 8 units = 44 square units

For triangle SVU:

Area(SVU) = (1/2) x 11 units x 8 units = 44 square units

Therefore, the total area of the polygon is:

Area = Area(STU) + Area(SVU) = 44 + 44 = 88 square units

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. The true statements are the center of the circle lies on the x-axis and the standard form of the equation is (x - 1)^2 + y^2 = 3. So, the correct answers are B and D.

To determine which statements are true about the circle with equation x^2 + y^2 - 2x - 8 = 0

First, we can rewrite the equation by completing the square

(x^2 - 2x + 1) + y^2 = 9

(x - 1)^2 + y^2 = 3^2

Therefore, the center of the circle is at (1, 0), which lies on the x-axis.

The radius of the circle is sqrt(3), which is not equal to 3, so the statement "The radius of the circle is 3 units" is false.

Since the center of the circle is on the x-axis, the statement "The center of the circle lies on the y-axis" is false.

The standard form of the equation is (x - 1)^2 + y^2 = 3, which is true.

Finally, the radius of the circle whose equation is x^2 + y^2 = 9 is 3 units, which is not the same as the radius of the given circle. Therefore, the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is false.

So, the correct options are B and D.

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The value of graph of function g (x) is,

⇒ g (x) = (x + 4)²

We have to given that;

The graph of function f (x) is,

⇒ f (x) = x²

Here, The graph of function g (x) is 4 unit left to the graph of f (x).

Hence, The graph of function g (x) is,

⇒ g (x) = (x + 4)²

Thus, The value of graph of function g (x) is,

⇒ g (x) = (x + 4)²

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The equation of the quadratic function C(t) is:

[tex]C(t) = -t^2 + 5[/tex]

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero. This function is a second-degree polynomial function, which means it has a degree of two.

To find the equation of the quadratic function C(t), we need to use the general form of a quadratic function:

[tex]C(t) = at^2 + bt + c[/tex]

where a, b, and c are constants to be determined.

We can use the given values of t and C(t) to form a system of equations and solve for the constants.

From the table, we have:

t = -2, C(t) = 1

t = -1, C(t) = 4

t = 0, C(t) = 5

t = 1, C(t) = 4

t = 2, C(t) = 1

Substituting these values into the equation of the quadratic function, we get:

[tex]a(-2)^2 + b(-2) + c = 1\\a(-1)^2 + b(-1) + c = 4\\a(0)^2 + b(0) + c = 5\\a(1)^2 + b(1) + c = 4\\a(2)^2 + b(2) + c = 1[/tex]

Simplifying each equation:

[tex]4a - 2b + c = 1\\a - b + c = 4\\c = 5\\a + b + c = 4\\4a + 2b + c = 1[/tex]

Using the third equation, we can immediately find that c = 5. Substituting this into the other equations, we get:

[tex]4a - 2b = -4\\a - b = -1\\a + b = -1\\4a + 2b = -4[/tex]

Simplifying further, we get:

2a - b = -2

a + b = -1

2a + b = -2

Solving for a and b using any method of solving linear equations, we get:

a = -1, b = 0

Therefore, the equation of the quadratic function C(t) is:

[tex]C(t) = -t^2 + 5[/tex]

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The equation of [tex]C(t) = -x^2 + 5.[/tex]

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the equation of the quadratic function C(t), we can use the vertex form of a quadratic function:

[tex]C(t) = a(t - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and "a" determines the direction and shape of the parabola.

From the given table, we can see that the vertex of the parabola is at t = 0, C(0) = 5. Also, since the parabola is opening downward, the coefficient "a" must be negative.

Using the vertex and one of the other points, say (-2, 1), we can find the value of "a":

[tex]1 = a(-2 - 0)^2 + 5[/tex]

1 = 4a + 5

4a = -4

a = -1

Therefore, the equation of C(t) is:

[tex]C(t) = -(t - 0)^2 + 5[/tex]

Simplifying, we get:

[tex]C(t) = -t^2 + 5[/tex]

Therefore, the correct option is [tex]C(t) = -x^2 + 5.[/tex]

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The equation could represent function g the result of this transformation is,

g (x) = - tan (1/2x)

Tangent function:

The tangent function is:

y = tan x

Since, Horizontally compressed by a factor of 1/2

Hence, Horizontally compressing by a factor of 1/2 is multiplying by 1/2.

So, It is Reflected over the x-axis.

g (x) = tan (1/2x)

Thus, Reflecting a function over the x-axis is the same as multiplying it by -1.

Then, g is given by:

g (x) = - tan (1/2x)

Thus, The equation could represent function g the result of this transformation is,

g (x) = - tan (1/2x)

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Answer:
The correct answer will be C. 3

Step-by-step explanation:

Hope this helps you :)

[tex]\cfrac{8}{13}\cdot \cfrac{7}{55}\cdot \cfrac{11}{2}\implies \cfrac{8\cdot 7\cdot 11}{13\cdot 55\cdot 2}\implies \cfrac{616}{1430}\implies \cfrac{(22)(28)}{(22)(65)}\implies \cfrac{28}{65}[/tex]

Answer:

28/65

Step-by-step explanation:

8/13×7/55×11/2

8/13×7/55=56/715

56/715×11/2=56/130=28/65

The interquartile range (IQR) of the data is 42.

The interquartile range (IQR) is the box plot showing the middle 50% of scores and can be calculated by subtracting the lower quartile from the upper quartile (e.g., Q3−Q1).

In the image, The data set is:

20 40 E 60 80 E 100​

Now, We have to find the interquartile range of the data.

The IQR is the difference between the upper quartile Q₃ and the lower quartile Q₁

Q₃ is the value at the right side of the box plot , that is

Q₃ = 62

Q₁ is the value at the left side of the box plot , that is

Q₁ = 20

then

IQR = Q₃ - Q₁ = 62 - 20 = 42

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Answer:

135 non union members

Step-by-step explanation:

sum the parts of the ratio, 8 + 5 = 13 parts

divide the amount of employees by 13 to find one part of the ratio.

351 ÷ 13 = 27 ← value of 1 part of the ratio, then

5 parts = 5 × 27 = 135 ← non union members

There are 135 nonunion members working for the company.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

Given that for every 8 union members, there are 5 nonunion members.

Here, the total number of employees can be represented as:

8x + 5x = 13x, where x is a constant.

Since the total number of employees is 351, so we can solve for x as follows:

13x = 351

x = 27

So, the nonunion members: 5x = 5 × 27 = 135

Therefore, there are 135 nonunion members working for the company.

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Answer:

Step-by-step explanation:

x^2 + 6x + 9

D = 6^2 - 9 * 4 = 36 - 36 = 0

x1= [tex]-\frac{6}{2}[/tex]=-3