A Petri dish contains 100 bacteria cells. The number of cells increases 5% every minute. How long will it take for the number of cells in the dish to reach 2000? Use logarithms to solve.

Answers

Answer 1

Using logarithm, the following equation will apply:
Y = P * [1 + z]^x
Where Y = 2000
P = 100
z = 5% = 0.05
x is the quantity we are calculating for
The equation becomes
2000 = 100 * [1+ 0.05]^x
Dividing both side by 100, we have
20 = 10 * [ 1 + 0.05]^x
Taking the log of both sides, we have
Log 20 = Log [1 + 0.05]^x
log 20 = x * log 1.05
x = log 20/ log 1.05 = 61.40
Thus, it will takes 61.40 minutes for the number of cells in the petri dish to reach 2000.

Related Questions

The product of 32 and an unknown number subtracted from 435 is 179 what is the value of the unknown number

Answers

Hello from MrBillDoesMath!

Answer: Case 1: approximately 429.4, Case 2: 8

Discussion:

Let the unknown be "x". The problem statement could mean either

32 * (435 -x) = 179 (#1)

435 - 32*x = 179 (#2)

It's unclear which one is wanted so we solve both of them.

----------------------------------------------#1

But for case #1

32 * (435 -x) = 179

32 * 435 - 32x = 179 or

13920 - 32x = 179

Add 32x to both sides

13920 = 179 + 32x

Subtract 179 from both sides:

13920 - 179 = 32x

Divide both side by x to get

x = (13920 -179)/32 = 13741/32 which is approximately 429.4

For case #2

----------------------------------------------#2

435 - 32x = 179. Add 32 x to each side

435 -32x + 32x = 179 + 32x. Subtract 170 from each side

435 -179 = 32x or

32x = 256 or x = 8

Regards, MrB

What happens to the average kinetic energy of water molecules as water freezes? A. It decreases as the water releases energy to its surroundings.
B. It increases as the water releases energy to its surroundings.
C. It increases as the water absorbs energy from its surroundings.
D. It decreases as the water absorbs energy from its surroundings.

Answers

Answer: Option (A) is the correct answer.

Explanation:

Kinetic energy is defined as the energy possessed by an object because of it's motion.

Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.

Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.

Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.

The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.

When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.

As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.

In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.

Therefore, the correct option is (a).

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complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions. Find 1/4 divided by 3/8

Answers

Multiplying is the opposite of dividing, so that's why you multiply it by the reciprocal.
1. 1/4 ÷ 3/8 is equivalent to 1/4 × 8/3
2. 1/3 × 8/3 = ?
3. 1 × 8 = 8
4. 3 × 3 = 9

for every 5 teachers there are 12 student. if there are a total 153 student and teachers how many teachers and student are present

Answers

5 +12 = 17

153 /17 = 9

9*5 = 45 teachers

9*12 = 108 studets

meredith bought 7 new t-shirts for $7.95 per shirt. if price included tax how much did she pay for all of the t-shirts? each step please

Answers

In order to solve this problem, all that you have to do is multiply 7 and $7.95. Since the price already includes tax, there is nothing else that you have to add.

Step 1: 7 x $7.95 = $55.65

Solution = $55.65

On a quiz worth 5 points, three students earned a 5, five students earned a 4, four students earned a 3,six students earned a 2 , nine earned a 1 and eight students earned a zero . What is the class average on this quiz

Answers

If you add them all together and divide the answer you get by 5 you should get 7

For which real numbers x and y is it true that x + y = x+y?

Answers

By the general application of cumulative property of addition :

x + y = y + x

For sure

Adina is constructing a line perpendicular to YJ . She has already constructed two arcs as shown. She moves her compass point to Y to construct an arc above the line. What must be true about the width of Adina’s compass opening before she draws the arc?

A. It must be narrower than it was when constructing the first two arcs. B. It must be the same as it was when constructing the first two arcs.
C. It must be wider than it was when constructing the first two arcs.

Answers

It has to be wider than the first two arcs or else you will just get two circles side by side with point c in common. I usually measure it to be the length of a point between the c and j. It is a good point to get the arcs to intersect.

The arc is every two-point smooth curve. The length of an arc is called the length of its arc. In a chart, a chart arc is an adjacent pair of vertices. A semicircle is called an arc, whose endpoints lie on a circle diameter.

It must be broader than the first two arcs or you'll only get two circles alongside. The length of a point between the c and j is measured. The arches are a good way to cross.The compass shall be set to a length broader than the length of YC when drawing arcs below and above the YJ line.The arc production passes, not giving a line perpendicular to YJ.

Therefore, the final answer is "Option C".

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Factor −1/2−1/2 out of −1/2x+6.

Answers

Final answer:

To factor out -1/2 - 1/2 from -1/2x + 6, multiply -1/2 by the expression inside the parentheses and distribute. Then, simplify and combine like terms to get the factored form: -3/2x - 6.

Explanation:

To factor out -1/2 - 1/2 from -1/2x + 6, you can rewrite the expression as (-1/2) * (x + 2(6)). Then, distribute to get (-1/2)x - (1/2)(2) * (x + 2(6)). Simplify further to get (-1/2)x - x - 6. Finally, combine like terms to get (-1/2 - 1)(x) - 6. Therefore, the factored form of the expression is -3/2x - 6.

compute the following 8c2•5c2

Answers

The question that we are given to compute is 8c² × 5c². Since this is multiplication, we can straight up multiply 8 and 5 to get 40. Now, we multiply c² by itself to get c⁴. Therefore, when we combine our products together, we get 40c⁴, which is your answer. Hope this helped!

The computation of 8C2•5C2 results in 280

The student asked: 'compute the following 8c2•5c2'.

We can solve this using the combinations formula, where nCr = n! / [r!(n-r)!].
Compute 8C2.-
8C2
= 8! / [2!(8-2)!]
= (8*7) / (2*1) = 28.
Compute 5C2.
5C2
= 5! / [2!(5-2)!]
= (5*4) / (2*1) = 10.
Multiply the results.
28 * 10 = 280.

Hence, the value of 8C2 • 5C2 is 280.

the mean age of a dance troupe is 14.2 years. A 7-year-old sibling is invited to join the troupe. How does the sibling’s age affect the mean?

A. The new mean age will be 10.6 years.
B. The new mean age will be greater than 14.2 years.
C. The new mean age will be less than 14.2 years.
D. The new mean age will still be 14.2 years.

Answers

The correct answer is c. There is no possible way to know how much the mean age decreases, but we know it definitely will (averages decrease as values less than the average are added to the data.)

The new mean age will be less than 14.2 years.

What is mean?

There are several kinds of mean in mathematics, especially in statistics. For a data set, the arithmetic mean, also known as arithmetic average, is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.

According to questions, the mean age of a dance troupe is 14.2 years.

A 7-year-old sibling is invited to join the troupe.

We have to find how does the sibling’s age affect the mean.

There is no possible way to know how much the mean age decreases.

But the new mean age will decrease definitely.

Hence we can conclude that Option C is correct answer.

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The floor at a roller skating rink is 72.25 feet long and 51.5 feet wide how much longer is the rank than it is wide

Answers

21.20 feet is the answer your looking for

It is 20.75 feet longer than the width.

Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.

Answers

This part of the plane is a triangle. Call it [tex]\mathcal S[/tex]. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that [tex]y=z=0[/tex] means [tex]5x=20\implies x=4[/tex], so that (4, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 20) are the other two vertices.

Next, we can parameterize the surface by

[tex]\mathbf s(u,v)=\langle4(1-u)(1-v),5u(1-v),20v\rangle[/tex]

so that the surface element is

[tex]\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=20\sqrt{42}(1-v)\,\mathrm du\,\mathrm dv[/tex]

Then the area of [tex]\mathcal S[/tex] is given by the surface integral

[tex]\displaystyle\iint_{\mathcal S}\mathrm dS=20\sqrt{42}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-v)\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle=20\sqrt{42}\int_{v=0}^{v=1}(1-v)\,\mathrm dv=10\sqrt{42}\approx64.8074[/tex]

Final answer:

The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.

Explanation:

To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.

Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:

Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx

And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.

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A local little league has a total of 85 players, of whom 80% are left-handed. How many left-handed players are there?

Answers

Final answer:

The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.

Explanation:

The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.

The calculation is as follows:

Left-handed players = 85 * (80/100)

= 85 * 0.80

= 68

So, there are 68 left-handed players in the local little league.

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Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80. What is the price of Mira’s breakfast,before tip?

Answers

Ok so
9×20%=1.80
So the original price of her breakfast is $9.00
hope this helps!

Hey there,
20% = $1.80
1% = $1.80 / 20%
= $0.09
100 % = $0.09 x 100
= $9

Hope this helps :))

~Top

What is 2 2/5 ÷ (- 1/4) And how?

Answers

-9.6 is the answer.
first you turn both fractions into decimals, then you just divide the two.

Turn 2 2/5 into a fraction of 12/5 and when dividing fractions, just flip and multiply! So 12/5 x -4/1 = your answer

How long will it take for the object to fall all the way down to the ground? The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h is the intial height is h(t)=-16t^2+h. The building is 162 feet tall.
Thanks so much!

Answers

Since the initial height of the bldg is 162 ft, h(t)= -16t^2+h becomes

-16t^2+162, or 16t^2 = 162. Taking the + square root of both sides,

we get t = 162/16 seconds, or 10 1/8 seconds.

Write the decimal 0.326 in to other forms

Answers

0.326

to get percent, move the decimal point over two spaces to the right:
32.6%

to get fraction, put it over 100 by moving the decimal spaces two to the right:
32.6/100

To get a fraction that is not include a decimal, write it over 1000 (at this case:
326/1000

hope this helps

The speed of the car was 45 mph. A driver noticed that while moving with this speed it took him 40 seconds to cross a bridge. On the way back crossing the same bridge, it took him 30 seconds. What was the speed of the car on the way back?

Answers

distance = speed*time

Each time the car travels the same distance across the bridge.

By setting the distances equal you get the following equation:

[tex]30x = 40*45 \\ \\ x = \frac{40*45}{30} = 60[/tex]

Answer: Car was going 60 mph

Answer:

Speed of car on the way back = 30 mph

Step-by-step explanation:

Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s

Time taken to cross bridge on the way = 40 seconds

Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m

Time taken to cross bridge on the way back = 30 seconds

Length of bridge = Speed of car on the way back x Time taken on the way back

800 = Speed of car on the way back x 30

Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph

Speed of car on the way back = 30 mph

What is the slope of the x axis

Answers

Answer: Zero slope

Step-by-step explanation: Since the x-axis is horizontal, it has a slope of 0. In fact, for any horizontal or flat line, the slope is always 0.

The variable that's used to represent slope is m. So in this problem, we would say that m = 0.

What operation extends this pattern? 100, 85, 70, 55... A) add 15 B) subtract 15 C) multiply by 15 Eliminate D) divide by 15

Answers

Hello! If you look at the pattern, 100 - 85 is 15, 85 - 70 is 15, and 70 - 55 is 15. You don't divide, because the numbers would be much smaller, or multiply, because the numbers would be much bigger. You would subtract 15 in order to get the next numbers. The answer is B.

G how many distinct ordered arrangements of the letters of the word boogaboo can be made?

Answers

In the word "boogaboo", there are eight (8) letters while there are only four distinct letters. The number of distinct ordered arrangements can be calculated through the equation,

n = 8!/(2!)(4!)

where there are 2 letter b's and 4 letter o's. The answer to this item is 840.

Answer: 840

Find a line perpendicular to – 5 x – 4 y = 19 that passes through ( – 5 , 11 )

Answers

Solve – 5 x – 4 y = 19 for y to obtain the slope: -5x - 19 = 4y, and so
the slope is (-5/4).

A line perpendicular to – 5 x – 4 y = 19 must have a slope which is the negative reciprocal of this (-5/4). That would be (+4/5).

Using the point-slope form of the eqn of a str line:

y-11 = (4/5)(x-[-5]), or (4/5)(x+5). This could, of course, be written in other (but equivalent) forms.

What are the values of the mean and standard deviation after converting?

Answers

Example:Pulse rates of women are normally distributed with a mean of 77.5beats per minute and a standard deviation of 11.6 beats per minute.a) What are the values of the mean and standard deviation afterconverting all pulse rates of women to z-scores usingz=(x−μ)/σ?µ = 0;σ= 1b) The original pulse rates are measured with units of “beats perminute.” What are the units of the corresponding z-scores?The z-scores are numbers without units of measurement.

Which of these equations have no solution? Check all that apply. A 2(x + 2) + 2 = 2(x + 3) + 1 B 2x + 3(x + 5) = 5(x – 3) C 4(x + 3) = x + 12 D 4 – (2x + 5) = (–4x – 2) E 5(x + 4) – x = 4(x + 5) – 1

Answers

Answer: A,B,E

Step-by-step explanation:

I just got done with the assignment and that was the answer

A delivery driver earns a fixed amount for each delivery she makes, and yesterday her average hourly wage was $16.50 an hour. If she worked 6 hours yesterday and made 11 deliveries, how much does she earn for each delivery made? A. $9.90 B. $5.50 C. $5.00 D. $9.00

Answers

The answer is D. $9.00
$16.50 x 6 = $99
so 99 divided by 11 is 9

Answer:

Option D - The driver earned $9 for each delivery.

Step-by-step explanation:

Given scenario is :

Hourly wage for the driver = $16.50

Total number of hours worked in a day = 6

So, total earning for the day = [tex]16.50\times6=99[/tex] dollars

Now, she made 11 deliveries in $99

So, each delivery cost = [tex]\frac{99}{11}=9[/tex]

Hence, the driver earned $9 for each delivery.

Solve the equation for x. (Round your answer to three decimal places.) arctan(4x − 4) = -1

Answers

take the inverse arctan on both sides:

4x-4 = tan(-1)

4x-4 = -0.01745

4x = 3.98255

x = 3.9255 / 4

x = 0.996

solve this system of linear equations. separate the x- and y- values with a coma. 6x+20y=-62
3x-9y=-12

Answers

Final answer:

To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.

Explanation:

To solve the system of linear equations:

6x + 20y = -62

3x - 9y = -12

We can use the method of substitution:

From the first equation, solve for x: x = (-62 - 20y) / 6Substitute the value of x into the second equation: 3((-62 - 20y) / 6) - 9y = -12Simplify and solve for y:

After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.

Mary made 1/8 of a batch of cookies in 1/10 pf an hour. How much time will she need to make 1 full batch of cookies?

Answers

Mary will need 48 minutes to make a full batch of cookies, as determined by setting up a proportion and then converting hours to minutes.

Mary made 1/8 of a batch of cookies in 1/10 of an hour. To find out how long it will take to make a full batch, we set up a proportion based on the information given. Since 1/8 of a batch takes 1/10 of an hour, we want to find out the time for 8/8 (a full batch), which is equivalent to 1.

Setting up the proportion, we can say that 1/8 of a batch is to 1/10 of an hour as 1 full batch (8/8) is to X hours:

1/8 batch : 1/10 hour = 1 batch : X hours

To solve for X, we multiply 1/10 by 8 because there are 8 parts of 1/8 in a full batch:

1/10 hour * 8 = 8/10 hours

Reducing the fraction 8/10, we get:

8/10 = 4/5 hours

To convert 4/5 of an hour to minutes, we multiply by 60:

4/5 hour * 60 minutes/hour = 48 minutes

Therefore, Mary will need 48 minutes to make 1 full batch of cookies.

what is the product of g and 7???

Answers

7 •g = 7g
Product always refers to a multiplication problem. So the product of g and 7 is 7g.

The product of the variables g and 7 is written as 7g.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the numbers are g and 7. The product will be written as,

Product = 7 x g

Product = 7g

Here, g is the variable and for different values of 'g', the formula will give the different values of the product.

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Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > 2.4b 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which students first step was incorrect, and why? Amelias, because the variable term must be isolated on the left side Luiss, because he flipped the inequality sign when he subtracted Shaunas, because she did not apply the subtraction property of equality properly Clarences, because the terms he added together were not like terms The field of artificial intelligence, which would not be possible without database technology, includes all but which one of these fields? To remove a worksheet group, you can right-click the sheet tab of a sheet in the group and then click ____ on the shortcut menu. In industrialized nations, childhood diseases have declined dramatically during the past half-century, largely as a result of Why did Congress pass the Volstead Act to go along with the Eighteenth Amendment? A caldera forms when _____.A- A volcano eruptsB- A hot spot developsC- Magma hardens in vertical cracksD- A volcano collapses The area near the Indus and Ganges rivers is one of the most densely populated areas of the South Asian subcontinent because of its a. lush rain forests. c. ocean ports. b. fertile land. d. high mountains. what would happen if the cell membrane were not selectively permeable? support your answer. Both jennifer and tony experienced traumatic head injuries. while jennifer finds it difficult to understand others, tony is able to understand what others are saying, but finds it difficult to speak even though there is nothing wrong with the muscles that control his speech. both jennifer and tony are suffering from _____. What does miss emily inherit from her father? When you reboot your system, the computer follows start-up instructions stored in this type of memory. multiple choice dram sdram cache flash? The hunger games that explores the interest in suffering as entertainment, comparing it to one or more current reality television shows in which participants also suffer. what words need to be capitalized in Thomas Jefferson wrote the Declaration of Independence for our country Hour truck can carry a 3/4 ton load. Each brick weighs 4 lbs and 14 oz. How many bricks can the truck carry How did women's suffrage change the role of women in society? The limiting factor of a desert biome is its _____. The greatest factor in the development of "skyscrapers" was rationalize the denominator of square root -36 over (2-3i)+(3+2i) Organisms in a community reflect the resources and climate of that community. Give some examples to illustrate this statement. What does francis say about atticus how do his comments illustrate that racism exists not just in the other residents of maycomb but within the finch family as well? Steam Workshop Downloader