World population is about P = 7.68(1.0103)', with Pin billions and t in years since 2020.
(a) What is the yearly percent rate of growth of the world population? % per year
(b) What was the world population in 2020? billion people What does this model predict for the world population in 2026? Round your answer to 3 decimal places. i billion people
(c) Use part (b) to find the projected average rate of change of the world population between 2020 and 2026. Round your answer to the nearest integer. million people per year

An equation in point-slope form for this line is y=6x+5.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that;

Point on a line (-1,-1)

Slope of the line 6

Now, substituting the values in the general formula of line

y+1=6(x+1)

y+1=6x+6

y=6x+5

Therefore, the equation with the given slope will be y=6x+5.

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The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

What is Factoring an expression?

A numerical or algebraic expression is factored when it is written as a product of factors. The distributive property can be used to factor expressions.

The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

The solutions for this equation would be x = √6 or x = -√6. These are the values of x that make the expression equal to zero.

Factoring the expression in this way can be useful in solving related equations or in finding the roots of a quadratic function. It also helps in visualizing the graph of the function, as the factored form shows the x-intercepts, which are the points where the graph crosses the x-axis.

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Answer:

(-9)×(-7/3)=9×7/3=3×7=21

Answer:

21

Step-by-step explanation:

-9 is equal to -9/1

the negative sign on the -7/3 can be put on the top or bottom

-9 -7 63

--- x --- = ---

1 3 3

63 divided by 3 equals 21 and is therefore in the simplest form

The best way to figure out if there is a solution to the equation:

 --> solve this whole thing algebraically

Let's solve:

 [tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]

If we get this kind of circumstance:

 --> where the left/right part of the equation are equal and cannot be

      solved further

     ---> the solution is all real numbers

Answer: solution is all real numbers

By using the substitution method, the value of x is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2y - 4x = 8                 .......equation 1.

3(x + 4) - 2y = 5          .......equation 2.

From equation 1, we have:

y = 2x + 4         .......equation 3.

By using the substitution method to substitute equation 3 into equation 2, we have the following:

3(x + 4) - 2(2x + 4) = 5

3x + 12 - 4x - 8 = 5

-x + 4 = 5

x = 4 - 5

x = -1.

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The width of the rectangle is [tex]4x^8y^6[/tex]inches.

Option A is correct.

What is the area of the rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:

A = l x w

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:

width = Area / length

Substituting the given values, we have:

width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]

Simplifying the expression, we get:

width = [tex]4x^{8}y^{6}[/tex]

Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.

Option A is correct.

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The Possible effects of incentives for political leaders includes options 1, 2, 3, and 4. These options elaborate the incentives of political leaders.

Favor programs with immediate benefits: Political leaders may be incentivized to prioritize policies or programs that provide immediate benefits to their constituents in order to increase their popularity and chances of reelection.

Implement policies that favor a small, powerful group: Incentives for political leaders may also lead them to implement policies or regulations that favor a small, powerful group, such as major donors or influential interest groups, at the expense of the general public.

Provide policies whose costs outweigh the benefits: Political leaders may be incentivized to implement policies that provide short-term benefits but have long-term costs or consequences, such as a large budget deficit or environmental degradation.

Favor programs with immediate costs: Alternatively, incentives may lead political leaders to prioritize programs or policies with immediate costs, such as increased taxes or reduced spending, to address pressing issues and avoid long-term consequences.

Therefore, options 1, 2, 3, and 4 describe possible effects of incentives for political leaders.

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____The given question is incomplete, the complete question is given below:

Select all the items that describe possible effects of incentives for political leaders. 1.favor programs with immediate benefits 2.implement policies that favor a small, powerful group 3.provide policies whose costs outweigh the benefits 4.favor programs with immediate costs

The equations that explains the process to find the number of square yards of fabric she will use and the number of square yards of fabric she will have left, using the addition of fractions are;

(3/8) + (2/8) = 5/8 square yards of fabric will be used

1 - 5/8 = 3/8 square yard of fabric will be left

A fraction is a representation of a part of a whole, consisting of a number in the numerator divided by another number in the denominator expressed as a quotient.

The amount of fabric Diana has = 1 square yard

Amount of fabric to make one pillow = 3/8 square yard

Amount of fabric required to make the other pillow = 2/8 square yard

Therefore, the amount of fabric Diana will use can be found by adding the fractions of the areas of the fabric she uses for each pillow as follows;

The number of square yard of fabric Diana will have left can be found from the difference between the initial number of square yards of fabric Diana has and the amount of square yards of fabric she will use.

Initial number of square yards of fabric = 1

Number of square yards of fabric she will use = 5/8

Therefore;

Number of square yard of fabric Diana has left = (Initial number of square yards of fabric) - (Number of square yards of fabric she will use)

Number of square yard of fabric Diana has left = 1 - 5/8 = (8 - 5)/8 = 3/8

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In linear equation, $ 618,418.80  will Andrea and Stanley save by choosing Mortgage A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Total Payback = Instalment Amount * No. of Instalments

Mortgage A:

=  $1621.39 * 360

= $ 583,700.40

Mortgage B:

=  $1717.83 * 360

=$ 618,418.80

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Answer:The answer is 2.5 pints.

The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.

Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.

We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.

The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.

The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.

The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:

$7.70x + ($150 - $5.00x) = $182.40

Expanding and simplifying the equation:

$2.70x = $32.40

Dividing both sides by 2.70:

$x = 12

So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

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Answer:

C. No real factors

Step-by-step explanation:

Not factorable

The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The variables for this problem are given as follows:

Hence after a time of two hours the battery level is found as the numeric value at x = 2.

The problem is incomplete, hence the general procedure to solve the problem is presented.

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The y-intercept of the line passing through the given points is -26 and the slope is -13/17

The y-intercept is the point where the graph intersects the y-axis.

Given that, the pair of coordinates of some points, we need to find the y-intercept,

To find the same, we will firstly find the equation of the line passing through these points,

We know that, the equation of a line passing through two points is given by,

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Considering the points, (34, -52) and (51, -65)

The equation will be,

y+52 = -65+52 / 51-34 (x-34)

y+52 = -13/17(x-34)

y+52 = -13x/17+26

y = -13x/17-26

Hence, the y-intercept of the line passing through the given points is -26.

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Answer:

Step-by-step explanation:

To solve this system of two equations with two variables (x and y), we'll use the substitution method. Here's how:

Solve one of the equations for either x or y, in terms of the other variable. Let's solve the first equation, 2x - 5y = 4, for x:

x = (4 + 5y)/2

Substitute the expression for x from step 1 into the second equation, 4x = 8 + 10y:

4(4 + 5y)/2 = 8 + 10y

Simplify the equation from step 2:

8 + 10y = 8 + 10y

Solve for y by subtracting 8 from both sides:

10y = 10y

Divide both sides by 10 to find the value of y:

y = y

Now that we have the value of y, we can substitute it back into the expression for x from step 1:

x = (4 + 5 *y)/2

So the solution to the system of equations is (x, y) = ((4 + 5 *y)/2, y=y).

Answer:

2.9375

Step-by-step explanation:

7 5/6 / 2 2/3 = 47/16 = 2 15/16 = 2.9375

The x-intercepts are (-2, 0), (-1, 0), (1, 0), and (2, 0).

What is meant by the x-intercept?

The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y coordinate equals zero, is the x-intercept for any curve.

The x-intercepts are the points where the graph meets the x-axis.

Which means that the coordinate of y will be zero.

It is given in the question that the graphed function will meet the x-axis at 4 points which are (-2, 0), (-1, 0), (1, 0), and (2, 0)

Therefore the x-intercepts of the function will be: (-2, 0), (-1, 0), (1, 0), and (2, 0).

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Answer: B)  (-1,0)

Step-by-step explanation:

Just took the test on edge

Answer:

Step-by-step explanation:

Two angles are said to be supplementary when their sum is equal to 180°.

Given angle 1 and 50° are supplementary.So, angle1+50°= 1880°

angle1 =180°-50°

angle 1=130°

Given 50° and angle 3 are supplementary

So,50°+ angle 3=18=0°

angle 3=130°

So angle 1 equals to angle

Answer:

Step-by-step explanation:

You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.

If x represents the cost of the goggles, then Winston's total spending is ...

  90.50 + x

If that is over is $150 budget, the relation is described by ...

  90.50 +x > 150

Subtracting 90.50 from both sides gives ...

  x > 59.50

This tells us the goggles cost more than $59.50.

<95141404393>

Answer:

Below

Step-by-step explanation:

(2x+15) / ( 3x+15)  =  11/14    cross multiply to get

28x + 210 = 33x + 165

45 = 5x

x = 9       so the larger number is   3 X 9 = 27  

                       (smaller number is 2 x 9 = 18)

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the solution:

Calculate the government deposit: For every $1.00 you deposit, the government deposits $2.00. So if you deposit the maximum of $100.00 each month, the government deposit would be $100.00 * $2.00 = $200.00.

Calculate the total deposit each month: The total deposit each month is the sum of your deposit and the government deposit, so it would be $100.00 + $200.00 = $300.00.

Calculate the number of months: You started with $100.00 and made the maximum deposit of $100.00 each month for 5 years. Five years is 5 * 12 = 60 months.

Calculate the total deposit over 5 years: Over 5 years, you made 60 deposits of $300.00 each, so the total deposit over 5 years would be 60 * $300.00 = $18,000.00.

Calculate the final balance: Adding the initial deposit of $100.00 to the total deposit over 5 years, the final balance in your account after 5 years would be $18,000.00 + $100.00 = $18,100.00.

So, at the end of 5 years, if you deposited the maximum of $100.00 each month into the College Savings fund, you would have $18,100.00 in your account.

Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:

I = P * r * t

I = 16000 * 0.05 * 1.5

I = 1200

The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:

A = P * (1 + r/n)^(nt)

A = 16000 * (1 + 0.05/2)^(2 * 1.5)

A = 16000 * (1.0253)^3

A = 16000 * 1.07897

A = 17253.576

The difference between the compound interest and simple interest is:

17253.576 - 1200 = 16053.576

So the difference between the simple interest and compound interest is 16053.576.

Step-by-step explanation:

Answer: 71/7

Step-by-step explanation:

I like this problem a lot!

Let the shorter leg length be x:

then the longer leg length is 3x - 9

the hypotenuse length is (3x - 9) + 2 = 3x - 7

Perimeter of Triangle = Sum of all 3 sides of a triangle

24 = x + (3x - 9) + (3x - 7)

24 = 7x - 16

40 = 7x

.: x = 40/7

.: hypotenuse = 3x - 7 = (120/7) - 7 = 71/7

Done!

Answer: 54.54 mph

Step-by-step explanation: To calculate the average speed of a car that traveled 300 miles in 5.5 hours, you can divide the total distance traveled by the total time taken: Average speed = Total distance / Total time-average speed = 300 miles / 5.5 hours = 54.55 miles per hour (mph)So, the average speed of the car is 54.55 mph.

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

piecewise function defines the function graphed between y=2x+3 and y=-1/3x+3.

How to compare linear equations?

The comparison method, a procedure for solving systems of independent equations, starts by rewriting each equation with the same variable as the subject. Any of the variables may be chosen as the first variable to isolate. Each equation is now an isolated-subject equation, and equation where one variable is isolated.

Given:

y = 2x+3

y = -1/3x+3

The left portion of the blue curve is y = 2x+3 but it is only graphed when x < 0 (we could argue that  but I'll set that aside for the other portion).

The right portion is the line y = -1/3x + 3 and it's only graphed when

Both lines have y-intercept 3.

The slopes are 2 and -1/3.

The equations are

y = 2x + 3; y = -1/3 x + 3e could have this piecewise function

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How these current asset may fit into your business, like mine, is explained as follows:

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The measure of the first angle is 128. 5 degrees

From the information given, we have that;

Let the second angle be x

We have the representation as;

3x - 26 + x = 180

collect the like terms, we get;

3x + x = 180 + 26

Add or subtract the like terms

4x = 206

Make 'x' the subject of formula by dividing by the coefficient of x, we get;

x = 206/4

divide the values

x = 51.5 degrees

Then, the angle is 128 .5 degrees

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Yes, the given statement is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that;

The statement is about the decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

Now, A fraction is terminating decimal as if the denominator of the fraction contains terms in the form of 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.

Then, It is said that, there is a digit in thousandth place.

Hence, the statement given is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.

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The table offers an average rate of change greater than the average rate of change of the function f(x) = x² + 2 · x - 1.

In this problem we need to determine two average rates of change, one from an equation and another from a table. Graphically speaking, average rate of change is the slope of a line secant to a curve and it can be computed by secant line formula:

m = [f(2) - f(- 2)] / [2 - (- 2)]

First, we proceed to determine the average rate of change for the function f(x) = x² + 2 · x - 1:

f(- 2) = (- 2)² + 2 · (- 2) - 1

f(- 2) = 4 - 4 - 1

f(- 2) = - 1

f(2) = 2² + 2 · 2 + 1

f(2) = 9

m = [9 - (- 1)] / [2 - (- 2)]

m = 10 / 4

m = 5 / 2

m = 2.5

And the average rate of change of the table:

m = (6.25 - 0.16) / [2 - (- 2)]

m = 0.09 / 4

m = 609 / 400

m = 1.523

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