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After considering all the given data and running a series of calculation we reach the conclusion that the probability of receiving both orders as the same colors is 0.2184, under the condition that a company has the information that 32% of their customers order their product in Black and 26% in White and 22% in Grey.

Then the evaluated probability of both orders being the same color can be found by applying summation of the probability of both orders being black, both orders being white, and both orders being grey.

Now, the probability of both orders being black is 0.32 × 0.32
= 0.1024.

Similarly the probability of both orders being white is 0.26 × 0.26
= 0.0676.

Lastly, the probability of both orders being grey is 0.22 × 0.22
= 0.0484.

Hence, the evaluated probability of both orders being the same color is 0.1024 + 0.0676 + 0.0484 = 0.2184 (rounded to four decimal places).
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Answer:

c=12.04

Explanation:

You can use the formula given: c=√a^2+b^2

c=√8^2+9^2=√64+81=√145=12.04

Answer:

 50 cm

Step-by-step explanation:

To solve this answer you can find the area of the small triangle, and multiply it by 2 to get the area of the top part.

Then you can find the area of one of the bigger triangles and multiply it by 2.

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To find the width of the suitcase, we need to use the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Given the volume of the suitcase as 8,556 cubic inches, the length as 32 inches, and the height as 15.5 inches, we can write the equation:

8556 = 32 × w × 15.5

Simplifying this equation, we can divide both sides by the product of 32 and 15.5:

8556 ÷ (32 × 15.5) = w

Solving for w, we get:

w ≈ 16.50 inches

Therefore, the width of the suitcase is approximately 16.50 inches.

Answer:

f(2) = 3

Step-by-step explanation:

At f(2) we can notice that there is 2 y-values (one is an open circle and another is a closed circle)

But, an open circle means that the function is not defined at that point
But a closed circle means that it is defined

So we ignore the open circle and the closed circle is 3

So f(2) = 3

Answer:{y,x}={-4,-1}

Step-by-step explanation:

Answer:

Step-by-step explanation:

Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].

To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.

The profit function is given as:

[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]

Taking the derivative of P(x) with respect to x, we get:

[tex]P'(x) = 2400 + 210x - 3x^2[/tex]

Setting P'(x) equal to zero and solving for x, we get:

[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]

Here, the critical points are x = 80 and x = -10.

To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:

[tex]P''(x) = 210 - 6x[/tex]

Evaluating P''(80), we get:

[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]

Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.

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Adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 1, 2, 1, and -5, multiplying -4(row1) will gives;

-4 × 1 = -4

-4 × 2 = -8

-4 × 1 = -4

-4 × -5 = 20

-4(row 1) + row 3 will result to:

-4 + 4 = 0

-8 + (-1) = -9

-4 + 6 = 2

20 + (-8) = 12

Therefore, adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

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By summing all the fractions that was left, we have 3 cups of flour left. The correct option is (B).

The "x" represents the quantity while the fractions represents the value.

To get the cups of flour left, we first multiply the number of "x" with the fraction and then add the resulting fractions together.

Cups left = 1 (1/8) + 1(3/8) + 2(1/2) + 2(3/4)

= 1/8 + 3/8 + 1 + 3/2

Find the LCM

= [tex]\frac{1 + 3 + 8 + 12}{8}[/tex]

= 24/8

Cups left = 3 cups

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The value of the function g(f(-4)) = 536. Option D

From the information given, we have that the functions are;

f(x)= 4x+5

g(x) = 4x^2 -5x - 3

To determine the composite function,  g(f(-4)), we need to first determine the value of the function f(x) at -4

Now, substitute the value, we have;

f(-4) = 4(-4) + 5

expand the bracket, we get;

f(-4) = - 16 + 5

Add the values

f(-4) = -11

Now, substitute the value in the function g(x), we have that;

g(f(-4)) = 4(-11)² - 5(-11) - 3

find the square and expand the bracket

g(f(-4)) =484 + 55 - 3

Subtract the values, we have;

g(f(-4)) = 536

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Answer:

  (-2, -1)

Step-by-step explanation:

You want the point that is 4 units left of (2, -1).

The x-coordinate of an (x, y) coordinate pair tells you the number of units to the right of the x=0 point. It increases for points farther right, and decreases for points farther left.

Moving left 4 units decreases the x-coordinate by 4 units. The x-coordinate of 2 becomes ...

  2 -4 = -2

The coordinates of the moved point are (-2, -1).

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The factorization of the polynomial is determined as (x + 6)(x - 2).

The factorization of the polynomial is calculated as follows;

4x² + 10 + x - 50 - x² + 4 + 11x

collecting similar terms, we will have;

3x² + 12x - 36

divide through by 3;

x² + 4x - 12

Factorize the expression as follows;

x² + 6x - 2x - 12

x (x + 6) - 2(x + 6)

(x + 6)(x - 2)

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Answer:

The surface area of the square pyramid is 18 km².

Step-by-step Explanation:

What is the surface area of a square pyramid with a slant height?

The surface area of a square pyramid with a slant height can be determined by the product of the base perimeter with the slant height divided by two.

Mathematically, it can be expressed as:

Surface Area S.A = P × l/2

where;

Side length (a) = 3

Base perimeter (P) = 4a = 4(3) = 12km

Slant length (l) = 3 km

Surface Area (S.A) = 12 × (3/2)

Surface Area (S.A) = 12 x 1.5 = 18 km²

Therefore, the surface area of the same pyramid is 18 square km.

[tex]\sf SA_{Pyramid} =\boxed{\sf 27km^{2}}.[/tex]

We're asked to calculate the surface area (SA) of a pyramid. Surface area of a tridimensional shape isn't more than calculating the area of all of its "faces" and then adding them all together. Some of these tridimensional shapes already have equations that provide a direct calculation of this parameters, without the need to add together the area of the different parts of the shape.

There's a developed formula for directly calculating the surface area of square pyramids, but in this case it is easier to just calculate the individual areas of each face and add them all together.

This is pretty easy to calculate, as the base forms the shape of a square. Therefore, multiplying the length and width of this square will give us that area:

[tex]\sf A_{Base} =lw=3km*3km=\boxed{\sf 9km^{2}} .[/tex]

Check attached image 1 to see where we got these values from.

So these faces form the sape of a triangle. Therefore, mul;tiplying their lengh by width and then dividing by 2 should give us the area.

[tex]\sf A=\dfrac{lw}{2} =\dfrac{(3km)(3km)}{2}=4.5km^{2}.[/tex]

Check attached image 2 to see where we got these values from.

This is the area of an individual triangular face of the pyramid, but we have a total of 4 faces. Hence, let's multiply this area by 4 to find the total area of all triangular faces:

[tex]4.5km^{2} *4=\boxed{\sf 18km^{2}}.[/tex]

So the total surface area, as stated at the beginning of this answer, is given by the addition of all individual areas from all the faces of the shape, so let's do just that:

[tex]\sf SA_{Pyramid} =9km^{2} +18km^{2}=\boxed{\sf 27km^{2}}.[/tex]

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∠WTA and ∠HTC are vertical angles. Thus, they are equal.

As WA || HC, that means ∠AWT and ∠THC are alternate interior angles and are equal. Additionally, ∠WAT and ∠TCH are also alternate interior angles and are equal.

∠WTA = ∠HTC, ∠AWT = ∠THC, and ∠WAT = ∠TCH

Since both triangles have the same angle measurements, they are similar.

The rotation transformation of the quadrilateral IJKL, to obtain the quadrilateral I'J'K'L', are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)

A rotation transformation is one in which the coordinates of a geometric figure are rotated about a point.

The coordinates of the vertex points on the figure are;

J(0, 2), K(2, 3), L(3, -1), and I(2, -3)

The coordinates of the point (x, y) following a rotation of 180° about the origin are (-x, -y)

Therefore, the coordinates of the image of the figure J(0, 2), K(2, 3), L(3, -1), and I(2, -3), following a rotation about the origin are;

J(0, 2) ⇒ J'(0, -2)  

K(2, 3) ⇒ K'(-2, -3)

L(3, -1) ⇒ L'(-3, 1)

I(2, -3) ⇒ I'(-2, 3)

Therefore, we get;

The coordinates of the image are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)

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An equation for this linear function that describes how height varies with age is y = 1/5(x) + 2.

The predicted height at 9 is 3.8 feet.

The predicted height at 31 is 8.2 feet.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Conversion:

1 feet = 12 inches

24 inches = 24/12 = 2 feet.

Next, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 2)/(10 - 0)

Slope (m) = 2/10

Slope (m) = 1/5

At data point (0, 2) and a slope of 1/5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 1/5(x - 0)  

y = 1/5(x) + 2

When x = 9, the predicted height is given by;

y = 1/5(9) + 2

y = 3.8 feet.

When x = 31, the predicted height is given by;

y = 1/5(31) + 2

y = 8.2 feet.

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Answer: 3.14 x 12 x 2

= 75.36

Step-by-step explanation:

Answer: 1st option

explanation: The ones that are crossed out include 1 whole number and 7 1/8 pieces. this is equal to 1 and 7/8. Then there is 3 whole 1 pieces so the answer is the 1st option

Answer:

All of them have a combined of 2,227 Stamps

Mean: 2014

Answer: c=10, b=5 root 3

Step-by-step explanation:

it is a 30-60-90 triangle (use sum of angles in a triangle theorem.)

5 is the leg oppoiste to the 30 degree, so it is half of the hypotenuse, which is c, so c=10

then just use pythagorean theorem and 100-25=75 so answer is root 75 simplified to 5 root 3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

The specified scalar is 12 as the result of u(v + w) is 12i + 12j.

The provided vectors are given to be u = 4i - j v = 3i + j w = i + 3j. First, we need to find the vector v + w,

v + w = (3i + j) + (i + 3j)

v + w = 4i + 4j

Now, we can find dot product, u(v + w),

u(v + w) = u(4i + 4j)

u(v + w) = 4ui + 4uj

Substituting the given values of u, we get,

u(v + w) = 4(4i - j)i + 4(4i - j)j

u(v + w) = 16i - 4j + 16j - 4i

Simplifying, we get,

u(v + w) = 12i + 12j

Therefore, the specified scalar is 12.

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Answer:

Correct ANSWER IS A

Step-by-step explanation:

For each coordinate pair (r,θ) listed in the table, first identify the ray on the graph created by the angle θ. On this ray, plot a point a distance of r from the pole.

The graph of the function "g", which is defined for all "real-numbers" is shown below.

The function "g" which is defined for all "real-numbers" is represented as :

g(x) = {2 if x<0,

         {-1 if x=0

         {-3 if x>0

this function means that, for every input-value, which is less than 0, the output will be always 2,

For the input-value "0", the output-value will be = -1;

For all the input-value which are greater than "1", the out will be always "-3",

So, from the above information, the graph is plotted below,

The red-line represents "2 if x<0", the green line represents "-3 if x>0".

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Therefore , the solution of the given problem of function comes out to be  f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.

On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

Setting the y-value (or output) of a function to zero and then solving for the corresponding x-values will allow us to determine the x-intercepts of the function.

The function in this instance is f(x) = (4x² - 36)/(x - 9)

=> 4x² - 36 = 0

To make the equation simpler, we can factor out a 4:

=> 4(x² - 9) = 0

We can factor further based on the difference of squares we now have:

=> 4(x + 3)(x - 3) = 0

We may determine the x-values where the function crosses the x-axis by setting each element to zero:

=> x + 3 = 0 or x - 3 = 0

To find x, solve for:

=> x = -3 or x = 3

The function f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.

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