Question 23
Springfield's population in 2019 was 202628 people and is projected to grow at a rate of 0.81 % each year. If the growth continues at this annual rate, what will the population be in 2046?
Round to the nearest person.

Answer: 56.70 g

Step-by-step explanation:

An outcome of a statistical analysis is a test statistic. The null hypothesis, which claims that there is no association between the variables or difference between the sample groups, is explained by the observed data's distance from it.

Calculate the test statistic for this problem ?

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If P value < α ; Reject H0 ; otherwise, fail to reject H0

A.) Left tail , Z = - 1.32 ; α = 0.10

We can use the P value calculator from Z score :

P value = 0.934

P value > α ; Hence, we fail to reject the null, H0

B.) Right-tailed test, z = 2.46, α = 0.01

P value from Z score calculator ;

P value = 0.0069

P value < α ; Hence, we reject the null, H0

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Answer:

Step-by-step explanation:

The intersection consists of the elements that are contained in all of the intervals.

(-2, 2) (-1, 4) (0, 6)

Correct me if im wrong

The actual distance is = 162.5mi

Acc to our question-

Hence,The actual distance is = 162.5mi

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The angle a formed at the exterior of the hexagon by a line that goes through a vertex to the center of the hexagon and a second line that touches the adjacent vertex is a = 30°

The properties of a regular hexagon includes;

There are 6 equilateral triangles in a regular hexagon

The triangle ΔOAC formed by the segment that extends into the hexagon is an equilateral triangle.

Therefore;

Triangle ΔABC is an isosceles triangle with segment AC ≅ Segment AB

Therefore;

Angle ∠C is congruent to angle ∠B (base angles of an isosceles triangle

∠C ≅ ∠B

m∠C = m∠B (definition of congruency)

m∠B = a

Therefore;

m∠C = m∠B = a

m∠C = a (substitution property)

From external angle to a triangle, postulate, we get;

m∠OAC = m∠B + m∠C

Therefore;

m∠OAC = a + a

60° = 2·a

a = 60°/2 = 30°

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Answer:

y=-6

Step-by-step explanation:

2.3y - 4.2 = -18

       +4.2     +4.2

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

2.3y = -13.8

divide by 2.3 on both sides

y = -6

The value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is 2.3y - 4.2 = -18.

We have to simplify the equation in order to find the value of y as,

2.3y - 4.2 = -18.

Rearrange the equation as

2.3y= -18+4.2

2.3y= -13.8

y= -13.8/2.3

y= 6

Thus, the value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

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Answer:

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

y - 3 = [tex]\frac{1}{4}[/tex] (x - 2 ) ← distribute parenthesis

y - 3 = [tex]\frac{1}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ( add 3 to both sides )

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form

Answer: 4.16 per pizza

Step-by-step explanation: 54.08 divided by 13 is 4.16

Answer:

2

Step-by-step explanation:
because 1. is true and 3. is true

A linear regression equation that represents the data set is y = 39.7x + 1127.8. Also, the number of new cases for 2011 is equal to 1525 cases.

In this scenario, the Year since 2002 (x) would be plotted on the x-axis of the scatter plot while the New cases (y) would be plotted on the x-axis of the scatter plot.

From the Excel sheet, you should right click on a data point on the graph (scatter plot), select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatter plot (see attachment) which models and shows the relationship given in the table, an equation for the linear regression is given by:

y = 39.7x + 1127.8

For 2011, the value of x is given by:

x = 2011 - 2002 = 9 + 1 = 10 years.

Now, we can determine the new cases for 2011:

y = 39.7(10) + 1127.8

y = 397 + 1127.8

y = 1524.8 ≈ 1525 cases.

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Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The value of addition for the equation (f + g) (-2) is 15 and the value of subtraction for the equation (f + g) (-2) is 39.

A function is a relationship that assigns exactly one output value to each input value. Like numbers and polynomials, functions can be added, subtracted, multiplied, and divided to create new functions. Here are the rules for performing these operations on functions.

Let f(x) and g(x) be two functions:

Addition:

We can add two functions:

(f + g)(x) = f(x) + g (x) ...... (1)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (1).

(f + g)(x) = 5x^2 + 7 + 3x - 6

(f + g)(x) = 5x^2 + 3x + 1 .......(2)

We have to evaluate the value of (f + g) (-2). Therefore, put the value of x = -2 in equation (2). We get,

(f + g) (-2) = 5 (-2)^2 + 3 x -2 + 1

(f + g) (-2) = 20 - 6 +1

(f + g) (-2) = 15

Hence, for the addition of the equation (f + g) (-2) the value is equal to 15.

Subtraction:

We can add two functions:

(f - g)(x) = f(x) - g (x) ...... (3)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (3).

(f - g)(x) = 5x^2 + 7 - (3x - 6)

(f - g)(x) = 5x^2 + 7 - 3x + 6

(f - g)(x) = 5x^2 - 3x + 13 ....... (4)

We have to evaluate the value of (f - g) (-2). Therefore, put the value of x = -2 in equation (4). We get,

(f - g)(-2) = 5(-2)^2 - 3(-2) + 13

(f - g)(-2) = 5 x 4 + 6 + 13

(f - g)(-2) = 20 + 6 + 13

(f - g)(-2) = 39

Hence, for the subtraction of the equation (f - g) (-2) the value is equal to 39.

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Using the formula of volume of cone, the height of the cone is 3/8.

In the given question,

We have to find the missing dimension of the cone.

Volume of cone is 1/18 pi, radius is 2/3 ft.

As we know that volume of cone is one third of the product of pi, square of radius and height.

The formula of cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

where V=Volume of cone

r=radius of cone

h=height of the cone

We know V=1/18 π, r=2/3 ft.

We don't know the value of h. So we find the value of h.

putting the value in formula

[tex]\frac{1}{18}\pi=\frac{1}{3}\pi\times\frac{4}{9}\times h[/tex]

Simplifying

[tex]\frac{1}{18}\pi=\frac{4}{27}\pi\times h[/tex]

[tex]\frac{\pi}{18}=\frac{4\pi}{27}\times h[/tex]

Multiply by 4/27π on both side

[tex]\frac{\pi}{18}\times\frac{27}{4\pi}=\frac{4\pi}{27}\times\frac{27}{4\pi}\times h[/tex]

Simplifying

[tex]\frac{1}{2}\times\frac{3}{4}=h[/tex]

Simplifying

h = 3/8

Hence, the height of the cone is 3/8.

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The correct input to the blank of the question is given below.

What are Triangle Congruence Theorems?

If the corresponding interior angles are equal in measure and the sides of two triangles are equal in size, then the triangles are congruent.

The missing part that completes the proof is given by:

1. Given.

2. Definition of linear pair.

3. m∠ABD + m∠CBD = 180°

4. 90° + m∠CBD = 180°

6. DB ≅ DB

7. HL Congruence Theorem

Hence, these are the missing part to complete the proof.

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The value of 6 is equal to 3.

Given that:

If 1=3, 2=3, 3=5, 4=4, 5=4.

So, we have to find the value of 6.

To calculate the value of 6 we have to think logically.

Looking at this question logically,

1 is written as ONE, so it contains three alphabets.

2 is written TWO, so it contains three alphabets.

3 is written as THREE, so there are 5 alphabets.

4 is written as FOUR, so it contains four alphabets.

5 is written as FIVE, so it contains four alphabets.

6 is written as SIX, so it contains three alphabets.

So, in this way, 6 can be written as 3.

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Answer:

x = 126

Step-by-step explanation:

The angle indicated with 126° and the angle represented with (5y - 4) are alternate angles and their measures are equal so we can write the following equation to find the value of y:

5y - 4 = 126 add 4 to both sides

5y = 130 divide both sides by 5

y = 26

x and the angle indicated with 126 are also alternate angles so

x = 126

The angle represented with (5y - 4) are the angle represented with (6z + 6) are supplementary angles and their sum is equal to 180, we can write the following equation based on this information:

6z + 6 + 126 = 180 add like terms

6z + 132 = 180 subtract 132 from both sides

6z = 48 divide bot sides by 6

z = 8

Answer:

B

Step-by-step explanation:

because im smart :) give me brainliest or else

Answer: 3.40687

Step-by-step explanation: 3.40687

If A varies jointly as b and inversely as d then value of A when b = 9 and d = 2 is 135/2.

What is proportionality?

If A  is inversely proportional to B, this is expressed as:

A α 1/B

A = k 1/B

where k is the constant of proportionality.

According to the given question:

A varies jointly with b and inversely with d

[tex]A \alpha \frac{b}{d}[/tex]

A = k b/d where k is proportionality constant

If A = 30, b = 6 and d = 3, finding the value of k

30 = k 6/3

k = 15

Now to find A when b = 9 and d = 2, using value of k

A = 15 x 9/2

A = 135/2

Hence the value of A is 135/2.

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The equation of the ellipse in vertex form is (x - 1)² / 25 + (y + 2)² / 4 = 1.

In this question we find a representation of an ellipse with a center at point (h, k) = (1, - 2). The vertex form of the equation of the ellipse is introduced below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Please notice that the major semiaxis is parallel to the x-axis and the minor semiaxis is parallel to the y-axis.

First, write the coordinates of the center of the ellipse:

(h, k) = (1, - 2)

Second, find the lengths of the semiaxes:

Major semiaxis

a = 0.5 · [6 - (- 4)]

a = 5

Minor semiaxis

b = 0.5 · [0 - (- 4)]

b = 2

Third, write the equation of the ellipse:

(x - 1)² / 25 + (y + 2)² / 4 = 1

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Answer:

u need a chart image

Step-by-step explanation:

The point of intersection is (3,3)

What is meant by intersection?

The intersection points show where both equations have their answers. To put it another way, the intersection point is the answer to both equations. There are multiple intersecting points if there are multiple solutions that satisfy both equations.

If we plot a function, y = f(x), and its inverse, y = f1(x), we can see that the inverse function is the exact opposite of the original function with regard to y = x.

Consequently, only when y = x can both intersect as show in the fig.

Therefore A place where the lines y and x cross must be there.

Find the spot that the line y = x meets at this time.

Of course, the line y = x is satisfied at only one point, which is (3,3).

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Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

As given in the question,

Given expression is equal to :

(3 x 10⁹) and (2 x 10⁹)

Apply law of indices of multiplication to get the product of the given expression

mᵃ × mᵇ = mᵃ⁺ᵇ

Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is equal to

(3 x 10⁹) and (2 x 10⁹)

= ( 3 × 2 ) × ( 10⁹ × 10⁹ )

= 6 × 10⁹ ⁺ ⁹

= 6 × 10¹⁸

Therefore, product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

The complete question is:

Find the product of (3 x 10⁹) and (2 x 10⁹). Write the final answer in scientific notation.

6 x 10⁸¹

6 x 100¹⁸

6 x 10¹⁸

6 x 10⁹

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The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million. There are summations with an infinite set of parameters.

As per the given,

Mohan has 2 current accounts, the first has a balance of $101.46.

The second has -$21.21.

Total amount of Mohan = 101.46 - 21.21 = $80.25

Eve's balance = -$45.91

Combined balance = $80.25 - $45.91 = $80.25

As per the given,

Eve has a savings account with $231.56 in it. She wants to buy a new coat for $75.00. She calculates that she will have $156.56

$231.56 = $156.56 - $75

$231.56 + $75 = $156.56

Hence "The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56".

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The end behavior of the following polynomial function is option A.

The leading term of the polynomial is 20x^20, degree of f(x) = 20, and the leading coefficient is 20.

Given function:

f(x)=−2x^3+20x^20+20x^18+60x^7+9

= 20x^20+20x^18+60x^7+2x^3+9

Here the degree is 20.

Leading term = 20x^20.

Leading coefficient = 20.

The degree is even and the leading coefficient is positive so end behavior is upward parabola which is option A .

Therefore the leading term of the polynomial is 20x^20, degree of f(x) = 20, and the leading coefficient is 20.

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$6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

Invested amount = $7000

Let x be the invested amount at 6% and y be the invested amount at 8%.

According to the question,:

x+y=7000......(1)

annual interest is $430.

Therefore Interest on x + interest on y = $430

Interest=(invested amount*rate*time)/100

Here Time is 1 year.

(6*x)/100+(8*y)/100=430

This shows, 6x+8y=43000.......(2)

From equation (1), we have:

x=7000-y.........(3)

Substitute the value of x in equation (2),

6(7000-y)+8y=43000

On simplifying, y=500

Put y = 500 in equation (3)

we get x=6500

Therefore $6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

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The correct options to the statements will be:

All the atoms in a composite are the same - False.

One example of a composite is glass reinforced plastic - True.

The properties of a composite are a combination of the properties of the materials used to make it - True

The materials used to make composites are always arranged in layers - False.

Composite materials are created by fusing two or more materials with very different properties. The different materials work together to give the composite its unique properties, but within the composite, the different materials can be easily distinguished - they do not dissolve or blend into each other.

A composite material is made up of two materials that have distinct physical and chemical properties. When they are combined, they form a material that is specialized to perform a specific function, such as becoming stronger, lighter, or electrically resistant. They can also help to increase strength and stiffness.

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The solution to the equation are as follows.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂                [tex]e^{\sqrt{-3 -sin²(x)x} }[/tex]

What is differential equation?

In arithmetic, a equation is associate equation that relates one or a lot of unknown functions and their derivatives.

Main body:

Find the first derivative.

dy/dx=r[tex]e^{rx}[/tex]

Find the second derivative.

d²y/dx² =r² [tex]e^{rx}[/tex]

Substitute into the differential equation.

r²[tex]e^{rx}[/tex]+4[tex]e^{rx}[/tex]=cos ²x

Factor [tex]e^{rx}[/tex]out of r²[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]=cos²x

Factor [tex]e^{rx}[/tex] out of 4[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+[tex]e^{rx}[/tex]⋅4=cos²x

Factor out of [tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]

[tex]e^{rx}[/tex](r²+4)=cos²x

Since exponentials can never be zero, divide both sides by

[tex]e^{rx}[/tex]r²+4=cos²x

Use the double-angle identity to transform

cos²x to 1−sin²(x).

r² +4=1−sin²(x)

Subtract 4 from both sides of the equation.

r²=1−sin²(x)−4

Simplify the right side.

r² = -3 -sin²x

r = √-3 -sin²x

By the principle of superposition, the general solution is a linear combination of the two solutions for a second order homogeneous linear differential equation.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂

Hence the differential solution is as follows.

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a. The function m = 200 - 50v is interpreted as

m = amount left

200 = amount available for buying video games

50 = cost per video game

v = number of video games

b. The domain of the function is 0 < v ≤ 4

the domain is discrete

c. explanation of the graph is below

In the graph, the input values is the number of video games, v while the output value is amount, m(in dollars) left for buying games.

The domain is controlled by the input values. considering the amount set out for games which is 200 we solve for v at zero amount

0 = 200 - 50v

50v = 500

v = 4

The maximum number of video games the amount can buy is 4. For the minimum we can not buy 0 video game but the graph can show amount available before buying the game.

The domain starts from 0, with 0 not inclusive to 4 with 4 included

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