The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)

The Gompertz model of tumor growth is a mathematical model that describes the growth of a tumor over time. It is characterized by two parameters, the intrinsic growth rate (r) and the carrying capacity (K), and is described by the following differential equation:

dn/dt = rn(1 - n/K).where n is the size of the tumor and t is time.

To classify the fixed points of the Gompertz model of tumor growth using linear stability analysis, we first need to find the fixed points by setting dn/dt = 0 and solving for n. The fixed points are the values of n that make the tumor size constant. In this case, the fixed point is n* = K.

Next, we need to linearize the system around the fixed point by using the Jacobian matrix. The Jacobian matrix for the Gompertz model is:
J = [dr/dn, d(rn(1-n/K))/dn]
[-rn(1-n/K)/K, rn(1-n/K)+(r*n/K^2)]

In the Gompertz model, the fixed point is n* = K, and the eigenvalues are -r and r/K, which are both negative. This means that the fixed point is stable, and the tumor size will converge to the carrying capacity K if perturbed.

To learn more about Gompertz Model:

https://brainly.com/question/13720402

https://brainly.com/question/18175560

#SPJ4

Answer:

There are several lines of evidence that scientists use to determine the relative age of the Earth and its various features. These include:

Stratigraphy: This refers to the study of rock layers and the sequence in which they were formed. Scientists use stratigraphy to determine the relative ages of different rock layers and the fossils they contain. The principle of superposition states that in any undisturbed sequence of rocks, the oldest rock layers will be at the bottom and the youngest will be at the top.

Fossil record: Fossils are the remains of plants and animals that lived in the past. By studying the fossils in rock layers, scientists can determine the relative ages of different rock formations and the organisms that lived in them. Fossils of extinct species found in lower rock layers are older than those found in higher rock layers.

Radiometric dating: This is a method that uses the decay of radioactive isotopes in minerals to determine the absolute age of rocks and minerals. Scientists can use radiometric dating to determine the age of a rock or mineral, and by comparing the ages of different rocks and minerals, they can determine the relative ages of different rock formations and the Earth's surface features.

By using the method of successive differences, the next number in the given sequence 3, 9, 20, 36, 57, 83, 114 is 150.

In Mathematics, a difference table can be defined as a type of table that is constructed by subtracting adjacent elements (entries) in a sequence, and then repeating the process with next those elements (entries).

Number            Difference from previous             Difference of differences

3

9                                         6                                          

20                                       11                                               5            

36                                       16                                              5          

57                                       21                                              5          

83                                       26                                             5          

114                                       31                                              5  

150                                      36                                             5        

First column: 9 - 3 = 6; 20 - 9 = 11; ....... 150 - 114 = 36.

Second column: 11 - 6 = 5; 16 - 11 = 5; ...... 36 - 31 = 5.

Read more on sequence here: brainly.com/question/27877463

#SPJ1

The gross pay mike for last week is $210.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Mike earns 5.00 per hour overtime is paid at the time and half of his regular rate worked 42 hours last week.

Since it is not mentioned that mike worked overtime or not so we will consider this a normal work hour for a week is 42 hours.

Thus total he earns = 42*5

total he earns = 210$

If he works overtime,

for every hour he worked overtime he would get = 1.5* 5

for every hour he worked overtime he would get = 7.5

Therefore, For the week mike's gross pay is $210.

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

Answer:

[tex]b = P - a - c[/tex]

Step-by-step explanation:

Notice that there are 3 terms on the right hand side. You want to isolate b in order to solve for it.

I find it less confusing to place term containing the variable you want on the left hand side. (As long as it is positive).

[tex]a + b + c = P[/tex]

To isolate b subtract a and c from both sides

[tex]b = P -a - c[/tex]

petroleum formation happens When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.

Dead creatures are broken down into their basic chemicals through the process of decomposition by bacteria and fungus. The cycle can be completed by plants absorbing and using these substances once again. Because of how they decompose dead organic stuff, decomposing bacteria and fungus are referred to be saprophytic.

Oil and gas are created from organic material that has been decomposed and altered over millions of years, mostly as sediments on the seafloor.

Fuels known as petroleum products are created from crude oil and the hydrocarbons found in natural gas. Coal, natural gas, and biomass can also be used to make petroleum products.

Plant and animal remains are used to create petroleum. Animals and plants that pass away sink and land on the seafloor. These extinct animals and plants decayed millions of years ago and mingled with sand and silt.

Therefore, we can say Petroleum is produced. Dinosaurs became extinct 65 million years ago, and when their corpses decomposed, petroleum was created. Petroleum doesn't form until hundreds of millions of years. Oil was created in chilly climates.

Learn more about decomposition here:

https://brainly.com/question/8009068

#SPJ1

Answer: - 4/5x + 1.8

Step-by-step explanation:

"-":  because the slope is negative

"4/5": because its the slope

"x": because it is part of 'mx + b'

"1.8": because it's the y-intercept that fits this equation

Answer:

y = -4/5x + 1.8

Step-by-step explanation:

1st find the slope, m,  using these 2 points:  (-4,5) and (6,-3)

m = (-3-5) / (6--4) = -8/10 = -4/5

Now use the point (-4, 5) in the the point-slope form to find b:

y - 5 = -4/5(x - -4)

y - 5 = -4/5(x + 4)

y - 5 = -4/5x - 16/5

y = -4/5x -16/5 + 25/5 = -4/5x + 9/5

Now write the equation in slope-intercept form:

y = -4/5x + 1.8

Answer:

.023

.75 X .33=.2475/11=.0225 rounded to .023

Step-by-step explanation:

Sam Is Building A Table for her gaming setup.The Length of the table is .75x.33 if she doubles the length of it then divides it by 11 then what will be the length of the table?Round to the nearest thousandths to solve your problem.

P.S:Mark Me Branlisist

If Kaido's age is x, Hiroshi's age is y and Saitama's age is z, then ratio value for their ages is x : y : z.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

Let the age of Kaido be represented as x.

Let the age of Hiroshi be represented as y.

Let the age of Saitama be represented as z.

The ratio of Kaido's age to Hiroshi's age can be given as -

Kaido's age : Hiroshi's age

Substituting the values in the expression -

x : y

The ratio of Kaido's age to Saitama's age can be given as -

Kaido's age : Saitama's age

Substituting the values in the expression -

x : z

The ratio of Hiroshi's age to Saitama's age can be given as -

Hiroshi's age : Saitama's age

Substituting the values in the expression -

y : z

The ratio of Kaido's age to Hiroshi's age to Saitama's age can be given as -

Kaido's age : Hiroshi's age : Saitama's age

Substituting the values in the expression -

x : y : z

Therefore, the ratio expression is obtained as x : y : z.

To learn more about ratio from the given link

https://brainly.com/question/30182280

#SPJ1

A standard form is a form of writing equations, numbers, or expressions using a certain set of rules.

solve the equation in standard form -2x²+8x=-1 ?

vertex is (2/-7)

opening down

x=h=8/-2(2)=4

INC(∞,-2) DEC(2,-∞)

D(-∞,∞)

R(∞,-7)

Reference yes dilution by 2

To learn more about standard form refers  to:

https://brainly.com/question/19169731

#SPJ1

Answer:

Step-by-step explanation:

The solution of the given functions (f+g)(x) is 2x²+x-5.

This connection is typically represented as y = f(x), or "f of x," where y and x are coupled so that for any value of x, there is a certain value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.

Here, the given functions are,

f(x) = x/2 - 2

g(x) = 2x ^ 2 + x - 3

(f+g) x = f(x) + g(x)

(f+g) x = x/2 - 2 + 2x ^ 2 + x - 3

(f+g) x = (3x)/2 - 5 + 2x ^ 2

(f+g) x = 2x ^ 2 + (3x)/2 - 5.

= 2x²+x-5

To learn more about functions refer to:

https://brainly.com/question/10473672

#SP1

These mathematical operations can be solved in the given manners.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given some fractions to solve for understanding, I will solve two questions with the same denominator and two with different denominators one with a whole number and one fraction.

Since the base is the same

=> 6/4

=> 1.5

We can write 2 /5 as 4/10 since their values are the same

=> 6/10 ÷4/10

=> 6/4

=> 1.5

we can write 1/4 as 6/24 and 1/6 as 4/24 to make the denominator same.

=> 6/24/4/24

=> 4/4

=> 1.5

We can write 2/9 as 4/18 and 5/6 as 15 / 18 to make the denominator the same

=> 4/18/15/18

=> 4/15

=> 0.266

Therefore, The given Mathematical operations are being solved In the s

same manner

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

No, what they said is not fact.

The statement "producing great engineers who benefit science and technology in India is the most important function of IITs" and "IITs are greatly improving the image of India in the West" are both important functions of IITs, and the priority of these functions may depend on individual perspectives and goals.

Some people might argue that producing engineers is more crucial for the development of India's technology and economy, while others might argue that improving the image of India in the West is equally important for increasing its global recognition and competitiveness. Both functions play important roles and it is a matter of perspective which one is considered more important.

Correct Question :

Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west

Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.

What they said is fact or not? Explain.

To learn more about fact here:

https://brainly.com/question/29646299

#SPJ4

In the end, the following is an illustration of a point that cannot appear on the graph of y = f(x): (-7, 1).

Substances and their modifications, equations and surrounding structures, objects and their placements, and locations where they can be found are all included in the study of mathematics. The relationship between a group of inputs, each of which produces related output, is referred to as a "function." A function is a relationship between both inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, many-to-one functions, within functions, and on functions.

given

The task's purpose makes it clear that the point on the graph of y = f(x) that cannot be found.

The definition of a function, f(x), states that it is a relation that assigns just one value of y to each value of x.

As a result, the statement above suggests that the x-value -7 can only be given one y-value, which is 0, if the point (-7, 0) is on the graph of the function y = f(x).

In the end, the following is an illustration of a point that cannot appear on the graph of y = f(x): (-7, 1).

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

Answer:

(-7, -7) you cannot have the same x

example:

The point (6,0) is on the graph of the function y=f(x) . Which point cannot be on the graph of y=f(x)?

(6, 3)

(4,6)

(3,8)

(4,8)

you cannot choose (6, 3)

a) (PA) P is a tautology because P is logically equivalent to P v F, and P v F is logically equivalent to P.

b) p (pv) is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p.

c) p + ( pa) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p v (p v A).

d) (p) - () is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p v F.

e) (P+) - P is a tautology because P+ is logically equivalent to P v T, and P v T is logically equivalent to P.

f) (p) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p.

Learn more about logically equivalent here:

https://brainly.com/question/17363213

#SPJ4

Answer:

√365 cm

Step-by-step explanation:

We can begin by using the formulas for the area of a rectangle and a square to set up an equation. Let x be the length of the sides of the square that is cut out of each corner of the rectangle.

The area of the original rectangle is 40cm * 89cm = 3560cm^2.

The area of the square that is cut out of each corner is x^2.

The area of the remaining base of the box is 2100cm^2.

So, we have:

3560cm^2 - 4x^2 = 2100cm^2

Solving for x, we get:

x = √(3560cm^2 - 2100cm^2)/4 = √(1460cm^2)/4 =√365cm

So the length of the sides of the square is √365 cm

if i helped you, can you mark my answer as best?

The five number summary of the set of numbers is :

A five number summary is a way to summarize a set of numerical data by providing five key values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.

For the set of numbers 34, 35, 37, 38, 42, 45, and 49, the five number summary would be:

The minimum value is 34, the lowest value in the set.

The first quartile, also known as Q1, is the value that separates the lowest 25% of the data from the rest of the data, which is 37.

The median is the middle value, which is 38.

The third quartile, also known as Q3, is the value that separates the highest 25% of the data from the rest of the data, which is 42.

The maximum value is 49, the highest value in the set.

Find out more on five number summary at https://brainly.com/question/24809873

#SPJ1

The entire expression is the product of two terms and 8x+5 is the sum of two terms.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The expression 4(8x+5)

Evaluating the expression we get 4(8x+5)=32x+20

The entire expression is the product of two factors 4&(8x+5)

Also the expression (8x+5) has two terms and therefore its a binomial

Thus it is the sum of two terms.

Hence, The entire expression is the product of two terms and 8x+5 is the sum of two terms.

Learn more about the algebraic expressions here:

https://brainly.com/question/29159730

#SPJ1

There are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.

What is a monomial ?

Monomial is polynomial in which it has only one term.

Given ,

To find Which property would you use to simplify this monomial division problem.

For example :

4a^3 - 10a^2 + 5a  /  2a

Now the polynomials ( 4a^3 - 10a^2 + 5a) is written as numerator and the monomial (2a) is written as denominator

Therefore,

we get 4a^3 - 10a^2 + 5a  /  2a .

Now we observe that there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.

4a^3 / 2a  -  10a^2 / 2a  + 5a/2a

Therefore, there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.

To learn more about Monomial from the given link.

https://brainly.com/question/9183135

#SPJ1

Work Shown:

y = (1/2)x+8

2y = 2*( (1/2)x+8 )

2y = x + 16

2y - 16= x

-16= x-2y

x-2y = -16

Side note: I multiplied both sides by 2 in the second step to clear out the fraction.

The answer x-2y = -16 is in standard form Ax+By = C

A = 1, B = -2, C = -16

The simplification of the given expression after addition = 130.

Addition is defined as one of the arithmetic operations that is used for the combination of two of more values.

The given values from the question above;

67 + 63 = 130

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

The numbers to 3 significant figures are as follows:

0.0230 ≈ 0.0230

0.035 ≈ 0.0350

0.804 ≈ 0.804

3.150 ≈  3.15

140 ≈  140

509 ≈ 509

The eroding rate of the beach in millimetres per day is 0.109 mm per day.

Significant figures are the number of digits in a value. In other words, significant figures are the digits of a number that are important in terms of accuracy and precision.

Therefore, let's find the 3 significant figures of the numbers.

0.0230 ≈ 0.0230

0.035 ≈ 0.0350

0.804 ≈ 0.804

3.150 ≈  3.15

140 ≈  140

509 ≈ 509

A particular beach is eroding at a rate of 4cm per year. Let's convert to millimetres per day.

Therefore,

4 cm = 40 mm

365 days = 40 mm

1 day  = ?

Hence,

eroding rate = 40 / 365 = 0.10958904109 per day

eroding rate = 0.109 mm per day

learn more on significant figure here: https://brainly.com/question/29153641

#SPJ1

Answer:-3

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis so in this case it is -3.

Eta-squared is a small effect size that means the difference between the sample of workers with high-stress careers and the general population is statistically significant, but not clinically meaningful.

Eta-squared is a proportion of variation explained by a statistical model or an experimental design. It is used in ANOVA and other types of regression analysis to determine how much of a dependent variable's variation may be attributable to the independent variable (s).

In the given question, Eta-squared is computed by taking the square of the t-value (2.5 in this example) and dividing it by the sum of the t-value and degrees of freedom squares (49 in this case). The result is an eta-squared value of 0.050.

This eta-squared value corresponds to a modest impact size. This suggests that the gap between the sample of high-stress employees and the overall population is minor but statistically significant. In other words, high-stress professionals may sleep less than the general population, but the difference is not significant enough to be clinically significant.

To know more about eta-squared, visit

brainly.com/question/14298919

#SPJ1

1. At 4.142s the first shell will hit the first enemy ship.

2. At 3.536s the second shell will hit the second enemy ship.

3. The two shells will be 677.1 meters apart when they hit their respective targets.

To solve this problem, we can use the equations for the horizontal and vertical motion of a projectile.

The horizontal velocity of a projectile can be found using the equation: [tex]v_x = v_0 * cos\theta[/tex] where,

The vertical velocity of a projectile can be found using the equation:

[tex]v_y = v_0 * sin\theta[/tex]

The horizontal displacement of a projectile can be found using the equation:

[tex]x = v_0 * cos\theta * t[/tex]

The vertical displacement of a projectile can be found using the equation:

[tex]y = v_0 * sin\theta * t - (1/2)gt^2[/tex] where,

1. To find the time that the first shell will hit the first enemy ship, we can use the equation for the horizontal displacement:

[tex]t = x / (v_0 * cos\theta)[/tex]

t = 2000m / (800m/s * cos(45))

= 4.142s

2. To find the time that the second shell will hit the second enemy ship, we can use the equation for the horizontal displacement:

[tex]t = x / (v_0 * cos\theta)[/tex]

t = 2000m / (1000m/s * cos(60))

= 3.536s

3. To find the distance between the two shells when they hit their respective targets, we can use the equation for the horizontal displacement:

[tex]x_1 = v_0 * cos\theta * t \\x_2 = v_0 * cos\theta * t[/tex]

x1 = 800m/s * cos(45) * 4.142s

= 2858.9m

x2 = 1000m/s * cos(60) * 3.536s

= 3536m

x2 - x1 = 3536m - 2858.9m

= 677.1m

So the two shells will be 677.1 meters apart when they hit their respective targets.

Learn more about projectile motion here:

https://brainly.com/question/15358092

The complete question is:

A destroyer simultaneously fires two shells at two different enemy ships. The first shell has an initial speed of 800 m/s and is fired at an angle of 45 degrees. The second shell has an initial speed of 1000 m/s and is fired at an angle of 60 degrees. The distance between the two enemy ships is 2 km.

1. At what time will the first shell hit the first enemy ship?

2. At what time will the second shell hit the second enemy ship?

3. How far apart will the two shells be when they hit their respective targets?

#SPJ4

Answer:

-1/2

Step-by-step explanation:

use any difference in Y

divided by the difference in X.

ΔY = 3-2 = 1

ΔX=-4-(-2)=-2

1/(-2) = slope

196 millilitres of tomato paste for 16 litres of spaghetti sauce.

=======================================================

Explanation:

We're told that 12 litres of sauce goes with 147 millilitres of paste.

Divide the larger value over the smaller: 147/12 = 12.25 exactly.

Do the same thing to each of the answer choices A through D.

Optionally we could represent the results in a table like so

[tex]\begin{array}{|c|c|c|c|} \cline{1-4}\text{Choice} & \text{Paste} & \text{Sauce} & \text{Paste/Sauce}\\\cline{1-4}\text{A} & 94 & 8 & 11.75\\\cline{1-4}\text{B} & 108 & 9 & 12\\\cline{1-4}\text{C} & 196 & 16 & 12.25\\\cline{1-4}\text{D} & 169 & 14 & 12.071 \ \text{(approx)}\\\cline{1-4}\end{array}[/tex]

Spreadsheet software is handy if you go this route. You don't have to worry about the units in this case.

Choice C is the only option that yields the ratio 12.25, which means it's the only possible answer.

For these traditional cooking measurements, there are no specific definitions. The majority of sources, however, claim that a dash is roughly 1/8 of a teaspoon, a pinch is 1/16 of a teaspoon, and a smidgen is 1/32 of a teaspoon.

The Complete Question.

To Learn more About dash Refer To:

https://brainly.com/question/27828140

#SPJ1