Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.

In square prism , A cracker box in the shape of a square prism with a base side length of   [tex]SA - \frac{2S^{2} }{4S} = h[/tex].

What is square prism?

The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.

                                    Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.

we know that'

The formula to calculate the surface area of a square prism is

          [tex]Q = 2s^{2} + 4sh[/tex]

  subtract 2s² both sides

    SA - 2s² = 4sh

  Divide by 4s both sides

     [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

   Rewrite

   [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

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According to the preceding statement, then standard deviation becomes 4.19 if the sample variance is given as 17.56.

A measurement of a data set's departure from the mean is referred to as "standard deviation" (or ""). Whereas a large variance shows that the numbers are more spread, a lower number suggests that its data are clustered around the mean. The standard deviation is a measure of how volatile your collected data is generally. It displays the standard deviation for every score with respect to the mean.

We must consider the square root of both the sample covariance matrix to determine the standard deviation.

= √17.56

≈ 4.19

Hence, their standard deviation is around 4.19

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Answer:

y=-3x+7

Step-by-step explanation:

find the slope which is (y1-y2)/(x2-x1). therefore the slope is -3. and then put it in point slope intercept form which is (y-y1)=m(x-x1) = (y-1)=-3(x-2) and simplified the expression is y=-3x+7.

Mr Smith looks their children 1 times 1

The geometric probability of the cube is 0.64

The complete question is added as an attachment

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

Next, we calculate the volumes of the cube and the cylinder using the following formulas

V(Cube) = l³

V(Cylinder) = πr²h

So, we have

V(Cube) = 3.2³ = 32.768

V(Cylinder) = 3.14 * (4.5/2)² * 3.2 = 50.868

The geometric probability of the cube is then calculated as

P = V(Cube)/V(Cylinder)

So, we have

P = 32.768/50.868

Evaluate

P = 0.64

Hence, the probability is 0.64

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The number of square units for the area of the square is greater than the number of units for the perimeter.

The area of a square is calculated using the formula below:

Area of square = (length of side)²

The length of the side of the square = 10 units

Ares of the square = 10 * 10

Area of the square = 100 units

The perimeter of a square = 4 * length of the side

Perimeter of a square = 4 * 10

The perimeter of a square = 40

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Complete question:

One side of a square is 10 units. Which is greater the number of square units for the area of the square or the number of units for the perimeter?

803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.

Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given values, we get:

Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8

= 401.92 + 401.92

= 803.84 square inches

the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.

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Answer:

y = 4x + 1

Step-by-step explanation:

Let's graph it in slope intercept form y = mx + b

m = the slope

b = y-intercept

m = 4

b = 1

So, the equation is y = 4x + 1

The values in the table using the expression (time=2 × no. of pages) will be 0.5, 5 and 8.5.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to produce a value.

Expressions can be simple or complex, and can involve arithmetic, algebraic, or logical operations. Some examples of expressions include:

In each of these examples, the expression consists of one or more terms that are combined using operations such as addition, subtraction, multiplication, division, or exponentiation.

Now,

As given pages = 8 and time= 16 minutes

this can be deduced by expression Time=2 × no. of pages

Then for time= 1,10 and 17 minutes

no. of pages will be 1/2,10/2 and 17/2.

Hence, the table will be:

Pages           8       0.5         5        8.5

Minutes      16        1           10       17

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The factor that both trinomials have in common is; C: (x + 2)

In mathematics, a polynomial is defined an expression that consists of variables that are also referred to as indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 7x - 18

The trinomial of james is;

x² - 7x - 18

Factorizing this gives;

x² + 2x - 9x - 18

= x(x + 2) - 9(x + 2)

= (x + 2)(x - 9)

The trinomial of Kaitlin is;

x² + 14x + 24

Factorizing this gives;

x² + 12x + 2x + 24

= x(x + 12) + 2(x + 12)

= (x + 2)(x + 12)

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The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)

In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:

d = √[(Δx)² + (Δy)²]

Where:

If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:

d = √[(3 - 1)² + (2 - 3)²]

d = √[2² + (- 1)²]

d = √5

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One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value. On the other hand,[tex]$x=y^2$[/tex]is not a function.

The graph of[tex]$y=x^2$[/tex] is a parabola that opens upwards, centered at the origin (0,0). The graph of [tex]$x=y^2$[/tex] is also a parabola, but it opens to the right, also centered at (0,0). Both graphs intersect at the origin, where x=y=0.

Another important similarity between the two graphs is that they are both symmetric with respect to the y=x line,

which is the line of symmetry for both graphs. This means that if we reflect one of the graphs across the line y=x, we get the other graph.

One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value.

On the other hand,[tex]$x=y^2$[/tex]is not a function, because for some y values there are two corresponding x values (one positive and one negative). This means that the graph of [tex]$x=y^2$[/tex] fails the vertical line test.

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16 + 5

Because Dan has 16 pencils and he gets 5 more

[tex](2x-1)^{2} = 25 \iff (2x-1)^{2} = 5^{2}\\[/tex]

[tex]x > 0 \implies 2x - 1 = 5 \iff 2x = 5 + 1 \iff 2x = 6 \implies \bf x = 3\\[/tex]

[tex](3y-1)^{2} = 36 \iff (3y-1)^{2} = 6^{2}\\[/tex]

[tex]y > 0 \implies 3y-1 = 6 \iff 3y = 6 + 1 \iff 3y = 7 \implies \bf y = \dfrac{7}{3}\\[/tex]

⇒

[tex]\dfrac{3x - y}{x+y} \cdot \dfrac{1}{7} = \dfrac{3(3) - \frac{7}{3} }{7(3+\frac{7}{3} )} = \dfrac{9 - \frac{7}{3} }{7(\frac{16}{3})} = \dfrac{\frac{27-7}{3} }{7(\frac{16}{3})}=\\[/tex]

[tex]= \dfrac{\frac{20}{3} }{\frac{112}{3}} = \dfrac{20}{3} : \dfrac{112}{3} = \dfrac{20}{3} \cdot \dfrac{3}{112} = \dfrac{20}{112} = \bf \dfrac{5}{28}\\[/tex]

Answer:

Red       100

Blue      150

Green    50

Purple    60

Step-by-step explanation:

The total number of people surveyed
= 20 + 30 + 10 + 12
= 72

The relative area of each pie in the pie chart will be in the ratio of

number of people who prefer a color ÷  total number of people

The central angles of each pie category = above ratio x 360°

These angles should add up to 360°

100 + 150 + 50 + 60 = 360

The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are R' (2, 1), S' (4, 2), T' = (5, 4), and U' = (3, 3).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle RSTU, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair R  = (1, -2) → Ordered pair R' = (-(-2), 1) = (2, 1).

Ordered pair S  = (2, -4) → Ordered pair S' = (-(-4), 2) = (4, 2).

Ordered pair T  = (4, -5) → Ordered pair T' = (-(-5), 4) = (5, 4).

Ordered pair U  = (3, -3) → Ordered pair U' = (-(-3), 3) = (3, 3).

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The inequality that can be use to represent the situation is 390 + 6x ≥ 739.

Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. Each set on sale contains 6 glasses.

Therefore, the  inequality that can be used to determine x, the minimum number of sets of glasses Latanya should buy can be calculated as follows:

Hence,

390 + 6x ≥ 739

where

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Answer:

See below.

Step-by-step explanation:

We are asked for a unknown number.

To find our number, we should use the Inverse Operation.

The Inverse Operation is the opposite operation.

For example: If we Multiplied, then we should use the Inverse Operation which is Dividing.

Let's divide 256 by -32 to identify our missing number.

Divide:

[tex]\frac{256}{-32} = -8[/tex]

Our missing number is -8.

The image triangle has vertices after the dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).

To find the image coordinates of a triangle after dilation, we need to multiply the coordinates of each point by the scale factor.

In this case, the scale factor is 3.

So the image coordinates of the triangle with vertices M(0,4), N(4,2), and P(2,-2) after dilation by a scale factor of 3 are:

M' = (3 * 0, 3 * 4) = (0, 12)

N' = (3 * 4, 3 * 2) = (12, 6)

P' = (3 * 2, 3 * (-2)) = (6, -6)

Hence, the image triangle has vertices M'(0,12), N'(12,6), and P'(6,-6).

In summary, the image coordinates of the triangle after dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).

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The profit made from Thembile selling the second hand sewing machine if the cost price is R5700 and the selling price is R8850 is R3150.

Profit/loss refers to the difference between the cost price and selling price of an item. When the difference is positive; it is profit. When the difference is negative; it is loss.

Cost profit = R5700

Selling price = R8850

Profit = Selling price - Cost price

= R8850 - R5700

= R3150

Ultimately, Thembile made a profit of R3150 on the second hand sewing machine.

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The proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is a proportional relationship between two scales.

{ 1 } -

We can write the proportionality constant (mm to cm) as -

{k} = (20 - 10)/(2 - 1)

{k} = 10

{ 2 } -

We can write the complete table as -

9 cm                  9 x 10 = 90 mm

12.5 cm             12.5 x 10 = 125 mm

50 cm               50 x 10 = 500 mm

88.49 cm          88.49 x 10 = 884.9 mm

Therefore, the proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

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The integer number that represents a temperature of 7 ºF below zero is given as follows:

-7 ºF.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For temperatures, we have that:

Hence the integer number that represents a temperature of 7 ºF below zero is given as follows:

-7 ºF.

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The answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

The central limit theorem states that if you take sufficiently large samples from a population, the samples' means will be normally distributed, even if the population isn't normally distributed.

(a) lim x → a [ f(x) + 2g(x)]

= lim x → a f(x) + 2 lim x → a g(x) (using algebraic limit theorem)

= 2 + 2(-4)

= -6

(b) lim x → a [h(x) − 3g(x) + 1]

= lim x → a h(x) - 3 lim x → a g(x) + lim x → a 1 (using algebraic limit theorem)

= 0 - 3(-4) + 1

= 13

(c) lim x → a [ f(x)g(x)]

= lim x → a f(x) * lim x → a g(x) (using algebraic limit theorem)

= 2 * (-4)

= -8

(d) lim x → a [g(x)]²

= [lim x → a g(x)]^2 (using algebraic limit theorem)

= (-4)^2

= 16

(e) lim x → a 3√6 + f(x) / 2g(x)

= [3√6 + lim x → a f(x)] / [2 lim x → a g(x)] (using algebraic limit theorem)

= [3√6 + 2] / [2(-4)]

= (-3√6 - 2) / 8

Therefore, the answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

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Answer:

The inverse of the function is

[tex]f^{-1} (x)=x^2-3[/tex]

Step-by-step explanation:

Given

[tex]f(x)=\sqrt{x+3}[/tex]

Find the inverse.

Write the function as an equation equal to [tex]y[/tex].

[tex]y=\sqrt{x+3}[/tex]

Interchange the variables.

[tex]x=\sqrt{y+3}[/tex]

Square both sides of the equation.

[tex]x^2=y+3[/tex]

Subtract [tex]3[/tex] from both sides of the equation.

[tex]y=x^2-3[/tex]

Replace [tex]y[/tex] with [tex]f^{-1} (x)[/tex].

[tex]f^{-1} (x)=x^2-3[/tex]

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Answer:

Net profit is the amount of money that a company has earned after deducting all of its expenses, taxes, and other costs from its total revenue. It is the final result of a company's income statement, which shows the revenue, expenses, gains, and losses incurred during a specific period of time, typically a year. Net profit is often used as a key measure of a company's financial performance and is a crucial metric for investors and stakeholders in evaluating the success of a business.

Step-by-step explanation:

The distance between points A and B is 6 units.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

We are given that;

The points= (-1.4) and B (5.-2)

Now,

To find the distance between points A (-1.4) and B (5.-2), we can use the distance formula:

d = [tex]\sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Substituting the values we have:

[tex]\sqrt{(5 - (-1))^2 + (-2 - (-4))^2}[/tex]

d = [tex]\sqrt{(5 + 1)^2 + (-2 + 2)^2}[/tex])

d = [tex]\sqrt{(6^2 + 0^2)}[/tex]

d = [tex]\sqrt{36}[/tex]

d = 6

Therefore, by the distance formula answer will be 6 units.

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Answer: Restaurant B

Step-by-step explanation:

First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:

14.52/11 = 1.32

Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:

2.58/2 = 1.28

Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.

Good Luck!

The range of values for length when the perimeter is between 82 feet and 124 feet is: 27 ≤ l ≤ 48

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter. The perimeter of the shape can be calculated by summing the measurements of its sides and edges. A rectangle's perimeter is equal to twice the product of its length and width.

Given a rectangular fence.

The perimeter P is at least 82 feet and is no more than 124 feet.

82 ≤ P ≤ 124

The width is 14 feet.

The range of values of the length is to be found.

Now,

Perimeter of rectangle = 2( length + width)

The lowest value of the perimeter is 82

82 = 2(l + 14)

82 = 2l + 28

54 = 2l

l = 27

The highest value of perimeter is 124

124 = 2(l + 14)

124 = 2l +28

96 = 2l

l = 48

Therefore the range of values for length when the perimeter is between 82 feet and 124 feet is:

                  27 ≤ l ≤ 48

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