what are her monthly payments

The correct representations of the given inequality -3(2x - 5) < 5(2 - x) include the following:

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numbers and variables in an algebraic equation, especially based on any of the following inequality symbols:

For this exercise, we would evaluate and simplify the given inequality so as to enable use determine its solution as follows:

-3(2x - 5) < 5(2 - x)

Opening the bracket, we have:

-6x + 15 < 10 - 5x (correct representation)

Rearranging the algebraic equation by collecting terms, we have:

-6x + 5x < 10 - 15

-x > -5

x > 5 (correct representation)

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The required pounds of peanut that can make one pound of peanut butter is given as 5 1/3

If  2/3 pounds of peanut = 1/8 pounds of peanut butter

? quantity of peanut = one pound of peanut butter

This would be better expressed in numbers as

2/3 = 1/8

? = 1

To solve for this , we would have to cross multiply

such that we would have

2/3 = 1/8?

to get the unknown, we have to divide through by 1/8

2/3 ÷ 1/8 = unknown

2/3 x 8/1

= 16/3

= 5 1/3

Hence the required pound that would be needed to make the peanut butter is given as 5 1/3

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Answer: x=25/4 or 6.25, y=79/16 or 4.9375

Step-by-step explanation:

Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.

[tex]7x^2+7y^2-28x+42y-35=0 \\ \\ x^2 +y^2-4x+6y-5=0 \\ \\ x^2+y^2-4x+6y=5 \\ \\ x^2-4x+4+y^2+6y+9=18 \\ \\ \boxed{(x-2)^2+(y+3)^2=18}[/tex]

So, the center is [tex](2,-3)[/tex] and the radius is [tex]3\sqrt{2}[/tex].

Answer:

D? I'm not sure tho so don't be mad if it's wrong

Answer: (0.4k+0.6w)

Step-by-step explanation:

the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.

The total volume of the solution as an algebraic expression is

0.4k + 0.6w.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount of acid added to the solution = 40% of k  

Amount of water added to the solution= 60% of w

Now,

The total volume of the solution.

= 40% of k + 60% of w

= 40/100 x k + 60/100 x w

= 0.40k + 0.60w

Thus,

The volume is 0.4k + 0.6w.

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After 9 months each car will have the same number of miles on it.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here,

Let miles per month be x.

then, by a linear equation, we get

4298 + x(426) = 6129 + x(223)

203x = 1831

x = 9 months

Hence, after 9 months each car will have the same number of miles on it.

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Equation for the perpendicular bisector of the line segment is  

2y = 3x +20.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

Given coordinates of the endpoints of a line segment  (-9, 3) and (-3,-1).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between  (-9, 3) and (-3, -1). :

slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 3/2

Now, we need to find the midpoint of the given coordinates.

[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - 1 = 3/2 (x + 6)

2y = 3x +20

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]

The standard deviation of the sampling distribution is 0.01767.

Standard deviation is a measure of the amount of variability or spreads in a set of data.

It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.

We have,

Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:

[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]

where p is the population proportion and n is the sample size.

In this case,

p = 0.53 (as given in the problem) and n = 400.

Substituting these values into the formula, we get:

[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]

(rounded to five decimal places)

Therefore,

The standard deviation of the sampling distribution is 0.01767.

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The proposition ~ (~ q ⇒ p) ⇒ ~ q represents a tautology, as it is true for all combinations of p and q.

Propositions are constructions that contains a truth value, which are two according to classical logic (T - true, F - false). There are simple propositions and compound propositions. Compound propositions are formed by combining simple propositions and operators. There are the following operators:

A tautology is a compound proposition that is always true. We can prove whether a proposition is a tautology by the use of a truth table:

p        q      ~ q       ~ q ⇒ p        ~ (~ q ⇒ p)       ~ (~ q ⇒ p) ⇒ ~ q

T        T        F              T                      F                           T

T        F        T              T                      F                           T

F        T        F              T                      F                           T

F        F        T              F                      T                           T

The proposition ~ (~ q ⇒ p) ⇒ ~ q is a tautology.

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Answer:

x= -2, -10

Step-by-step explanation:

(x+6)^2-16=0

(x+6)(x+6)-16=0

x^2+6x+6x+36-16=0

x^2+12x+20=0

10+2=12

10(2)=20

(x+2)=0

(x+10)=0

x= -2, -10

All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Birdseed that costs ​$0.67 a pound and sunflower seeds that cost ​$0.97 a pound. Angela​ Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for ​$0.79 per pound.

Assume that she used [x] pound and [y] pound of each type. We can write -

0.67x + 0.97y = 0.79 x 30

0.67x + 0.97y = 23.7

Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

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Answer:

3.45

Step-by-step explanation:

this is how it is supposed to be

The coordinates of P is ( -1 , 0.5) .

What is section formula ?

  We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.

Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex]  in the ratio of m:n then,

=>  (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]

Here A[tex](x_1,y_1)[/tex] =( -3,2) and  B[tex](x_2,y_2)[/tex]  = (5,-4)  and m:n = 2:6

Then,

=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]

=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]

=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]

=> (x,y) = (-1,0.5)

Hence the coordinates of P is (-1 , 0.5) .

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The four terms of the series will be equal to 14,20,26, and 32.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation for the series is given as, t(n) = 6n + 8. The series will be formed as,

t(n) = 6n + 8.

t(1) = 6 x 1 + 8 = 6 + 8 = 14

t(2) = 6 x 2 + 8 = 12 + 8 = 20

t(3) = 6 x 3 + 8 =  18 + 8 = 26

t(4) = 6 x 4 + 8 = 24 + 8 = 32

Therefore, the four terms of the series will be equal to 14,20,26, and 32.

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The expression that represents the number of tiles on Wendy's kitchen floor is B. 8 × 8t.

An expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Wendy lays rows of 8 tiles each to cover her kitchen floor.

Let t = the number of rows.

Therefore, the number of tiles on Wendy's kitchen floor will be:

= 8 × 8t.

Therefore, the correct option is B.

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The figure given can be classified into; rhombus, quadrilateral, square.

The correct answer option is option c

Quadrilateral: This is a polygon with four sides.

Rhombus: This is a parallelogram having all sides of equal length.

Rectangle: A quadrilateral having opposing sides parallel and four right angles.

Square: A polygon with four sides of equal length and four right angle.

Parallelogram: This is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

In conclusion, the figure can be classified into quadrilateral, rhombus and square.

Complete question:

The complete question is in the attached image.

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Using the corresponding angle theorem, the value of x is 15 and y is 12.

In the given question we have to find the value of x and y.

From the graph we can see that

From the corresponding angle theorem

4x+2=62

Subtract 2 on both side, we get

4x=60

Divide by 4 on both side, we get

x=15

So the value of x is 15.

Similarly from the corresponding angle theorem

12y=144

Divide by 12 on both side, we get

y=12

So the value of y is 12.

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Answer:

A 35%

Step-by-step explanation:

take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.

Answer:

a) 35%

Step-by-step explanation:

Given information,

→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.

Now we have to,

→ find the % increase of number of guests from first party to second party.

Let's solve the problem,

→ ((27 - 20)/20) × 100

→ (7/20) × 100

→ 0.35 × 100

→ 35%

Hence, the answer is 35%.

The number of months required to pay off the loan will be 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.

The number of the months will be calculated as,

N = ( 1178.8 - 547.30) / 42.10

N = 631.5 / 42.10

N = 15

Therefore, the number of months required to pay off the loan will be 15.

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Answer:

2 L

Step-by-step explanation:

If the first one is 12% then the 3% one would be 2L because of algebra

5.75 liters of 3 percent hydrogen peroxide solution are included by the company in the container.

A measurement used to determine a number's value out of 100 is the percentage.

Hydrogen peroxide solutions in various containers have concentrations of 35% and 3%.

Since the corporation wants an 8-liter container with a 12% hydrogen peroxide concentration.

Use mixture and allegation property,

35           3

       12

9       :       23

Total quantity = 23x + 9x = 32x

Since, the company wants 8 liters,

therefore, 32x = 8 ⇒ x = 1/4

3.5 percent hydrogen peroxide solution will be equal to = 23x = 23/4 = 5.75. 5.75 liters of 3 percent hydrogen peroxide solution are needed.

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=====================================================

Explanation:

Unfortunately the U from "universal set" and the union symbol look almost identical.

What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Feel free to use other notation if it makes better sense to you.

From this set, we'll erase items that are found inside set A = {f, g, p, q}

So we go from this

E = {f, g, h, p, q, r, x, y, z}

to this

A' = {h, r, x, y, z}

Everything found in here is guaranteed to not be inside set A.

------------------------

The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.

A' u B = {h, r, x, y, z}  U  {g, h, q, x, y}

A' u B = {h, r, x, y, z,        g, h, q, x, y}

A' u B = {g, h, q, r, x, y, z}

It's recommended you sort the items in a consistent fashion.

Set this result aside for now, and come back to it later.

------------------------

Go back to the set of everything, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'

C' = set of everything NOT found in C

C' = erase "p,q,x,y,z" from set E

C' = {f, g, h, r}

------------------------

To recap we found

Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.

The three items in common are: {g, h, r}  which forms the final answer.

Answer:

Step-by-step explanation:

Use identity:

Substitute values:

Answer:

(a - b)² = 9

Step-by-step explanation:

Expand (a - b)²:

[tex]\begin{aligned}\implies (a-b)^2&=a^2-2ab+b^2\\&=a^2+b^2-2ab\end{aligned}[/tex]

Given:

Substitute the given values into the expanded equation:

[tex]\begin{aligned}\implies (a-b)^2&=a^2+b^2-2ab\\&=15-2(3)\\&=15-6\\&=9\end{aligned}[/tex]

Therefore, (a - b)² = 9.

Answer:

2x – 4 – 1 + x

Step-by-step explanation:

Answer:

Step-by-step explanation:  -15

The required value lies Between 6 and 7, but closer to 6. Option C is correct.

Given that,
The square root of 50 minus 10 would be plotted on a number line.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

According to the question,
= √[50-10]
= √40
= 6.32
Which is closer to 6.

Thus, the required value lies Between 6 and 7, but closer to 6. Option C is correct.

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Answer:

the answer to 2dp is 2536.02