Solve for x and show work!

The spending would reach a figure of  1868 billon in the year 2031.

We know that we can be able to use a function to be able to show the relationship between variables and it can also serve as a model. In this case, we are modelling the spending by the use of the equation;

y = 1.48x^2 - 25.23x + 416.91

Let x be the number of years since 1990. Then we have that;

1868 =  1.48x^2 - 25.23x + 416.91

 1.48x^2 - 25.23x - 1451.1 = 0

When we solve the quadratic we have;

x =  41

In 41 years after 1990, the government spending would reach 1868 billon and that would be in 2031.

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If 3 < a < 4 and 4 then, 3 < a ≤ 4 is the relationship.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, A number 'a' which is 3 < a < 4 and 4.

This implies that the number 'a' is less than or equal to 4.

∴ 3 < a ≤ 4.

Q. Suppose  3 < a < 4 and a is also equal to 4, write this statement in inequality form.

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When constructing a perpendicular bisector of a segment, you should make arcs with the same radius from each endpoint as D. this makes the arcs parallel to the segment

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90-degree angle.

A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal segments. At the exact midpoint of the line segment, they divide it. The arcs with the same radius from each endpoint is important as this makes the arcs parallel.

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Answer:

  y -3 = -3(x +1)

Step-by-step explanation:

You want an equation for the line parallel to y=-3x+2 through the point (-1, 3).

The given line is written in slope-intercept form:

  y = mx +b . . . . . . . where m is the slope and b is the y-intercept

Matching your equation to this form, we see that ...

The parallel line will have the same slope: m = -3.

Another form of the equation for a line is "point-slope form." That is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

Perhaps you can see this would be useful for writing the equation of a line with slope -3 through the point (-1, 3).

  y -3 = -3(x +1) . . . . . . . line with slope -3 through point (-1, 3)

Answer: x<5. Work shown below! :)

Answer:

a. Angles x and y are supplementary because they are same side interior angles.

Angles x and y are supplementary because they are same side interior angles.

A line that goes through two lines in the same plane at two different points is called a transversal. When determining whether two or more other lines in the Euclidean plane are parallel, transversals play a role. Different kinds of pairs of angles are created when two lines intersect a transversal: alternate angles, corresponding angles, consecutive exterior angles, and consecutive interior angles. If the two lines are parallel, Euclid's parallel postulate states that consecutive interior angles are supplementary, that corresponding angles are equal, and that alternate angles are equal.

Given lines are parallel and cut by a  transversal,

and to find the statement for x and y

in figure x and y are interior side of both lines

statement for x and y is

Interior angles on the same side of a transversal are supplementary if it cuts through two parallel lines. Exterior angles on the same side of a transversal are supplementary if it cuts through two parallel lines.

Hence x and y are supplementary angles.

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The required cost for the ride in the Metro is obtained as $5.

The total cost can be calculated by multiplying the cost for one unit to the number of units.The cost for one unit is also called as unit rate. This method is based on the unitary method which states that the value of n number of quantities is equal to the product of n and the value of one quantity.

The cost of the ticket is given as $2.

And, the cost per stop is $0.50.

Now, in order to find the total cost of riding for 6 stops take the sum of fixed cost of ticket and the total cost for 6 stops as follows,

The cost of ticket + The cost for 6 stops

= 2 + 6 × 0.50 = 5

Hence, the cost for the total ride of the rider is $5.

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Answer:

$2,000

Step-by-step explanation:

A=P(rincipal)R(ate)T(ime)

1000*1*1=1000

1000(principal)+1000(interest)=2,000(total)

As a result, the singers can finish first, second, third, fourth, or fifth in 524,160 different ways.

Permutation, where order is important:

_nP_{r}=\dfrac{n!}{(n-r)!}

P r = (n−r)!n!

Combination of definitions (order is irrelevant):

_nC_{r}=\dfrac{n!}{r!(n-r)!}n C r equals r!(nr)!n!

with n!=n, cdot (n-1) ..., cdot 2..., cdot 1n!=n(n1)...2,1.

We want to know how many different ways we can choose five people from a group of 16 (ranked first, second, third, fourth, and fifth).

n=16 n=16 r=5 r=5 Because we are interested in the first, second, third, fourth, and fifth places, order is important (changing the first and second places results in different rankings and prizes for the people), so we need to use a "textbf permutation" permutation.

Analyze the permutation definition:

"Begin align*" means "16P_5" and "dfrac" 16! color#8895cetextDefinition combination &=dfrac16!11!&color#8895cetext Evaluate difference &=dfrac16cdot 15cdot 14cdot 13cdot 12cdot 11cdot 10cdot...cdot 111cdot 10...cdot 1

16!= 11!

16! = 11⋅10⋅...⋅1

16⋅15⋅14⋅13⋅12⋅11⋅10⋅...⋅1

=16⋅15⋅14⋅13⋅12

=524,160

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Full Question = There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth?

The weight of large box will be 45 pounds.

The weight of small box will be 30 pounds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The combined weight of a large box and a small box is 75 pounds.

And, The truck is transporting 55 large boxes and 70 small boxes.

Total weight of boxes = 4575 pounds

Now,

Let weight of large box = x

And, Weight of small box = y

Here, The combined weight of a large box and a small box is 75 pounds.

So, We can formulate;

⇒ x + y = 75   ...(i)

And, Total weight of boxes = 4575 pounds

So, We can formulate;

⇒ 55x + 70y = 4575   ...(ii)

Solve both equation as;

From (i);

x = 75 - y

Substitute in equation (ii), we get;

⇒ 55(75 - y) + 70y = 4575

⇒ 4,125 - 55y + 70y = 4575

⇒ 15y = 4575 - 4,125

⇒ 15y = 450

⇒ y = 30

And, x = 75 - 30 = 45

Thus, The weight of large box will be 45 pounds.

The weight of small box will be 30 pounds.

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Answer:

9t + 9e is your answer bro

The required top of the ladder from the ground is 7.14 ft.

A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any angle is a right angle.

To find the length in right angle triangle, use Pythagoreans theorem,

(hypotenuse)² = (base)² + (height)²

Given that,

The length of the ladder = 10 ft.

The distance of the house from the bottom of the ladder = 7 ft.

Let the length of the top of the ladder from ground is x ft.

To find the height of the ladder  from the ground,

Use Pythagoreans theorem,

(hypotenuse)² = (base)² + (height)²

(10)² = (7)² + (x)²

100 = 49 + x²

x² = 100 - 49

x² = 51

x = 7.1414

or x = 7.14 ft

The top of the ladder from the ground is 7.14 ft.

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y-intercept of the function is (0, 50), the slope of the function is 5, the equation of the line is  P(x) = 50 + 5x and it would take 189990 streams to profit  $950,000.

The x-intercept and y-intercept are the points where a centre line the x- and y-axes, respectively.

Given the following parameters

Fixed price = $50

The rate of change is $5 if streaming providers pay $ 5.00 per unit.

The necessary profit is provided as follows for the entire number of streams:

P(x) = 50 + 5x

The y-intercept is the location where x equals zero.

P(x) = 50 + 5x

P(0) = 50 + 5(0)

P(0) = 50

Thus, the function's y-intercept is (0, 50)

For the slope

mx = 5x

m = 5

Consequently, the function's slope is 5.

Equation of this line is P(x) = 50 + 5x

P(x) = 50 + 5x = 950000

5x = 950000 - 50

5x = 949950

x = 189990

Hence, it would take 189990 streams to profit  $950,000.

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Factorials and the binomial theorem are utilized in the binomial distribution, a discrete probability distribution. Checking the sample space is the first step in deciding whether or not to use a binomial distribution with a given data set.

The binomial distribution would apply if there were multiple trials of the same experiment and only two outcomes in the sample space.

S=T,H,THT,H,THH,HTH,HHT,HHH in this case.

∴ n(S)=8.

Thus, the probability of each and every outcome is 18.

When tossing three coins, let X be the number of heads.

There can be 0, 1, 2, or 3 heads.

Therefore, X's possible values are 0, 1, 2, and 3.

P(X=0) = P (no head) = P(T) = 18.

P(X=1) = P (getting a single head) = P(HorTHTorH) = 38.

P (X=P (getting 2 P (THH, HTH, HHT)=38.

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Answer:

To find the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, you would first need to find the coordinates of the vertices of the triangle when it is centered at the origin. This can be done by subtracting the coordinates of the original centroid, which is the point (3.33, -0.66) for triangle BCD, from the coordinates of each vertex. So the coordinates of vertex B would be (2 - 3.33, -1 + 0.66) = (-1.33, -0.34), the coordinates of vertex C would be (4 - 3.33, 1 - 0.66) = (0.67, 0.34), and the coordinates of vertex D would be (5 - 3.33, -2 + 0.66) = (1.67, -1.34).

To scale the triangle by a factor of 3, you would multiply the coordinates of each vertex by 3. So the coordinates of the scaled triangle would be (-3.99, -1.02) for vertex B, (2.01, 1.02) for vertex C, and (5.01, -4.02) for vertex D.

Therefore, the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, would be (-3.99, -1.02), (2.01, 1.02), and (5.01, -4.02).

On a graph of g(x) = -3x + 9 the x - intercept is identified to be

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

It is x - intercept where the line crosses the x axis and y intercept where the line crosses the y axis

On the graph, the point where the line crosses the x axis is noted and written in ordered pair in the for (a, b)

Where a represents values in the x direction and y are values in the y direction

From the graph, a = 3 and b = 0

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Answer:

The answer is C. (3, 0)

In a chi-square test for homogeneity of proportions,we test whether different populations have the same proportion of individuals with some characteristic.

Used to test whether different populations have the same proportion of individuals with a particular trait. Suppose we have three populations with four mutually exclusive characteristics. Randomly sample each population and create a crosstabulation or frequency table of the traits you are measuring. If you want to test whether there is an association between a population and a trait (for example, whether the population has a high frequency of one trait), perform a chi-square test to see if the result is significant must be confirmed.

If the chi-square test is significant, it only tells us that there is some relationship between the population and the trait, not how they are related. Also, not all traits need to be population related. For example, the chi-square test can be considered significant even if features A and B have very different distributions, and C and D have very different distributions, for different populations. If you want to measure whether a particular trait is influenced by the population, use an equal proportions test (I call it the z-test, or prop.test() in R) for exactly that trait. You can do. In other words, if the chi-square test reveals a significant relationship, it is appropriate to use prop.test() to more accurately determine the nature of the relationship between the two sets of categories.

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Answer:

I'm pretty sure the answer is 24.024

Step-by-step explanation:

300meters = 9 minutes

300+300=600

2/3 of 300=24minutes

800÷50=16

800÷33.3=24.024 minutes

Answer:

----------------------

Since Amy can swim 6 laps in 9 minutes, then it takes:

Number of laps in 800 m:

Time to swim 16 laps:

The correct answer is (C) 0.8. The correlation between two scores X and Y is equal to 0.8. If both the X scores and the Y scores are multiplied by 2, the correlation of the transformed scores would be 0.8.

The correlation between two variables measures the strength and direction of the linear relationship between them. It is calculated as the covariance of the two variables divided by the product of their standard deviations. When both the X scores and the Y scores are multiplied by 2, the covariance and standard deviations of the transformed scores are also multiplied by 2. Therefore, the correlation between the transformed scores is equal to the correlation between the original scores.

In this case, the correlation between the original scores is 0.8, and the correlation between the transformed scores is also 0.8.

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Answer:

Length = 11"  and  width = 8".

Step-by-step explanation:

let L be the length of the rectangle

and w be its width.

Formula (perimeter P of a rectangle) :

P = 2 × (L + w)

================================

Then

L = w + 3

and

P = 2 × (L + w)

  = 2 × (w + 3 + w)

  = 2 × (2w + 3)

  = 4w + 6

Solving the equation P = 4w + 6  for w :

P = 4w + 6

⇔

38 = 4w + 6

⇔

32 = 4w

⇔

w = 32 ÷ 4

   = 8

Determining the length L :

L = w + 3

⇔

L = 8 ÷ 3

  = 11

Conclusion:

L = 11  and  w = 8

Answer:

Width = 8"

Step-by-step explanation:

2(t+w) = 38              Eq. 1

t = w+3                     Eq. 2

t = length

w = width

From Eq. 2:

t+w = 38/2

t+w = 19

t = 19 - w                    Eq. 3

Replacing Eq. 3 in Eq. 2:

19 - w = w + 3

19 - 3 = w + w

16 = 2w

16/2 = w

w = 8

Frm Eq. 2:

t = w + 3

t = 8 + 3

t = 11

Check:

From Eq. 1

2(t+w) = 38

2(11+8) = 38

2(19) = 38

given that v1,v2 ,v3,v4 is linearly independent vector so in order for a set of vectors to be linearly independent it must satisfy the below conditon:

   [tex]x_1v1+x_2v2+x_3v3+x_4v4[/tex] =0  --(i)

  where [tex]x_1, x_2,x_3 ,x_4[/tex] is some real numbers.

a) so in order to show that v1,v2+v4,v3 is linearly independent we have to

check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have :

   [tex]x_1v1+x_2(v2+v4) +x_3v3[/tex]   ---(ii)

    where [tex]x_1, x_2,x_3[/tex] is some real numbers.

  after evaluating equation (ii) we have:

     [tex]x_1v1+x_2v2+x_3v3+x_2v4[/tex]  

     so the above equation is now transformed in the form of equation (i) where [tex]x_2 = x_4[/tex]  

and hence [tex]x_1v1+x_2v2+x_3v3+x_2v4[/tex] =0  ----(iii)

equation (iii) shows that the set of given vectors are linearly independent.

b)  so in order to show that v1 +v2, v3, v4  is linearly independent we have to check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have this equation:

   [tex]x_1(v1+v2)+ x_2v3 + x_3v4[/tex]      where [tex]x_1, x_2,x_3[/tex] is some real numbers.

  after evaluating equation (iv) we have:

     [tex]x_1v1+x_1v2+x_2v3+x_3v4[/tex]  

     so the above equation is now transformed in the form of equation (i) where the cofficient of v2 is also [tex]x_1[/tex]  

and hence [tex]x_1v1+x_1v2+x_2v3+x_3v4[/tex] =0  ----(v)

equation (v) shows that the set of given vectors are linearly independent.

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Complete question :

let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors a) v1, v2+v4, v3 and   b) v1 +v2, v3, v4 are also linearly independent.

The vectors v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent is hence proved.

let v be a real vector space.

The v1, v2, v3, v4 are vectors in v which are linearly independent.

V={v1, v2, v3, v4} then set V is called  linearly independent if [tex]\forall \alpha_i \in F \\[/tex].

∝1v1+∝2v2+∝3v3+..........+∝nvn=0

then, [tex]\forall \alpha_i =0 \\[/tex] i=1,2,3......n.

let ∝1,∝2,∝3,∝4 ε F

∝1v1+∝2(v1+v2)+∝3(v1+v2+v3)+∝4(v1+v2+v3+v4)=0

v1(∝1+∝2+∝3+∝4)+v2(∝2+∝3+∝4)+v3(∝3+∝4)+v4.∝4=0

Since  v1, v2, v3, v4 are linearly independent vectors.

So ∝1+∝2+∝3+∝4=0......(1)

∝2+∝3+∝4=0....(2)

∝3+∝4=0....(3)

∝4=0...(4)

Solving eq(1), (2), (3), (4)

we get ∝1=∝2=∝3=∝4=0

So according to definition of linearly independent vectors.

A set of vectors is called linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set. If any of the vectors can be expressed as a linear combination of the others, then the set is said to be linearly dependent.

So v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent vectors hence proved.

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Answer: f(x) = 1

Step-by-step explanation:

     They tell us what we need to do, we must substitute x for 0 in the original function to find the initial value.

         [tex]f(x) = (\frac{1}{4} )^x[/tex]

         [tex]f(x) = (\frac{1}{4} )^0[/tex]

         [tex]f(x) = 1[/tex]

     * Anything raised to the power of 0 is equal to 1.

If an organization selects 3 students to represent the district, the standard divisor needed to be eligible for representation of the region is 228.

The standard divisor is computed as the quotient of the total population divided by the number of representative seats required to be distributed.

The standard divisor explains the number of persons represented by a seat.

Regions     Number of Students

Region 15               315

Region 16              148

Region 17              221

Total number =    684

Number of students to represent the district = 3

Standard divisor = 228 (684 ÷ 3)

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A true statement for all genes , given Dr. Bert Vogelstein study on cancer , is D . They code for proteins with the same amino acid sequence .

Genes need a code in order to be able to produce proteins . The genetic code is the code that converts the data stored in DNA and RNA into organized amino acids and proteins . Additionally, every living thing has the same genetic code .

The reason for this, according to scientists, is that every single living organism , has a common evolutionary history .

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The area of the striped region (blue ones with angled strips on them) is equal to 3/4 square units.

First, we know that each square below is 1 square unit.

These squares are divided into rectangles of (1/2) by (1/6), then each one of these strips has an area equal to the product between the two dimensions, it gives:

(1/2)*(1/6) = 1/12 square units.

Now we need to count how many of the striped rectangles are, we can see that there are 9 of these, then the area of the striped region is:

A = 9*1/12 square units.

A = 9/12 square units

A = 3/4 square units.

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(a) The function over its practical domain x = 80±nπ  n∈(0, 1, 2, 3,..............)

(b) Point of maxima = (171.325, 15), (536.637, 15), (901.928, 15),................

Point of minima = (353.976, 9.326), (719.278, 9.328),...................

Inflection point = (80, 0), (262.651, 0), (445.301, 0),..................

In the given question, f(x)=2.836 sin(0.0172(x-80)) + 12.164

a. Using technology we have to obtain a printout of the function over its practical domain. Scale and label the axes appropriately.

f(x)=2.836 sin(0.0172(x-80)) + 12.164

f'(x) = 0 at 2.836×0.0172 cos(0.0172(x-80)) = 0

So x = 171.325, 353.976, 536.627, 719.278, .................

f''(x) = -2.836×(0.0172)^2 sin(0.0172(x-80)) = 0

So x = 80±nπ  n∈(0, 1, 2, 3,..............)

b. We have to label the maximum, minimum, and inflection points on the graph. We should label the points both in the form (x, f(x)) and (date, f(x)).

Point of maxima = (171.325, 15), (536.637, 15), (901.928, 15),................

Point of minima = (353.976, 9.326), (719.278, 9.328),...................

Inflection point = (80, 0), (262.651, 0), (445.301, 0),..................

Therefore, the graph of the aforesaid function is shown below. The greatest value of the function is 15 and the smallest value is 9.328. Additionally, the graph's values are labelled.

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When you multiply the diameter by 22/7,  you find the approximate not exact circumference of a circle.

What is the Circumference of a circle?

The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by it.

Pi ( written as the Geek letter π) is a universal constant found by dividing the circumference of a circle by its diameter. So if you measure the diameter of a circle you can calculate its circumference by multiplying by π.

Circumference = π * diameter.

It's value to the nearest hundredth is 3.14 but its actual value is a decimal number that goes on without bounds. That is in Maths it is irrational and can't be written accurately as a fraction.

For example:

What is the circumference of a circle that has a radius of 7cm?

Approximately 22 cm.

Exactly 7πcm

The ratio between the circumference of a circle and its diameter is π. We commonly write c=2π r, using the radius instead and doubling it.

One is 22/7, which is common in use and the other is 355113 ≈ 3.1415929,

which is less well-known but very accurate for the number of digits you have to remember.

In the given example, we are told that the diameter is 7 cm.

So using the common approximation π ≈ 22/7,

we find that the circumference is approximately:

(22/7)* 7 cm

= 22cm

Hence, when you multiply the diameter by 22/7,  you find the approximate not exact circumference of a circle.

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Answer:

[tex]681.25ft^2[/tex]

Step-by-step explanation:

The total area of the deck can be found with

[tex]A_t=A_0+A_a[/tex]

where

[tex]A_t[/tex] = total area of the new deck

[tex]A_0[/tex] = area of the original deck

[tex]A_a[/tex] = area of addition

The area of the addition can be found with

[tex]A_a=lw[/tex]

where

[tex]l[/tex] = length of addition

[tex]w[/tex] = width of addition

So,

[tex]A_t=400ft^2+(18.75ft*15ft)\\A_t=400ft^2+281.25ft^2\\A_t=681.25ft^2[/tex]

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 1.819, -0.1300048 and -1.4474respectively.

Equation: An algebraic expression composed of two expressions with the same value and the symbol "=" in between.

The given equation is

y = -0.0000084x³ + 0.00194x² -0.196x + 7.819

Where Y is the annual growth rate of  a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

y = -0.0000084(50)³ + 0.00194(50)² -0.196(50) + 7.819

y = 1.819

Therefore, the estimated average annual growth rate of the country's population for 1950 is 1.819.

The difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

y = -0.0000084(88)³ + 0.00194(88)² -0.196(88) + 7.819

y= -0.1300048

Therefore, the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

y = -0.0000084(110)³ + 0.00194(110)² -0.196(110) + 7.819

y= -1.4474

Therefore, the estimated average annual growth rate of the country's population for 2010 is 0.2236.

Therefore, population growth rates for a particular nation in 1950, 1988, and 2010 are, respectively, 1.819, -0.1300048 and -1.4474.

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The domain and range of the function are (-∞,∞) and (-∞,5). The greatest concentration will be 5.

The set of all values that a function can accept is known as its range, while the set of all values for which a function is defined is known as its domain.

The dependent variable's range is its domain, which is for the independent variable.

Part (A)

As per the given function C(t) = - 5t² + 10t

C'(t) = 0

-10t + 10 = 0

10t = 10

t = 1

C''(t) = -10 < 0

So, at t = 1 the function will be maximum.

C(1) = -5(1)² + 10 x 1 = 5

Thus, the range will be (-∞,5) and the domain will be (-∞,∞).

The range represents the amount of concentration while the domain is the time.

Part (B)

The graph of the function has been drawn below.

At t = 1 the C(t) is maximum as 5 thus it will be the maximum concentration.

Hence"The function's domain and range are  (-∞,∞) and (-∞,5), respectively. Five will have the highest concentration.".

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