A bacteria triples its original population in 25 hours (A=3A0). How big will its population be in 100 hours?

Answers

Answer 1

Answer:

81 times the original size.

Step-by-step explanation:

AA0ktA=3A0=?=?=25hours=A0ekt

Substitute the values in the formula.

3A0=A0ek⋅25

Solve for k. Divide each side by A0.

3A0A0=e25k

Take the natural log of each side.

ln3=lne25k

Use the power property.

ln3=25klne

Simplify.

ln3=25k

Divide each side by 25.

ln325=k

Approximate the answer.

k≈0.044

We use this rate of growth to predict the number of bacteria there will be in 100 hours.

AA0ktA=3A0=?=ln325=100hours=A0ekt

Substitute in the values.

A=A0eln325⋅100

Evaluate.

A=81A0

At this rate of growth, we can expect the population to be 81 times as large as the original population.

Answer 2

Answer:

81

Step-by-step explanation:


Related Questions

what is 2+2
it is very hard​

Answers

Answer:

4 is your answer :) yayy

Answer: Your answer is 4

Step-by-step explanation: If you have 2 blocks, and someone gives you 2 more, you now have 4 blocks in total. Hoped this helped you. Have a wonderful day!!!

A local little league has a total of 95 players, of whom 20% are right-handed. How many right-handed players are there?

Answers

80% of 95 is 0.80(95) = 76

There are 76 right-handed players.

Answer:

19

Step-by-step explanation:

20% of 95 is 19 :)

A desk fan has blades of 4 inches rotated at a rate of 249 revolutions per minute.

Answers

Ok_____________________

Frank's been traveling a lot lately as part of his job. During the past 30 days, he's been out of town 18 days. What fraction represents the number of the past 30 days that Frank has been out of town? Explain how you got your answer.

Answers

Answer:

18/30

Step-by-step explanation:

He has been out of town 18 out of the 30 days. You can simplify this to 6/10.

What is the first error Jordy made in his proof?
Choose 1 answer:
Jordy used an invalid reason to justify the congruence of a pair of sides or angles.
Jordy only established some of the necessary conditions for a congruence criterion.
Jordy established all necessary conditions, but then used an inappropriate congruence criterion.
Jordy used a criterion that does not guarantee congruence.

Answers

Answer:

D: Jordy used a criterion that does not guarantee congruence.

Step-by-step explanation:

Looking at the various steps, in step five, it says;

ΔABE ≈ ΔBCD

The reason for that is given as;

Angle - Angle - Angle congruence

Now, in test for congruence, we use any of the following criteria;

SSS: Side - Side - Side

SAS: Side - Angle - Side

ASA: Angle - Side - Angle

AAS: Angle - Angle - Side

RHS: Right angle - Hypotenuse - Side

Now, AAA was used and it's not part of the criteria to be used for congruence.

AAA is not used because it's possible for 3 angles to be equal and yet the triangles not congruent.

Thus, we can conclude that Jordy used a criterion that does not guarantee congruence.

Answer: Jordy used a criterion that does not guarentee congruence

Step-by-step explanation: Khan Academy

2x < 16
...................

Answers

Answer:

X could be any number from 1-6

Step-by-step explanation:

Because 2 multiplied by 1-6 equals a number lower than 16

A snail crawled ¾ inches in ⅕ of a minute. How long did it take the snail to crawl ½ an inch?

Answers

who tryna do all dis ..

Which expression is equivalent to 9+8 xn?
0 72n
O 9 + 8n
17 xn
0 9x (8 + n)

Answers

Answer:

17xn

Step-by-step explanation:

18 Graph the solution set for the inequality 4x – 3y > 9
on the set of axes below. Determine if the point
(1,-3) is in the solution set. Justify your answer.

Answers

Answer:

I think it's (-13,0)

Step-by-step explanation:

4x - 3y > 9

3y - 9 =x

y=-13

(-13,0)

Plz forgive me if i did that wrong I did try lol

A shopper needs 24 sandwich rolls. The store sells identical rolls in 2 differently sized packages. They sell a six-pack for $5.28 and a four-pack for $3.40. Should the shopper buy 4 six-packs or 6 four-packs?
6 four-packs is a better deal
4 six-packs is a better deal

Answers

4 six-packs is a better deal because it is $0.72 cheaper.
Hope it helps u!!!!!! ❤️

Find the slope of the line graphed below.

Answers

Answer:

Rise/Run= 1/2

Step-by-step explanation:

A gallon of milk cost $2.79 in 200.In 2015,it cost$3.98. Round to nearest tenths place . Write in Original,New,Change,Percent Proportion,Increase or Decrease,Solution Form

Answers

Answer:Is that the way the question was asked that's confusing

Step-by-step explanation:

Help me please I’ll mark as brainliest!!

Answers

Answer:

i wish i could help so sorry

Step-by-step explanation:

The unshaded regions are quarter circles. Which choice best approximates the area of the shaded region? Use ≈3.14. 24

Answers

Answer:

The probability that a point chosen at random will be in the shaded region is 0.25

Step-by-step explanation:

We have been given a small shaded circle inside a larger un-shaded circle. This is shown in the image attached below.

The area of smaller circle is 78.5 squares inches and the area of larger circle is 314 square inches. We have to find the probability that a point chosen at random will be in the shaded region.

Probability is defined as the ratio of Favorable outcome to the Total outcomes. In this case the favorable outcome is that the point should be inside the shaded region i.e. in an Area of 78.5 square inches. And the total outcome is that the point can be anywhere inside the larger circle i.e. within an Area of 314 square inches. Thus the probability that a point chosen at random will be inside the shaded region will be:

[tex]Probability =favorable-Outcome/total outcome[/tex]

[tex]=78.5/314[/tex]

[tex]=0.25[/tex]

Thus, the the probability that a point chosen at random will be in the shaded region is 0.25. This means there is a 25% chance that a randomly chosen point will be inside the shaded region.

1. What is the slope of this line?

(have this done correctly for brainiest)​

Answers

Answer:

4

Step-by-step explanation:

slope = dy/dx

We can see a dy (delta y) of 4 together with a dx of 1. In other words, when you step 1 to the right, you go up 4.

Answer:

the slope is-- 4/1 and the y intercept is where the line touches the vertical line. sorry the picture in not clear,so i could not see the number

Step-by-step explanation:

A red -tailed hawk can travel 50 miles when it flies against the wind In that same amount of time, the hawk can fly 90 miles when flying with the wind. How fast can the red-tailed hawk fly when the wind speed is 10 miles per hour?

Answers

Answer:

Against the direction of the wind is [tex]x-10=35-10=25\ \text{mph}[/tex] and with the wind is [tex]x+10=35+10=45\ \text{mph}[/tex]

Step-by-step explanation:

Let x be the speed of the hawk in still air

The speed of the wind is 10 mph

So speed of the hawk when flying against the wind is [tex]x-10[/tex] and with the wind is [tex]x+10[/tex].

Distance the hawk travels when going against the wind is 50 miles and going with the wind is 90 miles

The hawk covers the above mentioned distances in the same amount of time.

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\dfrac{50}{x-10}=\dfrac{90}{x+10}\\\Rightarrow \dfrac{50}{x-10}-\dfrac{90}{x+10}=0\\\Rightarrow \dfrac{50(x+10)-90(x-10)}{x^2-100}=0\\\Rightarrow 50x+500-90x+900=0\\\Rightarrow -40x+1400=0\\\Rightarrow x=\dfrac{1400}{40}\\\Rightarrow x=35\ \text{mph}[/tex]

The speed of the hawk in still air is 35 mph.

Speed of the hawk against the direction of the wind is [tex]x-10=35-10=25\ \text{mph}[/tex] and with the wind is [tex]x+10=35+10=45\ \text{mph}[/tex].

A bath tub in the shape of a rectangular prism is 20 meter long, 10 meter wide and 5 meter deep. How much water can it hold?

Answers

Answer:

1000 meters³

Step-by-step explanation:

20 x 10 x 5 = 1000

the units are in meters and you are measuring the volume so the units is meters³

Volume of rectangular prism is 1000 [tex]m^{3}[/tex]

1000 [tex]m^{3}[/tex] of water can a bath tub hold.

What is a rectangular prism?

"A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid."

Given

Length of a bath tub = 20 m

Width of a bath tub = 10 m

Height of a bath tub = 5 m

Formula to find the volume of the rectangular prism

Volume of the rectangular prism = length × width × height

= 20 × 10 × 5

=200 × 5

V = 1000 [tex]m^{3}[/tex]

Volume of the rectangular prism = 1000 [tex]m^{3}[/tex]

Hence, Volume of rectangular prism is 1000 [tex]m^{3}[/tex]

1000 [tex]m^{3}[/tex] of water can a bath tub hold.

Learn more about rectangular prism here

https://brainly.com/question/16154580

#SPJ2

When x increases from a to a+2, y increases by a factor of 16. For which function is the statement true?

A. y=2(4)^x
B. y=4x+2
C. y=2(16)^2
D. 16x+2

Answers

I believe the answer is d, but please correct me if I’m wrong!

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 50.2 min. PX> 50.2)( (Report answer accurate to 2 decimal places.) The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.3 and 50.8 min. P(50.3 X50.8)-| Let X have a uniform distribution on the interval (10, 16). Find the probability that the sum of 2 independent observations of X is greater than 29.

Answers

Answer:

a)  P(X > 50.2) = 0.90

b) P(50.3 < X < 50.8) = 0.25

c) P(X+Y >29) = 0.9167

Step-by-step explanation:

From the given information:

[tex]f(x) = \dfrac{1}{b-a} \ \ \ \ a<x<b[/tex]

[tex]f(x) = \dfrac{1}{52.0-50.0} \ \ \ \ 50.0<x<52.0[/tex]

[tex]f(x) = \dfrac{1}{2} \ \ \ \ 50.0<x<52.0[/tex]

a)

Let X be the random variable that follows a uniform distribution.

Such that [tex]X \sim U (50.0, 52.0)[/tex]

where;

a = 50

b = 52

[tex]P(X> 50.2) = \dfrac{b - x}{b-a}[/tex]

[tex]P(X> 50.2) = \dfrac{52 - 50.2}{52-50}[/tex]

[tex]P(X> 50.2) = \dfrac{1.8}{2.0}[/tex]

P(X > 50.2) = 0.90

b.)

To find the probability that the class length is between 50.3 and 50.8 min.

i.e.

[tex]P(50.3 <X<50.8) = \dfrac{(X_2-X_1)}{(b-a)}[/tex]

[tex]P(50.3 <X<50.8) = \dfrac{(50.8-50.3)}{(52-50)}[/tex]

[tex]P(50.3 <X<50.8) = \dfrac{(0.5)}{(2)}[/tex]

P(50.3 < X < 50.8) = 0.25

c)

Given that:

the interval = (101,16)

The probability that the sum of 2 independent observations of X is greater than 29 can be computed as follows.

here;

[tex]c = \dfrac{a+b}{2}[/tex]

where;

a = 10*2 = 20

b = 16*2 = 32

[tex]c = \dfrac{20+32}{2}[/tex]

c = 52/2

c =26

The required probability:

[tex]P(X+Y >29) = 1 - \dfrac{(b-x)\times 2}{(b-a) \times (b - c)}[/tex]

[tex]P(X+Y >29) = 1 - \dfrac{(32-29)\times 2}{(32-20) \times (32 - 26)}[/tex]

[tex]P(X+Y >29) = 1 - \dfrac{(3)\times 2}{(12) \times (6)}[/tex]

[tex]P(X+Y >29) = 1 - \dfrac{6}{72}[/tex]

P(X+Y >29) = 1 - 0.0833

P(X+Y >29) = 0.9167

Solve the equation for y.
2/5 x+y=3

Answers

Answer:

y=-2/5x+3

You subtract 2/5x from both Sides to get your answer

Consider these proportions: 4.5:1.5 6:2 7.5:2.5 9:3
Which of the following proportions belongs to the above set?
A 10.5:3.5 B 13:4 C 13.5:4.5 D 14:5

Answers

Answer:

 A

Step-by-step explanation:

plz help due in 5min​

Answers

Answer:

Justin, Louise, Franklin

Step-by-step explanation:

what is 3 divided by 80

Answers

0.0375 did you mean 80÷3 if so 26.6

A lawn-care company loses $130 as a result of a delay. The 4 owners of the company must share the loss equally. Which expression represents each owner’s share of the loss?

Answers

Answer:

$130/4

Step-by-step explanation:

Solve the given initial-value problem. (Use x as the independent variable.) 2y'y'' = 1, y(0) = 2, y'(0) = 1

Answers

Answer: y(x) = (2/3)*(x + 1)^(3/2) + 1/3.

Step-by-step explanation:

We have the differential equation:

2*y'(x)*y''(x) = 1.

y(0) = 2

y'(0) = 1.

I will use the change:

u = y'

u'= y''

Then we must solve:

2*u*u' = 1.

The product does not depend on x:

u*u' = 1/2.

By looking at the problem, i know that the functions must be something like:

u = a*(x + b)^n

Where a and b are real numbers.

u' = n*a*(x + b)^(n - 1)

such that:

(x + b)^n*(x + b)^(n - 1) does not depend on x

This means that:

(x + b)^n*(x + b)^(n - 1)  = (x + b)^(n + n - 1) = 0

n + n - 1 = 0

2n = 1

n = 1/2

Then:

u = a*(x + b)^(1/2)

u' = (a/2)*(x + b)^(-1/2)

The differential equation becomes:

u*u' = 1/2

a*(x + b)^(1/2)* (a/2)*(x + b)^(-1/2) = 1/2

(1/2)*a^2 = 1/2

a^2 = 1.

And by the initial conditions, we have:

y'(0) = u(0) = 1

then:

u(0) = a*(0 + b)^(1/2) = a*b^(1/2) = 1

now, if a = -1, then b^(1/2) must be negative, this can not really be then we must have:

a = 1

u(0) = 1*b^(1/2) = 1

then b = 1.

u(x) = (x + 1)^(1/2).

And remember that y'(x) = u(x).

Then we need to integrate u(x) over x.

let's use the change of variables:

w = x +  1

dw = dx

Then the integration of u(x) is:

y(w) = ∫(w)^(1/2)dw = (2/3)*w^(3/2) + c

where c is a constant of integration.

now we can go back to x:

y(x) = (2/3)*(x + 1)^(3/2) + c

And we know that:

y(0) = 1 = (2/3)*(0 + 1)^(3/2) + c

         1 = (2/3)*1 + c

1 - 2/3 = c

     1/3 = c

Then:

y(x) = (2/3)*(x + 1)^(3/2) + 1/3.

What is the area of the trapezoid shown?

Answers

Answer:

Answer is 74 square units

Step-by-step explanation:

I took the quiz.

Tia read 0.46 of the book assigned for class. Kiana read 33 out of the 72 pages. Who read more of the book?

Answers

Tia read more because 33 out of 72 pages is only 45% of it, but Tia read 46% of it.

The answer to Tia.

Have a good day :)

andreis grandfather offered to give him a

Answers

Answer:

girlfriend

Step-by-step explanation:

A truck weighs 16,000 pounds. What is the weight range in tons?

Answers

Answer:

8

Step-by-step explanation:

uh idrk all ik is that 16,000 punds = 8 tons

8
16,000 pounds equals 8 tons

The perimeter of a triangle is 25 cm. The first side is 3 cm longer than the second side. The third side is triple the length of the first side. Find the length of each side. (NEED HELP ASAP!! FIRST ONE GETS BRAINLY!!)

Answers

Step-by-step explanation:

Let second side = x

First side = 3+x

Third side = 3(3+x) = 9 +3x

The perimeter of a triangle = 25 cm

Perimeter = sum of all sides

So,

x + 3 + x + 9 +3x = 25

12 + 5x = 25

5x = 13

x = 2.6 cm

First side = 3 + x = 5.6 cm

Second side = x = 2.6 cm

Third side = 9+3(2.6) = 16.8 cm

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