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Answer:

We require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day

Step-by-step explanation:

Let n₁ be the population of A required and n₂ be the population of B required.

Now we require 2 units of the first nutrient for species A and one unit of the first nutrient for species B. The total nutrients required by species A is 2n₁ and that by species B is 1n₂ = n₂. So, the total nutrients required by both species A and B is 2n₁ + n₂. Since this equals the quantity of the first nutrient which is 10,560, then  2n₁ + n₂ = 10,560 (1)

Now we require 5 units of the second nutrient for species A and 6 units of the second nutrient for species B. The total nutrients required by species A is 5n₁ and that by species B is 6n₂. So, the total nutrients required by both species A and B is 5n₁ + 6n₂. Since this equals the quantity of the first nutrient which is 31,510, then  5n₁ + 6n₂ = 31,510 (2).

So, we have two simultaneous equations which we would solve to find the populations of A and B which satisfy both equations.

2n₁ + n₂ = 10,560  (1)

5n₁ + 6n₂ = 31,510 (2)

From (1) n₂ = 10,560 - 2n₁ (3)

Substituting equation (3) into (2), we have

5n₁ + 6(10,560 - 2n₁) = 31,510

expanding the brackets, we have

5n₁ + 63,360 - 12n₁ = 31,510

collecting like terms, we have

5n₁ - 12n₁ = 31,510 - 63,360

simplifying, we have

- 7n₁ = -31,850

dividing both sides by -7, we have

n₁ = -31,850/-7

n₁ = 4,550

Substituting n₁ = 4,550 into (3), we have

n₂ = 10,560 - 2(4,550)

n₂ = 10,560 - 9,100

n₂ = 1,460

So, we require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day

Number of Bacteria A and Bacteria B = 4550 and  1460 respectively,

Let the number of bacterias of Specie A and Specie B be = x and y respectively.

Given : 2 Nutrient Requirements of both species of Bacteria A and B , Total Nutrients available

To find : Number of Bacteria 1 and Bacteria 2

Nutrient 1 Constraint Equation : 2x + y = 10560

Nutrient 2 Constraint Equation : 5x + 6y = 31510

Putting the value of y from 1st equation in 2nd equation ;

5x + 6 (10560 - 2x) = 31510

5x + 63360 - 12x = 31510

63360 - 31510 = 7x

7x = 31850  

x = 31850 / 7 = 4550 { Bacteria A}

Putting the value of x in 1st equation,

2 (4550) + y = 10560

9100 + y = 10560

y = 10560 - 9100 = 1460 {Bacteria B}

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Step-by-step explanation:

Add parentheses around 1 + 1.

8 - 3 × 2 - (1 + 1) = 0

8 - 6 - 2 = 0

0 = 0

Answer: The answer is 0.

Step-by-step explanation: You'll need to add the parentheses around 1+1.

The solution:

Answer:

width = 15

Step-by-step explanation:

a² + b² = c² This the the formula

(PLUG IN)

8² + b² = 17²

64 + b² = 289 (subtract 64 on both sides)

b² = 225 (square root)

b = 15

Hope this helps ya!!

Answer:

38 degree

Step-by-step explanation:

all the angles of a triangle are 180 . a supplementary angle is 105 degree... first subtract 180 - 105 (A), because it is a supplementary angle , so 75 degrees then do 180 - ( 67 + 75 ) that is 38 = x

Answer:

2147.60

Step-by-step explanation:

Answer:

it's congruent

side-side -side

Answer:

not congruent because all the sides a different .

Answer:

1/2

Step-by-step explanation:

Answer:

I will assume you mean 0.015 out of 1.

It is 0.985

Step-by-step explanation:

Answer:

0.985

Step-by-step explanation:

The probability that a new fridge does not have a fault = 1 - 0.015

                                                = 0.985

Answer:

c isn't in the equation so I'm assuming you're solving for x

x=16

Step-by-step explanation:

3/4x+2=5/4x-6 start by subtracting 3/4x on both sides

2=2/4x-6 now add 6 to both sides

8=2/4x at this point you can simplify 2/4 to 1/2 just to make it easier to divide

8=1/2x divide 1/2 or 0.5 by 8

x=16

Answer: B. Longest side.

Step-by-step explanation:

Answer:

ANSWER

3pq−6hk+(−3qp+14kh)

⇒(3pq−3pq)+(14kh−6kh)[∴pq=qp]and

⇒0+8kh[kh=hk]

∴8khAns

Answer:

it takes 36 minutes to fill the bathtub using just hot water.

Answer: 8x - 1200

Step-by-step explanation: Because I did the problem

The profit function for Andrew's new product line is P(x) = 5x - 100.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The profit function P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x) = R(x) - C(x).

The revenue and cost functions for a new product line at his business are given by these functions. R(x) = 8x and C(x) = 100 + 3x.

Therefore, P(x) = 8x - (100 + 3x).

P(x) = 8x - 100 - 3x.

P(x) = 5x - 100.

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Answer:

Area of triangle = 34 in²

Step-by-step explanation:

Base = 4 inches

Height = 17 inches

[tex] \rm Area \: of \: triangle = \dfrac{1}{2} \times Base \times Height \\ \\ \rm = \dfrac{1}{2} \times 4 \times 17 \\ \\ \rm = 2 \times 17 \\ \\ \rm = 34 \: {in}^{2} [/tex]

Answer:

The required area of the ∆:

[tex] \boxed{ \rm{ar( \triangle) = 34 \: {inch.}^{2} }}[/tex]

Step-by-step explanation:

We have:

By using Formula, A = 1/2 * bh

⇒ ar(∆) = 1/2 × 4 × 17 inch²

⇒ ar(∆) = 2 × 17 inch²

⇒ ar(∆) = 34 inch²

Thus, The Area of Required ∆ is 34 inch²

Answer:

n=28 7 times 16=112divided by 4 =28

Step-by-step explanation:

Answer:

The correct equation is D.) 6x - 7y = -11

Step-by-step explanation:

Answer: 120 miles

Step-by-step explanation:

In one hour you travel 60 miles

In 2 hours you travel 120 miles

Hope this helps!

Answer:

it eats five mince meat everyday

Answer:

The two trangle's relation by S.AS

Step-by-step explanation:

Idono thes ansar gdau gdddhd hjkdbss hhfc

Answer:

Andre scored 14 points.

Equation: x = 14

Step-by-step explanation:

Let the number of points Andre scored be x.

Diego's points = x-9

Noah's points = (x-9) × 2

                       = 2x-18

Now, you know the exact value of Noah's points which is 10.

2x-18 = 10

Isolate the 2x.

2x = 10+18

    = 28

x = 28÷2

  = 14

Answer:

noah = 10 pts.

diego = 5pts. half as many as noah.

diego is 9pts less than andre.

if diego scored 5 and is 9 less than andre. andre scored 5+9

Andre scored 14pts

Step-by-step explanation:

The line of reflection is the vertical line x = 1.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

The line of reflection is the vertical line passing through the midpoint of segment AA'.

Since A'(2,5) and A(-4,5) have the same y-coordinate, their midpoint is on the line y = 5.

Therefore, the line of reflection is the vertical line x = 1.

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Answer:

shorts = 5and

t-shirts 7

Step-by-step explanation:

step one:

given

Let x= shorts and y= t-shirts

Trevor bought 12 shorts and t-shirts.

x+y=12----------1

sale for $12 each and

t-shirts were $6 each

12x+6y=102---------2

the sytems of equation is

x+y=12----------1

12x+6y=102---------2

Step two:

from 1,  x=12-y

put x=12-y in 2

12(12-y)+6y=102---------2

144-12y+6y=102

144-6y=102

144-102=6y

42=6y

y=42/6

y=7

put y=7 in  1

x+7=12----------1

x=12-7

x=5

shorts = 5and

t-shirts y

Answer:

-90%

Step-by-step explanation:

Change/ original x 100

9000-900= 8100

8100/9000= 0.9

0.9 x 100 = 90

Answer:

5th box  has 45 for  Cecilia and 15 for Cora

8th box  has 72 for  Cecilia and 24 for Cora

Cecilia's boxes numbers are 3 times of Cora's boxes numbers.

Step-by-step explanation:

This can be completed as follows .

                              0   1   2     3     4      5      6    7       8         9       10

Cora's boxes        0   3   6     9     12   15      18    21     24      27     30

Cecilia's boxes    0   9   18    27   36  45     54   63    72      81     90

The 5th box  has 45 for  Cecilia and 15 for Cora which means  Cecilia's  number is 3 times bigger than Cora's number in the 5th box.

The 8th box  has 72 for  Cecilia and 24 for Cora which means  Cecilia's  number is 3 times bigger than Cora's number in the 8th box.

As we see that the difference in numbers is of three times from the beginning to the end. Therefore we conclude that  Cecilia's boxes numbers are 3 times of Cora's boxes numbers.

Answer: 42 pages

Because

Answer:

y=2/3x + 4

Step-by-step explanation:

y=mx + b is the slope intercept form with b representing the y interept and m being the slope.

Answer:

x = 100

Step-by-step explanation:

(x - 20) + x = 180  

2x - 20 = 180

   + 20    +20

2x = 200

x = 200/2

x = 100

9514 1404 393

Answer:

  interval notation for all numbers except those that are at least -1 and less than 2.

Step-by-step explanation:

The ∪ between the two sets of brackets indicates the "union" of two sets. The brackets on the left indicate the interval ...

  -∞ < x < -1 . . . . . for a value represented by x

The curved brackets ( ) indicate the end values of the interval are not included, which is why the < symbol is used, and not the ≤ symbol.

The brackets on the right indicate the interval ...

  2 ≤ x < +∞ . . . . . for a value represented by x

The square bracket [ ] is used to indicate the end value is included, which is why the ≤ symbol is used in relation to the end-value 2.

By convention, the interval notation lists the left end of the interval first, and always uses curved brackets for infinity.