A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)

Answer:

Step-by-step explanation:

[tex]\mathrm{\cfrac{3^5\times\:10^5\times\:25}{5^7\times\:6^5}}[/tex]

Factor:

6^5= 2^5*3^5

10^5= 2^5*5^5

25 = 5^2

[tex]\mathrm{\cfrac{3^5\times\:2^5\times\:5^5\times\:5^2}{5^7\times\:2^5\times\:3^5}}[/tex]

3^5*2^5*5^5*5^2 = 3^5*2^5*5^7

[tex]\mathrm{\cfrac{5^7\times\:3^5\times\:2^5}{5^7\times\:2^5\times\:3^5}}[/tex]

Now, cancel common factor:-

[tex]\mathrm{3^5\times\:2^5\times\:5^7}[/tex]

[tex]\mathrm{1}[/tex]

-Hope this helps!

The age of a fossil can be determined using Carbon 14 dating. Carbon 14 dating is a method of determining the age of an object that is based on the decay of the isotope carbon-14. Carbon-14 has a half-life of approximately 5,730 years, which means that half of the initial amount of carbon-14 in a sample will decay in 5,730 years.

What is carbon dating in simple words?

Simply said, carbon dating is the process of using the presence of carbon 14 to estimate the age of ancient material (such as an archaeological or paleontological specimen).

If 32% of the initial amount of Carbon 14 in a sample remains, we can use the formula:

Age = t = (t1/2) * ln(2) / ln(A0/A)

Where t1/2 is the half-life of carbon-14 (5730 years), A0 is the initial amount of carbon-14 (100%), and A is the remaining amount of carbon-14 (32%).

Age = (5730) * ln(2) / ln(100/32)

Age = (5730) * 0.693 / (-1.51)

Age = 8129 years

So, approximately 8129 years have elapsed since the fossil was formed.

Note that this is an estimate and this method of dating can only be used for fossils that are less than about 60,000 years old. Also, this method assumes that the initial amount of carbon-14 in the sample is known, which can be affected by the environment and other factors that can affect the accuracy of the dating.

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An example of dilation math is a square of side 5 units can be dilated to a square of side 15 units, but the shape of the square remains the same.

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The maximum volume is 63.75 cubic cm. The rectangular is kind of shape that has lenght and width.

To find the dimensions of the rectangular solid that will result in a maximum volume, we can use the formula for the surface area of a rectangular solid, which is:

Surface Area = 2lw + 2lh + 2wh

where l is the length, w is the width (which is the same as the base of the square), and h is the height.

We can set up an equation using this formula, with the given surface area:

181.5 = 2lw + 2lh + 2wh

To find the maximum volume, we can take the derivative of the volume equation and set it equal to 0, then solve for the value of the variable.

The volume of the rectangular solid is V = lwh

The derivative of V with respect to l is : dV/dl = wh

The derivative of V with respect to w is : dV/dw = lh

The derivative of V with respect to h is : dV/dh = lw

Therefore, the maximum volume occurs when dV/dl = 0, dV/dw = 0 and dV/dh = 0

Since the base of the rectangular solid is a square, we know that l = w

If we substitute this value into the equation for the surface area, we get:

181.5 = 2l^2 + 2lh

Solving for h in terms of l, we get:

h = (181.5 - 2l^2) / (2l)

We can now differentiate this equation with respect to l, and set it equal to 0, then solve for l:

[tex]\frac{dV}{dl} = (2lh + l^2h - 2l^3) / l = 0\\2l(181.5 - 2l^2) + l^3 = 0\\2l(181.5 - 2l^2) = -l^3\\2(181.5 - 2l^2) = -l^2\\363 - 4l^2 = -l^2\\l^2 = 181.5 / 2\\l = \sqrt{\frac{181.5}{2} } \\I = \sqrt{90.75} \\I = 3.5[/tex]

So the dimensions that will result in a maximum volume are:

length (l) = 3.5 cm

width (w) = 3.5 cm

height (h) = (181.5 - 23.53.5) / (2*3.5) = 5 cm

The maximum volume is V = lwh = 3.53.55 = 63.75 cubic cm

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Quadrant Class 9 is a level of mathematics taught in secondary school in the United Kingdom. It is the equivalent of Algebra 1 and Geometry combined in the United States.

This class teaches students how to graph equations, solve equations, and use the properties of shapes to solve problems. Quadrant Class 9 also covers the basics of calculus, such as derivatives, integrals, and limits.

The main focus of Quadrant Class 9 is on graphing equations. Students learn how to plot points on a graph, connect the points to make a line or curve, and solve equations by finding the intersection of two lines. They also learn how to graph the solutions of inequalities and identify the domain and range of a function.

In addition to graphing, students learn how to solve equations using basic algebraic principles, such as the order of operations and the distributive property. They also learn how to solve systems of equations, manipulate polynomials, and find the roots of a quadratic equation.

Quadrant Class 9 also covers the basics of geometry, such as the Pythagorean Theorem, the properties of triangles, and the area and perimeter of shapes. Students learn how to use these skills to solve problems involving angles, area, and volume.

Overall, Quadrant Class 9 is a challenging and rewarding mathematics class that prepares students for higher-level math classes in the future.

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From the centre formula the distance is between two points in a plane.

A mathematical calculation known as the distance formula is used to calculate the separation between two points on a plane. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs, is the source of the distance formula which is the side opposite the right angle.

The distance formula is frequently shown as: d = √((x2 - x1)² + (y2 - y1)²). The first point's coordinates are x1 and y1, the second point's coordinates are x2 and y2, and d is the distance between the two points. It's crucial to keep in mind that this method only works when the two points are in a 2D plane.

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Answer:

A) 0

Step-by-step explanation:

h/4+(12-y)/3

-12/4+(12-3)/3

-3+(9)/3

-3+9/3

-3+3

0

Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.

Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.

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Answer:

Step-by-step explanation:

So we know what a gradient is = y=mx+c So you have to make a triangle with the 2 numbers touching a line and make a triangle the conects to both of them. and then you will get the answer

Applying the relation between the force and the distance between the two objects , the force between the objects when the distance between the objects is 7 meters is 0.21 N.

Force is a physical quantity that describes the interaction between two objects. It is the push or pull exerted on an object that changes or tends to change its motion. Force is measured in units of Newtons (N) and it can be a vector quantity, meaning that it has both magnitude and direction.

The unit of measurement for force is the Newton (N). It is important in physics because it is one of the fundamental quantities used to describe the motion and interactions of objects. Forces are responsible for changes in an object's motion, such as acceleration or deceleration, and they play a key role in many physical phenomena, including gravity, friction, and tension.

As given in the question , the force is 0.65 Newtons when the distance between the objects is 4 meters.

Let the force when the distance is 7 meters be F2.

So using the relation between the force and the distance , i.e Force is inversely proportional to the square of distance between the objects.

[tex]\frac{F2}{0.65} =\frac{4^{2} }{7^{2} }[/tex]

Therefore, F2 = 0.21 Newtons

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For each type of book, Elliott has 19 fiction books and 7 nonfiction books.

To solve for the number of fiction books (x), we can use the first equation of the system: x + y = 26. We know that the number of nonfiction books (y) can be represented by x - 12 (from the second equation of the system: x - y = 12).

So we can substitute x - 12 for y in the first equation:

Combining like terms:

Adding 12 to both sides:

Dividing both sides by 2:

Therefore, Elliot has 19 fiction books.

To solve for the number of nonfiction books (y), we can use the first equation of the system: x + y = 26 and input the value of x:

Therefore, Elliot has 7 nonfiction books.

This question is incomplete and should be written as:

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.

This system of equations models the number of books.

Elliot added the two equations and the result was 2x = 38. How many fiction and nonfiction books does Elliot have?

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Answer:

A)57   film a music video

Step-by-step explanation:

Let x represent measure of angle 1.

We have been given that measure of angle 3 is six more than twice the measure of angle 1. So measure of angle 3 would be .

We are also told that measure of angle 2 is 27 less than measure of angle 3, so measure of angle 2 would be .

We have been given that angle 1, angle 2 and angle 3 form a straight line, so the sum of angles 1, 2 and 3 would be 180 degrees.

Upon substituting the expressions for measure of angles, we will get:

Now, we will combine like terms.

The measure of angle 2 would be .

Therefore, the measure of angle 2 is 57 degrees.  

The numbers in the ascending order is given by A , where

-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

Let the set of numbers be represented as set P

The value of set P is P = { -4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73 }

On simplifying the equation , we get

The larger the negative number , the lesser is its value

And , larger the positive number , the greater is its value

So ,

The ascending order of the numbers are

-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

Hence ,

The ascending order is -73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

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The range of y=2x^(2)+12x-13 is all real number Option C

Generally, A quadratic function is a type of polynomial function that has the form

f(x) = ax^2 + bx + c,

where

a, b, and c are constants and x is the variable.

The graph of a quadratic function is a parabola that opens either upward or downward, depending on the value of a. The vertex of the parabola is the point (h, k), where h = -b/2a and k = f(h). The roots of the quadratic function, or the x-coordinates of the points where the parabola crosses the x-axis, can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.

The range of a quadratic function in the form of y = ax^(2) + bx + c is all real numbers for a ≠ 0, and for a = 0,

the range is {c}. In this case, a = 2, so the range of y = 2x^(2) + 12x - 13 is all real numbers.

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The range of the given quadratic equation is y ≤ 5.

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that, you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.  While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

For a quadratic function,  the range is defined from the y-coordinate of the vertex  ( [tex]y_v=\frac{-\Delta}{4a}[/tex]).

If a<0, the range is y≤ yv

If a>0, the range is y≥ yv

The question gives the following quadratic equation: -2x²+12x-13, then:

a=-2

b=12

c=-13

Δ= b²-4ac=12²-4*(-2)*(-13)=144-104=40

Therefore,

[tex]y_v=\frac{-\Delta}{4a}=\frac{-40}{4*(-2)}=\frac{-40}{-8}=5[/tex]

Thus, yv=5 and the range is ≤ 5.

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Answer:

-72

Step-by-step explanation:

-0.125x=16-7

-0.125x=

x=-72

Answer:

x = -72

Step-by-step explanation:

Given equation,

→ -0.125x + 7 = 16

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ -0.125x + 7 = 16

Subtract RHS with the number 7:

→ -0.125x = 16 - 7

→ -0.125x = 9

Divide RHS with the number -0.125:

→ x = 9 ÷ (-0.125)

→ [ x = -72 ]

Hence, the value of x is -72.

Answer:

Volume: 197.92

Formula: π r² h

Step-by-step explanation:

Answer:

the missing side is 29 so point D or bubble 2

Step-by-step explanation:

use the formula a^2 + b^2 = c^2

20^2 + 21^2 = ?^2 find the answer for the squared values

400 + 441 = ?^2 Add the values

841 = ?^2 in order to get rid of the power square root on both sides

_/- 841 = ? solve

29 = ?

Answer: e, a, f, c

Step-by-step explanation:

v evenly cuts through line tv and line VS. you can tell because the single line on each side....... rest should be correct

Answer:

1096.63316

Step-by-step explanation:

The minimum number of jumps required to reach the flag's height is 3.

Let n be the height of the flag. We can use a recursive approach to determine the minimum number of jumps it takes to reach the flag's height.

For n = 0, it takes 0 jumps to reach the flag's height.

For n = 1, it takes 1 jump to reach the flag's height.

For n > 1, we can calculate the minimum number of jumps using the following equation:

minJumps(n) = 1 + min(minJumps(n-1), minJumps(n-j))

Where minJumps(x) is the minimum number of jumps required to reach the flag's height from ground level x.

For example, if the flag's height is 5 and Bob can jump a height of 2, the minimum number of jumps required to reach the flag's height is 3.

minJumps(5) = 1 + min(minJumps(4), minJumps(3))

= 1 + min(1 + min(minJumps(3), minJumps(2)), 1 + minJumps(2))

= 1 + min(1 + 1, 1 + 1)

= 3

Therefore, the minimum number of jumps required to reach the flag's height is 3.

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To calculate the sale price, we need to find out how much the TV is discounted by, which we can do by multiplying the original price by the percentage discount (expressed as a decimal).

35% of the original price can be expressed as 0.35.

so,

Discount = 540 omr * 0.35 = 189 omr

To find the sale price, we can subtract the discount from the original price:

Sale price = Original price - Discount

Sale price = 540 omr - 189 omr

So the sale price is 351 omr.

Therefore , we may now say that the requisite unequal declaration is 4.50x+1.75y 50 if the expression problem is resolved.

In mathematics, an expression is made up of a claim, two or more integers or variables, and one or more arithmetic operations. This mathematical operation can multiply, divide, add, or remove numbers. The following is how an expression is put together: Expression: A variable or a number, a math operator, and a math operator.

Here,

$4.50 is the price per assignment.

The assignment cost "x" is equivalent to 4.50x as a result.

$1.75 for each task.

Therefore, the cost of assignment "Y" is 1.75Y.

Because of this, 4.50x+1.75y should be $50 maybe less.

As a result, the inequality declaration required is 4.50x+1.75y ≤50.

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Writing 5/x + 1 + 2/3x as a single fraction will result to (17 + 3x)/3x

The expression is written with parameters having unlike terns. The terms consist of the constant term and the variable parameters.

The constant terms are 1

terms with variables are 5/x and 2/3x

adding like terms gives

= 5/x + 2/3x

the LCM of x and 3x is 3x and this will be the common denominator

= (15 + 2) / 3x

= 17/3x

adding both together

= 17/3x + 1

the LCM of 1 and 3x is 3x and this will be the common denominator

= (17 + 3x) / 3x

The single fraction is (17 + 3x) / 3x

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Yes, a domain can be all numbers. This type of domain is called a numerical domain.

A numerical domain is a set of numbers that is used to define a function. It is usually represented by the formula D= {x: x is a real number}. This formula can be used to calculate the domain of a given function by determining which values of x, or the independent variable, produce a valid output. Numerical domains are becoming increasingly popular as they are easier to remember than domains composed of letters and hyphens. They can also be used to represent a business’s contact information, such as a phone number or street address. When registering a numerical domain, it is important to ensure that it is not already taken, as numerical domains are becoming increasingly sought after. For example, if a function is defined as f(x) = x2 + 3, then the domain would be all real numbers, since any real number would produce a valid output.

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a) The reason for which r > 3 is because a side length in a figure cannot assume a negative value.

b) The double inequality for r is given as follows: 3 < r < 8.

The perimeter of a rectangle of base b and height h is given by the equation presented as follows:

P = 2(b + h).

The dimensions for this problem are given as follows:

The perimeter of the rectangle is smaller than 26 cm, hence the inequality is defined as follows:

P < 26.

2(b + h) < 26

b + h < 13 (simplifying by 3 both sides of the inequality).

r + r - 3 < 13

2r < 16

r < 8.

Hence the double inequality is defined as follows:

3 < r < 8.

As a side length cannot be negative nor zero, hence it is also needed that r - 3 > 3 -> r > 3.

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Using synthetic division, the value of the remainder comes out to be -9.

What is synthetic division?

When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials. The ability to compute without writing variables when doing polynomial division with the synthetic division makes it an easier technique than the classic lengthy method, which is one of its advantages over the latter.

Two polynomials can be divided using the formula:

p(x)/q(x) = Q(x) + R/(q(x))

where,

The dividend is p(x).

The linear divisor is q(x).

The quotient is Q(x).

The remainder is R

Given expression is [tex]4x^{4} -3x^{3} +6x-10[/tex]

We have to divide this expression by (x + 1) by using synthetic division.

Expression given above can be written as,

4x⁴ - 3x³ + 6x - 10 = 4x⁴ - 3.x³ - 0.x² + 6x - 10

Now on dividing by x = -1 by synthetic division method, we get

-1 |  4     -3     0      6     -10

      -    -4      7     -7       1    

     4    -7      7     -1      -9    

Remainder of the synthetic division will be -9.

Hence, we rewrite the given expression as, [tex]4x^{3} -7x^{2} +7x+1 -\frac{9}{x-9}[/tex]

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