It took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, what was Luca's average trip?
-process

The area of the forest after 15 years will be 2189.4

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

i = The initial area of the forest = 4200km

r = Per year decrease is = 4.25%

n = Number of years = 15

The required formula is

The area of forest will be

A = i (1-r)^n

A = 4200(1-0.425)^15

A= 2189.4

Hence, the area of the forest will be 2189.4

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The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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Answer:

Step-by-step explanation:

The blanket that they should choose is the one for which the multiplication of dimensions result in the largest value.

The area of a rectangle of dimensions length and width is given by the multiplication of these dimensions, as follows:

Area = length x width.

Then, to obtain the area for each blanket, their dimensions must be multiplied.

Then the blankest with the greatest area is the one for which the multiplication of the dimensions will result in the largest value.

(applying the formula for the area of the rectangle).

The problem is incomplete, as the dimensions were not given, hence the answer is given in general terms.

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Answer: To determine whether the distance the puck travels per second is constant, we can use the concept of average speed. Average speed is defined as the total distance traveled divided by the time it takes to travel that distance.

If the average speed is constant, then the distance the puck travels per second is also constant. If the average speed is not constant, then the distance the puck travels per second will vary.

To determine the average speed, we need to know the total distance traveled and the time it took to travel that distance. Once we have this information, we can calculate the average speed by dividing the total distance traveled by the time it took to travel that distance. If the resulting value is constant, then the distance the puck travels per second is also constant.

Step-by-step explanation:

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

1/2 ÷ 2 1/4

1/2 ÷ 9/4

1/2 x 4/9 = 4/18 = 2/9

Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

Given that,

The equation f(x)=1.9(0.41)ˣ.

We have to state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.

We know that,

In order to translate their graphs over the 2D coordinate plane, I will offer the vertex form of an exponential equation for both the growth and decay functions.

In the case of growth, f(x) = a(1+r[tex])^{x-h}[/tex]+k, where b = 1+r

Decay is defined as f(x)=a(1-r)(x-h[tex])^{x-h}[/tex]+k, where b=1-r.

Consider the function  f(x)=1.9(0.41)ˣ.

We write as

f(x)=1.9(1-0.59)ˣ

So, initial value C is 1.9

Decay factor =0.41

Growth factor = 0.59

Therefore, Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

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Jahnay is making 6.5 cakes from the given ingredients.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Recipe: Makes 1 Cake =  120 g sugar + 130 g butter + 260 g flour + 3 eggs.

Jahnay is following this recipe to make cakes.

Jahnay uses 780 g of butter.

To find the number of cakes:

Use division operation,

780 ÷ 120,

= 780/120

= 78/12

= 6.5

Therefore, Jahnay makes 6.5 cakes.

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Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns,.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

Given : we prefer a histogram of the percentages in each age class rather than the countries

It's because Different years and countries may have different overall numbers of newborns, making a comparison based on the absolute numbers difficult

If we insist on using the absolute numbers,

The group with the most population would definitely result in higher results, and make it impossible for us to see the changes in weight that happen to average inborns.

Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns.

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According to the Central Angle Theorem, the central angle occupied by two points on a circle will always be twice the inscribed angle occupied by those same two points, therefore ∠ABC = 1/2 × 56 = 28°.

Since subtended and inscribed angles are mentioned in the definition, we must first understand them in order to understand the central angle theorem. An object at a specific outer position forms an angle known as a subtended angle.

If you disagree with that definition, think about this: On Earth, you are standing and gazing up at the sun. A triangle with three sides is created. The sun's height, the sun ray that travels from the bottom of the sun to your eyes, and these three directions are the three sides of the sun.

The Central Angle Theorem states that the central angle occupied by two points on a circle is always twice the inscribed angle occupied by those same two points.

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Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given : 9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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Step-by-step explanation:

please refer to the sketch

Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2

So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.

when reduced it would simplify back to 30/100.

You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.

Step-by-step explanation:

On solving the provided question, we can say that - the perimeter chest won't fit next to her bed, thus the answer is no.

The perimeter of a form is determined by the length of its contour. A rectangle or square's perimeter is determined by adding the widths of its four sides. In this instance, the rectangle's length and breadth are represented by x and y, respectively. The surface of a form is used to compute its area.

Given here is: In her room, it is 86 inches wide. The width of the bed is 76 inches.

She also wants to accommodate a chest of drawers that is 72 centimeters broad, which equals inches.

=> 90 cm = 24.6546536565 inches

and the space left in her room = 86-76=10 inches

thus, the chest will not fit next to her bed

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The solution of the equation x² - 4x + 6 = 0 using completing the square is x = 2 ± √(-2)

An equation is used to show the relationship between numbers and variables.

Polynomial can be classified based on degree of two as a quadratic equation.

Given the equation:

x² - 4x + 6 = 0

Solving using completing the square method:

subtract 6 from both sides:

x² - 4x = -6

add to both sides the square of half the coefficient of x:

x² - 4x + 4 = -6 + 4

(x - 2)² = -2

Taking square root of both sides:

x - 2 = ±√(-2)

x = 2 ± √(-2)

The solution is x = 2 ± √(-2)

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The given function will be represented by a straight line graph, as shown below in the attachment.

On a coordinate plane, functions can be graphed. To graph a function, first select several input values and compute the outputs. The x value is the independent variable, and the y value is the dependent variable. Plot the points and connect them with a line or a curve, depending on whether the function is linear or curvilinear.

Linear functions are written as y = mx + b, where m is the slope of the line and b is the y-intercept. A linear function's graph is a straight line that represents a constant rate of change between two variables. All other functions are curvilinear or non-linear.

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Answer:

x = -11, 2/3

Step-by-step explanation:

-3x^2-11x+2=0

-(3x^2+11x-2) = 0

3x^2 + 11x - 2 = 0

3x^2 + 33x - 22x - 2 = 0  ==> 33-22=11 and 33/11=3 and -22/11=-2

3x(x + 11) - 2(x + 11) = 0  ==> factor

(3x - 2)(x + 11) = 0

3x - 2 = 0                x + 11 = 0

3x = 2                x + 11 - 11 = 0 - 11

{ x = 2/3                         x = -11 } ==> x = -11, 2/3

According to the table, the Range of pools sold during this period is 8.

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, the range could also be defined as the difference between the highest observation and lowest observation. The obtained result is called the range of observation. The range in statistics represents the spread of observations.

Range = Highest Value – Lowest Value

Range = 18 – 10

Range = 8

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The multiplicative rate of change for the exponential function is 0.4.

The exponential function in mathematics is represented by the symbols f(x)=exp or ex. The word, unless otherwise stated, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

In mathematics, an exponential function has the following form: f (x) = an x, where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

Given: Exponential function [tex]$f(x)=2\left(\frac{5}{2}\right)^{-x}$[/tex]

To find The multiplicative rate of change for the exponential function.

Solution :

The general form of the exponential function is [tex]$f(x)=a b^x$[/tex]

where $b$ is the rate of change of the function.

First we write the given function In proper form:

[tex]$$\begin{aligned}& f(x)=2\left(\frac{5}{2}\right)^{-x} \\& f(x)=2\left(\frac{2}{5}\right)^x\end{aligned}$$[/tex]

The rate of change is [tex]$f(x)=a b^x$[/tex]

Therefore, The multiplicative rate of change for the exponential function Is $0.4$

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Number of Hours the band can record there music is 10hrs

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Word issues, also known as narrative problems, may be found in both daily life and the Common Core State Standards for every school level, from K to 12. For everything from counting pennies to calculating a gratuity, you can utilize the three primary forms of word problems: part-part whole, separate and join, and multiply and divide.

Total money the band has after selling the merch is = $375 + 200 = $575.

Rate for studio is $75 per day.

Total money left = $575 - 75 = $ 500

So number of Hours the band can record there music is= 500/50 = 10hrs.

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The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C

Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.

These involve certain functions of one, two or more angles.

They also are different from triangle identities, which involves angles and side lengths of a triangle.

To verify a trigonometric identity, we take the following steps;

Hence, the best option is C

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Answer:

b= 106 or b= -58

Step-by-step explanation:

word sentence

82= b-24

solution b equals 106

or

word sentence 82= 24-b

solution b equals -58

Step-by-step explanation:

I'm pretty sure it's 19200? or maybe im writing is wrong

Answer:

After 24 years population of the city will be 27000.

exponential function.

Step-by-step explanation:

in picture

Answer: The answer is 29,446,941,856

Step-by-step explanation:

Equations go into one of two categories: identities or conditional equations. An identity holds true for each value of the variables. A conditional equation is valid only for certain values of the variables.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true.

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Format in the example are Surds on the page above in own word is [tex]36z^{15} ,\ 100,\ 9^7,\ and \ 6r^3\\[/tex]

Surds are the root values for which there is no whole number representation. Indices represent the exponent or power of a value. For instance, the base is 3 and the index is 2 for the number 32. the index being 3/2.

These are the surds rules:

1) [tex](2z^3)^5=32^{15}[/tex]

2)  [tex]\sqrt[3]{1000*1000}=100[/tex]

3) [tex]\frac{9^{3} }{9^{-4} } = 9^7[/tex]

4) [tex](6r^{-3}) ^{-1} = 6r^3[/tex]

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The equation −12x+y=10 in slope-intercept form is y = 12x + 10

The general equation showing the slope-intercept form of a graph is represented as;

y = mx+ c

Given that;

From the information given, we have the equation as;

−12x+y=10

Now, let's make 'y' the subject of formula by

-12x + y = 10

Take '12x' to the other side of the equality sign

y = 10 + 12x

Make into slope-intercept form, we have

y = 12x + 10

Hence, the formula is y = 12x + 10

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The slope-intercept form of the equation of line −12x + y = 10 is y = 12x + 10.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the line;

−12x + y = 10

To rewrite in slope intercept form ( y = mx + b ), bring terms containing y to the left and x or constant terms to the write side of the equation.

−12x + y = 10

Add 12x to both sides

−12x  + 12x + y = 10 + 12x

y = 10 + 12x

Reorder in slope intercept form

y = 12x + 10

Therefore, the slope intercept form is y = 12x + 10.

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When Malia joined a gym 14 weeks after Jane did, the value of b was 5.

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.

A car's fuel capacity and efficiency, as well as how far it can go on a single charge of its electric battery, are important considerations. A nonproportional connection can be used to describe this.

a + b = 14

9 + b = 14

b = 14-9 = 5

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As determined in part, the ball reaches its highest point at time t is 2 seconds

S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.

The ball's starting speed is 64 feet per second.

(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).

(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.

(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.

v(t) = 32 - 16t = 0

or 16t = 32

out = 2 seconds.

As determined in part, the ball reaches its highest point at t = 2 seconds (c).

s(t = 2) = 32(2) - 16(2) (2)

2

or 32 feet if s(t = 2).

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