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 value of x in the equation 9(x − 6) = 8(x + 6) is 102.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that from the information given, the equation is illustrated as:

9(x − 6) = 8(x + 6)

9x - 54 = 8x + 48

Collect the like terms

9x - 8x = 48 + 54

x = 102

The value of x is 102.

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The lakefront company should make the investment as in 5 years they'll have a profit of 10000.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, the lakefront company is considering investing in a new dock that will cost 560,000.

So, a Capital cost of 10% is (560000/10) = 56000

The company's borrowing rate is 8%.

∴ SI = (560000×8×5)/100.

SI = 5600×8×5.

SI = 224000.

So, The total cost is (560000 + 56000 + 224000) = 840000.

After 5 years they can sell it for 300000.

And has a cash flow of 110000, so in 5 years it is 550000.

So, total earnings is (300000 + 550000) = 850000.

Total profit is (850000 - 840000) = 10000 so it is profitable.

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The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.

The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.

The new dimensions  of rectangle = 4mm and 9mm

The original dimension = 2mm and 4.5 mm

Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm

Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26

So, the new perimeter will be 2 times larger then the old perimeter

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The percentage of her students that ride the school bus every morning would be = 84%

A percentage expression is an representation of a data set to a fraction of 100.

The total number of students = 25 students

The number of students that ride the school bus = 21

To calculate the percentage of the students that ride the bus the following is done;

= 21/25 × 100

= 2100/25

= 84%

Therefore, the percentage of her students that ride the school bus every morning is 84%

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The required length of the longest side will be 28/5 cm in the triangle.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

We have been given that the three sides of a triangle are in the ratio of 3:5:7

Let's assume the sides are 3x, 5x, 7x

Since the perimeter of the triangle is 12 cm.

So, 3x+5x+7x = 12

Apply the addition operation,

15x = 12

x = 12/15

Reduce the above fraction to the simplest form

x = 4/5

So, longest side = 7x = 28/5 cm

Thus, the required length of the longest side will be 28/5 cm in the triangle.

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Answer:

5 weeks

Step-by-step explanation:

20 inches  /  ( 4 inches/week ) = 5 weeks

does it want the answer in a specific form?

slope intercept form; y = mx + b

slope = 2

b = -1

plug the values in

y = 2x -1 or y = 2/1x -1

Length of the rectangle is 25 and width of the rectangle is 14.

What do you mean by algebraic expression?

A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.

Any algebraic expression's variables, constants, terms, and coefficients.

A variable is a symbol that doesn't have a set value. Any value may be used.

It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.

Let the width of the rectangle be x

Length of the rectangle become  2x - 3

Perimeter of rectangle = 2(length + width)

78 = 2(2x - 3 + x)

78 = 2(3x - 3)

78 = 6x - 6

78 + 6 = 6x

84 = 6x

x = 84/6

x = 14

length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25

Width of the rectangle is x = 14

Therefore, length of the rectangle is 25 and width of the rectangle is 14.

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There are 3 tens in 7x30 or 30x7.

What is an equation?

A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.

Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.

An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.

Here, we have

7x30 = 7 x 10 x 10 x 10

The value of 7x30 = 210

Hence, there are 3 tens in 7x30 or 30x7.

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Answer:

1km\h

Step-by-step explanation:

like in physics, the calculation of speed is total distance divided by total time, you should do the same in math, and so you do 1 hour (60 minutes)  + 15 minutes which gives you 75 minutes, and then you divide 75 km by the time so it should look something like this:

[tex]\frac{75 km}{75 minutes}[/tex] which gives you 1

so raphael is going 1 km\h

Answer:

[tex]\huge\boxed{\sf v = 60\ km/hr}[/tex]

Step-by-step explanation:

Distance = S = 75 km

Time = t = 1.25 hours

Speed = v = ?

v = S/t

v = 75/1.25

v = 60 km/hr

[tex]\rule[225]{225}{2}[/tex]

Answer:

:))

Step-by-step explanation:

The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!

Answer: the equations has no solution

Step-by-step explanation:

[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]

The number of the digits after the decimal point is 7. The correct option is C.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,

P = 0.3568 x 0.042

P = 0.0149856

The number of the digits after the decimal is 7.

Therefore, the number of the digits after the decimal point is 7. The correct option is C.

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To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.

First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:

Total number of lines = 123 pages * 70 lines/page

= 8610 lines

Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:

Number of lines with 14 words = 8610 lines * 36/70

= 4380 lines

Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 14 words = 4380 lines * 14 words/line

= 61320 words

Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:

Number of lines with 18 words = 8610 lines - 4380 lines

= 4230 lines

Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 18 words = 4230 lines * 18 words/line

= 76140 words

Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:

Total number of words = 61320 words + 76140 words

= 137,460 words

To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.

It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.

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Eddie and Brad together shovel the snow in 1 hour 26 minutes.

Two or more expressions with an Equal sign is called as Equation.

Given that it takes Eddie 2 hours to shovel the snow from a driveway and sidewalk.

Brad can shovel the snow from the same driveway and sidewalk in 5 hours.

We now find how long would it take them working together to shovel the snow.

Eddie does 1/2 in 1 hour or x/2 in x hours

Brad does 1/5 in 1 hour or x/5 in x hours

the sum is 1 full job

(x/2)+(x/5)=1

multiply both sides by 10

7x=10

x=(10/7) hours or 600/7 minutes =86 minutes

As we know 1 hour has 60 minutes.

We can write 86 minutes as 1 hour and 26 minutes.

Hence, 1 hour 26 minutes is the time taken by Eddie and Brad to shovel the snow.

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Answer:

  2184

Step-by-step explanation:

You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.

The number of permutations of 14 flavors taken 3 at a time is ...

  14 × 13 × 12 = 2184

There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.

The formula for the number of n things taken k at a time is ...

  P(n, k) + n!/(n-k)!

For n=14, k=3, this is the product shown above.

Answer:

the answer will be the options A

{25} is the solution set of the equation  {10, 24, 25, 36}.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given set of equation is {10, 24, 25, 36}

Since, The equation is represented by the sentence that is 5/6 of a number is 30.

So the required solution,

5/6 of the number 30 = 25

The solution set of the equation is {25}.

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Answer:

The last option is the correct answer.

Step-by-step explanation:

Answer:

No real solutions.

Step-by-step explanation:

No real solutions.

Answer:

2. Definition of Midpoint

3. Vertical Angles Theorem

Step-by-step explanation:

Definition of Midpoint is the middle point of a line segment

Vertical Angles Theorem is proving angles that are opposite each other and formed by two intersecting straight lines, are congruent.

y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).

The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.

The standard form of an equation is y = mx+c.

Here given,

A line with a slope of -2/5 that passes through the point (2, -3).

Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,

-3 = -2/5 (2)+c

⇒ -3 = -4/5 +c

⇒ c = -3 + 4/5

⇒ c = (-15 + 4) / 5

=> c = -11/5

When m = -2/5  and c = -11 /5 are substituted in y = mx+c, we get

y = -2/5 x -11/5

As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.

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Answer:

  C.  2x+ 5y = −11

Step-by-step explanation:

You want the equation of the line with slope -2/5 through point (2, -3).

The equation of a line with slope m through point (h, k) can be written as ...

  y -k = m(x -h)

Then the equation of the line with slope -2/5 through point (2, -3) will be ...

  y +3 = -2/5(x -2)

We can put this in standard form by ...

  5(y +3) = -2(x -2) . . . . . multiply by 5

  5y +15 = -2x +4 . . . . . . eliminate parentheses

  2x +5y = -11 . . . . . . . . . add 2x-15 to both sides

The desired equation is 2x +5y = -11.

Answer:

2/5 ≠ 25

Step-by-step explanation:

Given question,

→ Is 2/5 equivalent to 25?

Let's check the problem,

→ 2/5 = 25

→ 0.4 ≠ 25

The equivalent fractions of 2/5 are,

→ 2/5 = 4/10

→ 2/5 = 6/15

→ 2/5 = 8/20

→ 2/5 = 10/25

Hence, 2/5 is not equivalent to 25.

Answer:

see explanation

Step-by-step explanation:

from the table we can obtain that

f(x ) = 6x³ + 8x - 12 ( 6  0  8  - 12 , being the coefficients of the polynomial )

f(x) is divided by (x + 7) , since evaluated at - 7

the quotient is

6x² - 42x + 302 ( 6  - 42  302, are the coefficients of the quotient )

with remainder - 2126

Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.

Here,

Given :

function :8-9x/5-4x

To find the inverse ,

Inverse of 8-9x. 8-5x 5 4x -4x+9

Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)

y= 8-9x 5-4x

Replace x with y

x = 8-9y/ 5-4y

Solve for y,

x = 8-97/ 5-4y

=>8-5x /-4x+9

Therefore , the inverse  function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .

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The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

What are the coordinates of the vertices of the triangle?

The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.

To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.

If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).

If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.

Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.

Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).

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Answer:

[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS

Step-by-step explanation:

[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.