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lidiya [134]
3 years ago
14

The question is below

Mathematics
1 answer:
Anna35 [415]3 years ago
8 0

Answer:

12) A = 27

13) B =  36

14) C = 25

15) D = 30

Step-by-step explanation:

We need to complete the ratio tables

We are given:

Footballs 15   5   20   C     D

Baseballs A   9    B    45   54

The table shows the ratio of footballs to baseballs.

We are given the ratio \frac{Football}{Baseball}=\frac{5}{9}

All other ratios will also be simplified to get \frac{5}{9}

12) Calculate A

Footballs = 15

Baseballs = A

Common ratio is 5/9, we need to find a number that multiplies by 5 to get 15, same number will be multiplied by denominator to get A.

We know that \frac{5\times3}{9\times3}= \frac{15}{27}

So, A = 27

13) Calculate B

Footballs = 20

Baseballs = B

Common ratio is 5/9, we need to find a number that multiplies by 5 to get 20, same number will be multiplied by denominator to get B.

We know that \frac{5\times4}{9\times4}= \frac{20}{36}

So, B = 36

14) Calculate C

Footballs = C

Baseballs = 45

Common ratio is 5/9, we need to find a number that multiplies by 9 to get 45, same number will be multiplied by numerator to get C.

We know that \frac{5\times5}{9\times5}= \frac{25}{45}

So, C = 25

15) Calculate D

Footballs = D

Baseballs = 54

Common ratio is 5/9, we need to find a number that multiplied by 9 to get 54, same number will be multiplied by numerator to get D.

We know that \frac{5\times6}{9\times6}= \frac{30}{54}

So, D = 30

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Answer:

The correct option is (D).

Step-by-step explanation:

The two expressions are:

\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7

On simplifying both the expressions we get:

\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1

Compute the value of both expressions for <em>x</em> = 2 as follows:

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The value of both expressions are same for <em>x</em> = 2.

Thus, the correct option is:

"They are equivalent because when x = 2, the two expressions have the same value."

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
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Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by \nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}

- (Gauss' theorem)Given a closed surface S, the following applies

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where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8

Hence, by the Gauss theorem we have that

\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

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Step-by-step explanation:

Let

x

be the kg of coffee of brand A in the mix and

y

be the kg of coffee of brand B in the mix.

The total kg must be

50

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+

y

=

50

The cost per kg of the mix must br

$

7.20

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6

x

+

8

y

, so the total cost per kg of the mix will be

6

x

+

8

y

50

.

6

x

+

8

y

50

=

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Now that we have our two equations, we can solve.

6

x

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⋅

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