Expand to write an equivalent expression: LaTeX: -\frac{1}{2}\left(-2x\:+\:4y\right)

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is the standard deviation.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The method of measuring dispersion most frequently employed is the standard deviation (SD). It is a measurement of data spread around the mean. The SD is calculated by multiplying the total squared departure by the mean by the total number of observations.

Variance is a measure of dispersion that, in contrast to the range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed.

Therefore, although Mean, Mode, and Median are the measures of central tendency, Standard Deviation, Variance, and Range are measures of dispersion.

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The lowest amount in pounds that Noah can pay to purchase pencils is ≥ 16.8 pounds.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Noah wants to buy exactly 84 pencils.

Pack of 10 pencils for 2 pounds.

So, the cost of each pencil is 2/10 =0.2 pounds

Then the cost of 84 pencils is

8 packs + 4 pencils

= 8×2+4×0.2

= 16+0.8

= 16.8 pounds

So, the cost of 84 pencils ≥ 16.8 pounds

Therefore, the lowest amount in pounds that Noah can pay to purchase pencils is ≥ 16.8 pounds.

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The length of the diagonal of the rectangle is 24cm.

The diagonal of the rectangle equals the square root of the width squared plus the height squared.

The width of the rectangle is indicated by the letter “w” and the length of the rectangle is indicated by "l".So, the diagonal of a rectangle formula is expressed as d = (l² + w²),

According to the question,

A rectangle is 22 inches long and 10 inches wide.

To observe the diagonal we use the Pythagorean Theorem:

Let, x = hypotenuse

22² + 10² = x²

⇒484 +100 =x²

⇒x = 24.14 =24

So, the length of the diagonal of the rectangle is 24cm.

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The cash received by Shamar from bank deposit ticket is (c) $908.11

When making a deposit into a bank account, a bank customer typically includes a little paper document called a deposit slip.

A deposit slip includes the date, the depositor's name, their account number, the sums being deposited, and a breakdown of the type of deposit (cash, checks, or a particular amount of cash the depositor wants back from a check deposit).

The deposit slip is evidence that the bank confirmed receiving the customer's funds.

In this problem, the total amount deposit through check or other mode is $1108.11 and $ 200 deducted by bank as processing fee.

So the final amount or cash Shamar received is

= $1108.11 - $ 200.00

= $ 908.11

The cash received by Shamar from bank deposit ticket is (c) $908.11

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The point where he  buried his treasure is (6.28,9.84)

First of all, we are going to find the equation of the line which describes the first path crossed by the horseman.  In order to find it we have to take into account that the vector V  provides us with the direction of this path. We can associate the direction with the slope of the line. The slope is defined by the ratio of vertical changes to horizontal changes between two points.  

According to the V=6i+5j, we can determine that:

Vertical change (y)= 5

Horizontal change (x)=6

Slope=\frac{5}{6}

Now, using the point-slope form:

y-y₁=m(x-x₁)

The chosen point is the point where the horseman began riding (-2,5). Therefore:

m=5/6

y1=5

x1=-2

y-5=5/6(x+2)

y=5x/6-10/3

Since the horseman at some point turned at a right angle towards village B  and he unchanged his direction until arrived in village B, the second path must be described by a line perpendicular to the first path.  

We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1

m₁=5/6

m₂=-1/m₁=-6/5

In order to find the equation of the second path, we will use again the point-slope form.

The chosen point is the point where is located Village B (2,11)

y-11=-6/5(x-2)

y=-6x/5+13.4

The coordinates of the point where the horseman buried a jar full of silver coins correspond to the intersection of path 1 and path 2. Therefore we are going to equal the two equations of each path.

5x/6-10/3=-6x/5+13.4

Solving this equality for x

X=6.28

Replacing this value in any of the equations of the paths

Y=9.84.

Finally, the point where he buried his treasure is (6.28,9.84).

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If he had $5 left to put aside for bait, he start with $2.

Let 2x be amount of money Thomas started with.

He spent spent half of what he had plus $5 at the first store.

So the expression should be x + 5.

So, we have left money = 2x - (x+5)

Left Money = 2x - x - 5

Left Money = x - 5

he spent half of what was left plus $4 in second store.

So the expression should be = (x - 5)/2 + 4

Now he has left money = 2x - [(x - 5)/2 + 4]

left money = 2x - (x - 5)/2 - 4

After solving, we get

left money = 3x/2 - 3/2

left money = 3(x-1)/2

At the third store, he spent half of the remainder plus $3.

So the expression should be = \frac{3(x-1)/2}{2} + 3

Now he has left money = 2x - \frac{3(x-1)/2}{2} + 3

Now simplifying

Left Money = 2x - 3(x-1)/4 + 3

After solving we get;

Left money = 5x/4 + 15/4

Left money = (5x+15)/4

According to question, he had $5 left. So

(5x+15)/4 = 5

Multiply by 4 on both side, we get

(5x+15) = 20

Subtract 15 on both side, we get

5x = 5

Divide by 5 on both side, we get

x = 1

He start with money 2x = 2*1 = $2

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335 students of fourth graders voted for the Falcon.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:

  Commutative and associative properties hold true for fractional       addition and multiplication

Using proportions, it is found that 335 students voted for the Falcon. In total, 536 students voted for a mascot. The proportion that voted for the Falcon is 5/8 of the total number of students. To find the number of students that voted for the Falcon, we multiply the proportion of 5/8 by the total of 536, thus: 335 students voted for the Falcon.

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If Rachel found this rate of change for the scenario represented in the table.  you can conclude from her work that:

1. The function is continuous.

3. The scenario is represented by a linear function, since the rate of change is constant.

5. For every additional hour, 53 cups of juice are poured.

Rate of change can be defined as the rate in which a variable is changing as a result of another variables.

You can conclude from her work that the function is continuous, the scenario is represented by a linear function due to the fact that the rate of change is constant and lastly based on the table for every additional hour, 53 cups of juice are poured.

Therefore the correct option is 1,3,5.

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The complete question is:

Rachel found the following rate of change for the scenario represented in this table.

A 2-column table with 5 rows. Column 1 is labeled Time (hours) with entries 4, 5, 6, 7, 8. Column 2 is labeled Berries picked with entries 128, 181, 234, 287, 340.

What can you conclude from her work?

Check all that apply.

The scenario is represented by a linear function,

since the rate of change is constant.

The scenario is represented by a nonlinear function,

since the rate of change is constant.

The berries are picked at a constant rate of 53 per

hour.

The berries are not picked at a constant rate.

Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.

Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.

First, let's use the sine function to find the value of KL:

sin(40) = KL/ML

KL = (sin(40))(ML)

KL = (sin(40))(8)

Next, let's use the cosine function to find the value of MK:

cos(40) = MK/ML

MK = (cos(40))(ML)

MK = (cos(40))(8)

Finally, let's use the tangent function to find the value of mZK:

tan(40) = KL/MK

mZK = tan(40)

To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.

sin(40) = 0.766

cos(40) = 0.644

tan(40) = 1.193

KL = (0.766)(8) = 6.128 ≈ 6.1

MK = (0.644)(8) = 5.152 ≈ 5.2

mZK = 1.193

So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.

Answer:

To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.

Given:

angle K = 40°

ML = 8

KL = 2

We can use the sine function to find the value of angle M:

sin(M) = KL / ML

sin(M) = 2 / 8

sin(M) = 0.25

So M = arcsin(0.25) = 14.04 (approximately)

Next, we can use the cosine function to find the value of MK:

cos(M) = ML / KL

cos(M) = 8 / 2

cos(M) = 4

So MK = 4

Lastly, we can use the tangent function to find the value of angle L:

tan(L) = KL / MK

tan(L) = 2 / 4

tan(L) = 0.5

So L = arctan(0.5) = 26.57 (approximately)

So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.

If the plant is n inches then,

the actual plant = 2n feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

The garden club at central middle school is planting a flower bed.

A scale drawing of the flower is shown.

The scale 1 in:2 ft

The scale factor,

the model = 1 inch

Then the actual plant = 2 feet.

If the plant is n inches then,

the actual plant = 2n feet.

Therefore, If the plant is n inches then, the actual plant = 2n feet.

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A) The slope of the line is 2.

B) the linear equation is y = 2x - 7

C) y-intercept = -7

   x-intercept = 3.5

A general linear equation can be written as:

y = m*x + b

Where m is the slope.

If the line passes through two points (x₁, y₁)and (x₂, y₂), then the slope is:

m = (y₂ - y₁)/(x₂ - x₁)

In this case these points are (-3, 7) and (2, -3), then the slope is:

m = (-3 - 7)/(2 + 3) = 2

Then the line is something like:

y = 2x + b

To find the value of b we can replace the values of the point (2, -3), we will get:

-3 = 2*2 + b

-3 - 4 = b

-7 = b

y = 2*x - 7

C) the y-intercept is the value of y when x = 0.

y = 2*0 - 7

y = -7

The x-intercept is the value of x when y = 0.

0 = 2*x  -7

7 = 2x

7/2 = x

3.5 = x

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Answer:

I think it is (8,16).

Car 'B' travels the farthest on one gallon of gas.

From the table of the number of miles car a can drive for different amount of gas, car 'A' needs 8 gallons of gas to cover 200 miles.

So, in one gallon of gas, a car 'A' would cover 25 miles.

By unitary method we will find the remaining values.

Let a car drive 't' miles in 4 gallons of gas

Using unitary method,

t = 25  × 4

t = 100 miles

So, we can say that the rate of the number of miles driven per amounts of gas for car 'A' is 25 miles per gallon.

Car b can travel 140 miles for every 5 gallons of gas.

So, the rate for car B is 140/5 = 28 miles/gallon

And from the graph, the rate for car 'C' would be 81/3 = 27 miles/gallon

Thus, car B is the fastest.

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Find the complete question below.

If Dan Elliott uses inline banking to pay 9 bills , a printed statement , 2 out of network transactions and cash advance of $200 , then the total fees for the month is $221.45  .

The Basic monthly charge for the bank is = $6.95  ;

The cost of 1 bill payment is = $0.50 , and Dan Elliott paid 9 bills ,

So , Cost of 9 Bill payment is = 9 × 0.50 = $4.5  ;

the charge for printing the statement is = $4 ;

The Surcharge for 1 out of network transaction is = $3 , and

Dan Elliott made 2 Out of Network transactions ,

So , Surcharge for 2 Out of Network transactions = $3 × 2 = $6 ;

he also has a cash advance of $200 ;

The Total Fees can be calculated by Adding all the charges that means :

Total Fees = Basic Charge + Bill Payment + Statement + ATM Surcharge + Cash Advance Fees ;

Substituting the values :

we get ;

Total Monthly Fees = $6.95 + $4.5 + $4 + $6 + $200

= $221.45

Therefore , The total fees for the month is $221.45  .

The given question is incomplete , the complete question is

Dan Elliott uses online banking. He pays the basic monthly charge, 9 bills, and requests a printed statement. He also has ATM transactions that include 2 out of networks transactions and a cash advance of $200. 0. What are his total fees for the month ?

The Charges are as follows : Basic Monthly Charge is $6.95 ;

1 bill payment costs $0.50 ; A printed statement costs $4 ;

The Out of network Surcharge is  $3 .

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c=14+xh is the  equation that represents the relationship between h and c.

An expression is combination of variables, numbers and operators.

Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.

Let h represent the duration of a rental in hours and c represent the total cost of the rental.

We have to find the  relationship between h and c.

c=14+xh

Here x represents the dollar.

Hence, c=14+xh is the  equation that represents the relationship between h and c.

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Answer:

1. y=29

2. m= -8

3. x=10

Step-by-step explanation:

1. Add the numbers

y+y+1+y+2=90

y+y+3+y=90

combine like terms

3y+3=90

Subtract 3 from both sides

3y+3-3+90-3

3y=87

Divide both sides by the same factor

3y/3 = 87/3

y=29

2. Distribute

5(m+4)=-20

5m+20=-20

Subtract 20 from both sides

5m+20=-20

5m+20-20+-20-20

Simplify

5m=-40

Divide both sides by the same factor

5m/5 = -40/5

m= -8

3. Add 8 to both sides

3x-8=2x+2

3x-8+8+2x+2+8

Simplify

3x=2x+10

Subtract 2x from both sides

3x=2x+10

3x-2x+2x+10-2x

x=10

Answer: 6.1 or 6 1/10

Step-by-step explanation:

4+1 = 5

1/2 + 3/5 = 5/10 + 6/10

5/10 + 6/10 = 11/10

11/10 = 1 1/10

1 1/10 + 5 = 6.1 or 6 1/10

If f(3) = 3 - |2x - 5| is given then the value of f(0) + f(-4) would be -8.

What is the function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided.

To find f(3), we need to plug in x = 3 into the equation:

f(3) = 3 - |2(3) - 5| = 3 - |6 - 5| = 3 - |1| = 3 - 1 = 2

To find f(0), we need to plug in x = 0 into the equation:

f(0) = 3 - |2(0) - 5| = 3 - |-5| = 3 - 5 = -2

To find f(-4), we need to plug in x = -4 into the equation:

f(-4) = 3 - |2(-4) - 5| = 3 - |-9| = 3 - 9 = -6

Now we can add f(0) + f(-4) = -2 + (-6) = -8

Hence, if f(3) = 3 - |2x - 5| is given then the value of f(0) + f(-4) would be -8.

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To represent the number of boxes sold when the total sales are equal to $1600 on a number line, we can simply mark the x-coordinate of the point (420,1600) on the number line.

The point of intersection between the horizontal line y = 1600 and the graphed function b) = 3.756 + 25x is (420,1600), which means Alan would have to sell 420 boxes to make $1600 in total sales.

To represent the number of boxes sold when the total sales are equal to $1600 on a number line, we can simply mark the x-coordinate of the point (420,1600) on the number line. To the left of this point, the number of boxes sold would be less than 420, and to the right of this point, the number of boxes sold would be more than 420. At the point (420,1600), Alan would have sold exactly 420 boxes and made a total of $1600 in sales.

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After performing the division , the missing term in the problem is (2x³ + 5x² + 9)/(x + 3) = (2x² -x +3) .

The problem is (2x³ + 5x² + 9)/(x + 3) ;

that means , we have to divide , the expression "2x³ + 5x² + 9" by "x + 3" ;

first we multiply (x+3) by 2x² ;

the expression becomes : 2x³ + 5x² + 9

                                           -2x³ - 6x²

                                                    -x²  +  9

next we multiply by -x :               -x²  - 3x                      

                                                             3x + 9

next we multiply by 3 :                        -3x - 9

                                                                      0   .

So , dividing the "2x³ + 5x² + 9" by "x + 3" , we get the remainder is 0 and the quotient is 2x² - x + 3 .

Therefore , the missing term is 2x² - x + 3 .

The given question is incomplete , the complete question is

Which is the missing term in this problem ?

(2x³ + 5x² + 9)/(x + 3) = ______  ;

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For the inequality "2(34 + 12) > 5b" that contain a variable "b" , then the numbers that make this inequality true are (a) 16 , (b) 18 .

The inequality containing the variable "b" is ⇒ 2(34 + 12) > 5b  ;

simplifying the inequality ,

we have ;

⇒ 2×(46) > 5b  ;

⇒ 92 > 5b ;

(a) Substituting value of b = 16 ,

we get ; 92 > 5×16

⇒ 92 > 80 , TRUE  .

(b) Substituting value of b = 18 ,

we get ; 92 > 5×18

⇒ 92 > 90 , TRUE  .

(c) Substituting value of b = 19 ,

we get ; 92 > 5×19

⇒ 92 > 95 , FALSE  .

(d) Substituting value of b = 20 ,

we get ; 92 > 5×20

⇒ 92 > 100 , FALSE  .

Therefore , the inequality is TRUE for two values of b that are (a) 16 , (b) 18.

The given question is incomplete , the complete question is

This inequality 2(34 + 12) > 5b ;  contains a variable "b". Choose ALL numbers that make this inequality true.

(a) 16

(b) 18

(c) 19

(d) 20

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The width of the swimming pool is 1.624yards.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Here, we have,

a swimming pool can hold 9.745 cubic yards of water.

i.e. V = 9.745

it has a length of 3 yards and a height of 2 yards.

i.e. l= 3

    h=2

so, width = w = V/(l*h)

i.e. w = 1.624

Hence, the width of the swimming pool is 1.624yards.

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The output of a classification system is usually a discrete value, usually a label or class, which represents the predicted result of the model.

A classification system can be expressed mathematically using a decision boundary. This boundary is defined by a decision function that maps the input data to a discrete output. The decision boundary is determined by setting a threshold for the output of the decision function, such that if the output exceeds the threshold, the predicted class is labeled as a "positive" output and if the output is below the threshold, the predicted class is labeled as a "negative" output.

The output of a regression system is usually a continuous value, which represents the predicted result of the model. A regression system can be expressed mathematically using a linear equation which maps the input data to a continuous output. The equation is determined by fitting a line to the data, such that the line best fits the data points. The value of the output is then calculated by evaluating the equation at a given point in the input data.

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The graph of the quadratic function y = x² + 2x - 5 is given by the image at the end of the answer.

The domain and range are given as follows:

The domain of a function is the set that contains all the possible input values for the function, hence in the graph it is composed by the values of x of the function.

The range of a function is the set that contains all the possible output values for the function, hence in the graph it is composed by the values of y of the function.

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The distance between (-6 5) and (-6 -3.5) is 14.71 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-6, 5) and (-6, -3.5) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-6 - 6)² + (5 - -3.5)²}

d =√{144 + 72.25}

d = √216.25

d = 14.71 units

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Answer:

D and C

Step-by-step explanation:

C:  Has a negative slope which will go down

D:  Has a negative slope which will also go down

=> Convert feet into yards.

660 feet = 220 yards.

=> Convert feet into inches.

660 feet = 7920 inches.

Now, According to the question:

=> Convert feet into inches.

660 feet = 7920 inches

Formula: multiply the value in feet by the conversion factor '12'.

So, 660 feet = 660 × 12 = 7920 inches.

=> Convert feet into yards.

660 feet = 220 yards

Formula: divide the value in feet by 3 because 1 yard equals 3 feet.

So, 660 feet = 660/3

     660 feet = 220 yards.

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Answer:

x intercept = 1.66666...

y intercept = 2.5

The x intercept is approximate. The 6's go on forever. The y intercept is exact without any rounding done to it.

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

Explanation:

Plug in y = 0. Then solve for x to get the x intercept.

3x+2y = 5

3x+2*0 = 5

3x = 5

x = 5/3

x = 1.66666...

The 6's go on forever.

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

Plug x = 0 into the equation and solve for y. This will get us the y intercept.

3x+2y = 5

3*0+2y = 5

0+2y = 5

2y = 5

y = 5/2

y = 2.5

This value is exact without any rounding

Sylvan made a mistake computing the quotient in the problem.

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: 1.6 divided by 0.4

We know 1.6 can be expressed as 1.6=0.4×4

x ÷ y = z.

1.6÷0.4=4

Division method is nothing but the inverse of multiplication.

Divide 1.6 by number 0.4.

Solution:1.6÷0.4=1.6/0.4 with remainder zero

                          =4

Thus the quotient should have been 4

But according to Sylvan 1.6/0.4=0.4 which is not correct.

Hence, Sylvan computed the wrong quotient.

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