A teacher plans to use a 40-inch long roll of string to form a border around a rectangular space on her bulletin board reserved for student use. What is the maximum amount of space, in square inches, that she can reserve on her bulletin board using this roll of string?

The total population, h(x): of bison in the two regions 0f the park X years after 2010 is h(x) = 1050(1.14)ˣ. So the option a is correct.

The following functions represent the population of bison in two regions of a wildlife park; where X is the number of years since 2010.

f(x) = 600(1.14)ˣ

g(x) = 450(1.14)ˣ

We must tell the function that represents the total population of bison in the two park regions x years after 2010.

h(x) = Total Population

So, h(x) = f(x) + g(x)

Now put the value of f(x) and g(x)

h(x) = 600(1.14)ˣ + 450(1.14)ˣ

Take (1.14)ˣ on both side, we get

h(x) = (600 + 450)(1.14)ˣ

h(x) = 1050(1.14)ˣ

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The complete question is:

The following functions represent the population of bison in two regions of a wildlife park; where X is the number of years since 2010.

f(x) = 600(1.14)ˣ

g(x) = 450(1.14)ˣ

Which function represents the total population, h(x): of bison in the two regions 0f the park X years after 2010?

h(x) = 1,050(1.14)ˣ

h(x) = 1,050(2.28)²ˣ

h(x) = 1,050(1.14)²ˣ

h(x) = 1,050(2.28)ˣ

Andy should write $507.18 for the balance on January 30. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations can be used to express any real number.

1. To determine the total of the numbers, use the addition operator ('+').

2. Use the sign "-" when subtracting to find the differences between the numbers.

3. Multiply when the result is the product of the numbers.

4. Dividing the numbers produces their quotient.

We are given that the amount balance on January 24 is $104.47 and she deposited $407.71 on January 30.

So, the amount Andy should write for the balance on January 30 is

⇒$104.47 + $407.71

⇒$507.18

Hence, Andy should write $507.18 for the balance on January 30.

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Luca picks his number first. then, craig picks a number from the remaining cards, these two events are Dependent.

Total number of cars are 25,

Luca picks randomly a card so probability is now 1/25 and total number of cars are now 24.

If craig have to pick then the probability of it becomes 1/24 as one card was already picked by the Luca,

So this indicated that these two events are Dependent.

In probability, dependent events are those whose occurrence influences the likelihood of occurrence of another event. Imagine there are 3 red and 6 green balls in a bag. One after the other, two balls are taken out of the bag.

Let A represent the first draw's red ball draw and B represent the second draw's green ball draw. If the first draw's ball is not put back in the bag, then A and B are dependent events because P(B) changes depending on whether the first draw's ball was red or green.

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Step-by-step explanation:

A line that is parallel to another line has the same slope but a different y-intercept. The slope of the line through the points (1,-2) and (-6,3) can be found using the slope-point formula:

slope = (y2 - y1) / (x2 - x1) = (3 - (-2)) / (-6 - 1) = 5/7

So, a line that is parallel to this line would have the same slope of 5/7. To find an equation for a line with this slope that passes through a different point, we can use the point-slope formula:

y - y1 = m * (x - x1)

Where m is the slope and (x1, y1) is a point on the line. We can choose any point to use in this formula, but a common choice is the origin (0,0). So, plugging in the values we have:

y - 0 = 5/7 * (x - 0)

y = 5/7 * x

This is the equation for a line that is parallel to the line through the points (1,-2) and (-6,3) and passes through the origin.

The equation of the line to commute the time is written as y = -1/2x + 24.5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The given points are (1,24) and (15,17). To write the equation of the line first calculate the slope of the line and then find the y-intercept of the line.

Slope =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 17 - 24 ) / ( 15 - 1 )

Slope = -7 / 14

Slope = -1 / 2

The y-intercept is:-

y = mx + c

24 = -1/2 + c

c = ( 48 + 1 ) / 2

c = 49 / 2

c = 24.5

The equation of the line can be written as:-

y = mx + c

y = -1/2x + 24.5

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The solution of the piecewise function at the given values of the independent variable g(0) is 5, g(-7) is 12 and g(2) is 7.

This is an example of a piecewise function, which is a function composed of two or more parts, each part being defined by a separate equation.

In this function, the first part is defined as g(x) = x+5 if x >= -5, and the second part is defined as g(x) = -(x+5) if x < -5.

To evaluate the function at the given values of the independent variable, we can simply substitute the values into the appropriate equation.

At x = 0,

=> g(0) = 0+5 = 5.

At x = -7,

=> g(-7) = -(-7+5) = 12.

And at x = 2,

=> g(2) = 2+5 = 7.

Therefore, the values of the function are 5, 12, and 7 respectively

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The total Messages that Tammy, Felipe, and David sent are 30, 50, and 45 messages respectively.

Let's denote the number of text messages sent by Tammy as x, Felipe as y, and David as z. Based on the information given, we have:

y < x and z = 3y.

The total number of messages they sent is x + y + z = x + y + 3y = 4y + x.

Since the total number of messages sent is not specified, we can choose an arbitrary value for the total number of messages. Let's choose 90 messages. Then, we have:

4y + x = 90

x = 90 - 4y.

Substituting z = 3y into x = 90 - 4y, we get:

3y = 90 - 4y

7y = 90

y = 90/7 = 15.

Plugging y = 15 into x = 90 - 4y, we get:

x = 90 - 4 * 15 = 30.

Therefore, Tammy sent 30 messages, Felipe sent 15 messages, and David sent 45 messages.

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The pattern tells that the amount raised by Robert in 26th mile is $90.

What is a pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

The amount of money raised by Robert for first mile = $5

The amount of money raised by Robert for second mile = $6

The amount of money raised by Robert for third mile = $7.2

The difference between amount raised in first and second mile = $1

The difference between amount raised in second and third mile = $1.2

Similarly, the difference between amount raised in third and fourth mile will be = $1.4

Similarly, the difference between amount raised in fourth and fifth mile will be = $1.8

Following this pattern the difference between 25th and 26th mile will be = (26 × 0.2) + 0.4 = $5.8

Now, the amount raised in 26th mile = 84.2 + 5.8 = 90

Therefore, the amount raised is $90.

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The picture below shows the graph of the  inequality of x² ≤ 4

Option C is correct.

In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.

A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

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The measures of x, y and z are 40⁰, 90⁰ and 50⁰

A triangle is a three-sided polygon that consists of three edges and three vertices.

We know that co-interior angles are supplementary.

∠APQ+∠CPQ=180⁰

x+∠CPQ=180⁰

x+140⁰=180⁰

x=40⁰

∠BPR+∠PRD=180⁰

z+130⁰=180⁰

z=50⁰

Now, angles x, y and z form a line, hence they sum up to 180∘.

x+y+z=180⁰

40⁰+y+50⁰=180⁰

y=90⁰

Hence, the measures of x, y and z are 40⁰, 90⁰ and 50⁰

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The question is not complete, similar kind of question is given below.

In the given figure, AB || CD. Find the measure of x, y and z.

The expressions that show the number of students for each activity are;

Note that this is a fraction problem.

We are given;

Total number of students in the middle school = x

A) From the given table, we can deduce that;

B: Now, the expression to show the students that like either drama or dance is;

(1/7)x + 26 + (1/7)x + 22

⇒(2/7)x + 48

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Full Question:

A middle school with x students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

Therefore , the solution of the given problem of expression comes out to be C) -3.5 , D) -0.75 and E) -1/3 .

Math requires the use of arithmetic, algebra, and divisions. They result in the following when combined: An equation, some statistics, and a mathematical function Values, factors, and mathematical processes like adding, addition and subtraction, complex numbers, and division can all be found in a statement of fact. Different words and terms can be analysed and evaluated.

Here,

Thus , numbers below is less than -1.2

C) -3.5

D) -0.75

E) -1/3

Therefore , the solution of the given problem of expression comes out to be C) -3.5 , D) -0.75 and E) -1/3 .

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The complete question is "Which of the numbers expressions below is less than zero? Select all that apply.

A) 1.2

B) 7/2

C)-3.5

D)-0.75

E)-1/3"

When solving problems that contain exponents, we must know the value of both elements for the result to be correct. This ability can be improved by knowing how to multiply very well.

An exponent is a mathematical expression that tells us that a value must be multiplied by itself a certain number of times, the most common exponent is the square in which a value must be multiplied by itself once, for example:

To improve in problems with exponents we must know how to multiply very well because this is the basic operation that is most related to solving exponents.

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the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞)

A function is described as a relation among a fixed of inputs having one output every. In easy words, a feature is dating among inputs in which every entry is associated with precisely one output.

Given, The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours

Part A:

f(x) = 20x + 80

F(2) = 20*2 + 80

F(2) = 120

g(x) = x + 2

g(2) = 2 + 2

g(2) = 4

Part B: f(x) divided by g(2)

=> f(x) / g(2)

=> (20x + 80 ) /4

=> 5x + 20 (since, g(2) is 4)

Part C:  the domain of f divided by g of x

So,

f(x) / g(x ) = (20x + 80)/(x +2)

=>  (20x + 80)/(x +2)

Since Denominator can not be zero.

Therefore, the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞).

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Answer: The lateral surface area of the cylinder can be found using the formula: πr h, where r is the radius and h is the height of the cylinder.

Given that the height of the cylinder is 22 ft, and the diameter is 6 ft, the radius can be found by dividing the diameter by 2: r = 6 / 2 = 3 ft.

So the lateral surface area of the cylinder is: πr h = π * 3 * 22 = 66 * π ≈ 208.36 sq ft.

Rounding to the nearest hundredth, the lateral surface area of the cylinder is 208.36 sq ft.

Step-by-step explanation:

Step-by-step explanation:

4(a- 7) = 4×a-(7×4)

= 4a-(28)

= 4a-28.

Both graphs show the same relationship between Clem's waist height and time, but the exponential graph shows a more rapid increase in Clem's waist height over time.

Both graphs depict the relationship between Clem's waist height and time. The first graph is linear and is represented by the equation y = 2x + 3, where y is Clem's waist height and x is the amount of time that has passed. The second graph is exponential and is represented by the equation y = 2^x + 3. Both graphs show that Clem's waist height increases with time – the difference is that the linear graph shows a steady, linear increase, while the exponential graph shows an exponential increase. For example, if Clem's waist height was 3 inches at the start, then after 1 hour it would be 5 inches on the linear graph, but 8 inches on the exponential graph. This difference can be seen in the calculations: 1 hour on the linear graph would be 3 + (2 x 1) = 5 inches, while 1 hour on the exponential graph would be 3 + (2^1) = 8 inches.

In summary, both graphs show the same relationship between Clem's waist height and time, but the both graphs show the same relationship between Clem's waist height and time, but the exponential graph shows a more rapid increase in Clem's waist height over time.

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Answer:

The dimensions of a cylinder that will maximize volume would be radius = 10 cm and height = 30 cm.

Answer:

18

Step-by-step explanation:

56 copies

sold 1/4 *56 = 14 copies

42 copies left

4/7 * 42 = 24 copies sold

remaining 42-24 = 18

Not merely a cluster of random elements, a narrative presents an ordered series of events connected by the logic of cause and effect.

A narrative depicts an ordered set of events linked by the logic of cause and effect, not just a collection of random pieces. In tales, the sequence of events is linear, making it evident to the viewer the motivation behind and effects of character behavior.

The sequence of events in a story is referred to as the story. Simply put, sequencing a story is determining the beginning, middle, and end of the story as a first step toward retelling the events in a logical order.

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Answer:

Step-by-step explanation:

99x99= 9801

Answer: 9,801

Step-by-step explanation: first you write the numbers down like this

99

x99

then you multiply the numbers

Answer:Irrational,2/9,22/100 11/50, Irrational, No Fraction Given, Perfect Square, Non-Perfect Square

Step-by-step explanation:Best fit options for each question.

[tex]8-6n=-58\\6n=66\\n=11[/tex]

[tex]11\in\mathbb{N}_+[/tex] therefore it is.

-58 is not a term of this sequence.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We can check if -58 is a term of this sequence by substituting -58 for n in the formula for the nth term:

8 - 6n

= 8 - 6(-58)

= 8 + 348

= 356

Since -58 does not result in 356, we can conclude that -58 is not a term of this sequence.

Thus,

-58 is not a term of this sequence.

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0.028. is the probability .

Describe probability using an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

Total sample space = 6*6 = 36

A) Sample space for sum of 1 = 0

So probability of getting a sum of 1 = 0

B) sample space for sum of 5 = {(1,4) , (2,3), (3,2), (4,1)}

So probability of getting a sum of 5 = 4/36 = 0.11

C) sample space for sum of 12 = (6,6)

S, probability of getting a sum of 12 = 1/36 = 0.028.

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Answer:

-6

Step-by-step explanation:

using the rules of exponents

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

• [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]

then

- 18 × [tex]9^{-\frac{1}{2} }[/tex]

=-  18 × [tex]\frac{1}{9^{\frac{1}{2} } }[/tex]

= - 18 × [tex]\frac{1}{\sqrt{9} }[/tex]

= - 18 × [tex]\frac{1}{3}[/tex]

= -6

Answer: The answer should be -6

Step-by-step explanation:

18(9^−1/2)

= −18(9^−1/2)

= (−18)(0.333333)

= −6

So, what you want to do is first solve 9^-1/2, it will come out to be about 0.333333

You are going to put 0.333333 in for 9^-12 and then multiply:

-18(9^-1/2) = (-18)(0.333333)

(-18)(0.333333) = -6

The distance further you have to walk is 5 / 8 miles.

You want to walk from home to a shoe store that is 7/8 miles away. You stop for a rest after 1/4 miles. The distance you have to walk can be calculated as follows:

Therefore,

distance you have to walk = 7 / 8 - 1 / 4

distance you have to walk =  7 - 2 / 8

distance you have to walk = 5 / 8

Therefore, the distance you have to walk is 5 / 8 miles

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The rational number representation of Micah withdrawing $4.50 from his bank account is -4.5.

A rational number is any fraction with non-zero denominators. A rational number can be written as a fraction with a numerator and denominator that are both integers.

In this case, we can write $-4.50$ as the fraction $\frac{-450}{100}$, where the numerator represents the amount of money withdrawn (in cents) and the denominator represents the unit of currency used (in this case, 100 cents = 1 dollar).

So, the rational number representing the amount of money withdrawn from Micah's bank account is {-450} / {100}$ = -4.5.

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the sin(Ф) trigonometric function can be used to calculate its y component.

What is vector?

Latin word for "carrier" is "vector." Point A is transported to point B by vectors. The direction of the vector AB is the direction in which point A is moved in relation to point B, and the magnitude of the vector is the length of the line connecting the two points A and B. The terms Euclidean vectors and spatial vectors are also used to refer to vectors. Having both magnitude and direction, vectors are geometrical objects. An arrow pointing in the direction of a vector's magnitude and a line representing the vector's direction can be used to depict a vector. Since they have starting and ending points, vectors are symbolized by arrows.

component of a vector along the y-axis is a product of the length of vector and the sine of the angle of a vector with the x-axis.

the trigonometric function can be used to calculate its y component.

Then sin(Ф) trigonometric function can be used to calculate its y component.

Hence the sin(Ф) trigonometric function can be used to calculate its y component.

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