Find the midpoint between each pair of points.
13. (7,-2) (-4,2)
BONUS POINTS IF RIGHT

Doing moves to keep an equation balanced is a powerful part of solving equations, but thinking about what the structure of an equation tells us about the solutions is just as iimportant

Sometimes it’s possible to look at the structure of an equation and tell if it has infinitely many solutions or no solutions. For example, look at

2(12x + 18) + 6 = 18x + 6(x + 7)

Using the distributive property on the left and right sides, we get

24x + 36 + 6 = 18x + 6x + 42

From here, collecting like terms gives us

24x + 42 = 24x + 42

Since the left and right sides of the equation are the same, we know that this equation is true for any value of x without doing any more moves!

Similarly, we can sometimes use structure to tell if an equation has no solutions. For example, look at

6(6x + 5) = 12(3x + 2) + 12

If we think about each move as we go, we can stop when we realize there is no solution

1/6 · 6(6x + 5) = 1/6 · (12(3x + 2) + 12) Multiply each side by 1/6

6x + 5 = 2(3x + 2) + 2 Distribute 1/6 on the right side.

6x + 5 = 6x + 4 + 2 Distribute 2 on the right side.

The last move makes it clear that the constant terms on each side, 5 and 4 + 2, are not the same. Since adding 5 to an amount is always less than adding 4 + 2 to that same amount, we know there are no solutions.

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The equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y - 0 = 1/3(x - 5). The correct option is b. y - 0 = 1/3(x - 5)

From the question, we ae to write the equation of a line that has the given slope and x-intercept.

From the equation for the point-slope form of a line,

y - y₁ = m(x - x₁)

Where m is the slope

and (x₁, y₁) is a point on the line

From the given information,

m = 1/3

and

The x-intercept is 5, that is, (5, 0)

Thus,

The equation of the line is

y - 0 = 1/3(x - 5)

Hence, the equation is y - 0 = 1/3(x - 5)

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To add 2 1/2 + 4/5 using a number line, we can start by marking off the whole numbers along the number line. Then, we can divide each whole number into equal parts to represent the fractions. For example, if we divide each whole number into fifths, we can mark off 2 1/5, 2 2/5, 2 3/5, etc.

After the above, the next thing is that we can find the point on the number line that represents 2 1/2 by starting at 2 and moving 1/5 of the way to the right. Similarly, we can find the point that represents 4/5 by starting at 4 and moving 1/5 of the way to the right.

Finally, to add the two numbers, we can simply move from the point that represents 2 1/2 to the point that represents 4/5. The final point we reach will be the sum of 2 1/2 + 4/5. In this example, the final point will be 3 3/10.

Therefore, 2 1/2 + 4/5 will be 3 3/10.

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Answer:

the solution and explanation/work is in the images

Answer:

x+5 > 12

Step-by-step explanation:

A number plus 5 is greater than 12 represents x + 5 > 12.

numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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Answer:

The first one

sorry if I'm wrong

The function shown in the graph is f(x)=3x-2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points.

(0, -2) and (2,4)

m=6/2=3

Now let us find y intercept.

4=3(2)+b

4=6+b

-2=b

Hence, the function shown in the graph is f(x)=3x-2.

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Answer:

Step-by-step explanation:

3/5 because 10 is their GCF

Answer:

The answer is 3/5

Step-by-step explanation:

30/50 > 6/10 >3/5

Just divide 30/50 (both numbers by 5) and then divide 6/10 (both numbers by 2). Hope this helped :)

Classifying  the scenarios as an observational study, an experiment, or a sample survey.

Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

Scenario B: Eight students were chosen at random from the cafeteria and asked if their favorite sport was soccer- a sample survey

Scenario C: To determine which drug is most effective in treating the common cold, drug A or drug B, cold patients were randomly given one of the two drugs and the results were compared-  a sample survey.

Scenario D: To determine which hair growth treatment was most effective in regrowing hair, GrowHair or ReGain, participants were assigned a treatment to determine which showed the most new hair growth- experiment.

Scenario E: Students who were taught reading by two different methods are compared in terms of their reading standardized test scores  observational study.

Scenario F: Ten employees are randomly selected and asked whether they would be in favor of a new management position in their department- a sample survey.

Sample Survey can be defined as the way in which people are randomly choose or pick from a large population so as to draw or reach a conclusion.

Observational study is a type of research method in which  people are be observed before conclusion are drawn.

Experiment study is research method in which something is been  tested before conclusion are reach.

Therefore Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

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Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1).

Factors are the positive integers that can divide a number evenly in mathematics. Say we want to create a product by multiplying two numbers. The factors of the product are the number that is multiplied. Each number has its own factor.

Examples of factors in real life include putting candies in a box, arranging numbers in a pattern, giving chocolates to kids, and many more.

Factors are the figures that can divide an amount precisely. As a result, there is no remainder after division. Factors are the sums of numbers that you multiply to produce another number. A factor is therefore the divisor of another number.

Using the formula

a³ – b³ = (a – b)(a² + ab + b²)

8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)

8m³ - 1³ =  (8m – 1)(8m² + 8m + 1²)

8m³ - 1³ =  (8m – 1)((8m)² + 8m + 1²)

8m³ - 1³ =  (8m – 1)(64m² + 8m + 1)

8m³ - 1³ =  (8m – 1)(64m² + 8m + 1)

Thus, Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1)

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Answer:

the patient would receive 375 mL of fluid in 3 hours.

Step-by-step explanation:

To calculate the amount of fluid a patient would receive in 3 hours, we can use the formula:

Flow rate (mL/hr) = Total volume (mL) / Time (hr)

Flow rate = 1000 mL / 8 hr = 125 mL/hr

To find the amount of fluid a patient would receive in 3 hours, we can use the formula:

Volume = Flow rate x Time

Volume = 125 mL/hr x 3 hr = 375 mL

So the patient would receive 375 mL of fluid in 3 hours.

In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

BD = 88

BC = 27

CD = 61.

Given that BD is equal to 7x, BC is equal to 4x, and CD is equal to 5x,

It is evident from the above figure that Points B, C, and D are parallel. On line segment BD, point C is located.

BD = BC + CD

In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

7x - 10 = (4x - 29) + (5x - 9)

When we combine similar phrases, we obtain

7x - 10 = (4x + 5x) + (-29 - 9 )

7x - 10 = 9x - 38

38 plus 38 on either side.

7x - 10 + 38 = 9x

7x + 28 = 9x

Take 7x away from both sides.

28 = 9x - 7x

28 = 2x

By 2, divide both sides.

14 = x

Consequently, x has a value of 14.

BD  = x - 10 = 7(14) - 10 = 88

88 units are BD's worth.

BC = 4x - 29 = 4(14) - 29 = 27

BC has a value of 27 units.

CD = 5x - 9 = 5(14) - 9 = 61.

The CD is worth 61 units.

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19/6 * 3+2, expression is equivalent to 19÷6•3+2

Expressions that are equivalent do the same thing even when they have distinct appearances.

When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

We may be given equations with algebraic expressions on both sides in some situations.

The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F

Hence, 19/6 * 3+2, expression is equivalent to 19÷6•3+2

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The required solution of the given inequality 2x < 8 is x < 4.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given  inequality is

2x < 8

According to given question we have

Write inequality

2x < 8

Divide both sides by 2 we get,

x < 4

Therefore, the required solution of the given inequality 2x < 8 is x < 4.

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On solving the provided question, we can say that by percentage, 19.7% 0f female = 19.7/100 * 54 = 10.638

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

by percentage,

male = 2139

female  = 54

19.7% 0f female = 19.7/100 * 54 = 10.638

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The approximate number of packets containing blades with no defective is :  9802

We are given the probability of defect per blade = 1/500 = 0.002

The general formula for Poisson distribution is;

Pₓ (k) = (x^k)/k × e⁻ˣ

Where;

k = The number of defective blades in a packet.

For a packet of 10 blades the mean number of defect is;

x = 0.002 × 10

x = 0.02

When there is no defective in a consignment, then it means k = 0

Thus;

Pₓ(0) = (0.02⁰ / 0!) × e^(-0.02) = 0.980199

The approximate number of packets containing blades with no defective is : 10000 × 0.980199 = 9802

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Answer:

Every 10 seconds is 1 gallon

The line parallel to Line 1 which is given by the equation: −6y + 3x = 12 and passes through (−1, − 5) is written in slope intercept form as

\y = 0.5x - 4.5

A linear function consists of functions where the variables has exponents of 1. the relationship is expressed in the slope intercept form as below.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The given equation is rewritten in slope intercept form as follows

−6y + 3x = 12

−6y = 12 - 3x

y = 1/2 x - 2

the slope is 1/2

equation of the line of slope = 1/2 passing through point (-1, -5) is calculated using the point slope formula which is

(y - y') = m(x - x')

(y + 5) = 1/2(x + 1)

y + 5 = 1/2 x + 1/2

y = 1/2 x + 1/2 - 5

y = 0.5x - 4.5

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25.6

The question is asking for the difference between 4000 compounded interest and 4000 with simple interest.

So simply calculate 4000 compounded by 8% per annum for 2 years:

4000(1+0.08)^2=4665.6

Now calculate 4000 with simple interest of 8% per annum for 2 years:

4000(1+0.08×2)=4640.

Now subtract the simple interest amount from the compounded amount:

4665.6-4640=25.6

Hope that helps :)

Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9)

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations.  Each change must be carried out, and you must be able to tell which transformations have been carried out. The function translation and transformation guidelines are: F (x) + b moves the function up by b units. The function is moved downward by f (x) b. The function is moved left b units by the formula f (x + b).

given

(2 , -6 )

under this (x, y) → (x-2, y-3)

( 2 - 2, -6 , -3 )

(0 , -9)

Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9) .

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The expression, 5 ÷ 3, in standard form, would be 1. 67 x 10⁰.

For the purposes of representing large or small numbers in mathematics, a standard form of a number is essentially mentioned. To represent such numbers in standard form, we employ exponents.

It would be easier to understand the correct definition of standard form if you used decimal numbers and adhered to specific restrictions. As is well known, fractions are expressed more simply as decimal numbers.

Basically, in standard form, we try to ensure that only one digits is to the left of the decimal point and then to the right are the rest of the digits in the number. The position of the number is then reflected as a power of 10.

First, solve 5 ÷ 3 :

= 5 / 3

= 1. 667

The result already has only one number to the left of the decimal so the power of 10 would be 0:

= 1. 667 x 10⁰

This is because every number to the power 0, is 1 and so 1.667 x 10⁰ would be the same as 1. 667 x 1 which is correct.

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Answer:

Step-by-step explanation:

In order to properly fit the website for Faria mobile devices such as tablets and smartphones, the company will need to make sure that the website is optimized for different screen sizes. The original website was designed for a screen dimension of 16" x 9", but mobile devices have varying screen sizes. The company can use the dimensions listed in the table to ensure that the website looks and functions properly on the five mobile devices they are researching.

The value of -0.6675 for the correlation coefficient of X and Y indicates that there is a negative correlation between the two variables.

The correlation coefficient, denoted as p, is a measure of the linear relationship between two random variables X and Y. It is defined as the ratio of the covariance of X and Y to the product of their standard deviations:

p = cov(X,Y) / (stdDev(X) × stdDev(Y))

To compute the correlation coefficient, we need to first calculate the covariance and the standard deviations of X and Y.

Since the marginals pdfs of X and Y are the same, we know that the expected value (mean) of X is equal to the expected value of Y, which is denoted as Mu x = Mu y = A.

The expected value of XY is given as E(XY) = 2/5.

The covariance of X and Y is defined as E((X-Mu x )(Y-Mu y )), which simplifies to E(XY) - Mu x × Mu y

Substituting the given values, we have:

cov(X,Y) = E(XY) - Mu x × Mu y = 2/5 - A²

To calculate the standard deviation of X and Y, we need to calculate the variance first. The variance of X is defined as E(X²) - (Mu x )²,

which can be easily calculated by replacing x with y in fx(x) and applying the same formula.

The standard deviation is the square root of the variance, so we have:

stdDev(X) = √(variance(X)) = √(E(X²) - (Mu x )²)

stdDev(Y) = √(variance(Y)) = √(E(Y²) - (Mu y )²) = √(E(X²) - (Mu x )²)

Now we can substitute these values into the formula for p:

p = cov(X,Y) / (stdDev(X) × stdDev(Y)) = (2/5 - A²) / (√(E(X²) - (Mu x )²) × √(E(X²) - (Mu x )²)).

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Inferential statistics is a branch or method of statistics that makes the use of various analytical tools to draw or conclude inferences about the population data from sample data. Apart from inferential statistics, another part is descriptive statistics forms another branch of statistics.

Inferential statistics help to make conclusions about the population while descriptive statistics summarizes the features of the data set.

Inferential statistics helps to develop a good grasp of the population data by analyzing the samples obtained from it.

It helps in making concept about the population by using different analytical tests and tools.

Inferential statistics can be classified into two types of hypothesis testing and regression analysis. Hypothesis testing also includes the use of belief intervals to test the parameters of a population.

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The measure of angle S in ΔRST to the nearest degree is 44°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know sine rule of a triangle ABC is, a/sinA = b/sinB = c/sinC.

Given, In ΔRST, m < R = 100°, r = 20, and t = 12.

Therefore,

r/sinR = t/sinT.

20/sin100° = 12/sinT.

20.30 = 12/sinT.

sinT = 12/20.3.

sinT = 0.59.

T = sin⁻¹(0.59).

T = 36°.

We know the sum of all the interior angles in a triangle is 180°.

Therefore, m∠R + m∠T + m∠S = 180°.

100° + 36° + m∠S = 180°.

m∠S = 180° - 136°.

m∠S = 44°.

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The differential equation of y'' + 3y' + 2y = 1/4+ex is

               [tex]y=c_{1} e^-^2^x+c_{3} e^-^x+4e^-^2^xln(4+e^x)+e^xln(4+e^x)[/tex]

The given differential equation is y'' + 3y' + 2y = 1/4+ex

As we are considering the LHS part looks like a Quadratic equation.

y''+3y'+2y=m²+3m+2

m²+3m+2=0 ---(1)

finding the roots for eq(1)

m²+2m+m+2=0

m(m+2)+1(m+2)

(m+2) (m+1)=0

m=-2,m=-1

Yc=C₁e⁻²ˣ+C₂eˣ   ----(2)

equation (2) is called a complementary function.

A complementary function is only one part of the solution to a linear, and autonomous differential equation.

An ordinary differential equation (ODE) defines the sum of a function and its derivatives. When the explicit functions y = f(x) + cg(x) form the solution, g is called the complementary function; f is the particular integral.

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Answer:

357

Step-by-step explanation:



The meaning of the y-intercept in this situation is ,

''For every additional mile the cab travels, the total fee increases by $12.00.''

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

From the table, we have the following parameters:

Points (x, y) = (2, 5) and (15.00, 19.50)

So, we would calculate the slope as follows:

Slope = (19.50 - 5)/(15.00 - 2)

Slope = 14.50/13

Slope = 1.11

Hence, We get;

Fixed fee = $15 - (1.12 x 2)

               = $15 - 2.24 ≈ $12.00

So, We get;

For every additional mile the cab travels, the total fee increases by $12.00.

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Answer:

parallel

Step-by-step explanation:

solve for the second equation so y is by itself

y=-2x+3

their slopes are the same so they're parallel

Answer:

[tex]c = \sqrt{74}[/tex]

Step-by-step explanation:

To find the distance between the two, we will use the Pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]). To find a and b, we need to subtract the distances between the y coordinates and the x coordinates respectively. For the x coordinates, we have 8 - 1 = 7 units. For the y coordinates, we have 7 - 2 = 5. Plugging this into our equation gives us:

[tex]7^{2} + 5^{2} = c^{2}[/tex]

We will simplify our exponents:

[tex]49 + 25 = c^{2}[/tex]

Then adding them together gives us:

[tex]74 = c^{2}[/tex]

Then, we square root both sides giving us:

[tex]\sqrt{74} = c[/tex]

Then, we cannot simplify past this, since 74's prime factorization doesn't allow it. So, [tex]c = \sqrt{74}[/tex].

Hope this helped!