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From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65

An exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.

In this problem, we have to calculate the rate of increase per year.

Data;

rate = 2%

P = 3000

The exponential growth can be calculated by;

A = P(1 + r)ⁿ

In year 1

A = 3000(1 + 0.02)¹

A = 3060

In year 4

A = 3000(1 + 0.02)⁴

A = 3247.3

a)

The average rate of change from year 1 to year 4 will be

A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1

A = 62.43

The average rate of change from year 1 to year 4 is 62.43

b)

The average rate of change from year 5 to year 8 is calculated as

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5

A = 67.57

C)

The rate of change increase can be calculated as;

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1

A =65

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957÷3=319 this divide answer i hope help you

Answer:

510 miles

Step-by-step explanation:

                                       A                     B

Rate                               80                  120

Time                                 x                     x - 2

Distance        

Distance = rate x time

A's distance

d = 80x

B's distance

d = 120(x -2)          

The distances equal each other when B catches up to A.  Set the equations equal to each other and solve for the time

80x = 120(x -2)  Distribute the 120

80x = 120x - 240  Subtract 120x from both sides

-40x = -240    Divide both sides by -40

x = 6

After 6 hours, B caught up with A.  Substitute 6 for t and find the distance. You can use A or B.    

d= 80x

d = 80(6)

d = 480

We need to add another 30 miles to get to the next town.

480 + 30 = 510

The value of the function h(x) is x² -  4x +6 and 4-6 x².

Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.

Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).

Therefore, we get

f(x) = x² and  we have g(x) = 4x - 6

h(x) = f(x) - g(x)

h(x) =   x² -  4x +6

h(x) = f(g(x))

     =  x²( 4x - 6)

     = 4-6 x²

h(x) is the inverse of g(x)

   = inverse of 4x - 6

   = 1/ 4x - 6

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Answer:

The answer is C

Step-by-step explanation:

You have to divide both numerators then the denominater.

So, it would look like:  160 over 90 x 100 over 290

160x100=16   90x290=25     16/25

The equations that are true for x = –2 and x = 2 are:

x^2-4=0 and 4x^2 = 16

We can determine the equations that are true for x = –2 and x = 2 by testing the given options:

After testing the options option  1 ; x^2-4=0 putting x = 2 or -2 into the equation will give zero.  

(2^)2-4=0

(-2)^2-4=0

Then option 4: 4x^2 = 16

4(2)^2 = 16

4(-2)^2 = 16

Therefore, option 1st and 4th are correct.

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The total number of employees that this company would be said to have is given as 122424

How to solve for the number of employees in the company

We know that the number of employees in one country is 22400, and that this represents 18.3% of the company's employees in total.

We can use this information to set up a proportion to find the total number of employees in the company.

Employees in one country / Total employees = 18.3 / 100

22400 / X = 18.3/100

To find the total number of employees, we can cross-multiply and divide:

X = (22400 * 100) / 18.3

X = 122424

So the company has a total of 122424 employees.

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Answer: y= -6x+4/5

Step-by-step explanation: We will compare these equations with standard form y=mx+c where m is the slope of the line and c is the y-intercept.

for line y= -6x+4/5

on comparing with y= mx+c

we have m= -6 and c= 4/5.

So, the first option is correct.

laucs ori nisiquiera estoy en universidad estoy en eseyo pe

Answer:

which one is correct about HRM?

The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.

In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.

By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.

For example, if 3 shirts are ordered, then x = 3 and the expression becomes:

So the total cost of the order would be $26.

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D. mz1 = 45° and mz2 = 45 are complementary angles (mz1 + mz2 = 90°), but neither angle is obtuse (greater than 90°), so the guess is wrong. This is a counter-example to show.

A supplementary angle is an angle where the sum of two angles is 90 degrees. That is, if angle A and angle B are complementary, angle A measurement + angle B measurement = 90 degrees. Supplementary angles may be adjacent (having a common vertex and edge) or non-adjacent (having no common vertex or edge), but they always complement each other.

There are various kinds of angles to study.

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The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

According to the graph -

The perpendicular measures 4 units.

The base measures 3 units.

To find the hypotenuse g apply the Pythagoras theorem -

(hypotenuse)^2=(base)^2+(perpendicular)^2

(g)^2=(3)^2+(4)^2

(g)^2=9+16

(g)^2=25

g=[tex]\sqrt{25}[/tex]

g=5

Therefore, line segment g measures 5 units.

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Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram.

The complete question is,

Which of the following attributes of a parallelogram leads to the conclusion that every square can be categorized as a parallelogram? Choose each option that applies.

four equal sides

two pairs of diametrically opposed equal angles

diagonals are cut in half.

two sets of parallel, opposed sides.

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The length of segments TA and TB are both 4 cm.

To solve this problem, we can use the properties of circles and the relationship between the radius and the diameter.

Since the radius of the circle with center T is 4 cm, the diameter of this circle is 2 * 4 = 8 cm.

Since the length of segment ST is 9 cm, the diameter of the second circle is also 9 cm.

Since the radius of the circle with center T is 4 cm, the radius of the second circle is also 4 cm.

Since the two circles intersect at points A and B, the segments TA and TB are equal in length.The length of segment TA and TB is the radius of the second circle, which is 4 cm.

Therefore, the length of segments TA and TB are both 4 cm.

The figure is attached

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The blank spaces of the statement coefficient: The number in BLANK of the variable within the BLANK BLANK are, front, addition, subtraction.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

We know a coefficient is a constant value combined with a variable.

For example, In 7x the coefficient of x is 7.

Given, A fill-in-the-blank statement,

coefficient: The number in BLANK of the variable within the BLANK BLANK.

Therefore,

coefficient: The number in front of the variable within the addition subtraction.

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Check the picture below.

Answer:

It is in its simplest form

Step-by-step explanation:

The number of atoms that are there in 400 grams of hydrogen will be 2.408 × 10^26.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

In this case, there are 6.02 × 10^23 atoms in 1 gram of hydrogen.

The number of atoms that are there in 400 grams of hydrogen will be:

= 6.02 × 10^23 × 400

= 2408 × 10^23

= 2.408 × 10^3 × 10^23

= 2.408 × 10^26

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Answer: 130

Step-by-step explanation:

The original price of the sweater is $303.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.

The discounted price is $91

Let the original price of the sweater be x.

So, 30% of x=91

30/100 ×x=91

0.3x=91

x=91/0.3

x=$303

Therefore, the original price of the sweater is $303.

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There are 34 ways by which  pairs of potential clients can be randomly chosen from pool or eight candidates.

We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.

As such we would have the use of the formula for combination as follows;

C = n!/r!( n - r)!

C = 8!/2!(8 - 2)!

C = 8 * 7 * 6!/2! 61

C = 8 * 7/ 2 * 1

C = 28

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Answer:

There is a root between x=3 and x=5.

Step-by-step explanation:

Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.

The length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).

What are the distance formula and midpoint of a segment?

The distance formula is a mathematical formula that can be used to determine the distance between two points in a coordinate plane. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

The midpoint of a segment is a point that is exactly in the middle of a line segment. Given the endpoints of the line segment, (x1, y1) and (x2, y2) the coordinates of the midpoint, (x, y) can be calculated using the following formulas:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

The given points are (-8, 6) and (-2, -2).

Given two points A(x1, y1) = (-8, 6) and B(x2, y2) = (-2, -2), we can use the distance formula to find the length of the line segment AB. The distance formula is:

[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\\\d= \sqrt{((-2) - (-8))^2 + ((-2) - (6))^2}\\\\d=\sqrt{36 + 64}\\\\d=\sqrt{100}\\\\d=10[/tex]

The length of AB would be 10.

To find the coordinates of the midpoint of AB, we can use the midpoint formula:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

Plugging in the values for A and B, we get:

x = (-8 + (-2)) / 2 = -5

y = (6 + (-2)) / 2 = 2

The coordinates of the midpoint of AB are (-5, 2).

Hence, the length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).

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Answer:

both are right

Step-by-step explanation:

2/5x = 14

multiply both sides by 5/2:

(5/2)(2/5)x = 14(5/2)

x = 70/2 = 35

However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right.  Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

Answer:

Step-by-step explanation:

Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:

(PR)/(JK) = (PQ)/(JL) = (36)/(18)

Cross multiplying and solving for PR, we find:

PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36

The coordinate of the point C is (0, a)

From the question, we have the following parameters that can be used in our computation:

A = (0, a)

B = (b, 0)

As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.

This means that we start by calculating the equation of the altitude from B to line AC.

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the above as a guide, we have the following:

slope = (y₂ - y₁)/(x₂ - x₁)

This gives

m(BC) = (0 - 0)/(b - 0) = 0

y-intercept (c) = a

So the equation of the line BC is

y = 0 * x + a

y = a

For line AC, we have

m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.

This means that the equation of the line AC is

x = 0

The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)

At this stage, we have the coordinates of the points from lines AC and BC to be

(0, a) and (0, a)

Next, we calculate the C as follows

C = Midpoints of (0, a) and (0, a)

This gives

C = 1/2 * (0 + 0, a + a)

Evaluate

C = (0, a)

Hence, the coordinate of C is (0, a)

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The value of (2/3 - 5/6) / 3/4 is -2/9.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

(2/3 - 5/6) / 3/4

2/3 - 5/6

= (4 - 5)/6

= -1/6

Now,

(-1/6 )/(3/4)

= -1/6 x 4/3

= -4/18

= -2/9

Thus,

The value is -2/9.

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