The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.

The graph of the system of equations is shown below, and the solution is: (6, 1).

When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.

In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.

The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.

Both lines intersect at point (6, 1).

Therefore, the solution is (6, 1)

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to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-6}{2 +1} \implies \cfrac{ -6 }{ 3 } \implies \text{\LARGE -2}[/tex]

Answer:

The slope is 2

Step-by-step explanation:

To find the slope you divide the rise by the run. Rise being how many units it goes up or down) (run being how many units it goes to the side).

In this case the rise is -2 and the run is -1.

See in the picture, for every 2 units the line goes down, it moves one unit to the right.

so, -2/-1= 2

There would be 52 atoms after 25 years and it would take 13 years for half the number of atoms to remain.

We know that the term radioactive decay has to do with the break down of a substance to form the daughter nuclei of the particular element. In this case, we have the decay function of the element to be; A(t) =200e^-0.054t.

t is the time taken for decay.

Now in 25 years we would have;

A(t) =200e^-0.054(25)

A(t) = 52 atoms

The time that it would take for half of the original number to remain is obtained from;

100 = 200e^-0.054t

100/200 = e^-0.054t

0.5 = e^-0.054t

ln(0.5) = -0.054t

t = ln(0.5)/-0.054

t = 13 years

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Answer:

a) 23,1 milions

b) en 2013 - 2014

Hello,

I hope you and your family are doing well!

To find the mean of a set of numbers, you need to add up all of the numbers and divide the sum by the total number of numbers in the set.

In this case, the mean would be calculated as follows:

(678 + 592 + 652 + 800 + 502 + 396 + 502 + 301) / 8 = 515.25

So the mean of this data set is 515.25.

The mean is a measure of the central tendency of a data set and can be used to represent the entire set of numbers by giving a single value that is representative of the set as a whole. It is also known as the average.

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To find a book it is necessary to write the name "a vacation trip" in the search engine and add the word PDF to obtain better results.

To download a book from the Internet it is necessary to review various pages since some do not contain the complete book and others may have some type of virus that can damage the device.

In the same way, there are some platforms or applications that require a subscription payment to be able to access the content in an unlimited way.

¡Hope this helped!

The elevation needs to be smaller than the decrease of the elevation like this.

What is the elevation on the number line?

The elevation of a location describes its height above or below the sea level, which has an elevation of 0. Elevations below the sea level are represented by negative numbers, and elevations above the sea level are represented by positive numbers.

Whatever number is larger than the number of the elevation of the bottom of the harbor

the elevation needs to be smaller than the decrease of the elevation like this.

e.g.

The temperature elevated by 28 degrees and then decreased by 30 degrees.

Hence, the elevation needs to be smaller than the decrease of the elevation like this.

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The two column proof in completed as follows

Statement                                                 Reason

1 line UV ≅ line ST                                  Given

2 line QR ≅ line PQ                                Given

3 line OT ≅ line OU                                Given

4 line PV ≅ line RS                                 Given

5 PT = PQ + QT                                      Additive Property of Length

6 RU = QR + QU                                     Additive Property of Length

7 PY = QR + QU                                      Substitution

8 PT = RU                                               Transitive Property of Equality

9 TV = UV + TU                                      Additive Property of Length

10 SU = ST + TU                                     Additive Property of Length

11 TV = ST + TU                                      Substitution

12 SU = TV                                             Transitive Property of Equality

13 ΔSUR ≅ ΔVTP                                   SSS

14 ∠V ≅ ∠S                                            CPCTC

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Side - Side - Side = SSS rules to ensure that the the triangles are congruent

The SSS have it that the two triangles being compared should have their three sides being are equal then the triangles are congruent

Achieving the SSS rules then by Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠V ≅ ∠S

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You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.

A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors

Let x be number of pounds of cheaper candy and y represent that of expensive candy.

Then, x + y = 55.2----(1)

And

2x + 8.9y = 55.2(2.5) = 138

2x + 8.9y = 138---------(2)

On solving above two equation, we get

x = 51.2

y = 4

Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib

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Answer:

[tex]\textsf{A)} \quad -\dfrac{9}{5}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given sum:

[tex]\displaystyle \sum^{\infty}_{n=1} -3\left(\dfrac{3}{8}\right)^n[/tex]

Therefore, the first term in the series is:

[tex]a_1=-3\left(\dfrac{3}{8}\right)^1=-\dfrac{9}{8}[/tex]

The common ratio, r, is:

[tex]r=\dfrac{3}{8}[/tex]

Substitute the first term, a, and common ratio, r, into the formula:

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{1-\frac{3}{8}}[/tex]

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{\frac{5}{8}}[/tex]

[tex]\implies S_{\infty}=-\dfrac{9}{5}[/tex]

Therefore, the sum of the given series is:

Answer: x=3

Step-by-step explanation:

When you plug in each number only 3 is the right answer.

A. 8(-4)-4=2(2(-4)+4)

-36=8 False

B. 8(12)-4=2(2(12)+4)

92=56 False

C. 8(0)-4=2(2(0)+4)

-4=8 False

D. 8(3)-4=2(2(3)+4)

20=20 True

Answer:

the chance to pull a blue marble is 3/20

the chance to pull a yellow marble is 5/20

The value of ∠ A = 40°,∠C = 70° and AC = 12

What is value ?

Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. Consider the number 45, for example. Here, the fourth digit is in the tens column.

If triangle is isosceles it means the two sides and angles are equal

∴ BC = AC

 AC = 8 cm

A + B + C = 180

A = 180 - 70 -70

∠A = 40°

∠C = 70°

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The value of x would be 11° and the value of y would be 6.

What are congruent triangles?

Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.

ΔRWS ≅ ΔTUV

As both triangles are congruent then we can say that

∠S ≅ ∠V

so ∠S = 29°

Now in ΔRWS,

By using the sum of all angles of the triangle property, we can write

∠R +∠W + ∠S = 180°

(8x - 27)° + 90° + 29° = 180°

8x = 180° - 92°

8x  = 88°

x = 88/8

x = 11°

Now Side RS ≅ Side TV

         3y + 7 = 25

         3y = 25 - 7

         3y = 18

            y = 18/3

            y = 6

Hence, the value of x would be 11° and the value of y would be 6.

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Answer:

Step-by-step explanation:

Answer:

z = -8

Step-by-step explanation:

6(z-1) + 14 = -40

6z - 6 + 14 = -40   Distribute the 6

6z + 8 = -40   Combine Like Terms

6z = -48   Subtract 8 on Both Sides

z = -8   Divide by 6 on Both Sides

The maximun value (63) is located at point (1, 2).

Check attached image 1.

The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.

In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.

Check attached image 2 to see the extreme values.

Point A is located at: (-3, -2)

Point B is located at: (-3, -4)

Point C is located at: (3, -4)

Point D is located at: (1, 2)

Given function: [tex]P=10x+6y+41[/tex]

Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.

Evaluating the points:

[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]

The maximun value (63) is located at point (1, 2).

There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.

Translate the graph [tex]5[/tex] units right, reflect over the [tex]x[/tex]-axis, and then perform a vertical stretch with a factor of [tex]3[/tex].

Answer:

Step-by-step explanation:

You want to know the values of x and y in the given figure.

The left-side triangle has angles marked as congruent. Hence it is an equilateral triangle, which also has congruent sides.

  8y = 40

  y = 40/8 = 5

The angle at the middle of the longest line is supplementary to the adjacent angle in the equilateral triangle, hence is 120°.

The marked side length of 40 and the equilateral triangle side length of 40 mean the triangle on the right is an isosceles triangle with an a.pex angle of 120°. Its congruent base angles (x°) must be (180° -120°)/2 = 30°.

  x° = 30°

The values of x and y are 30 and 5, respectively.

angle A = 63.7°, B= 26.3°, D= 49° , then angle C = 221

Two shapes that are the same size and the same shape are congruent.Congruent shapes are shapes that are exactly the same.

The corresponding sides are the same and the corresponding angles are the same.

This means the corresponding angles of the two shapes are equal.

With this, angle A = 63.7°, angle B= 26.3° , angle D =49°

The sum of angles in a quadrilateral is 360°

therefore angle C = 360-(63.7+49+26.3)

C = 360-139

C = 221°

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Answer:

Step-by-step explanation:

It will lie in quadrant 3

Step-by-step explanation:

Here, we want to know where the resulting image will lie after the rotation

After the rotation, it is expected that the resulting image will lie in quadrant 3

First 90 to quadrant 1

second 90 to quadrant 2

Third 90 to quadrant 3

Answer:

B is the correct answer

Step-by-step explanation:

i think:)

The first numSelected of the selected elements to an array selectedData is assigned in the programme.

The program for the given condition is-

function selectedData = SelectLogicalN( dataMatrix, logicalSelect, numSelected )

% SelectLogicalN: Return the first numSelected values of input 2D

% array dataMatrix indexed by localSelect indexing array.

%Inputs: dataMatrix - input data matrix (2D array)

%logiccalSelect - logical indexing array, can be 2D or linear

%numSelected - number of indexed elements to return in selectedData%

%Outputs: selectedData - column vector of logically indexed elements to return

dataMatrix = dataMatrix(logical(logicalSelect));

% assign tempSelected with logically indexed elements of dataMatrixtemp

Selected = dataMatrix

% find the size of tempSelected

s=size(tempSelected);

% remove the last element from the temp

SelectedselectedData =tempSelected

(1:s-1)end

Thus, the first numSelected of the selected elements to an array selectedData is assigned in the programme.

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Answer:

Area = 28.27 in²

Step-by-step explanation:

Now we have to,

→ find the area of the circle.

Formula we use,

→ π × r²

Now the required area will be,

→ π × r²

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

The probability of choosing a random number that starts with 6 from this group is 1/5 Or 0.2.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, All three-digit numbers that can be created from the digits 0-9.

So, The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 total of 10 digits.

No. of even digits is 4 and the number of odd digits is 5.

The total number of 3 digits that can be formed where the first and last digits must be even and no digit can repeat and can start with 0 is,

= 5×10×4.

= 200.

The number of digits starts with 6 in this group is,

= 1×10×4.

= 40.

∴ The probability of choosing a random number that starts with 6 from this group is (40/200) = 1/5 Or 0.2

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A farmer needs to pack 2,903 apples into crates to ship to supermarkets. Each crate can hold only 30 apples. Choose true or false for each statement.

A. The farmer needs 96 crates to ship out all apples. False

B. The farmer needs 97 crates to ship out all the apples. True

C. At least one of the crates will not be filled to capacity. True

D. To determine the number of crates needed, divide 30 by 2,903. False

Answer:

A. False, you will need another crate in order for all of the apples to be shipped to the supermarkets.

B. True, this will hold all of the apples with some extra space left in the last crate.

C. True, 2,903 divided by 30 is 96.76666666666667. Meaning that one of them won't have exactly 30 apples.

D. False, you divide 2,903 by 30.

The linear function g(x) = 3 · x + 6 has the following features:

Domain: - ∞ < x < + ∞

Range: - ∞ < y < + ∞

x-Intercept: (- 2, 0)

In this problem we must determine the domain, the range and the x-intercept of a linear function, that is, a polynomial of the form y = m · x + b, where m is the slope and b is the x-intercept. We must find the information by understanding the following features:

If we know that the function is g(x) = 3 · x + 6, then its domain and range are - ∞ < x < ∞ and - ∞ < y < ∞ and its x-intercept is:

0 = 3 · x + 6

- 3 · x = 6

x = - 2

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Step-by-step explanation:

The given function is g(x) = 3x + 6.

Domain: The domain of a function is the set of all possible input values (x) for which the function is defined. Since the function is a linear equation, it is defined for all real values of x. Therefore, the domain of the function is: Domain: -∞ < x < ∞ Range: The range of a function is the set of all possible output values (y) that the function can produce. The slope of the given function is positive (3), so the function increases without bound as x increases.

Therefore, the range of the function is: Range: -∞ < y < ∞ x-intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. 0 = 3x + 6 -6 = 3x -2 = x Therefore, the x-intercept is (-2, 0).

So, the correct option is: Domain: -∞ < x < ∞; Range: -∞ < y < ∞; x-intercept (-2, 0).

Hello,

I hope you and your family are doing well!

To solve this problem, you need to set up a proportion using the information given in the problem. Let x represent the number of miles the family will travel during the next 4 hours. The proportion will look like this:

318 miles / 6 hours = x miles / 4 hours

To solve for x, you can cross-multiply and solve the equation:

318 miles / 6 hours = x miles / 4 hours

6 hours * 318 miles = 4 hours * x miles

1848 miles = 4x miles

x = 462 miles

Therefore, if the family continues at the same rate, they will travel a total of 462 miles during the next 4 hours.

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Answer:

Step-by-step explanation:

You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.

We can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...

  m = ∆a/∆p = 100/(-1) = -100

The y-intercept (b) can be found by solving the slope-intercept equation for b:

  y = mx +b

  b = y - mx

For (x, y) = (3.50, 250), the value of 'b' is ...

  b = 250 -(-100)(3.50) = 600

The slope-intercept equation for 'a' in terms of p is ...

  a = -100p +600

The value of 'a' for p = 1.50 is ...

  a = -100(1.50) +600

  a = 450

They will sell 450 items if the price per item is $1.50.

We might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.

An equation is a claim that shows the equality of two mathematical expressions.

For instance, the equal sign separates the two equations that make up the equation 3x + 5 = 14: 3x + 5 and 14.

So, we need a total of x pounds of mixed nuts.

Peanuts weigh 0.70 pounds in this combo.

Three pounds of peanuts are used to create the 20% mixture, or 0.20*15.

The equation we got: 0.70 x + 3 = 0.40(x + 15)

Now, solve as follows:

0.70 x + 3 = 0.40(x + 15)

0.70 x + 3 = 0.40(x + 15)

0.70x + 3 = 0.40x + 6

0.70x - 0.40x = 6 - 3

0.30x = 3

x = 10 pounds

Therefore, we might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.

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