54. Suppose the population of a country is currently 8,100,000. Studies show this
country's population is increasing 2% each year.
a. What exponential function would be a good model for this country's
population?
b. Using the equation you found in part (a), how many years will it take for the
country's population to reach 9 million? Round your answer to the nearest
hundredth.

When the two lines makes angle of 90 degree , then the lines are known as Perpendicular Lines .

What are Perpendicular Lines ?

Two lines are said to be perpendicular to each other if the straight line  makes an angle of 90 degree with another line. 90 degree is also called a Right Angle and is represented by a little square between two perpendicular lines .

when the two lines intersect at a right angle, they are said to be perpendicular to each other.

For Example : In a football field all the four corners of a football field are perpendicular to each other.

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The set of numbers x such that 0 ≤ x ≤ 5 is an interval containing 0, 5, and all numbers between 0 and 5.

Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers.

In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing 0, 1, and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).

Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.

Complete Question:

What is the interval of 0,5 ?

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The x-intercept of the graph of y = x² - 4x + 4 is x = 2.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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The four names of an angle are acute angle, right angle, obtuse angle, and reflex angle.

An acute angle measures less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle measures greater than 90 degrees but less than 180 degrees.

A reflex angle measures greater than 180 degrees but less than 360 degrees.

It's worth noting that these names are based on the measure of the angle, an acute angle is less than 90 degrees, a right angle is exactly 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees.

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It will take 13 weeks to gather funds that sum up to $4500.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: I have $2485 and I save $155 weekly

Thus amount left to be gathered is $4500-$2485=2015

If I save $155 weekly then we get = $2015/$155

                                                        =13 weeks

Hence, It will take 13 weeks to gather funds that sum up to $4500.

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The length of the cuboid is 56 cm.

The breadth of the cuboid is 40 cm.

The height of the cuboid is 16 cm.

A cuboid is a three-dimensional shape where the volume is given by

Length x width x height.

We have,

Volume of a cuboid = 35840 cm³

The ratio of length, breadth, and height of the cuboid = 7:5:2

This means,

Length = 7x

Breadth = 5x

Height = 2x

Now,

(7x)(5x)(2x) = 35840

70x³ = 35840

x³ = 512

x = ∛512

x = 8

Now,

Length = 7x = 7 x 8 = 56 cm

Breadth = 5x = 5 x 8 = 40 cm

Height = 2x = 2 x 8 = 16 cm

Thus,

The length, breadth, and height of the cuboid are 56cm, 40cm, and 16 cm.

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The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.

When the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.

the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13

then;

probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13

probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13

probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13

Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13

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Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21

Jamal, a camp counsellor, purchased meal tickets at an arts festival for his ravenous kids. The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.

A camp counsellor purchased meal tickets at an arts festival for her ravenous kids.

The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.

Let x be the number of hot dogs and y be the number of burgers. In all, campers are allowed to utilise up to 21 tickets.

Thus, inequality in its most basic form explains this circumstance.

= 5x + 4y ≤ 21

Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21

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Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.

The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.

In cartesian plane the reference axis are named as X - axis and Y -axis.

In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.

The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.

hence, tan angle = 2/3

for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.

Finally, the distance of 2/3 from the horizontal axis is 2.

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Answer: Choice 2

Step-by-step explanation:

A table of equivalent ratios for the number of treasure chests and hours that Hannah recovered is as follows:

Treasure chests      Hours

8                                  4

12                                 6

10                                 5

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 4/8

Constant of proportionality (k) = 0.5.

When hours y = 6, the number of treasure chests x is given by:

x = y/k

x = 6/0.5

x = 12.

When treasure chests x = 10, the number of hours y is given by:

y = kx

y = 0.5(10)

y = 5.

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Complete Question:

Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests every 4 hours.

Complete the table using equivalent ratios. Select all the answers that will fill the table.

The direction of A with respect to B. N B 73° N A is 287

A direction is the way that something is moving, directing, or moving toward something or someone. The directions could be Up, Down, Left, and Right, or North, South, East, and West.

The ability to specify where one thing is in relation to another is known as position in mathematics. Defining direction entails explaining the direction in which something moves, such as forward, backward, or in a full or half turn.

It is possible to define direction using relative terms like up, down, in, out, left, right, forward, backward, or sideways. A direction can also be denoted by one of the four cardinal directions: north, south, east, or west.

Angles at a point add up to 360 degrees.

⇒ Bearing from A to B is = 360° - 73° = 287°.

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The linear relation y = |2x - 5| is a function which has it's domain along     (-∞, ∞) and it's range at [0, ∞)

A linear relation is a relationship between two variables (x and y) in which the points, when plotted on a graph, form a straight line. This means that for a given change in the independent variable (x), there will be a corresponding, predictable change in the dependent variable (y).

In this given relation, we can graph the absolute function and determine it's range and domain.

Using a graphing calculator;

y = |2x - 5|

The x-intercept of the relation is 2.5 and it's y-intercept is 5

The domain of the relation is (-∞, ∞)

The range of the relation is [0, ∞)

The relation y = |2x  5| is a function which is known as an absolute function

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The total sale price of n shirts can be found using the following expression:

total sale price = n * (26.99 - 5.99)

This expression first calculates the sale price of a single shirt by subtracting the discount from the original price, and then multiplies that value by the number of shirts to get the total sale price.

For example, if Mia bought 3 shirts, the total sale price would be 3 * (26.99 - 5.99) = 3 * 21 = 63.

Answer$84:

Step-by-step explanation:

Answer: 25%

Step-by-step explanation:  

The inequality be -4 ≤ x ≤ 2,300

If x is a real number, we have infinite solutions.

If x is an integer number, we have 2,305 solutions.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

Let the given data be 3, -4, 0, and 2,300 are solutions.

If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}

Let the inequality be -4 ≤ x ≤ 2,300

The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.

Here x exists a real number, then we contain infinite solutions.

If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)

the number zero (1)

We would have: 4 + 2,300 + 1 = 2,305 integer solutions.

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The inequality be -4 ≤ x ≤ 2,300

If x is a real number, we have infinite solutions.

If x is an integer number, we have 2,305 solutions.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

Let the given data be 3, -4, 0, and 2,300 are solutions.

If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}

Let the inequality be -4 ≤ x ≤ 2,300

The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.

Here x exists a real number, then we contain infinite solutions.

If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)

the number zero (1)

We would have: 4 + 2,300 + 1 = 2,305 integer solutions.

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The algebraic description of the transformation of B(x, y) = B'(y + 0, 0 - x)

The algebraic description of the transformation of K(x, y) = K'(y + 0, 0 - x)

The endpoints of the new line segment are B'(4, -1) and K'(-3, -4).

As per the given data BK has endpoints B(1, 4) and K(4, -3).

Rotate BK clockwise 270 degrees about the origin.

Every point of a source image is transformed in a plane via a rotation that rotates it around a fixed point at a specific angle and direction. The fixed point is referred to as the rotational center.

The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.

Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees anticlockwise.

Now, it would be (x, y) = (-y, x)

We have;

R (x, y) to R' (y, -x)

The algebraic description is simply written as;

R (x, y) = R'(y + 0, 0 - x)

B (x, y) = B'(y + 0, 0 - x)

K (x, y) = K'(y + 0, 0 - x)

To get the new endpoints, we simply write the transformation as shown;

B(1, 4) becomes B'(4, -1)

K(4, -3) becomes K'(-3, -4)

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The function that will define the situation is y = 10x

The domain:  {0, ∞)

The range: {0, ∞)

The function that will define the situation is a linear function of the form

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = there is no condition defined here hence = 0

m = cost of per hour = $2.50

x = time in hours

y =  amount paid in hours

y = 10x

The domain in this case is time from 0 to infinity {0, ∞)

The range is also {0, ∞)

there are no limitations to hep set the range and domain

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The intervals that are equivalent to each inequality are given as follows:

The interval notation of an inequality of lower bound a and upper bound b is given as follows:

(/[a,b]/).

The closing notation can be in either parenthesis or brackets, as follows:

For the first interval, 2 < x ≤ 5, it is an open interval at the lower bound of 2 and closed at the upper bound of 5, hence the notation is given as follows:

(2,5].

For the second interval, x > 7, we have that it has only a lower bound of 7, which is open. Hence, the upper bound is of infinity, and an infinite bound is always open, hence the notation is given as follows:

(7, ∞).

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Answer:

64(ab÷c²)

step by step:

(when you multiply two similar bases you can add their exponents but when dividing similar bases you subtract their exponents)

for example

a³x a= a⁴

a²÷ a= a²-¹= a

so

4a³x 16a⁰b¹÷ 1ac²=

64a³b÷ac²

64a²b/c²

Answer:

2 pounds of cheese

Step-by-step explanation:

First, we have to find out how much did she pay by taking

$5.00 - $1.40 = $3.60

So, she paid $3.60 in total. Then we find how many pounds of cheese she bought by taking

3.60 / 1.80 = 2 pounds of cheese

So, she bought 2 pounds of cheese.

Answer:

$220

Step-by-step explanation:

first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,

then we calculate the amount she made by selling each type.

Eq.1 : No. of Type1 bracelets Selena made = 9

         Amount she sold them for = $12

         Amount she made by selling them = 9*12

                                                                                   = $108

Eq.2 : No. of Type2 bracelets Selena made = 14

          Amount she sold them for = $8

          Amount she made by selling them = 14*8

                                                                               = $112

Now we calculate the Total Amount she made

we add both of the amounts

$108 + $112

= $220

Hope this helps :)

The coefficient of the expression 3x² is the number 3 and constant term is 20

What are the coefficients?

The coefficients are the numbers on the left side or before each variable.

What is an algebraic expression?

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

Number 3

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FG is not a defined term, so there is no way to determine its value.

FG is not a defined term, so there is no way to determine its value. This means that we cannot assign a numerical or other value to it. In order to determine the value of FG, we would first need to identify the context in which it is being used, as different contexts may assign different meanings to the same term. Once the context has been established, we can then look up the definition of FG in order to understand what it means in that particular context, and then assign a value to it accordingly. For example, if FG stands for "Frequency Generator" in a physics context, then it would likely have a numerical value associated with it.

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A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The correct answer Is option c) 6.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The diagram shows us a triangle [tex]$\mathrm{ABC}$[/tex], which

[tex]$$m \angle A=m \angle C=63^{\circ}, \quad A B=3 x$$[/tex]

units and [tex]$B C=(4 x-2)$[/tex] units.

The task Is to determine the length of the slde [tex]$\mathrm{AB}$[/tex].

[tex]$\mathrm{ABC}$[/tex] has the following

[tex]$$m \angle A=m \angle C$$[/tex]

In a triangle, we understand that

If the measurements of two angles are equal, then the lengths of the sides or each side are also equal.

so we must have

[tex]B C=A B \\\Rightarrow 4 x-2=3 x \Rightarrow 4 x-3 x=2 \Rightarrow x=2 .\end{aligned}$$[/tex]

As a result, [tex]$\mathrm{AB}$[/tex] will be of length

[tex]$$A B=3 x=3 \times 2=6$$[/tex]

As a result, the side [tex]$A B$[/tex] is 6 units long.

Therefore, the correct answer Is option c) 6.

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The x-intercept for the graph of y is found to be at x = 2.

The quadratic equation given is

y = x² - 4x + 4

Put y = 0

0 = x² - 4x + 4

It becomes perfect square for (x - 2).

It can be written as;

(x - 2)² = 0

Take square root on the both sides

x - 2 = 0

x = 2

Thus, the x-intercept for the graph of y is found to be at x = 2.

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The correct question is-

What is the x-intercept of the graph of y = x² - 4x + 4?

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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