The table represents a proportional relationship. Write an equation to represent the relationship.

Paul's pig pen has a width of 2 feet and an area of 16 square feet is the true statement.

The area of Rectangle is length times of width.

This is a simple calculus problem but it can be solved without calculus, as follows:

let L=length of the pen and W = width

2(L + W) = 20  

L + W = 10

L = 10 - W

Let A = area of the pen

A = Length × Width = 10W - W²

Sketch this parabola which has a positive maximum which occurs at W = 10/2

This means the area is maximum when w = 2, in other words the maximum area occurs when the rectangle is a square.

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

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The statement in algebraic terms is given by 8z-89/8

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The statement " 11¹/₈less than the product of 8 and the number z"

The translation of the statement in the form of an algebraic expression is given by

8z - 11¹/₈

8z-89/8

Hence, The statement in algebraic terms is given by 8z-89/8

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Answer: The graph of f(x) = 2^x and g(x) = 2^x +2 are the same.

Explanation: The functions f(x) = 2^x and g(x) = 2^x + 2 are identical. The only difference between them is the constant term in the second function. This constant term does not change the shape, direction or the relative position of the graph of the function, it only shifts the graph along the y-axis. Because both functions have the same base, the graphs will have the same shape, direction and relative position, regardless of the constant term.

Mean is 27 and SD is 2 then the normal curve ​with highest range would be at domain 27.

The mean is the average of a set of numbers. It is calculated by adding all the numbers in the set together, and then dividing by the number of values in the set.  It is calculated by adding up all the numbers in the set, dividing by how many values there are in the set, and then multiplying by that number. The average of a group of numbers is called the mean.

Mean is 27 and SD is 2

a) P(23<x<27)= P((23-27)/2<z<(27-27)/2)=P(-2<z<0)=P(z<0)-P(z<-2) or P(z<0)-(1-P(z<2))

From normal distribution table we get 0.5-(1-0.9772)=0.4772

b) P(x>31)=P(z>(31-27)/2)=P(z>2) or 1-P(z<2)=1-0.9772=0.0228

c) P(x<29)= P(z<(29-27)/2)=P(z<1)=0.8413

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Parallelograms are quadrilaterals with two sets of parallel sides

Slope Formula: y2-y1/x2-x1

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

KL: 12-7/6-2 = 5/4

LM; 13-12/13-6 = 1/7

MN: 8-13/9-13 = 5/4

KN: 7-8/9-2 = 1/7

We can identify this as a parallelogram since it has congruent angles and sides, which are found on a parallelogram.

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Answer: $3.22 tax

Step-by-step explanation:

7/100 x 46 = $3.22

Answer:3.22$

Step-by-step explanation:3.22$ in the USA

Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".

In this sequence, we can see that the difference between consecutive terms is -6x - 5.

The 9th term of an arithmetic sequence can be found by using the formula:

a_n = a_1 + (n-1)d

Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.

Given the sequence -5x + 2, -11x - 3, -17x -8, ...

The 9th term is:

-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38

Therefore the 9th term of the arithmetic sequence is -53x -38.

Step-by-step explanation:

After solving the value of y is 541.

The value of set A is 281, 268, 225, 290. So

The mean of set A = (281 + 268 + 225 + 290)/4

The mean of set A = 1064/4

The mean of set A = 266

The value of set B = 392, 512, 413, 422, у

The mean of set B = (392 + 512 + 413 + 422 + у)/5

The mean of set B = (1739 + y)/5

The ratio of Mean of Set A : Mean of Set B = 7 : 12

So, 7x = 266

Divide by 7 on both side, we get

x = 266/7

x = 38

Now, 12x = 12 × 38 = 456

The mean of set B = 456

(1739 + y)/5 = 456

Multiply by 5 on both side, we get

1739 + y = 2280

Subtract 1739 on both side, we get

y = 541

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The complete question is:

Here are two sets of numbers, A and B.

 Set A                            Set B

281  268                     392  512  413

225  290                        422  у

Mean of Set A : Mean of Set B = 7 : 12.

Work out the value of y.

The quotient for the given expression is 8x^2-8x+14 and the remainder is -19.  The solution has been obtained using the method of long division of polynomial.

What is polynomial long division?

A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

Using Polynomial Long Division,

Dividing :  8x^3 + 6x - 5 ("Dividend")

By         :    x+1   ("Divisor")

Dividend              8x^3  +  0x^2  +  6x  -  5

- divisor  * 8x^2   8x^3  +  8x^2        

Remainder                     -  8x^2   +  6x  -  5

- divisor  * (-8x)               -  8x^2   -  8x    

Remainder                                       14x  -  5

- divisor  * 14                                     14x +  14

Remainder                                               - 19

Quotient :  8x^2-8x+14

Remainder:  -19

Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.

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Answer: 3.6e+18

Step-by-step explanation: (400 x 9 = 3,600) 10 to the power of 15= 1,000,000,000,000,000 or quadrillion. 9x1,000,000,000,000,000=9e+15x400=3.6e+18

[tex]4y-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies 4\stackrel{y}{\left( -\cfrac{1}{2} \right)}-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies -2-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( -2-\cfrac{1}{2} \right)=6\left( \cfrac{x}{3}-\cfrac{5}{2} \right)}\implies -12-3=2x-15 \\\\\\ -12-3+15=2x\implies 0=2x\implies \cfrac{0}{2}=x\implies \boxed{0=x}[/tex]

The x-intercept of (-2, 0) has both functions. The behavior of the function g(x) for x ⇒ -∞ then g(x) → ∞. The y-intercept of the function f(x)  is (0, 6). And both functions have real roots.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = x³ - 2x² - 5x + 6

g(x) = - x³ + 4x

The factor of the function f(x) is given as,

f(x) = 0

x³ - 2x² - 5x + 6 = 0

(x + 2)(x - 1)(x - 3) = 0

x = -2, 1, 3

The factor of the function g(x) is given as,

g(x) = 0

- x³ + 4x = 0

x = 0, 2, -2

The y-intercept of the function f(x) is given as,

f(0) = (0)³ - 2(0)² - 5(0) + 6

f(0) = 6

The y-intercept of the function g(x) is given as,

g(0) = - (0)³ + 4(0)

g(0) = 0

The graph of the function is given below.

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Step-by-step explanation:

1. MN || LO - ( PARALLEL LINES ) .

2. <NMO = <LOM - ( GIVEN ) .

3. <MLO = <ONM - ( REFLEXIVE PROPERTY ) .

4. ..... - ( AAA S-C ) .

Answer:

f(g(0)) = 12

Step-by-step explanation:

to find f(g(0)) , evaluate g(0), then substitute the value obtained into f(x)

g(0) = 0 + 4 = 4 , then

f(4) = 3(4) = 12

Answer:

w = 11 , x = 25

Step-by-step explanation:

for Δ ABC ≅ Δ TUV, then corresponding sides must be congruent, that is

AB = TU and BC = UV ( using these to create 2 equations )

- 9x + 20w + 89 = 4w + x + 15 ( subtract 4w + x + 15 from both sides )

- 10x + 16w + 74 = 0 → (1)

and

x + w + 41 = - 18w + 11x ( subtract - 18w + 11x from both sides )

- 10x + 19w + 41 = 0 → (2)

multiplying (2) by - 1 and adding to (1) will eliminate x

10x - 19w - 41 = 0 → (3)

add (1) and (3) term by term to eliminate x

0 - 3w + 33 = 0 ( subtract 33 from both sides )

- 3w = - 33 ( divide both sides by - 3 )

w = 11

substitute w = 11 into either of the 2 equations and solve for x

substituting into (1)

- 10x + 16(11) + 74 = 0

- 10x + 176 + 74 = 0

- 10x + 250 = 0 ( subtract 250 from both sides )

- 10x = - 250 ( divide both sides by - 10 )

x = 25

thus the values x = 25 and w = 11 will make the triangles congruent

The required monthly payment for 6.4% of interest is $16846.6.

Interest is the cost of borrowing money or the fee you charge to lend it. Most frequently, interest is shown as an annual percentage of the loan amount. The interest rate for the loan is denoted by this proportion. ​

We have,

Purchasing price = $200,000

Down payment = 5% of $200,000

= $10000

Remaining Amount = $190000

Interest of one year = 6.4%

Amount of interest =  6.4% of $190000

Amount of interest = $12160

Total amount = f $190000 + $12160

Total amount = $202160

Monthly payment = $16846.6

Thus, required monthly payment is  $16846.6.

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The bar representing her 7-day vacation will have a class width of 16 - 22 and a height of 1.

The frequency distribution of a collection of data reveals how frequently each unique value appears.

The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.

In the given histogram class width(horizontal width)  represents the number of days and frequency(vertical height) represents the number of vacations taken.

Therefore, The 7-day vacation yet she took this summer will be represented by a bar having a class width 16 - 22 and a height of 1.

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Jessica gets more rocks to skip across the surface of the pond than Henry.

To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.

For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.

For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.

Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.

We will multiply the numerator and denominator of Henry's ratio by 12 to get -

5/9 x 12/12 = 60/108

Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -

7/12 x 9/9 = 63/108

Comparing the numerators we get 60<63.

This implies that 60/108 < 63/108.

Therefore, Jessica gets more rocks to skip across the surface of the pond.

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The complete question is -

Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks

Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond​?

The range of the function is (d) [150, 275]

The graph that completes the question is added as an attachment

From the graph, we have the following properties:

The range is simply the amount of values between the y axis

In this case represented by the graph, we have:

Minimum y value = 150

Maximum y values = 275

Sinfe both values are inclusive, the range would be [150, 275]

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The monthly payment during the initial period is  about $1,682.94

The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM

The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.

Let us assume that m represents the initial monthly payment.

[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]

where, M is the monthly payment during the initial period

P is the amount on loan

r is the interest rate = 5% = 0.05

n is period = 30 × 12 = 360

Here, P = $313,500

r = 5%

r = 0.05

n =  30 × 12

n = 360

Substituting these values in the above formula we get,

[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]

M  ≈ 1,682.94

Therefore, the monthly payment is about $1,682.94

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As per the given mortgage, the remaining balance be after the first 5 years is $678125

Here Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-years 5/1 ARM at 3. 5% with a 2/7 cap structure.

As we know that the formula for the calculation is written as

=> (Mortgage X Rate)/ 12 months

And then we have to subtract the Monthly PI payment from monthly interest on payment.

When we apply the value on it, then we get,

($465,000 x 3.5)/12

= $135625

Then the amount after 5 years is calculated as,

⇒ $135625 x 5

= $678125

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The long division problem can be used to prove the formula for factoring the difference of two perfect cubes (a-b)(a²+ab+b²).

The difference of two perfect cubes: a³-b³  = (a-b)(a²+ab+b²)

let the two perfect cubes be a³ and b³. Factoring the  difference between these two perfect cubes we have: a³ - b³

First, we need to factorize (a-b)³:

(a-b)³ = (a-b) (a-b)²

(a-b)³ = (a-b)(a²-2ab+b²)

(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³

(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²

(a-b)³ = a³-b³ - 3a²b+3ab²

(a-b)³  = (a³-b³) -3ab(a-b)

Then we will make a³-b³ the subject of the formula from the result equation;

a³-b³ =  (a-b)³+ 3ab(a-b)

a³-b³  = a-b{(a-b)²+3ab}

a³-b³  = a-b{a²+b²-2ab+3ab}

a³-b³  = (a-b)(a²+b²+ab)

a³-b³  = (a-b)(a²+ab+b²)

The long division problem that can be used is (a-b)(a²+ab+b²).

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The slope and the intercept of the function f(x) = -x + 5 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The function for this problem is defined as follows:

f(x) = -x + 5.

Comparing to the standard definition of a linear function, we have that:

The problem asks for the slope and the intercept of the function f(x) = -x + 5.

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The answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a. The solution has been obtained by using the concept of exponents.

What is an exponent?

The exponent of a number shows that how many times a particular number has been multiplied by itself. For instance, the number 2^4 means that we are multiplying the number 2 itself by four times. It is enlarged to 2*2*2*2. An exponent is also known as a number's power. One may use a whole number, fraction, negative number, or decimal.

We are given [tex]\sqrt[4]{125a^{4} }[/tex]

This can be also written as (125a^4)^1/4

Splitting the power, we get

⇒[tex]a^{4^{1/4} } 125^{1/4}[/tex]

⇒a 125^0.25

⇒a 3.34

⇒3.34a

Hence, the answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a.

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Since there are multiple questions so, the question answered above is

[tex]\sqrt[4]{125a^{4} }[/tex]

The number of hamsters as a function of the cycle number, c, can be represented by the equation:

f(c) = 5 * 3^c

This equation was determined by the fact that the population triples every cycle and the starting number of hamsters is 5. The function notation is f(c) which represents the number of hamsters as a function of the cycle number. The base of the equation is 3, which represents the rate at which the population triples. The exponent is c, which represents the cycle number. The coefficient is 5, which represents the starting number of hamsters.

The number of terms in the algebraic expression 6y + 14 is 2 terms

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

6y + 14

Consider an expression given as

ax + b

The number of terms in the expression is 2 and the terms are ax and b

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

6y + 14 has 2 terms

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Complete question

Identify the number of terms and then the resend themselves for each algebraic expression

6y + 14

This statement is False.

The formula provided in the statement is used to calculate the variance of the sample mean difference between two independent samples, but it is not necessarily true that the sample variances, and , are independent of one another.

The sample variances are calculated based on the data from their respective samples, and thus their relationship will depend on the specific data and the underlying population distributions.

For example, let's consider two samples of size n = 25, one from a normal population with mean 100 and variance 10, and another one from a normal population with mean 110 and variance 20. The sample variances for each sample are:

S1² = 9.6 and S2² = 20.8

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1 gallon of water must be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7%.

Let x = amount of water required

7 gallons + x gallons = (x + 7) gallons of mixture

For x gallons of water, we have 0 gallons of insecticide

For 7 gallons of 8% insecticide solution, we have 0.08(7)=0.56 gallons of insecticide

According to the question, we get the equation as follows

0.07(x + 7) = 0.56

7(x + 7) = 56

x + 7 = 8

x = 1 gallon

Therefore, the amount of water that needs to be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7% is 1 gallon.

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A perfect square is a number obtaining by squaring a whole number

A perfect square can be defined as a number that is being expressed as the product of an integer by itself.

It is also seen as the second exponent of an integer.

In determining the perfect of a number, when you multiply an integer which could be a “whole” number, positive, zero or negative) by itself, the product of the multiplication is termed a square number, or a perfect square.

Perfect square is also described as a number made by squaring a whole number.

Some perfect squares in mathematics are;

Number 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 139, 144, etc

Hence, a perfect square is described as a number that is the product of an integer with itself.

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