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How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 50%

Answer:

the substance in chart above

Step-by-step explanation:

that has greatest number of atom is each molecule

The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is \(-8.6+3.15\).

What is formula for slope and intercept is?

\($$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$\)

The slope is

\($$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$\)

The intercept is

\($$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$\)

The regression equation is

\($$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$\)

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\(x^4+4x^3-8x-32=0\)  

Can be factoried into:

\((x^3-8)(x+4)=0\\\)

Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.

First we'll do:

\(x^3-8=0\)

We're looking for what number cubed is equal to 8, which is 2.

Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.

Second we'll do:

\(x+4=0\)

This one's pretty easy, x will be -4.

So your solutions are:

x = 2, -4

The solutions of the polynomial \(x^{4}\) + 4x³ - 8x - 32 = 0 are 2 and -4.

Polynomials are sums of terms of the form k⋅xⁿ.

where k is any number

n is a positive integer.

Example:

2x + 4x - 7 is a polynomial

We have,

\(x^{4}\) + 4x³ - 8x - 32 = 0 _______(1)

Divide into two parts.

\(x^{4}\) + 4x³

-8x - 32

Take out the common from each part.

x³ ( x + 4 )

- 8 ( x  + 4 )

Now,

We have,

x³ ( x + 4 ) - 8 ( x  + 4 ) = 0

We can write this as:

(x³ - 8) (x + 4) = 0

Now,

We need to find the x values.

x³ - 8 = 0

x³ = 8

x = ±2

Put x = 2 in (1)

\(x^{4}\) + 4x³ - 8x - 32 = 0

x = 2

16 + 32 - 16 - 32

0 = 0

x = 2 is satisfied

Put x = -2 in (1)

16 - 32 + 16 - 32 = 0

-64 ≠ 0

x = -2 is not satisfied

x + 4 = 0

x = -4 putting in (1)

256 - 256 + 32 - 32 = 0

0 = 0

x = -4 is satisfied

Thus the solutions of the polynomial \(x^{4}\) + 4x³ - 8x - 32 = 0 are 2 and -4.

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Answer:

  y > -x -3

Step-by-step explanation:

The graph is shaded above the dashed line, indicating y-values in the solution are greater than those on the line, so your inequality will start with ...

  y >

The y-intercept of the line is (0, -3), so the "b" value in ...

  y > mx +b

will be -3.

The line has a rise of -3 for a run of 3 (between the marked points), so the slope is ...

  m = rise/run = -3/3 = -1

Then the inequality you want is ...

  y > -x -3

Answer:

As Per Provided Information

Radius of cylindrical shape silo 9 ft

Height of cylindrical shape silo 41 ft

We have been asked to determine the volume of cylindrical silo .

\( \boxed{\sf \: Volume_{(Cylindrical\:Silo)} = \pi {r}^{2}h}\)

Substituting the given value in above formula and we obtain

\( \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times {9}^{2} \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 81 \times 41 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 3.14 \times 3321 \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10427.94 \: {ft}^{3} \\ \\ \\ \qquad\longrightarrow\sf \:Volume_{(Cylindrical\:Silo)} = 10428 \: {ft}^{3}\)

Answer:

Volume is 10428 cubic ft.

Step-by-step explanation:

Given :-

To find:-

Solution:-

Putting the known values ,

Volume:- 3.14 × 9² × 41 cubic ft.

Volume :- 10427.94 cubic ft.

rounding off to nearest whole number ,

Volume :- 10428 cubic ft.

Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

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Answer:

0.035 x 2^10

Step-by-step explanation:

(0.035). * (2^10) = (0.035) * (1,024) = 35.84

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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The term formula for a geometric progression where the second term is 54, the fourth term is 6, and the common ratio is 0.5 is Un = 108 * (0.5)n-1.

In a Geometric Progression (G.P.), each term is the product of the previous term and a constant multiplier (known as the common ratio). To begin, identify the common ratio (r) by using the formula r = Un / Un-1. If the second term is 54 and the fourth term is 6, then the common ratio (r) is √(6/54) = 0.5.

Once we have established the common ratio, we can find an arbitrary term of the progression using the formula Un = U1 * r(n-1). However, since we don't know the first term, we can derive it from U1 = U2 / r, substituting our given values, we find U1 = 54 / 0.5 = 108.

Now, we can substitute U1 and r into our term formula to find any term (n) in the series: Un = 108 * (0.5)n-1.

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Answer:

h=2A/b

Step-by-step explanation:

I did the test

A differential equation is an equation that includes an unknown function and its derivative. A differential equation describes a relationship between a function and changes in the function.

Differential equations are very important in higher mathematics and also in disciplines where mathematics is used. In subject areas such as physics, engineering, meteorology and economics, differential equations are used to describe connections and development processes.

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Answer: 2. They are congruent angles.

Step-by-step explanation:

      Angle 1 and angle 3 are vertical angles. In other words, they are "opposite" each other.

     Vertical angle pairs are congruent angles, meaning the answer to this question is;

              2. They are congruent angles.

Answer: They are congruent angles.

Step-by-step explanation: Complementary means the two angles equal 90°, supplementary angles are next to each other and equal 180° together, and it's obviously not a right angle, (angle that equals 90°) so we know they are congruent angles (this means that they are the same)

hope this helps!

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Answer:  4n-3

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

Explanation:

day 1 = 1 sold

day 2 = 5 sold

day 3 = 9 sold

day 4 = 13 sold

Each time we're going up by 4. This is effectively the slope of the line since it represents the rate of change. The starting amount sold (1) is the y intercept

So we go from y = mx+b to y = 4x+1

Afterward, replace x with n to get 4n+1

On day n = 0, we have 4n+1 = 4(0)+1 = 1 sold. While this is correct, it doesn't really help to start with day 0 and it's better to start with day 1 instead.

What we can do is replace n with (n-1) and then simplify

4(n-1)+1 = 4n-4+1 = 4n-3

Now plugging in n = 1 leads to 4n-3 = 4(1)-3 = 1

Plugging in n = 2 leads to 4n-3 = 4(2)-3 = 5

and so on.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

141036.25

Step-by-step explanation:

Answer:

141036.25

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Dimension of the rectangular fence:

Length = 30 ft

Width = 25 ft

Perimeter of the rectangular fence = 2(L + W)

= 2(30 + 25) = 2(55)

Perimeter = 110 ft

Fencing cost per foot = $4.05

Fencing cost for 110 ft = 110 × 4.05 = $445.50

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The amount in year 6 is $1282.5.

What is simple interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

rate of interest = 7%

time = 1 year

Amount on first year = $950

First we will calculate simple interest for 5 years, because amount is available for 1 year.

SI =PRT

SI = 950(7/100)1

SI = $332.5

Therefore, the amount after 6 years = 950+332.5

=$1282.5

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Answer:

H = 2S+4

H = M-2

M-2 = 2S+4

M-6 = 2S

M-6/2 = S

The equation that shows Silas's age, S, in terms of Mark's age is

S = (M - 6)/2.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Silas's age = S

Mark's age = M

Hailey's age = H

Now,

H = 2S + 4

H = M - 2

This means,

2S + 4 = M - 2

2S = M - 2 - 4

2S = M - 6

S = (M - 6)/2

Thus,

Silas's age is (M - 6)/2.

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hope it helps :-) good morning ☀️.

Answer:

Step-by-step explanation:

1.

\((-4)(-9)\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a,\:-\left(-a\right)=a\\=4\times\:9\\= 36\)

2.

\((-4)(9)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=-4\times\:9\\\\\mathrm{Multiply\:the\:numbers:}\:4\times\:9=36\\=-36\)

3.

\((6)(6)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=6\times\:6\\\\\mathrm{Multiply\:the\:numbers:}\:6\times\:6\\=36\)

4.

\((-6)(-6)\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a,\:-\left(-a\right)=a\\=6\times 6\\\\\mathrm{Multiply\:the\:numbers:}\:6\times\:6\\=36\)

5.

\((6)(-6)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=-6\times 6\\\\\mathrm{Multiply\:the\:numbers:}\:6\times \:6=36\\=-36\)

The theme is the underlying message, lesson, or central idea conveyed by the narrative or story.

Both a narrative and a story share several common elements that contribute to their structure and presentation. These elements include characters, setting, plot, conflict, and theme.

Characters are essential components of both narratives and stories. They are the individuals or entities that drive the events and experiences within the narrative or story. The setting is the time and place in which the events occur and provide the context for the story.

The plot refers to the sequence of events that unfold and create a structure for the narrative or story. Conflict represents the central problem or challenge faced by the characters and is often a driving force behind the plot's progression.

These shared elements create a framework for both narratives and stories, enabling the development and communication of experiences, ideas, and emotions to the audience. They contribute to the engagement, coherence, and impact of the narrative or story, regardless of the medium or genre in which they are presented.

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Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Answer:

31 degrees

Step-by-step explanation:

90-59

=31

~rere

Answer:

<b = 31 °

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles

So . .

Because the sum is 90 subtract!

<b = 31 °

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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Answer:

18 cheese pizza's

Step-by-step explanation:

3-7

6*7=42 pepperoni pizza's

3*6=18 cheese pizzas

Answer:

C. =

Step-by-step explanation:

This is because 18% is 18/100. You could find the answer one of two ways. Divide by two or multiply by 2.

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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