In a lab experiment, 2400 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 19 hours. How long would it be, to
the nearest tenth of an hour, until there are 3300 bacteria present?

Answers

Answer 1

Answer:

It takes 8.7 hours for there to be 3300 bacteria present.

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for population growth is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate.

2400 bacteria are placed in a petri dish.

This means that [tex]P(0) = 2400[/tex]

So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 2400(1+r)^t[/tex]

The conditions are such that the number of bacteria is able to double every 19 hours.

This means that [tex]P(19) = 2P(0)[/tex]. We use this to find 1 + r.

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]2P(0) = P(0)(1+r)^{19}[/tex]

[tex](1+r)^{19} = 2[/tex]

[tex]\sqrt[19]{(1+r)^{19}} = \sqrt[19]{2}[/tex]

[tex]1 + r = 2^{\frac{1}{19}}[/tex]

[tex]1 + r = 1.03715504445[/tex]

So

[tex]P(t) = 2400(1+r)^t[/tex]

[tex]P(t) = 2400(1.03715504445)^t[/tex]

How long would it be, to the nearest tenth of an hour, until there are 3300 bacteria present?

This is t for which [tex]P(t) = 3300[/tex]. So

[tex]P(t) = 2400(1.03715504445)^t[/tex]

[tex]2400(1.03715504445)^t = 3300[/tex]

[tex](1.03715504445)^t = \frac{3300}{2400}[/tex]

[tex]\log{(1.03715504445)^t} = \log{\frac{33}{24}}[/tex]

[tex]t\log{1.03715504445} = \log{\frac{33}{24}}[/tex]

[tex]t = \frac{\log{\frac{33}{24}}}{\log{1.03715504445}}[/tex]

[tex]t = 8.7[/tex]

It takes 8.7 hours for there to be 3300 bacteria present.


Related Questions

PLEASE HELP!Write the standard form of equation with p=sqrt3, 0=150°

Answers

Answer:

I heard it's not b

Step-by-step explanation:

was A the correct answer?

Find the missing side. Round to the nearest tenth

Answers

Answer:

x = 12.5

Step-by-step explanation:

From the diagram,

Applying

tanФ  = Opposite/Adjacent...................... Equation 1

From the diagram,

Given: Opposite = 16, Adjacent = x, Ф = 52°

Substitute these values into equation 1

tan52° = 16/x

make x the subject of the equation

x = 16/tan52°

x = 16/1.27994

x = 12.5.

The difference between an observational study and an experiment is that

Answers

Answer:

An observational study is a study based on data while as an experiment, your actually using that data and carrying out different procedures with it.

Answer:

in an observational study, the researchers do not control treatment, and in an experiment, they do (B)

Step-by-step explanation:

PLEASE HELP ILL GIVE BRAINLIEST !!

FAKE ANSWERS WILL GET REPORTED.

Answers

Answer:

b ≈ 3.9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg b is another leg c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

a = 1

c = 4

Step 2: Solve for b

Substitute in variables [Pythagorean Theorem]:                                            1² + b² = 4²Evaluate exponents:                                                                                         1 + b² = 16[Subtraction Property of Equality] Subtract 1 on both sides:                         b² = 15[Equality Property] Square root both sides:                                                    b = √15[√Radical] Evaluate:                                                                                         b = 3.87298Round:                                                                                                               b ≈ 3.9

The results of a survey of 38 students and the foreign language they are studying are shown in the two-way frequency table. Language Gender Chinese French Spanish Total Girl 4 7 10 21 Boy 1 1 15 17 Total 5 8 25 38 What fraction of the surveyed students are taking Chinese? of the surveyed students are taking Chinese.

Answers

Answer:

5/38

Step-by-step explanation:

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

The numerator is the number above. While the denominator is the number below

an example of a fraction =  [tex]\frac{4}{5}[/tex]

4 is the numerator while 5 is the denominator

fraction of the surveyed students are taking Chinese = total number of students surveyed / total number of students surveyed

5/38

Help me I need help ASAP pls

Answers

Answer:

Step-by-step explanation:

-37/4

Answer: 2 1/4

Step-by-step explanation: 5 + 3/4 -3 = 1/2 5 - 3 = 2

50 POINTS!!!!
Analyze the graph of the cube root function shown
on the right to determine the transformations of the
parent function. Then, determine the values of a, h,
and k in the general equation.
y = a3x - h + k
h =
k=

Answers

Answer:

Let's solve for h.

y=a3x−h+k

Step 1: Flip the equation.

a3x−h+k=y

Step 2: Add -a^3x to both sides.

a3x−h+k+−a3x=y+−a3x

−h+k=−a3x+y

Step 3: Add -k to both sides.

−h+k+−k=−a3x+y+−k

−h=−a3x−k+y

Step 4: Divide both sides by -1.

−h

−1

=

−a3x−k+y

−1

h=a3x+k−y

Answer:

h=a3x+k−y

Let's solve for k.

y=a3x−h+k

Step 1: Flip the equation.

a3x−h+k=y

Step 2: Add -a^3x to both sides.

a3x−h+k+−a3x=y+−a3x

−h+k=−a3x+y

Step 3: Add h to both sides.

−h+k+h=−a3x+y+h

k=−a^3x+h+y

Answer:

k=−a^3x+h+y

Step-by-step explanation:

The required values are h = 1 and k = 4 the given cube root function.

What is the cube root function?

The cube root function is a function that takes the cube root of its input. The formula for the cube root function is:

f(x) = ∛x

The graph is given in the question, as shown.

To find the symmetric center of the cube root function, we need to find the point on the function that is equidistant from the two opposite sides of the function graph.

Since the given cube root function is an odd function, it is symmetric about the point (1, 4).

So, the symmetric center of the cube root function is the point (1, 4).

Thus, h = 1 and k = 4

Therefore, the required values are h = 1 and k = 4 the given cube root function.

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The complete question would be as:

Yonghui works as a waiter in a Chinese restaurant. He got $104 tip on Monday and $59 more on Tuesday. How much did he get on Tuesday?

Answers

Answer:

163$

d#ddddddddddddd

Step-by-step explanation:

104+59=163

At 7 p.m the temperature was 15 F in the next 2 hours, the temperature fell 15F


Select all true statement based on the the above information.



A. The temperature was 30 F at 9 pm


B.The temperature was 0 F at 9 pm


C. The change in temperature from 7 PM to 9 PM is represented by -15



D. The change in temperature from 7 PM to 9 PM is represented by 15.


E. The expression 15+( -15) represents the temperature change

F. The expression 15+15 represents the temperature change

Answers

Answer:

The answer is 0

Step-by-step explanation:

Because if the tempurature was 15 and it dropped 15 = 0°

Solve for h.
h − 999 = –341

Answers

i think h is 658 i could be wrong

Answer:

Step-by-step explanation:

=> h=-341+999

=> h= 658

Make me the brainliest pls :))

A pound of chocolate costs 8 dollars. Kala buys p pounds. Write an equation to represent the total cost c that Kala pays.

Answers

Answer:

8p=c

Step-by-step explanation:

For questions like this, it isn't asking for a numerical answer or anything complicated. It's mainly just using common sense and figuring out what you would do if you had actual numbers instead of variables. You would multiply the amount of pounds (p) by the cost per pound of $8, and that would be your answer (c). I hope I could help.

Find a positive angle less than 360° that is coterminal with the given angle.
560

Answers

Answer:

200

Step-by-step explanation:

brainliest?

15-2X = -45 how do I show My work for this?

Answers

Answer:15-2x=-45

15-2=13

13=-45

Step-by-step explanation:

I hope that helps you!

Answer:

x = 30

Step-by-step explanation:

15 - 2x = -45

+ 2x to both sides

15 = 2x - 45

+ 45 to both sides

60 = 2x

divide both sides by two

x = 30

Figure abc is a triangle with a base of 22 inches if abc is dilated by a scale factor of 0.5 what will be the base of the figure

Answers

Answer:

11

Step-by-step explanation:

Scale factor 0.5 means 1/2

so multiply base length with scale factor

22×0.5 = 11

Anyone know the answer ?

Answers

Answer:

C

Step-by-step explanation:

The mean is 6.41428571429

five different names were put into a hat. A name is chosen 111 times and the name Karen is chosen 29 times. What is the experimental probability of the name Karen being​ chosen? What is the theoretical probability of the name being​ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.

Answers

Answer:

Step-by-step explanation:

As the name Karen is chosen 29 out of 111 times,

the experimental probability of the name Karen being​ chosen = 29/111

As five different names were put into a hat,

the theoretical probability of one name like Karen being​ chosen = 1/5

If the number of names in the hat were different, the experimental probability will still depend on the outcomes. If it is 29 out of 111 times, then the probability stays the same.

But the theoretical probability will be 1 out of the number of names. So it will change.

Answer:

Step-by-step explanation:

P(experimental) = outcome = 29/111

P(theoretical) = P(equal chance) = 1/5

P(expt) no change w/ no. of names

P(theo) changes w/ no. of names

Find the volume of cylinder

Answers

Answer:

1539.4 rounded

Step-by-step explanation:

Have a great day

Choose the best answer to complete the sentence.
If a point lies on the angle bisector of an angle, then it is
[Select)
from the two sides of the angle.
B

Answers

Answer:

Equidistant

Step-by-step explanation:

When we have a point lying on the angle bisector, it stands at an equal distance from the two sides of the angle

The purpose of the angle bisector is to divide the angle into two different equal parts

So, for a point to lie on this, it means it of the same distance from the two points of the angle

Find the surface area of the composite figure.
3 cm
12 cm
2 cm
6 cm
10 cm
8 cm

Answers

Answer:

I think it is 34,560

Step-by-step explanation:

3 x 12 x 2 x 6 x 10 x 8 = 34,560

The surface area of the given figure is 394 square cm.

What is a surface area?

Surface area refers to the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units, such as square meters (m²) or square feet (ft²).

The surface area will be calculated by calculating the area of each face and then adding all the areas,

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

Therefore, the surface area of the figure will be 394 square cm.

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Khan Question :) Please do help no links pls

Answers

Answer:

sqrt(41)

Step-by-step explanation:

Using pythagoras theorem

In a cookie jar there are 9 sugar cookies and 12 snickerdoodle cookies. The cookie are randomly mixed together in the jar. What is the probability of pulling two of the same types of cookies out of the cookie jar in a row without replacement?

Answers

Answer:

The probability of pulling two of the same types of cookies in a row without replacement is [tex]\frac{51}{105}[/tex].

Step-by-step explanation:

There are a total of 21 * 20 = 420 different outcomes (After you take one cookie out, you aren't replacing it, so there will be 20 cookies in the jar on the second grab). There are a total of 9 * 8 = 72 different combinations of two sugar cookies, and 12 * 11 = 132 different combinations of two snickerdoodle cookies, so the total probability of pulling two of the same types of cookies in a row without replacement is [tex]\frac{132+72}{420} = \frac{204}{420} = \frac{51}{105}[/tex].


1. Define: (1) factor (ii) multiple. Give five examples of each.it

Answers

Answer:

A factor is a number that when its multiplied with another number, gives a product of a given number. Example: The factors of 21 are 7,3,1 and 21. A multiple is a number that can be divided by another number a certain amount of times evenly (without a remainder). Example: Some multiples of 4 are: 8, 12, 16, and 20.

Find the length of the missing side.
14.5 m
7.3 m
X

Answers

Answer:

x=  12.528

*rounded is 12.53 or 12.5

Step-by-step explanation:

7.3 ^2 + x^2 = 14.5^2

53.29 + x^2 = 210.25

-53.29            -53.29

x^2= 156.96

x= 12.528

Kelly purchased 9 planters for a total of $63. She wants purchase another 20 planters at the same unit price.
How much will 20 planters cost?

Answers

Answer

140 :D

Explanation
It’ll be 140, because that’s how much they cost

The following list shows three factors that can either increase or decrease the probability of a Type II error. The sample size is increased. The significance level is increased. The standard error is increased. Which factors alone will cause the probability of a Type II error to increase?

Answers

Answer:

Standard Error is increased.

Step-by-step explanation:

Type 2 error is failure to reject a false null hypothesis. This is a 'false negative' result of hypothesis testing, represented by beta 'β'.

Power of test is 1 - β, which shows probability of accurately stating  a null hypothesis false, when it is actually false.

Increased sample size increases the power of test accuracy, hence reduces type 2 error. Increased level of significance implies higher probability of rejecting a true null hypothesis, ie type 1 (false positive) error. So, it decreases type 2 error.

Standard Error increase implies lower level of t statistic , ie = (x - u) / (s / √ n) Lower the t value, higher is the probability of not rejecting null hypothesis, which implies higher chance of type 2 error.

Type II error is 1 - power of the test. The factor that can alone make the type II error to increase is: Option C: The standard error is increased.



What is Type I and Type II error?

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false). It is 1 - statistical power of the test. Thus, increasing power of the test decreases this error.

How are the type I error and type II error are related to level of significance?

The probability of committing the type I error is called the significance level of the hypothesis test.

And the more we increase the level of significance, the less area the test statistic gets to fall in, and its chances of falling in region outside level of significance increases, which makes us to reject the null hypothesis more probable, thus, decreasing its chance of tagging as negative, not mattering if true or false.
Thus, increasing level of significance increases the type I error but decreases the type II error.

How is standard error related to type II error?

If it is increases, the likely area for test statistic falling increases, thus, increasing probability of tagging the null hypothesis tagging to be true, so increasing result of test being declared negative, thus, increasing type II error.

How is type II error and sample size related?

Increasing sample size increases statistical power, thus, decreasing the type II error.

Thus, for the given case, as the sampling size is increased, the type II error will decrease, as the significance level is increased, the type II error will decrease, and as the standard error is increased, the type II error will increase with it.

Thus, out of the given factors, only the last factor (increasing the standard error) makes the type II error to get increased.

Thus, the factor that can alone make the type II error to increase is: Option C: The standard error is increased.

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Directions: Use the information given to write the equation of the circle in standard form.
16. center:(-10,-4), point on circle: (4, -2) 17. center: (-9, -3), point on circle: (-11, 2) 18. center: (5.-7), point on circle: (-3,-1)
19. center: (8,2), point on circle: (14,-1) WO​

Answers

Answer:

subject?

Step-by-step explanation:

PLSS HELP
A paper store spent 1/4 of all the money they earned in December to buy new inventory. It used 1/2 of the rest of the money to pay bills. Then, they still had $3,000 left over. How much money did the store earn in December? ​

Answers

Answer:

$8,000

Step-by-step explanation:

Let the store earned $x in December.

Therefore,

Money spent to buy new inventory [tex] =\frac{1}{4} x[/tex]

Remaining money [tex] = x - \frac{1}{4} x =\frac{3}{4} x[/tex]

Money used to pay bills [tex] =\frac{1}{2} \times \frac{3}{4} x=\frac{3}{8} x[/tex]

Money still left over = $3,000

Total money earned in December [tex]= \frac{1}{4} x+ \frac{3}{8} x+3,000[/tex]

[tex]\therefore x= \frac{1}{4} x+ \frac{3}{8} x+3,000[/tex]

[tex]\therefore x= \frac{2}{8} x+ \frac{3}{8} x+3,000[/tex]

[tex]\therefore x= \frac{5}{8} x+ 3,000[/tex]

[tex]\therefore x- \frac{5}{8} x=3,000[/tex]

[tex]\therefore \frac{8x-5x}{8} =3,000[/tex]

[tex]\therefore \frac{3x}{8} =3,000[/tex]

[tex]\therefore x =3,000\times \frac {8}{3}[/tex]

[tex]\therefore x =1,000\times 8[/tex]

[tex]\therefore x =\$8,000[/tex]

Thus, total money earned in December is $8,000.

Given
A ∆GHJ with k
GH
L on GI
are K and L the midpoints of GH and GJ respectively?
is KL || HJ?
is HJ = 2KL?​

Answers

Answer:

Is there diagram for this?

Vector V has components of (6,9) determine the angle in degrees that vector vee makes with the X axis

Answers

Given :

Vector V has components of (6,9).

To Find :

The angle in degrees that vector V makes with the x-axis.

Solution :

The x-component of vector is, x = 6 units.

The y-component of vector is, y = 9 units.

So, the angle the vector makes from the horizon is :

[tex]\theta = tan^{-1}{\dfrac{y}{x}}\\\\\theta = tan^{-1}{\dfrac{9}{6}}\\\\\theta = 56.31^o[/tex]

Hence, this is the required solution.

Heather had 20 stickers. She bought 27 stickers from a store in the mall and got 6 stickers for her birthday. Then Heather gave 4 of the stickers to her sister and used 11 to decorate a greeting card. How many stickers does Heather have left?​

Answers

Answer:

38 stickers

Step-by-step explanation:

20+27=47

47+6=53

53-4=49

49-11=38

20+27+6-(4+11)=38 stickers

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