How is the logarithmic function y log x defined?

a. The exponential function that is good model for the country population is:

Pₙ = 8100000(1.02)ⁿ ,

b. It will take 5.27 years to reach 9 million.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.

a. Given,  initial population P₀ = 8100000, Rate of increase R = 2%.

If a constant rate of growth be R% per annum,

then function for population after n years

Pₙ = P₀ x (1+R/100)ⁿ

Population Pₙ = 8100000 × (1+2/100)ⁿ

Pₙ = 8100000(1.02)ⁿ

b. Let after x years population will be 9 million.

then,

9000000 = 8100000 (1 + 2/100)ˣ

(1 + 2/100)ˣ = 9000000/8100000

(1.02)ˣ = 90/81

(1.02)ˣ = 1.11

Taking log on both sides

ln (1.02)ˣ = ln (1.11)

ln(a)ⁿ = n ln(a)

x ln(1.02) = ln (1.11)

x = ln(1.11)/ln(1.02)

x = 5.27 years

Hence, the population will reach 9 million in 5.27 years.

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Answer:

12.5

Step-by-step explanation:

We see in the other triangle that the ratios is 2:5 (4 to 10).

Therefore, assuming they are similar, we can assume the ratio is the same for the missing triangle.

So,

10/4 = 2.5

5(given) x2.5 =  12.5

Answer:

7.7

Step-by-step explanation:

10² - 4² = 84

√84 = 9.16 so 9.2

now we now have the hypotenuse of the other triangle

9.2² - 5² =59.64

√ 59.64 = 7.72 so 7.7

Answer:

2. one angle is 108, and other is 72

3. x is 12

Step-by-step explanation:

the ratio is 3:2.

3x + 2x = 180

5x = 180

x = 36

36 x 3 = 108

36x 2 = 72

so that is why the two angles re 108and 72.

for the last question, 37 plus 41 plus x = 90

37 plus 41 is 78

90 - 78 = 12

so that is why x is 12.    

Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.

[tex]P-9=-3w+9-9[/tex]

[tex]p-9=-3w[/tex]

[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]

[tex]-\frac{P-9}{3} =w[/tex]

Answer: 2.4

Step-by-step explanation:

we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.

hope that helps...

Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below

Here,

Spread it all out here first:

4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10

The mean is calculated by dividing total total by the total number of scores. Add up each number.

There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75

To get the median, identify the middle number among all the other numbers.

Sadly, there is no "center number" given that there are 16.

Add the ninth and eighth numbers together, then divide by to find the middle.

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A plot point example contains a point in a story that defines the turning point in the story.

A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.

Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.

An example of plot point is :

In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.

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The total amount of solid sphere chocolate in the box is 1695.6 cubic centimeters.

The space occupied within an object's borders in three dimensions is referred to as its volume.

The volume or the space inside the borders of the sphere is given by the formula:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Given that the diameter is 6cm, the radius r = 3cm.

Substituting the value of radius in volume we have:

[tex]V = \frac{4 (3.14)(3)^3}{3}[/tex]

[tex]V= 113.04[/tex]

The box contains 15 candies hence the total volume will be:

V = 15 * 113.04

V = 1695.6 cubic centimeters.

Hence the total amount of chocolate in the box is 1695.6 [tex]cm^3[/tex].

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The equation is

log ( milligrams of drug A ) =3 - 0.0737 ( Time)

As per the details  stated above,

Curved relationship between the number of milligrams of drug A is  (x) still in the body and the number of hours since drug A was delivered (y)

The co-efficient of the constant is 3.00

the co-efficient of the time is -0.0737

the SE  co-efficient of the constant is 0.4017

the SE co-efficient of the time is 0.005

the t-ratio of the constant is 7.481

the t-ratio of the time is -14.74

now the equation formed is

logarithm of drug A in milligrams is  (The co-efficient of the constant - the co-efficient of the time )

that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).

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Answer:

8 + 56d

Step-by-step explanation:

We will open the parentheses, multiplying the stuff outside by the stuff inside. So, we get:

8*1 + 8*7d

Then, we can simplify by giving us:

8 + 56d

Hope this helped!

Answer:

1.52cm rounded

1.524 exact

Step-by-step explanation:

For this, we use the basic conversion of 1 inch is 2.54 cm.

We can do:

2.54 cm x 0.6 inch = 1.52 cm rounded.

Answer:

1. 360

2. Yes because in a regular hexagon all angles are congruent so the exterior angles are as well

3. (i) 60 (ii) 120

4.

(i) 1. 360 2. Yes because in a regular octagon all angles are congruent so the exterior angles are as well 3. (i) 45 (ii) 135

(ii) 1. 360 2. Yes because in a regular 20-gon all angles are congruent so the exterior angles are as well 3. (i) 18 (ii) 162

Step-by-step explanation:

Works for each polygon

1. First take the number of sides and subtract it by 2 then multibly that by 180

6-2=4x180=720

Then divide by the number of angles and subrtact that number by 180 to find the measure of one exterior angle

720/6=120

180-120=60

Then multiply by the number of exterior angles

60x6=360

2. Regular polygons always have equal angles so the exterior angles are as well

3. Put in your numbers from earlier

(i) 60 (ii)120

Hope this helps! :)

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Given:

The quadratic equation is:

[tex]12a^2+9a+7=0[/tex]

To find:

The solution of the given equation in simplest form by using the quadratic formula.

Solution:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]12a^2+9a+7=0[/tex]

Here, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]

[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]

[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex]              [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]

The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].

Therefore, the correct option is B.

The number of phones sold is 26 and the number of accessories sold is 30.

An equation is said to be linear if the maximum power of the variable is usually 1.  A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.

In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.

Given that

Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.

On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold. ​

Let x and y be the number of phones and accessories

Given that

Cameron made a total of $361 in commission

=> 11x + 2.5y = 361  ----- (1)

Total number of phones and accessories sold

=> x + y = 56

Multiply by 11

=> 11x + 11y = 616 ----- (2)

Do (2) - (1)

=> 11x + 11y - ( 11x + 2.5y) = 616 - 361

=> 11x + 11y - 11x - 2.5y = 255

=> 8.5y = 255

=> y = 255/8.5

=> y = 30  

Substitute y = 30 in x + y = 56  

=> x + 30 = 56

=> x = 26

Therefore,

The number of phones sold is 26 and the number of accessories sold is 30.

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Answer:

m=3n

Step-by-step explanation:

3 movies per month. So 3 n per m.

Answer:

n=3m

Step-by-step explanation:

n is number of movies

3 is the 3 movies per month

m is each month

so it's n=3m

Answer:

c. the sample portion is unbaised

Step-by-step explanation:

plato

Answer:

(9, -5)

Step-by-step explanation:

The vector AC has coordinates (27, -18), because:

21 - (-6) = 27

-13 - 5 = -18

If the ratio of AB to BC is 5 to 4, it means that

AB = [5/(5+4)]AC = (5/9)AC

Therefore, we have

AB = (5/9)AC = (5/9) (27, -18) = (15, -10)

Which means that:

xB - xA = 15 <=> xB - (-6) = 15 <=> xB + 6 = 15 <=> xB = 9

yB - yA = -10 <=> yB - 5 = -10 <=> yB = -10 + 5 <=> yB = -5

So B has coordinates (9, -5).

Answer: 4y (4y^2-2y-5)

Step-by-step explanation:

Answer:

20 + 2x = 180

Step-by-step explanation:

20 + 2x = 180

2x = 160

x = 80

Answer:

x = 60

Step-by-step explanation:

Let the two opposite angles be equal and let's call them y.

Because of the theory of angles on a straight line 120 +y = 180

y = 60

Because of the theory of angles on a straight line 2x + y = 180

2x + 60 = 180

2x =  120

x = 60

Alternatively. (also a lot easier)

120 and 2x are opposite angles so they are equal and so;

2x = 120

x = 60

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Answer:

slope is zero

Step-by-step explanation:

slope is the difference of the y-values over the difference of the x-values

(-3-(-3)) ÷ (5-2)

0/3

The process of finding the horizontal asymptote and y intercept is explained below.

In order to find the steps, we must know that what is meant by asymptote and intercept.

The process of finding the asymptote is defined as the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

If the degree of numerator is less than degree of denominator then horizontal asymptote at y = 0

Where as if the degree of numerator is greater than degree of denominator by one then there is no horizontal asymptote

Finally if the degree of numerator is equal to degree of denominator then the horizontal asymptote at ratio of leading coefficients.

As per the definition of intercept we have identified that the point that will intersect at the y axis is referred as the y intercept.

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Answer:

around 18.094 liters

Step-by-step explanation:

Answer:

Around 18.0942683 Liters

Answer:

(y-5)^2=14(x+7/2)

Step-by-step explanation:

The equation for a parabola with a focus at (0,5) and a directrix at x = -7 is (y - 5)² = 14 (x + 3.5).

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

Given,

Focus of the parabola at (0, 5).

Directrix is x = -7.

The parabola is horizontal parabola since the directrix is a vertical line.

Equation of the parabola is of the form,

(y - k)² = 4p (x - h)

Here (h, k) is the vertex.

Vertex of the parabola is the mid point of focus (0, 5) and the point (-7, 5).

(h, k) = ([tex]\frac{0 + -7}{2}[/tex], 5) = (-7/2, 5)

Now, p is the distance from vertex to focus.

p = 0 - -7/2 = 7/2 = 3.5

So the equation is,

(y - 5)² = 4× 3.5 (x - -3.5)

(y - 5)² = 14 (x + 3.5)

Hence the equation is (y - 5)² = 14 (x + 3.5).

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Answer:

$720

Step-by-step explanation:

The formula is:

A = P(1 + rt)

We know

P = $6000

r = 3% = 0.03

t = 4 years

A = 6000( 1 + 0.03 x 4) = $6720

Now we have to find the interest by taking

$6720 - $6000 = $720

So, he earns $720 in interest in 4 years.

Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."

Algorithms exist to identify, solve, and frequently automate a solution to a particular problem; regardless of the situation, they are essentially problem solvers of expression.

In area of beginning textbooks, algorithms are typically introduced as "a set of phases to solve a problem."

Here,

Alternatively, a Turing computer that halts for all inputs cannot recognize a language for whose membership cannot be determined by an algorithm.

It is known as undecidable language.

There is no Turing Machine for an undecidable language that accepts the language and decides on each input string (TM can make decision for some input string though).

When the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."

Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."

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