Factor the quadratic expression
4a²+27a+18

It becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

Logarithms arise in problems of exponential growth

and decay because they are inverses of exponential functions. Because of the Laws of Logarithms, they also turn out to be useful in the measurement of the loudness of sounds, the intensity of earthquakes, and other processes that occur in nature

We can write an exponential function to represent the situation.

We know that the current population is 100,000.

The population doubles each day.

The standard exponential function is given by P(t) = A (2)^t

Since our current population is 100,000, a = 100000.

Since our rate is doubling, r = 2.

So

P(t) = 100000 (2)^t

We want to find the population five days ago.

So, we can say that t = -5. The negative represent the number of days that has passed.

Therefore

P(-5) = 100000 (2)^-5 =100000*(1/32) =3125

However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.

We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:

P(t) = A (2)^t

After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:

100000 =A[tex]2^5[/tex]

And solving for A, we acquire     :[tex]\frac{100000}{2^5}[/tex]

                                                      =3125

So, our function in terms of the original day is:

P(t) = 3125 (2)^t

So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

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The absolute value of a given number is said to be the positive version of that number. For example, the absolute value of -5 is + 5, which can be written as: − I5 | = 5. Other examples of absolute values ​​of numbers: |−9| = 9, |0| = 0, − |−12| = −12, etc.

Absolute Value Equation:

An absolute value function is an algebraic function whose variables lie within the absolute value bar. This function is also called the modulus function, and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. In general, the absolute value function can be expressed as f(x) = a |x - h| + k, where a represents how much the graph stretches vertically, h represents the horizontal shift, and k represents the vertical shift of the graph for f(x) = |x|. represents If the value of 'a' is negative, the chart opens downwards, if positive, the chart opens upwards.

Now that we understand the meaning of the absolute value function, we understand the meaning of the absolute value equation f(x) = a |x - h|. + k and how the values ​​of a, h, and k affect the value of the function.

The vertex (x) = a |x - h| + k of the absolute expression f is given by (h, k). You can also use the vertices of f(x) = a |x - h| Find + k using the formula (x - h) = 0 . When determining the value of x, substitute that value into the formula to find the value of k.

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The slope of 5x 2y =- 3 is -5/2.

To find the slope of the equation 5x 2y =- 3, we need to rearrange it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

We start by rearranging the equation 5x 2y = -3 so that all the terms with y are on one side and all the terms with x are on the other side.

5x -2y = -3

Now, we divide both sides by -2 to isolate y.

-5x/2 = y + 3/2

Finally, we subtract 3/2 from both sides to get the equation in the slope-intercept form.

-5x/2 = y - 3/2

Therefore, the slope of the equation 5x 2y = -3 is -5/2.

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The commission the salesperson would receive is $490.

What is a commission?

A commission is a payment made to an individual, such as a salesperson or agent, for services rendered or a good sold. The commission is typically a percentage of the sale or revenue generated. This percentage is known as the commission rate.

To find the commission a salesperson would receive from selling a car, we need to multiply the commission rate (5%) by the car's value ($9,800).

The commission rate is given as a percentage, so we need to convert it to a decimal to do the calculation. We can do this by dividing the percentage by 100.

So 5% = 5/100 = 0.05

Then to find the commission the salesperson would receive we multiply:

Commission = 0.05 * $9,800

Commission = $490

Hence, the commission the salesperson would receive is $490.

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On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Surface  Area of central park = 2.5 × 0.5 = 1.25 square mile

1 acre = 1/640 square mile

1.25 square mile = 1.25 ÷ 1/640 = 800 acre

Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people

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function f(x) = 75 - 4.5 w.

where w = number of weeks.

this question is related to function and solution is as follows,

The owner of a mall Restaurant bought rice = 75 kg

Each week, the restaurant use rice = 4. 5 kg

so we have to make an equation of function by which we can find out the remaining rice after w number of weeks,

f(x) = 75 - 4.5 w

where ,w = number of weeks

example, find out rice after 6 weeks

number of weeks (w) = 6

put it in the function,

f(x) = 75 - 4.5(6)

f(x) = 75 - 27

f(x) = 48.

so the function is ,f(x) = 75 - 4.5 w.

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The area of the semi-circle with the radius of 4.1 mm, round to the nearest tenth is 52.8 mm²

The area of the semi-circle will be calculated by the formula -

Area = 1/2πr², where r is the radius of the circle.

Keep the values in formula to find the value.of area of semi circle

Area = 1/2×3.14×4.1²

Performing multiplication on Right Hand Side of the equation to find the area of the semi-circle

Area = 52.78 mm²

Round off the nearest tenth

Area = 52.8 mm²

Thus, the area of semi-circle with mentioned radius is 52.8 mm².

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Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

A linear model is the one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "mathematical expression having two variables" both y and x are different factors. Bivariate linear equations are two-variable linear equations. There are several uses for linear equations: , all result in zero. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. Y=mx+b is the formula for an equation, where m stands for the slopes and b for the y-intercept.

Here,

Given : 2x + 3 =0

thus,

To find that it is linear equation in two variable is given  equation

As,

We can see there is only one variable that is x.

So , it is not a linear equation in two variables.

Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

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Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

The initial pressure is 70 N / 0.2 m^2 = 350 Pa (Pascals). If the force is increased by 10 N and the area is increased by 10 cm^2, the new pressure is 80 N / 0.3 m^2 = 266.67 Pa

To calculate the percentage change in pressure, we divide the change in pressure by the initial pressure and multiply by 100:

So Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

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The percentage markup the store made before selling those speakers

are 136.33%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A store bought a set of speakers for $82.86 and sold them for

$195.82.

So, The amount of profit is $(195.82 - 82.86).

= $112.96.

Now, The markup percentage can be obtained by the concept of the percentage change.

Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,

= (112.96/82.86)×100%.

= 136.33%.

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According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.

The direction that each person is facing is crucial when arranging the people.

In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.

Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.

There are two different ways to arrange the groups so they can sit together.

2! = 2 * 1

2! = 2ways

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both Square and Rectangle

because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)

Answer: 7 13/15

Step-by-step explanation:

First of, you have to get your common denominator, as it's impossible without one.

The closest common denominator is 15, and it will ask you for a simplified version.

Multiply the 2/3 in 5 2/3 by 5 on both sides to get 5 10/15

Multiply the 1/5 in 2 1/5 by 3 on both sides to get 2 3/15

Then add up your sum.

5 10/15+2 3/15=7 13/15

Answer:

7 13/15

Step-by-step explanation:

5 2/3+2 1/5

We need to get a common denominator for the fraction

3*5 = 15

2/3 *5/5 = 10/15

1/5 * 3/3 = 3/15

5 10/15 + 2 3/15 = 7 13/15

Answer:

I hope this helps you...

please mark me as brainliest..

The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

What is the equation of the parabola?

The equation can be written as

f(x) = 1/(4p)(x -h)^2 +(k-p)

where (h, k) is the focus, and p is half the distance between focus and directrix.

Here, We have the upward parabola;

Focus at (9,27)

P/2 = 27-19 = 8        Nature of focus

P = 16

so (x-9)^2 = 2py = 32y

y = 1/32(x-9)^2 + 19

The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

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The required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Given expression x + 7,
The expression can be translated as a number increase by 7 or the Addition of the number and 7.

Thus. the required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

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Answer:

yes, the board is long enough

Step-by-step explanation:

5.5 in x 4 walls = 22 inches

The board is 24.5 in, so there is enough.

24.5 > 22, there is an extra 2.5 in left over.

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers.

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Wind direction [Mode] is South west

The [Mean] temperature is  

The  [Bimodal] pavement is  Dry Wet

From the question the first question is to determine the wind direction

Generally from the wind direction would be the data with the highest frequency on the wind column i.e the mode of the data, this because this variable(wind direction ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )

So

The mode is Southwest

This means that the wind direction is Southwest

From the question second question is to determine the temperature

Generally given that their are are no outlier that will skew the data we can obtain the temperature by calculating the mean for the temperature column

This is mathematically represented as

T = 89+86+....+93+93/8

T = 91

From the question, the first question is to determine the  pavement

Generally from the pavement would be the data with the highest frequency on the pavement i.e the mode of the data, this because this variable(pavement ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )

From the table we see that the pavement that the pavement column is bimodal

So the mode is Dry Wet

This mean that the pavement is Dry Wet

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The function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

What is the function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

For Option A, the total amount earned can be represented by the function:

f(x) = 100 + 10x

where x is the number of days in February (x = 28 for a standard non-leap year)

For Option B, the total amount earned can be represented by the function:

f(x) = (1/100) * 2^x

where x is the number of days in February (x = 28 for a standard non-leap year)

the above function will be in cents, to get dollar values divide it by 100.

hence, the function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

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Step-by-step explanation:

the center of the circle is (−3,5) and radius is 16 =

Fencing that Luke and Seth did each buy is 72 feet

Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.

Seth's garden is square, so it has four times the perimeter.

The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).

We also know that Luke and Seth should buy the same amount of fences. So:

4x = 2(x + 3) + 2(x/2)

Solving this equation for x gives x = 6 feet.

So Seth's yardage is 6 feet and Luke's yardage is 9 feet.

So the fence required for Seth's garden is 46 = 24 feet

and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.

So the total fencing required is 24 + 45 = 72 feet.

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Step-by-step explanation:

to find the equation of any line we have to first find the slope. the slope formula is:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

our slope here would be 8/13

now we input the points in the equation

y = mx + b

then we find b to be -3(7/13)

so the final equation would be:

[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]

When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y=6-2x\implies 2y=-2x+6\implies y=\cfrac{-2x+6}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -1 \implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1} \implies 1}}[/tex]

so we're really looking for the equation of a line whose slope is 1 and it passes through (6 , -7)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{6}) \implies y +7= 1 (x -6) \\\\\\ y+7=x-6\implies {\Large \begin{array}{llll} y=x-13 \end{array}}[/tex]

Answer: Kayden needs 12 more meters of railing.

Step-by-step explanation:

To find the perimeter of the roof garden I added up all the numbers you listed (12m+3m+7m+10m+20m+10m) to get a total perimeter of 62 meters.

Since Kayden already has 50 meters of railing we can subtract that from the total he needs to get the remaining amount needed.

62m - 50m = 12 meters of railing remaining.

Answer:  To solve this problem, we can use the fact that a cubic centimeter of osmium has a mass of about 23 grams and the information provided about the chemist's amount of osmium.

First, we can divide the total mass of osmium by the mass of a cubic centimeter of osmium to find out how many cubic centimeters of osmium the chemist has. The equation would look like this:

2,530 grams / 23 grams/cubic centimeter = 110 cubic centimeters

So, the chemist has approximately 110 cubic centimeters of osmium.

It's worth mentioning that an exact value would require additional information as 23 grams per cc is an approximate value and also any impurities or loss of material in the sample also effect the total mass.

Step-by-step explanation:

Answer:

2^x=1

x=0

32•x=0

32.0=0

maybe