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notsponge [240]
2 years ago
6

Round final answers to 3 decimal places.

Mathematics
1 answer:
irina [24]2 years ago
6 0

There are 651.335 million cells in the petri dish after 11 hours and the cells will reach 1 billion cells after 14.068 hours

<h3>How to determine the number of cells after 11 hours?</h3>

The given parameters are:

At t = 0, Bacteria = 140 million

At t = 6, Bacteria = 320 million

This can be represented as:

f(0) = 140

f(6) = 320

An exponential function is represented as:

f(t) = f(0) * r^t

When t = 6, we have:

320 = 140 * r^6

Divide both sides by 140

r^6 = 2.28571428571

Take the 6th root of both sides

r = 1.15

So, we have:

f(t) = f(0) * 1.15^t

Substitute f(0) = 140

f(t) = 140 * 1.15^t

After 11 hours, we have:

f(11) = 140 * 1.15^11

Evaluate

f(11) = 651.33

Hence, there are 651.335 million cells in the petri dish after 11 hours

Time to reach 1 billion cells

This means that

f(t) = 1 billion i.e. 1000 million

So, we have:

1000 = 140 * 1.15^t

Divide by 140

1.15^t = 7.14285714286

Take the logarithm of both sides

t * log(1.15) = log(7.14285714286)

Divide both sides by log(1.15)

t = 14.068

Hence, the cells will reach 1 billion cells after 14.068 hours

Read more about exponential functions at:

brainly.com/question/2456547

#SPJ1

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Triangle ABC is graphed in Quadrant I of a coordinate plane, and none of the vertices have an x-coordinate or
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Answer:

Step-by-step explanation:

D. the corresponding sides of triangle ABC and triangle A'B'C' are congruent

because the sides do not change their length when we rotate the triangle

8 0
3 years ago
State whether the lines are parallel, perpendicular,or neither.
cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

  • Two lines are parallel if their slopes are equal.
  • Two lines are perpendicular if the product of their slope is -1

We also know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept

Given the lines

1)

  • y = 6х - 3

Comparing with y=mx+b, the slope of y = 6х - 3:

m₁=6  

  • y = - 1/6x + 7

Comparing with y=mx+b, the slope of y = - 1/6x + 7:

m₂=-1/6

As

m₁ × m₂ = -1

6 ×  - 1/6 = -1

-1 = -1

Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.

2)

  • y = 3x + 2

Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3  

  • 2y = 6x - 6

simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.

i.e. m₁ = m₂ → 3 = 3

Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

3)

  • 8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4  

  • x + 4y = - 1

simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

As

m₁ × m₂ = -1

4 ×  - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

4)

  • 3x+2y = 5

simplifying to write in slope-intercept form

y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

m₁=-3/2  

  • 3y + 2x = - 3

simplifying to write in slope-intercept form

y = -2/3x - 1

Comparing with y=mx+b, the slope of y = -2/3x - 1:

m₂=-2/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

5)

  • y - 5 = 6x

simplifying to write in slope-intercept form

y=6x+5

Comparing with y=mx+b, the slope of y=6x+5:

m₁=6  

  • y - 6x = - 1

simplifying to write in slope-intercept form

y=6x-1

Comparing with y=mx+b, the slope of y=6x-1:

m₂=6

As the slopes of y - 5 = 6x and y - 6x = -1 are equal.

i.e. m₁ = m₂ → 6 = 6

Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

6)

  • y = 3х + 9

Comparing with y=mx+b, the slope of y = 3х + 9:

m₁=3  

  • y = -1/3x - 4

Comparing with y=mx+b, the slope of y =  1/3x - 4:

m₂=1/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

8 0
2 years ago
200 kg of brass is melted down and cast into ornamental frogs, each weight 3/20kg. How many frogs are made?
Savatey [412]

Answer:

1,333 frogs

Step-by-step explanation:

okay so we know that mass remains conserved no matter where you are.

same here ^^

if the total mass of brass is 200 kg

the total mass of the new frogs formed from it when put together will be the same :)

and if there were n such frogs formed

we have,

total mass = n × mass of each frog

200 = n × 3/ 20

n = 4000/ 3

so it becomes something like 1,333.33

that is nearly 1,333 frogs can be made out of 200 kg of brass each weighing 3/ 20kg (the last ones a bit less to make upto 200kg)

5 0
3 years ago
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the ne
SVEN [57.7K]

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

y=-4}x\\ 4=-4x\\x=-1

8 0
3 years ago
If c=4 and the problem is c to the third power/2 what is the answer?
tiny-mole [99]

c=4\\\frac{c^3}{2}\\\frac{(4)^3}{2}\\\frac{64}{2}\\32

When c = 4 and it is applied to this equation, the answer is 32.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

6 0
3 years ago
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