Paul wants to create a rectangular pig pen using 20 feet of fencing or less. To help determine the possible areas of the pig pen, Paul created a quadratic inequality. A(w) represents the possible total areas in feet2 of the pig pen with respect to width, w, in feet. The graph of the quadratic inequality is shown below:
Which of the following statements could be true about Paul's pig pen?

Select ALL that apply
Paul's pigs will have the maximum possible area if the pen has a width between 3 and 4 feet.


Paul's pig pen has a width of 3 feet and an area of 2 feet2.


With a pen width of 7 feet, Paul could still place 4 pigs in the pen and get them each an average space of approximately 5 feet2.


Paul's pig pen has a width of 2 feet and an area of 16 feet2.


Paul's pig pen h as a width of 16 feet and an area of 8 feet2.

By applying the proportional relationship formula, the height of the barn is 45 ft.

In a proportional relationship, each pair of data points is related in the same way, typically by multiplying them together. A proportionate relationship can be seen in a set of numbers, an equation, or a graphical representation. In this case, we are given that :

The height of the farmer (X1)  = 6 ft

The height of the farmer’s shadow (Y1) = 10 ft

The height of the barn with farmer’s shadow (Y2) = 75 ft

To calculate the actual height of the barn (X2), we can use this following formula:

X1 : Y1 = X2 : Y2

6 : 10 = X2 : 75

X2 = (6 : 10) x 75

X2 = 45

Thus, the height of the barn is 45 ft

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Correct option is A, (1,2) is the correct option for the given system of equations.

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system).

The number of equations must match the number of unknowns for a system to have a singular solution.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

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(3,2) the eqaition would be y=3/2x+3

The slope of a line in the xy plane b = 13/3

The slope of a line in the xy plane can be calculated by using the equation m = (y2-y1)/(x2-x1). In this equation, m is the slope, x1 and y1 are the coordinates of the first point, and x2 and y2 are the coordinates of the second point.

Using this formula, we can solve for b.

m = (y2 - y1) / (x2 - x1)

8/3 = (b - (-1)) / (2 - (1/2))

24/3 = (b + 1) / (5/2)

24/3 * (5/2) = (b + 1)

40/3 = b + 1

40/3 - 1 = b

b = 13/3

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Answer:

Quadratic

Step-by-step explanation:

The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches it maximum height and then starts dropping back to ground at increasing speeds due to positive acceleration exerted by the force of gravity.

The flight path of the parabola can thus be modeled by height as a function of elapsed time

h = f(t) where f(t) is a quadratic equation in t with the general form being

a · t² +b · t  + c

We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever

The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However we know from observation that the firework has the highest speed at the moment of launch

Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.

The note says:
Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.

Indeed the actual path of the firework is a reflection of the graph about the x axis. so that it is a downward facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.

The height would be the y axis and time t the x-axis

The answer is 4^2. Step-by-step explanation: This is because 4 squared is 4*4 which equals 16.

On solving the linear equations x + 3y = 5 and -3x - 2y = 20, the value for x is x = -10 and the value of y is y = 5. When solved independently the value is obtained as -2x + y = 25.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - x + 3y = 5

The second linear equation is - -3x - 2y = 20

On evaluating individually the equation obtained is -

-3x - 2y + x + 3y = 20 + 5

-2x + y = 25

Multiply equation (1) with 3 -

3(x + 3y) = 5 × 3

3x + 9y = 15.....(3)

Adding equation (3) and (2) -

-3x - 2y + (3x + 9y) = 20 + 15

-3x - 2y + 3x + 9y = 35

-2y + 9y = 35

7y = 35

y = 35/7

y = 5

Substituting the value of y in equation (1) -

x + 3y = 5

x + 3(5) = 5

x + 15 = 5

x = 5 - 15

x = -10

Therefore, the value of x and y is -10 and 5 respectively.

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Answer:

The new printer prints 100 pages about 4 minutes faster than the old printer

The new printer prints 22 move pages per minute than the old printer

Step-by-step explanation:

New printer's equation

y = 37x

Old printer's equation

y = 15x  

Since the graph is proportional you can take any ordered pair (except (0,0) and put it the form y/x to find the slope. For example, The point (2,30) 30/2 = 15 or the point (4, 60) 60/4 = 15 and so on.

The difference between the rates is 22 pages a minute (37 - 15).

Substituted in 100 for y and solve for x (minutes)

New:

y = 37x

100 = 37x  Divide both sides by 37

100/37 =37x/37

3 = x  This is rounded

This means that it takes about 3 minutes to print 100 pages.

Old:

y = 15x

100 = 15x  Divide both sides by 15

100/15 = 15x/15

7 = x   This is rounded

This means that it takes about 7 minutes to print 100 pages.

The new printer can print the same amount of page (100) in 4 less minutes (7-3)

The point where the two lines intersect each other is (2,5).

What are simultaneous equations?

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an endless number of solutions.

When two lines intersect each other, the point of intersection is a point common to both lines.

This can be found by solving simultaneous equations.

The given equations of the two lines are

3x+y = 11

4x-y = 3

Adding the above equations, we can remove the y variable.

The result is 7x = 14

x = 2

Now we substitute this value of x in either of the above equations to get the value of y.

3 * 2 + y = 11

y = 11 -6 = 5

Therefore the point where the two lines intersect each other is (2,5).

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The equation which represents Lisa's earnings, e, relative to the number of hours, h, that she works assume a proportional relationship is e = 7.5h

Amount Lisa makes for babysitting = $30

Number of hours Lisa babysit = 4 hours

Total earnings = e

Number of hours = h

If the relationship is proportional, then

k = constant of proportionality

e = k × h

30 = k × 4

30 = 4k

divide both sides by 4

k = 30/4

k = 7.5

So therefore,

e = k × h

e = 7.5 × h

e = 7.5h

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Answer:

Step-by-step explanation:

A sample of size 40 is a valid sample size and could result in a sample statistic, as explained above, the correct answer is B.

What is the sample statistic?

A sample statistic is a measure calculated from a sample of the population, while a population parameter is a measure calculated from the entire population. Therefore, a sample statistic may differ from a population parameter due to sampling variability.

Out of the options provided, only option B (40) could result in a sample statistic but not a parameter.

This is because a sample of size 40 is a subset of the population, and a statistic calculated from this sample (such as the sample mean or sample proportion) would be a sample statistic.

Option C (4000) would result in both a sample statistic and a population parameter because a sample consisting of the entire population is a census, and any measure calculated from this sample would also be a parameter.

Option A (both 40 and 4000) and option D (neither 40 nor 4000) are not correct because 4000 is not a valid sample size, as it includes the entire population and would therefore be a census.

Hence, a sample of size 40 is a valid sample size and could result in a sample statistic, as explained above, the correct answer is B.

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The mixed fraction in the simplest form is 21/20, and the snowfall in December was almost 5 times more than the snowfall in January.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 seems to be the quotient and 1 is the remainder. An amalgam of a whole integer and a legal fraction is a mixed fraction.

Given that the amount of snowfall in January was:

[tex]1 \frac{1}{20}[/tex]

To convert the mixed fraction to simplest form, multiply the denominator with the value and add it to the numerator:

[tex]21/20 = 1.05[/tex]

The amount of snowfall in December is:

[tex]5 \frac{2}{24} = 5 \frac{1}{12}[/tex]

To convert the mixed fraction to simplest form, multiply the denominator with the value and add it to the numerator:

[tex]\frac{61}{12} = 5.08[/tex]

Hence, the snowfall in December was almost 5 times more than the snowfall in January.

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Step-by-step explanation:

please see the attached fir details

If a new I phone costs $799 and is estimated to lose 25% of its value every six months after its purchase ,then the value of phone after 2 years is $253  .

The cost of new i phone is = $799 ;

the percent loss in the value after every 6 month is = 25% = 0.25  ;

in 2 years , there are 4 period of six months , so , n = 4  ;

The depreciated value of i phone can be calculated by formula ;

⇒ Value = Cost × (1 - 0.25)ⁿ ;

Substituting value of n =4 and cost = $799 ;

⇒ Value = 799 × (1 - 0.25)⁴ ;

⇒ Value = 799 × (0.75)⁴ ;

⇒ Value = 799 × (0.75)⁴ ;

⇒ Value = 799 × 0.31640625 = 252.8085 ≈ 253 .

Therefore , the value of the phone after 2  years is $253  .

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The expression of (²/₃)⁻¹ without an exponent is given as;

3/2

The different laws of exponents are;

1) Power Law of Exponents which is expressed as; (x^m)ⁿ = x^(mn)

2) Quotient Law of Exponents is expressed as; x^m ÷ x^n = x^(m - n)

3) Product Law of Exponents is expressed as; x^(m) * x^(n) = x^(m + n)

4) Law of Reciprocal is expressed as; a⁻ⁿ = 1/aⁿ

Now, we want to rewrite the expression (²/₃)⁻¹ without using an exponent.

From the law of reciprocal of exponents we can say that;

(²/₃)⁻¹ = 1/(²/₃)

= 3/2

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Answer: 40 cm

Step-by-step explanation: 2/5 x 100 =

200/5 = 40

When using percent slope to get tree height, the tree is the rise, and the horizontal distance from the tree with the ground is the run. We can simply measure our horizontal distance from the tree, and we have instruments for gauging the percent slope to the top of a tree.

Hence, with those two measures (run and %slope) we can solve for rise.

You Total up all the trees.

let the average of number of trees are:

3+3+8+10+5+2=31

then you subtract the amount of trees under 75 feet in height.

31-8-3-3=14

divide the number of trees 14 under 75 ft in height by the total amount of trees31.

14/31=0.4516

0.4516=45.2

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180 - 115 = 65

4k + 5 + 6k + 10 + 65 = 180

10k + 80 = 180

10k = 100

k = 10

Answer: To find the values that make the inequality -v <= -8 true, we can first isolate v on one side of the inequality. We do this by adding v to both sides:

-v <= -8

v >= 8

This inequality states that the only values that make it true are those greater than or equal to 8.

Another equivalent inequality in terms of v would be v>=8

So, the values that make the inequality -v <= -8 true are v >= 8

Step-by-step explanation:

The correct answer is Between 157,500 and 968,187 phones.

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George is not correct because we can find the least common multiple of 8 and 6 which is 24. This allows us to solve the problem with simple numbers and ease our calculations to get the answer in the simplest form.

The equation solved by George is 3/8 - 1/6 = 18/48 - 8/48

To solve the given fractions in the simplest form, we will find the common denominator which would be the least common multiple of both denominators.

we can see that the numbers in the denominator are 8 and 6.

Multiples of 8: 8, 16, 24, 32, 40,...

Multiples of 6: 6, 12, 18, 24, 30,...

Hence, LCM of 8 and 6 is 24.

thus we can solve the equation as follows -

3/8 - 1/6

= 3*3/8*3 - 1*4/6*4

= 9/24 - 4/24

= 5/24

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For given frequency table the relative frequency table with percentage is given in image.

What is a frequency table ?

A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.

e.g.

A, A, A, B, B, B, B, C, C, D

Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:

Frequency of A = 3

Frequency of B = 4

Frequency of C = 2

Frequency of D = 1

Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.

Now,

To find the percentage for relative frequency table we used (given value/Total people)*100.

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The area of the shaded part of the rectangle is 152 cm².

The area of the shaded part is the difference between the area of the larger rectangle and the smaller square.

Area of the shaded part = area of the larger rectangle - area of the square

Area of the larger rectangle = length x width

12cm x 18cm = 216 cm²

Area of the square = length²

= 8² = 64 cm²

Area of the shaded part = 216 - 64 = 152 cm²

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Answer:

Step-by-step explanation:

The number O is the Hcf of the two numbers L and O. This is only possible if the number O is the highest common factor of the two.

The highest number among all of the common factors of something like the given numbers is known as the HCF (Highest Common Factor) for two or more numbers.

Similarly, for the given question.

The number O is the Hcf of the two numbers L and O. This is only possible if the number O is the highest common factor of the two.

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The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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Mrs. Byrne mowed 1/4 of her lawn. Her son mowed 2/7 of it.  Mrs. Byrne mowed most of the lawn. The lawn still needs to be mowed is 13/28.

Mrs. Byrne mowed of his lawn = 2/7

Her son mowed of his lawn = 1/4

We firstly equal the denominator of both fraction by taking the LCM of both numbers.

The LCM of 7 and 4 is 28.

So we multiply and divide by 4 in the fraction 2/7 and by 7 in fraction 1/4. Now,

Mrs. Byrne mowed of his lawn = 2/7 × 4/4 = 8/28

Her son mowed of his lawn = 1/4 × 7/7 = 7/28

Now we compare the both fraction 8/28 and 7/28. The 8/28 is greater than 7/28. So we can say that Mrs. Byrne mowed most of his lawn.

The total lawn is 28/28.

So, the remaining lawn for mowed = 28/28 - (8/28 + 7/28)

The remaining lawn for mowed = 28/28 - (8 + 7)/28

The remaining lawn for mowed = 28/28 - 15/28

The remaining lawn for mowed = (28 - 15)/28

The remaining lawn for mowed = 13/28

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The complete question is:

Mrs. Byrne mowed 2/7 of his lawn. Her son mowed 1/4 of it. Who mowed most? How much of the lawn still needs to be mowed?

for any value of n, the nth term of the equation will be:

Aₙ = -3* 2ⁿ⁻¹

A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.

From the general formula of the nth term of the geometric sequence:

Aₙ = A₁* rⁿ-1

Given a geometric sequence:

-3, -6, -12, 24,.....

From the general formula of the nth term of the geometric sequence:

Aₙ = A₁* rⁿ⁻¹

in our case

a₁ = -3

ratio(r) = -6/-3 = 2

Thus for any value of n, the nth term of the equation will be

Aₙ = -3* 2ⁿ⁻¹

For instance,

8th term of the given sequence:

A₈ = -3* 2⁸⁻¹

A₈ = -3* 2⁷

A₈ = -384

Therefore, for any value of n, the nth term of the equation will be

Aₙ = -3* 2ⁿ⁻¹

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Answer: B. x + 52

Step-by-step explanation:

The unknown number is represented as x.

The phrase "52 more than" means adding 52 to something

From this we can say that the expression is B. x + 52