Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 19,660 units of the first nutrient and 31,890 units of the second nutrient. Each bacterium of species A requires 4 units of the first nutrient and 5 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 6 units of the second. What populations of each species can coexist in the environment so that all the nutrients are consumed each day?

Answers

Answer 1

Answer:

4570 species of the type A and 1540 species of the type B.

Step-by-step explanation:

A:

1st: 4 units

2nd: 5 units

B:

1st: 1 unit

2nd: 6 units

A=x, B=y

4x + 1y = 19820  units of the first nutrient

5x + 6y = 32090  units of the second nutrient

5x + 6*(19820-4x) = 32090.

       32090 - 6(19820-4x)

x= ------------------------------------- = 4570

                     5-24

y = 19820 - 4*4570 = 19820 - 18280 = 1540.

ANSWER:  4570 species of the type A and 1540 species of the type B.

Hopes this solves it.

Answer 2

The populations of each species can coexist in the environment so that all the nutrients are consumed each day are 4530 and 10600

What are simultaneous equation?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given;

Each day the environment is supplied with 19,660 units of the first nutrient and 31,890 units of the second nutrient

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

Now,

Let the number of bacteria of Specie A and Specie B be x and y respectively;

To find : Number of Bacteria 1 and Bacteria 2

Nutrient 1 Constraint Equation : 4x + y = 19660

Nutrient 2 Constraint Equation : 5x + 6y = 31890

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

5x + 6 (19660 - 4x) = 31890

5x + 117960 - 24x = 31890

117960 - 31890 = 19x

19x = 86070

x = 86070 / 19 = 4530 { Bacteria A}

Putting the value of x in 1st equation;

2 (4530) + y = 19660

9060 + y = 19660

y = 19660 - 9060= 10600{Bacteria B}

Therefore, the solution of equations will be 4530 and 10600

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Related Questions

There are 40 students in a summer cohort. Of those students, 20 are taking an accounting course, and 25 are taking a Spanish course. A total of eight students are taking both courses. How many students are not taking either course

Answers

Answer: 3

Explanation:

Students that takes course one or both courses.

20 + 25 = 45

Students that take course. Not including both courses students.

45 - 8 = 37

Students that doesn’t take course.

40 - 37 = 3

Please I need help Please I need help Please I need help Please I need help Please I need help

Answers

Answer:

please help my friend 99ooooooooooooooooooooooooooooooooooo9ooooo my mjjjkjjidhjubsjuxsvuvjxehxf

PLEASE HELP!!! I will give you brainliest!

Answers

Answer:

6

Step-by-step explanation:

The range of the middle 50% is the right side of the box subtracting the left side of the box

14-8

6

I need a step by step correct answer bc i need to get in this college please help :(

Answers

Answer:

please mark me brainliest

Step-by-step explanation:

-6÷3×2+3÷3

using Bodmas(bracket of division multiplication addition and subtraction)

-2×2+1

-4+1

-3

hey please help i’ll give brain

Answers

Answer:

81-1 nine

90-81

9

Step-by-step explanation:

Answer:

[tex]9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ thank \: you[/tex]

Sophie bought snacks for her team's practice. She bought a bag of chips for $2.49 and
a 12-pack of juice bottles. The total cost before tax was $27.57. Write and solve an
equation which can be used to determine x, how much each bottle of juice costs?

Answers

equation: $27.57 = $2.49 + 12x

Solve the compound inequality. Graph the solution

Answers

Answer:  Choice B

Work Shown:

[tex]-2 \le 2x-4 < 4\\\\-2+4 \le 2x-4+4 < 4+4\ \text{ ... add 4 to all sides}\\\\2 \le 2x < 8\\\\2/2 \le 2x/2 < 8/2\ \text{ ... divide all sides by 2}\\\\1 \le x < 4\\\\[/tex]

This says that x is between 1 and 4; it can equal 1, but it can't equal 4.

To visually represent this, we'll have a closed circle at 1, an open circle at 4, with shading in between these circles. This is represented by graph B.

What is the percentage change from 99 to 35

Answers

Step-by-step explanation:

(35-99):99*100 =

(35:99-1)*100 =

35.353535353535-100 = -64.65

Percentage change from 99 to 35 is -64.64% .

Negative sign indicates that the number is decreased from the initial value.

Percentage change : When a number is increased or decreased from its original value is termed as percentage change.

Given, that number changes from 99 to 35.

Formula of percentage change  =  [tex]\frac{Final - Initial}{Initial}[/tex] × [tex]100[/tex]

Final number = 35

Initial number = 99

Substitute the values in the above formula,

Percentage change = [tex]\frac{35 - 99}{99} *100[/tex]

Percentage change = -0.6464 *100

Percentage change = -64.64%

Negative sign indicates that the number is decreased from the initial value.

Know more about percentage change,

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help plz (ASAP) thanks

Answers

Answer:

D

Step-by-step explanation:

thank uu

Answer:

the yellow answer is false; second answer

Step-by-step explanation:

x + 2x + 3x = 6 . Find x

Answers

Answer:

1

Step-by-step explanation:

x + 2x + 3x = 6

Add the like terms,

6x = 6

=> x = 6/6

=> x = 1

Step-by-step explanation:

x+2x+3x=6

x+5x=6

6x=6

x=6÷6

x=1

find a rational number halfway in between the two numbers. 1/3 and 3/10

Answers

Answer:

39/60 is a rational number halfway b/w the given numbers.

Step-by-step explanation:

Add both of these numbers and then divide the result by 2.

(1/3+3/10)/2

=((30+9)/30)/2

=(39/30)*1/2

=39/60

what are some objects that start with s because i have to do my name using objects

Answers

Answer:

Saddle.

Sage.

Sail Boat.

Salad.

Salamander.

Salami.

Salmon.

Salt.

Step-by-step explanation:

Answer: string, shoes, sun, scissors, sand, stapler, safe, soap, salt, salmon, sailboat, scarf, seat,


Angle X measures 110 degrees. If angle X is rotated 60 degrees, what is the measure of angle X'?

Answers

Answer:

170 degrees

Step-by-step explanation:

110+ 60= 170

x angle = 170 degrees

What is six hundred five thousand, five hundred written in standard form

Answers

Answer:

the answer is in given bellow:

605500.

Pleaseee help ill mark brainliest please include explanation too

Answers

Answer:

TO place the triangle ABC on EDF flip the triangle so the you get the mirror image of the triangle and then place it on top of the triangle EDF

hope this helps!

the distance between the points (-1,3) and (2,-1) is?

Answers

Answer:

It is 5.83 units

Step-by-step explanation:

[tex]{ \bf{length = \sqrt{ {(x_{1} - x _{2} ) }^{2} + {(y _{1} - y_{2})}^{2} } }}[/tex]

x1 is -1

x2 is 2

y1 is 3

y2 is -1

[tex] = \sqrt{ {( - 1 - 2)}^{2} + { \{3 - ( - 2) \}}^{2} } \\ \\ = \sqrt{9 + 25} \\ = \sqrt{34} [/tex]

can someone explain to me how to do both of this question? tyvm

Answers

Answer: Hope this helps :)

Step-by-step explanation:

a) =Let the boys be x

girls = x-10

so

x + x - 10 = 50

or, 2x = 60

so, x = 30

boys = 30

girls = 30-10 = 20

Therefore, 30 boys participated in the activity.

b) = Let the zilong's stamp be x and miya's stamp be y

so

first

x+y = 40

y = 40-x

now

x - 10 = 2y

x-10 = 2(40-x)

x-10 = 80-2x

or, 3x = 90

so, x = 30

then y = 40-x

        y = 40-30 = 10

Therefore, Zilong had 30 stamps and Miya had 10 stamps before.

what is the answer to this? please

Answers

Step-by-step explanation:

hopefully it makes sense and is visible

:)

Jocelyn is going to the amusement park, where she has to pay a set price of admission
and another price for tickets to go on each of the rides. The total amount of money
Jocelyn will spend is given by the equation y 3.5x + 28, where y represents the
total amount of money, in dollars and cents, and x represents the number of rides
Jocelyn goes on. What could the number 28 represent in the equation?

Answers

$28 is the set price of admission that she has to pay when entering.

least common multiple of 2 and 3?i forgot how to do this completly over the summer lol

Answers

Answer:

6

Step-by-step explanation:

Multiples of 2: 2, 4, 6, 8, 10

Multiples of 3: 3, 6, 9, 12, 15

Brainliest, please!

5 An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.​

Answers

Answer:

a₁ = - 16 , a₂₁ = 24

Step-by-step explanation:

The nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂ = - 14 , then

a₁ + d = - 14 → (1)

The sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Given S₂₁ = 84 , then

[tex]\frac{21}{2}[/tex] [ 2a₁ + (n - 1)d ] = 84 ( multiply both sides by 2 )

21(2a₁ + 20d) = 168 ( divide both sides by 21 )

2a₁ + 20d = 8 → (2)

From (1) d = - 14 - a₁ ← substitute into (2)

2a₁ + 20(- 14 - a₁) = 8 , that is

2a₁ - 280 - 20a₁ = 8

- 18a₁ - 280 = 8 ( add 280 to both sides )

- 18a₁ = 288 ( divide both sides by -18 )

a₁ = - 16

Substitute a₁ = - 16 into (1)

- 16 + d = - 14 ( add 16 to both sides )

d = 2

Then

a₂₁ = - 16 + 20(2) = - 16 + 40 = 24

how can i solve that equation

Answers

Answer:

C and E

Step-by-step explanation:

[tex]3 \tan( \beta ) = 2. \: \: \: \: \tan( \beta ) = \frac{2}{3} [/tex]

[tex] \frac{h}{x} = \tan( \beta ) = \frac{2}{3} [/tex]

[tex]if \: \: h = 2 \: \: \: x = 3 \: \: \: and \: \: \: t = \sqrt{ {h}^{2} + x } [/tex]

C. [tex]t = \sqrt{13} [/tex] ✅

○♧○♧○♧○♧○♧○♧○♧○♧○♧○♧○♧○

[tex] if \: \: \: h = 4 \: \: \: \: x = 6 \: \: \: and \: \: \: t = \sqrt{ {h}^{2} + {x}^{2} } [/tex]

E. [tex]t = 2 \sqrt{13} [/tex] ✅

The dot plot below shows the numbers of years of experience of the teachers at City High School.
++
0 2 4 6 8 10 12 14 16 18 20
Years of Experience
Determine where a gap is present in the data set.
between 14 and 18 years
between 5 and 7 years
oooo
between 2 and 4 years
between 11 and 19 years
Submit
Reset

Answers

Answer: Between 14 and 18 years

Step-by-step explanation:

There are no dots in that area.

write each equatiom as a single power of 10​

Answers

Answer:

It is 10²

Step-by-step explanation:

[tex] \frac{ {10}^{3} . {10}^{4} }{ {10}^{5} } = \frac{ {10}^{(3 + 4)} }{ { {10}^{5} }} \\ \\ = \frac{10 {}^{7} }{ {10}^{5} } \\ \\ = {10}^{(7 - 5)} \\ = {10}^{2} [/tex]

Answer:

10²

Step-by-step explanation:

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

Then

[tex]\frac{10^{3}.10^{4} }{10^{5} }[/tex]

= [tex]\frac{10^{(3+4)} }{10^{5} }[/tex]

= [tex]\frac{10^{7} }{10^{5} }[/tex]

= [tex]10^{(7-5)}[/tex]

= 10²

a triangle has sides with lengths of 33 centimeters, 75 centimeters, 89 centimeters. is it a right triangle?

Answers

Step-by-step explanation:

By pythagoras triplet

sum of square of bigger side should be equal to sum of square of remaining two sides

so 75² + 33² = 5625 + 1089 = 6714

and 89² = 7921

here 6714 is not equal to 7921

so this triangle is not right angled triangle

MARK AS BRAINLIST IF IT IS USEFUL

Two functions are given ; f(x) = x^2+2x-1 and g(x) =5x+3 . Find the value of x if f(x) = g(x). . Also find f(-4) and g(9

Answers

Answer:

Explanation:

Find x:

f(x) = g(x)

x^2+2x-1 = 5x+3
x^2+2x-5x-1-3 = 0
x^2-3x-4 = 0
(x-4)(x+1) = 0
=> x-4 = 0 => x = 4
=> x+1 = 0 => x = -1

Find f(-4):

(-4)^2 + 2(-4) - 1
= 16 - 8 - 1
= 7

Find g(9):

5(9) + 3
= 45 + 3
= 48

Solve the equation. (find x)​

Answers

Answer:

Step-by-step explanation:

[tex](x^2-3x+1)^{(2x^2+x-6)}=1\ we \ take \ the \ logarithm\\\\(2x^2+x-6)*ln(x^2-3x+1)=0\\\\(2x^2+x-6)=0\ or\ x^2-3x+1=1\\\\1)\\2x^2+x-6=0\\2x^2+4x-3x-6=0\\2x(x+2)-3(x+2)=0\\(x+2)(2x-3)\\x=-2\ or\ x=\dfrac{3}{2} \\\\2)\\x^2-3x=0\\x(x-3)=0\\x=0\ or\ x=3\\\\sol=\{-2,0,\dfrac{3}{2},3\}\\[/tex]

what is the total value in fraction​.

Answers

Answer:

When we divide a whole into equal parts, each part is a fraction of the whole. For example, Fraction of a collection: Fractions also represent parts of a set or collection.

if my answer helps you than mark me as brainliest

if LN=9x-39, LM=47, and MN=3x+10 find MN

Answers

Answer:

11

Step-by-step explanation:

ML+LN=MN solve for x

(47)+(9x-39)=(3x+10) = 1/3

x = 1/3

plug into MN

3(1/3)+10=11

when f(x)=2x-2 what is the domain?​

Answers

Answer:

d: x3R

Step-by-step explanation:

Step 1: What is asked

A domain is for what values of x in the graph is defined such as when y = 2, x is equal to 2.

Step 2: Solve

Since this is a linear equation the domain would be every x value do it would be: d: x3R (x belongs to all real numbers)

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