population every generation. This sequence represents the number of

bacteria for the first few generations:

150, 450,1350, ...

What is the explicit formula for the number of bacteria in generation n?

**Answer:** bn= 150*3^(n-1)( bn is a quantity of bacteria in generation n)

**Step-by-step explanation:**

It looks like geometrical sequence, each next generation is three times greater than previous one. So the r of this sequence is 3.

The first generation has 150 representatives, so b1=150

The formula of geometrical sequence is bn=b1*r^(n-1)

(in our case bn is a quantity of bacteria in generation n)

so bn= 150*3^(n-1)( bn is a quantity of bacteria in generation n)

Point W is on line segment V X. Given VX = 18 and VW = 14 determine the length W X

**Answer: WX = 4**

**Concept:**

Here, we need to know the idea of segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

**Solve:**

Given information

VX = 18

VW = 14

Given expression deducted from the segment addition postulate

WX = VX - VW

Substitute values into the expression

WX = 18 - 14

Simplify by subtraction

WX = 4

Hope this helps!! :)

Please let me know if you have any questions

What is (x)

9.4x+17.5

**Answer: x=1.8617 **

**Step-by-step explanation: 9.4x+17.5 9.4x/9.4=17.5/9.4 x=1.8617 **

step by step

6x+1<9-2x

2x-1 less than or equal to 5x+20

3-(2x-7) less than or equal to 34-6x

**Answer:**

6x+1<9-2x

6x+2x<9-1

8x<8

x<1

2x-1 ≤ 5x+20

2x-5x≤20+1

-3x≤21

x≥-7

3-(2x-7) ≤ 34-6x

3-2x+7 ≤ 34-6x

-2x+6x ≤ 34-3-7

4x ≤ 24

x ≤ 6

Write an equation in slope-intercept form of a line that passes through the point (-4,9) and has a slope of 1/2.

**Answer:**

y = 1/2x + 11

**Step-by-step explanation:**

y = 1/2x + b

9 = 1/2(-4) + b

9 = -2 + b

b = 11

PLEASE HELP COMPARING RATIOS

*Answer:*

8 minutes per customer in Restaurant One.

6 minutes per customer in Restaurant Two.

7 minutes per customer in Restaurant Three.

Restaurant Two had the fastest service.

*Method:*

I divided the time it took – for example – 48 divided by 6. I would do this because I wanted to find out each person took (6 people), and the amount of time it took for each person to get their food. I would use division for this problem because I am finding how much each person took out of the whole time.

Answer

The 2nd restaurant is the fastest

Step-by-step explanation:

I. Compare Time per Customers

When 1st restuarant = 48/6 = 9

2nd restuarant = 42/7 = 6

3rd restuarant = 63/9 = 7

Given if in 1 min, I can serve 20 customers = 1/20 = 0.05

in 1 min, He can serve 10 customers = 1/10 = 0.1

See the different? I can serve better than him.

So The answer is the 2nd restuarant.

Hope that help :D

help if you can id appreciate it

Less than 14 means

x < 14

**Answer:**

A. x < 14

**Step-by-step explanation:**

'<' = "less than"

'=' = "equal to"

'>' = "greater than"

What is 3(x-6)+12=6(x+1)-3x show your work.

**Answer:**

No solution.

**Step-by-step explanation:**

3(x - 6) + 12 = 6(x + 1) - 3x

3x - 18 + 12 = 6x + 6 - 3x

3x - 6 = 3x +6

-6 = 6

-6 ≠ 6

How many meters does a runner cross in a circular runway with radious of 100 meters [R=3, 14]

diameter = 2 * radius = 200m

circumference (length of the outside of the circle = diameter * pi = 200 * 3.14

= 628m

circumference (length of the outside of the circle = diameter * pi = 200 * 3.14

= 628m

simplify 2 root 3 + 3 root 3 - 4 root 3

**Answer:**

√ 3

**Step-by-step explanation:**

2√3 + 3√ 3 - 4√ 3

5√3 - 4√ 3

1√3

=> **√
3**

**Answer:**

→ 2√3 + 3√3 - 4√3

= (2+3-4)√3

= (5-4)√3

= √3

Therefore, ** √3** is the right answer.

The side of a cube is 3^4 centimeters long. What is the volume of the cube?

**Step-by-step explanation:**

v=s^3 s=3^4=81

v=(81)^3

v=531,441 cm^3

what is the answer to 90π + 2π(7.5)2

**Answer:**

635.75

**Step-by-step explanation:**

90π + 2π(7.5)²

~Simplify

90π + 2π(56.25)

~Multiply

282.5 + 2(176.625)

~Simplify

282.5 + 353.25

635.75

All this was simplified using PEMDAS.

Best of Luck!

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?

**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.

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

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

To learn more about simultaneous **equations** :

brainly.com/question/16763389

#SPJ2

The length of each side of an equilateral triangle having an area of 9√3 cm² is

**Answer:**

6 cm

**Step-by-step explanation:**

Let each side of the equilateral triangle be *a*.

Given, area of an equilateral triangle = 9√3 cm2

Area of an equilateral triangle = (√3)/4 × (Side)²

=> (√3)/4 × a² = 9√3

[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]

=> a² = 36

[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]

∴ Side = 6 cm [taking positive square root because side is always positive]

another easy question pls answer

**Answer:**

22.5 degrees and 67.5 degrees

**Step-by-step explanation:**

complementary angles add up to 90°

x + 3x = 90°

4x = 90

90/4 = x

x = 22.5

The first angle is 22.5

The second angle is 3 times as much

22.5 x 3 = 67.5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

s= zh - 2zt^3 solve for z

Hi ;-)

[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]

**Answer:**

z = [tex]\frac{s}{h-2t^3}[/tex]

**Step-by-step explanation:**

Given

s = zh - 2zt³ ← factor out z from each term

s = z(h - 2t³ ) ← divide both sides by h - 2t³

[tex]\frac{s}{h-2t^3}[/tex] = z

Which is the graph of the equation y- 1= 5(x-3)?

**Answer:**

linked below

**Step-by-step explanation:**

If you use desmos, it show this which is the correct graph :)

PLEASE HELP YOU WILL GET A BRAINLY AND A LOT OF POINTS

A) 9 plus 4

B) 13

C) x plus 5

D) 5

E) 4

Hope this is right sorry if it’s wrong

B) 13

C) x plus 5

D) 5

E) 4

Hope this is right sorry if it’s wrong

Alex had $29 in a bank account. He withdrew $13 for pizza and then $18 for a movie. How much money does Alex have left in his account?

**Answer:**

-12

**Step-by-step explanation:**

18 plus 13 is 41 29 subtracted from 41 is -12

**Answer:**

**- $2**

**Step-by-step explanation:**

Alex withdrew money twice, or he subtracted those amounts from the total that he had.

In this case, he withdrew $13 first, and then $18, or:

13 + 18 = 31

$31 dollars in all.

Alex had $29. Subtract the total that he withdrew from the amount he had:

29 - 31 = -2

Alex has - $2, or he owes the bank $2 with interest.

~

please help me it’s my last question

One circle is 360°, that means, 180° is half of the circle.

Then, the required rotation may be performed according to this property. For more details see the attached picture.

2 multiplied by b is equal to 8

**Answer:**

2*b = 8

b=4

**Step-by-step explanation:**

2*b = 8

Divide each side by 2

2b/2 =8/2

b=4

2/3=1/2x+2y can someone help

I believe that the answer is 4

suppose a 13 foot ladder is leaning against a building. Reaching to the bottom of a second floor window 12 ft above the ground. How far is the base of the ladder from the building? Round your answer to the nearest 10th

5 ft

4ft

3ft

6ft

**Answer: First Choice. 5ft**

**Step-by-step explanation:**

Here we need to know the idea of the Pythagorean theorem.

Since a building is straight, the base angle is a right angle, thus it would be a **right triangle**.

Pythagorean Theorem: a² + b² = c²

**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)

**Solve:**

Given information

a = 12 ft

c = 13 ft

b = unknow base length

Given formula for Pythagorean Theorem

a² + b² = c²

Substitute values into the formula

12² + b² = 13²

Simplify exponents

144 + b² = 169

Subtract 144 on both sides

144 + b² - 144= 169 - 144

b² = 25

Square root both sides

√b² = √25

[tex]\boxed{b=5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

I wrote a cheque for $10 and he threw my 2 dollar how much do I have left

**Answer:**

you have $ 8

**Step-by-step explanation:**

cheque wrote ,=$10

and he threw =$2

then total $ left will be $8

please mark me brainleast

When p= 12, t= 2, and s= 5, r= 18. If rvaries directly with p and inversely with the product of sand t, what is the

constant of variation?

**Answer:**

15

*Brainliest, please!*

**Step-by-step explanation:**

r = kp/(st)

p = 12, t = 2, s = 5, r = 18

18 = k(12)/(2)(5)

18 = 12k/10

12k = 180

k = 15

Sin A 4/5.

Find

COSA + tan A

**Answer:**

**Step-by-step explanation:**

The opposite side (the one not connected to A) = 4

The hypotenuse is 5

The adjacent side needs to be found for the cosine and the tangent.

a^2 + b^2 = c^2

a = opposite side = 4

b = adjacent side = ?

c = hypotenuse = 5

4^2 + x^2 = 5^2

16 + x^2 = 25

x^2 = 25 - 16

x^2 = 9

x = sqrt(9)

x = 3

cos(A) = adjacent / hypotenuse = 3/5

Tan(A) = opposite / adjacent = 4/3

cos(A) + tan(A) = 3/5 + 4/3

cos(A) + tan(A) = 9/15 + 20/15 = 29/15

Given: SinA = 4/5

To find: CosA + TanA

Solution:

16/25 + Cos²A = 1 [Sin²A + Cos²A = 1]

Cos²A = 1 - 16/25

Cos²A = 25 - 16/25

Cos²A = 9/25

CosA = 3/5

We know that TanA = SinA/CosA

TanA = (4/5)/(3/5)

TanA = 4/3

CosA + TanA = 3/5 + 4/3 = 29/15

To find: CosA + TanA

Solution:

16/25 + Cos²A = 1 [Sin²A + Cos²A = 1]

Cos²A = 1 - 16/25

Cos²A = 25 - 16/25

Cos²A = 9/25

CosA = 3/5

We know that TanA = SinA/CosA

TanA = (4/5)/(3/5)

TanA = 4/3

CosA + TanA = 3/5 + 4/3 = 29/15

Find the distance between the two points rounding to the nearest tenth (if necessary).

(5,-5) and (8,-8)

**Answer:**

4.2

**Step-by-step explanation:**

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

d=sqrt[(5-8)^2+(-5+8)^2]

d=sqrt[(-3)^2+(3)^2]

d=sqrt[9+9]

sqrt18=4.24

HELP!! Use the properties of addition to simplify this expression. 6-8 +6f-2f

**Answer:**

-2 + 4f

**Step-by-step explanation:**

6 - 8 + 6f - 2f

2(3 - 4 + 3f -f) [Distributive Property]

=> 2(-1 + 3f - f)

=> 2(-1 + 2f)

**=> -2 + 4f**

**Answer:**

4f-2

**Step-by-step explan:**

**6-8+6f-2f**

**6-8+4f**

**4f-2**

PLZ HELPP

Q: Nitrates are organic compounds that are a main ingredient in fertilizers. When those fertilizers run off

into streams, the nitrates can have a toxic effect on

fish. An ecologist studying nitrate pollution in two

streams measures nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. The parallel dotplots display the data.

1. Explain what the dot above 12 in the Stony Brook graph represents.

By looking at the** dot graph**, we can see that the single **dot **above 12 in the Stony Brook** graph**, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L

To understand this, first I want to give a brief explanation of how these **graphs** work.

You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.

Each of these 42 places is represented with a **dot** in the corresponding graph. Now looking at the graph, the position of the **dots **represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 **dots** for 42 places).

So, having a single **dot** above 12 in the Stony Brook** graph**, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of **12 mg/L**

If you want to learn more, you can read:

https://brainly.com/question/16354226

Which fractions are equal to 0.375?

The fraction that is equal to 0.375 is 3/8.

Hope this helps! :)

9. 6(0.4 +0.3) =

I need it now!!!!!

:)

**Answer:**

4.2

**Step-by-step explanation:**

0.4+0.3=0.7

0.7x6=4.2

**Answer:**

4.2

**Step-by-step explanation:**

6(0.4+0.3)

=> 6(0.7)

=> 6 x 0.7

=> **4.2**

please i need to know
help plz answer quickly
what is the median of these numbers? 4, 14, 7, 8, 12, 12, 5, 10
(a. Find the distance around the park to the nearest yard.39The distance is aboutyards.b. A new path and a bridge are constructed from point Q to the midpoint M of PR Find QM to the nearest yard.QMydc. A man jogs from P to Q to M to R to Q and back to P at an average speed of 150 yards per minute. To the nearelong does it take him to travel the entire distance?It takes aboutminutesType here to con
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Please help me with this
What are the main problems created by lack of transportation system? Discuss with your friends and present the conclusion in the class.
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6 bannas cost $0.75. How much do 20 bannas cost
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Which of the following is a correct citation for this website for a Works Cited page? article title: Vaccines for All!author: Dr. Vaccinate Vannpublisher: BigPharmaWebsite address: www.bigpharma.comWeb Title: BigPharmadate published: 19 Sept. 2005Vann, Vaccinate MD. "Vaccines for All!" BigPharma.com. BigPharma. 19 Sept.2005. www.bigpharma.com.Vaccinate Vann. "Vaccines for All!" BigPharma.com. BigPharma. 19 Sept. 2005www.bigpharma.com."Vaccines for all!" BigPharma.com BigPharma. Dr.Vaccinate Vann 19 Sept.2005. www.bigpharma.com.
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