I might need some help with this question

I Might Need Some Help With This Question

Answers

Answer 1

Step-by-step explanation:

12/18   =  16/24

Simplify the fractions on both sides

2/3    =     2/3


Related Questions

What single percentage change is equivalent to a 9% increase followed by a 14% decrease?

Answers

Assume the number 100. 100*1.09=109. You then do 109*0.86=93.74.

So the overall decrease is 6.26%.

find c
A. square root of 7 and 2
B. 14
C. 7
D. square root of 7 and 3


can you please help.​​

find cA. square root of 7 and 2B. 14C. 7D. square root of 7 and 3can you please help.

Answers

Answer:

3.74-a

7

2.64

4.58

Step-by-step explanation:

hope it helps please mark me as brainlist

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

Answers

The given points, only the point (4, -9, -8) lies on line 1.

To determine whether certain points lie on the line 1, which is perpendicular to the plane x - 2y - 4z = 5 and contains the point (2, -5, 0), we can check if the coordinates of those points satisfy the equation of the line.

The direction vector of the line 1 is perpendicular to the plane and can be determined from the coefficients of x, y, and z in the plane equation. In this case, the direction vector of the line is (1, -2, -4).

Now, we can write the parametric equation of the line l as:

x = 2 + t * 1

y = -5 + t * (-2)

z = 0 + t * (-4)

To check if a point (x₀, y₀, z₀) lies on the line 1, we need to find a value of t that satisfies the parametric equations.

Let's consider the following points and determine if they lie on line 1:

Point (3, -6, -4)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (3, -6, -4) into the parametric equations:

x₀ = 2 + t * 1 --> 3 = 2 + t --> t = 1

y₀ = -5 + t * (-2) --> -6 = -5 - 2 --> t = -1

z₀ = 0 + t * (-4) --> -4 = 0 - 4t --> t = 1

The value of t is not consistent across all equations, so the point (3, -6, -4) does not lie on line 1.

Point (2, -5, 0)

This point is given as the point that line 1 contains. Therefore, it lies on line 1.

Point (4, -9, -8)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (4, -9, -8) into the parametric equations:

x₀ = 2 + t * 1 --> 4 = 2 + t --> t = 2

y₀ = -5 + t * (-2) --> -9 = -5 - 2t --> t = 2

z₀ = 0 + t * (-4) --> -8 = 0 - 8t --> t = 1

The value of t is consistent across all equations, so the point (4, -9, -8) lies on line 1.

Therefore, among the given points, only the point (4, -9, -8) lies on line 1.

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The complete question is:

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

100 points & brainliest!! ONLY IF U ANSWER CORRECTLY, IF YOU DONT ILL REPORT.

100 points & brainliest!! ONLY IF U ANSWER CORRECTLY, IF YOU DONT ILL REPORT.

Answers

Total objects

As

\(\\ \sf\longmapsto Unit\:price=\dfrac{Sale\: Price}{No\:of\: units}\)

\(\\ \sf\longmapsto Unit\:Price=\dfrac{D_2({E_2)}}{C_2}\)

Or

\(\\ \sf\longmapsto Unit P=\dfrac{E_2(D_2)}{C_2}\)

Answer:

= D2/E2

Step-by-step explanation:

See attached

Number of units in cell E2, Total price in D2

The formula for unit price is:

= D2/E2
100 points & brainliest!! ONLY IF U ANSWER CORRECTLY, IF YOU DONT ILL REPORT.

Name the marked angle in 2 different ways.

Name the marked angle in 2 different ways.

Answers

The names of the marked angles are <JIK and <KIJ

How to name the marked angle?

From the figure, we can see that the angle is marked at point I

At the point where it is marked, the angle extends to lines J and K

This means that the angle can be named as JIK

Alternatively, the angle can be named as KIJ

Hence, the names of the marked angles are <JIK and <KIJ

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name a fraction that is equivalent to three fourths. then, describe how the numerator and denominator changed.

Answers

\(\frac{6}{8}\) is a fraction that is equivalent to three fourth, or \(\frac{3}{4}\). The numerator and denominator are changed by multiplying and dividing the original fraction by the same natural number as 2.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction followed by simplification. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions. An equivalent fraction can be obtained by multiplying and dividing the same natural number with the given fraction. As of the query, \(\frac{3}{4}\) is an improper fraction, whose equivalent fractions can be obtained as follows:

Multiplying natural numbers lie 2, 3, 4... with the given fraction:

\(\frac{3}{4}\) × \(\frac{2}{2}\) = \(\frac{6}{8}\)

Hence, 6/8 is an equivalent fraction of 3/4. Other than this, we can also obtain more equivalent fractions in the same manner.

\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)

Hence, 9/12 is also equivalent to 3/4 when reduced to lowest terms. Similarly, we can find that 12/16, 15/20, and 18/24 are also equivalent fractions of 3/4.

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NUMBER SENSE Find the measure of each angle.
The measure of one interior angle of a parallelogram is 0.25 times the measure of another angle.
The measure of the smaller interior angle is
and the measure of the larger interior angle is

Answers

The measure of the angles in the parallelogram are 144 and 36 degrees.

What is a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles are also equal.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Angles in a parallelogram

a + b + c + d = 360

Opposite angles are equal, so

2a + 2(0.25a) = 360

2a + 0.5 = 360

2.5a = 360

a = 360/ 2.5

a = 144

the other angle = 180 - 144 = 36 degrees

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Consider △RST and △RYX.

Triangle R S T is shown. Line X Y is drawn parallel to side S T within triangle R S T to form triangle R Y X.

If the triangles are similar, which must be true?

StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction

Answers

Answer:

B. \(\frac{RY}{RS}\) = \(\frac{RX}{RT}\) = \(\frac{XY}{TS}\), must be true.

Step-by-step explanation:

Similar figures are figures whose angles and sides are similar with respect to a definite ratio when compared.

From the given question, note that ΔRXY is within ΔRST. Given that the two triangles are similar, then their sides can be compare in a form of ratio as:

\(\frac{RY}{RS}\) = \(\frac{RX}{RT}\) = \(\frac{XY}{TS}\)

Therefore by comparing the length of sides of the triangles, option B must be true.

The dimensions of one of two triangles that are similar can be obtained

from the other triangle by multiplying by a scale factor.

The statement that must be true is; \(\displaystyle \underline{ \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}}\)

Reasons:

The given relationship between the triangles are;

Line XY is drawn within ΔRST to form ΔRYX.

XY is parallel to ST

Given that we have;

Point X on side RT and point Y on side RS of ΔRST

ΔRST is similar to ΔRYX, we get;

The ratio of the corresponding sides are equal, which gives;

\(\displaystyle \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}\)

Therefore;

The option that gives the statement that must be true is; \(\displaystyle \underline{\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}}\)

which is the same as the option; StartFraction RY Over RS EndFraction =

StartFraction RX Over RT EndFraction = StartFraction XY Over TS

EndFraction.

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M\QRX=
80
360
180
129
Pls help

M\QRX= 80 360 180 129 Pls help

Answers

Answer:

129

Step-by-step explanation:

The sum of all the angles in a triangle is 180 degrees.

49 + 80  + <QRP = 180

<QRP = 51

The sum of the angles across a straight line is also 180:

<QRP + <QRX = 180

51 + <QRX = 180

<QRX = 129

HELP! Determine whether option A or B is a better deal?

Option A) 12 binders for $30
Option B) 7 binders for $16.80

Answers

A option A

Step-by-step explanation:

according to if the binders its so important you need to buy it for $30 but its not really important buy for 16.80 and if you want to use for 1 time buy 7 binders but if you want to use much times buy for $30 and you need to see if that really care because you need to see if was a good material

3[(x^3 -7x+1) - (x+4)]
О А. 3х³ - 24х-9
О B. х-8х-3
0 С. 3x²-5x-6
O D. 3x²-6x+15

Answers

Answer:

A

Step-by-step explanation:

You have to simplify the brackets in turn.

3 times x^3- 7x+1 = 3x^3- 21x+ 3

then do 3 times x + 4= 3x + 12

you then add them all together, if they have a power add them, if they just have an x add them, and if they are just a number add them.

So it goes to 3x^3- 24x - 9,

this is because 3x^3 cant be added/ subtracted by anything, -24x is made from -21x- 3x, and -9 is made from 3 - + 12, so this means 3 - 12 = -9.

I hope this helps, have a lovely day.

line k in the xy-plane has slope the negative of the fraction 2 p over 5 and y-intercept the point with coordinates 0 comma p, where p is a positive constant. what is the x-coordinate of the x-intercept of line k ?

Answers

The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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Given:BK=CH Which additional congruence statement could you use to prove that ∆BJK ≅ ∆CFH by the HL Theorem?

Given:BK=CH Which additional congruence statement could you use to prove that BJK CFH by the HL Theorem?

Answers

Answer:

B

Step-by-step explanation:

The hl theorem says that if we have two right triangles that have a congruent hypotenuse and a congruent leg, the two triangles are congruent

in this case the exercise says the two leg are congruent, so we have to say that the two hypotenuse are congruent

So

JB congruent to FC

It’s b lol







but ima just add on bc it has to be 20 characters long lol

A customer in a coffee shop purchases a blend of two coffees: Kenyan, costing $3.50 a pound, and Sri Lankan, costing $5.60 a pound. He buys 3 lb of the blend, which costs him $11.55. How many pounds of each kind went into the mixture

Answers

Answer:

10.55.

Step-by-step explanation:

no

For each of the descriptions below, identify the degree and cardinalities of the relationship, and express the relationships in each description graphically with an E−R diagram (You will need to take a screenshot of your ERD and insert it to your solution in the word document) a) A book is identified by its ISBN, and it has a title, a price, and a date of publication. It is published by a publisher, each of which has its own ID number and a name. Each book has exactly one publisher, but one publisher typically publishes multiple books over time. In addition, a book is written by one or multiple authors. Each author is identified by an author number and has a name and date of birth. Each author has either one or multiple books; in addition, occasionally data are needed also regarding prospective authors who have not yet published any books.

Answers

The ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

Based on the given description, we can identify the following relationships and their characteristics:

1. Book - Publisher Relationship:

  - Degree: 1-to-1 (One book has exactly one publisher)

  - Cardinalities: Each book is associated with one publisher, and one publisher can publish multiple books over time.

  - Graphical Representation: The Book entity will have a foreign key referencing the Publisher entity.

2. Book - Author Relationship:

  - Degree: Many-to-Many (One book can have multiple authors, and one author can write multiple books)

  - Cardinalities: Each book can have one or multiple authors, and each author can write one or multiple books.

  - Graphical Representation: To represent the many-to-many relationship between Book and Author, we will introduce a junction table or associative entity, commonly known as the "BookAuthor" entity. It will have foreign keys referencing both the Book and Author entities.

3. Author - Prospect Relationship:

  - Degree: 1-to-0 or 1 (One author can have either zero or one prospect status)

  - Cardinalities: Each author can either have no prospective status (if they have published books) or have a prospective status (if they haven't published any books yet).

  - Graphical Representation: The Author entity will have an attribute indicating the prospect status, such as a boolean flag.

Overall, the ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

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Matrix Metro is a city with m rows and n columns of buildings, with roads connecting these houses to form a grid. Amy is visiting and wants to walk around the city. Help Amy find the length of the longest path that she can walk (i.e. she never walks to the same building twice). Provide a brief explanation as to why it is the maximum. You can assume m, n >= 2.

Answers

The longest path that Amy can walk in Matrix Metro is equal to min(m,n)*2-1.

To see why, imagine that Amy starts at any building in the city. Without loss of generality, let's assume she starts at the bottom left corner of the city.

From this point, she has two options: continue walking to the right or turn up. If she continues walking to the right, she will eventually reach the rightmost column of the city and will have to turn up.

Since Amy cannot visit the same building twice, she can visit at most min(m,n) buildings in each row or column. If she visits all min(m,n) buildings in each row or column, she will visit a total of 2*min(m,n) - 1 buildings.

Therefore, the length of the longest path that Amy can walk in Matrix Metro is min(m,n)*2-1, and this is the maximum because Amy cannot visit any more buildings without visiting the same building twice.

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Marty, Doc, and Einstein are all traveling very fast in
their cars. Marty and Doc's position over time are
shown below in the tables. Einstein only collected two
data points during his trip; after 3 hours he travelled
240 miles and after 4 hours he travelled 320 miles.
Who drove the fastest? Show work. Explain on the
lines below.

Marty, Doc, and Einstein are all traveling very fast intheir cars. Marty and Doc's position over time

Answers

Answer:

Doc drove the fastest.

Step-by-step explanation:

The first thing you want to do is figure out how many milese they are traveling per hour. We know that Einstein has these two time stamps  (hour/miles) ; 3/240 and 4/320.

so divide the hour by the number of miles:

3÷240=80

just to make sure I did the four hour one as well;

4÷320=80

Do the same thing for doc and marty!

Doc

4÷340=85

Marty

4÷100=0.04

The answer that you get from the division problems is the number of miles that they travel each hour.

Hope this helps!

a parking meter that is 1.6m tall costs a shadow of 3.6m long. at the same time, a tree costs a shadow 9m long. which proportion could be used to fin the height of the tree?

Answers

well, 1.6m:3.6m, so then for 9m, we would divide 1.6 by 3.6, which is 0.444444... So, we multiply 9 by 0.444444, which is 3.9999996. We can round this to 4, so 9m:4m. The 9m tall tree casts a shadow of 4m.

The tree casting a shadow of 9 meters is actually 20.25 meters in height.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The information's given that a parking meter that is 1.6m tall costs a shadow of 3.6m long. at the same time, a tree costs a shadow 9m long.

The height of the sign that casts a shadow of 1.6 meters is = 3.6

Then the height of the tree that casts a shadow of 9 meters

= (3.6/1.6) x 9 meters

= 20.25 meters

Therefore, the height is actually 20.25 meters.

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A pocket contains 3 pennies, 2 nickels, 1 quarter and 4 dimes. What is the probability of randomly choosing a dime, replacing it, and then drawing a penny?​

Answers

The probability of both events happening together (drawing a dime and then drawing a penny) is equal to the product of their individual probabilities: (4/10) * (3/10) = 12/100 = 6/50 = 3/25.

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain to occur.

Explain the term events

An event is any outcome or set of outcomes of an experiment or situation. In probability, an event can be a simple event (a single outcome) or a compound event (a combination of outcomes).

According to the given information

The probability of choosing a dime is 4/10 because there are 4 dimes in the pocket and 10 coins in total.

The probability of choosing a penny is 3/10 because there are 3 pennies in the pocket and 10 coins in total. Since we are replacing the dime after we choose it, we can assume that we have 4 dimes and 10 coins again for the second draw.

Therefore, the probability of drawing a penny after drawing a dime is also 3/10.

The probability of both events happening together (drawing a dime and then drawing a penny) is equal to the product of their individual probabilities: (4/10) * (3/10) = 12/100 = 6/50 = 3/25.

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The number of board games cannot be negative. Write this constraint.

The number of role-playing games cannot be negative. Write this constraint

The number of board games cannot be negative. Write this constraint.The number of role-playing games

Answers

Step-by-step explanation:

回答 你今天在做什么 我父亲是一个地球仪 并将其邮寄给今日印度的中央政府组 为年轻人提供在线学习 答案是肯定的 我不确定你是否

Select the correct answer from each drop-down menu.
Sam’s teacher wrote two Boolean expressions on the whiteboard. Identify the names of the laws of these expressions.

Expression 1: X (Y + Z) = X.Y + X.Z

Expression 2: X(Y.Z) = (X.Y)Z = X.Y.Z

The first expression is known as the
law. The second expression is known as the
law.

Answers

The first expression  X (Y + Z) = X.Y + X.Z is distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z is associative property of multiplication.

According to the question,

We have the following two expressions:

X (Y + Z) = X.Y + X.Z

X(Y.Z) = (X.Y)Z = X.Y.Z

Now, the distributive property of multiplication states that the number outside the bracket is multiplied into each number within the bracket and the sign remains the same.

For example, 2(5+7) is 2*5+2*7.

The associative property of multiplication states that the result of the multiplication of numbers is same even when the bracket is changed from one number to another.

Hence, the first expression  X (Y + Z) = X.Y + X.Z is distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z is associative property of multiplication.

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According to the Boolean algebra, the first expression  X (Y + Z) = X.Y + X.Z uses distributive property of multiplication and

The second expression X(Y.Z) = (X.Y)Z = X.Y.Z uses the associative property of multiplication.

Boolean Algebra:

Basically, Boolean algebra is a branch of mathematics that deals with operations on logical values with binary variables.

And there are three properties in Boolean algebra.

They are, Commutative, associative, and distributive properties.

Given,

Sam’s teacher wrote two Boolean expressions on the whiteboard. Identify the names of the laws of these expressions.

Expression 1: X (Y + Z) = X.Y + X.Z

Expression 2: X(Y.Z) = (X.Y)Z = X.Y.Z

Here we need to find the name of the property used by the teacher on those two expression.

While we looking into the question,

We have the give the two expressions:

They are

=> X (Y + Z) = X.Y + X.Z

=> X(Y.Z) = (X.Y)Z = X.Y.Z

When we take the first expression,

X (Y + Z) = X.Y + X.Z

That states that the distributive property of multiplication is used here and the process of the distribution property is the number outside the bracket is multiplied into each number within the bracket and the sign remains the same.

Similarly, when we take the second expression

X(Y.Z) = (X.Y)Z = X.Y.Z

That uses the associative property of multiplication which is the result of the multiplication of numbers is same even when the bracket is changed from one number to another.

Therefore, the first expression  X (Y + Z) = X.Y + X.Z uses the distributive property of multiplication and the second expression X(Y.Z) = (X.Y)Z = X.Y.Z uses the associative property of multiplication.

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Question content area top
Part 1
Reasoning The number of pizzas is in a proportional relationship to the weight of the shredded cheese toppings. When​ shredded, a​ 50-lb block of cheese is enough to make 150 large pizzas. Find the constant of proportionality. Use pencil and paper. Explain how you can use a constant of proportionality to find how much cheese is on one slice of pizza if there are 8 slices per pizza

Answers

there is approximately 0.0139 pounds of shredded cheese toppings on each slice of pizza. To find the constant of proportionality, we can use the formula:

k = y/x

where k is the constant of proportionality, y is the number of pizzas, and x is the weight of shredded cheese toppings.

From the given information, we know that when a 50-lb block of cheese is shredded, it is enough to make 150 large pizzas. Therefore, we can set y = 150 and x = 50:

k = 150/50

k = 3

So the constant of proportionality is 3. This means that for every 3 pounds of shredded cheese toppings, we can make 1 large pizza.

To find how much cheese is on one slice of pizza if there are 8 slices per pizza, we can use the fact that there are 150 pizzas for every 50 pounds of cheese:

3 pounds of cheese = 1 large pizza

50 pounds of cheese = 50/3 large pizzas

If we divide the 50 pounds of cheese by the total number of pizza slices (150 x 8 = 1200), we get the amount of cheese per slice:

50/3 pounds of cheese ÷ 1200 slices = 0.0139 pounds of cheese per slice

Therefore, there is approximately 0.0139 pounds of shredded cheese toppings on each slice of pizza.

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Simplify the expression
6x -(5x-4)

Simplify the expression 6x -(5x-4)

Answers

Answer:

x + 4 OR 1x + 4

Hope this helps, thank you !!

Simplify the expression 6x -(5x-4)

(hurry) pls help me ‍♀️

(hurry) pls help me

Answers

Answer:

C)

a)30

c)55

d)92

...........

Find a formula for a geometric sequence that begins 100, 120, 144, ....

Answers

Answer:

\(b_{n} =b_{1} r^{n-1} =100*1.2^{n-1}\)

Step-by-step explanation:

first number is \(b_{1} =100\)

the cammon ratio is \(r=\frac{120}{100} =\frac{144}{120}=1.2\)

so \(b_{n} =b_{1} r^{n-1} =100*1.2^{n-1}\)

A psychologist conducts a study and finds that d = -63. This effect size would most likely be described as small medium large an error because d cannot be negative

Answers

d)An error because d cannot be negative.

According to the data, effect sizes such as Cohen's d typically range from 0 to positive values, and negative values do not make sense in this context. Therefore, an effect size of d = -63 is likely an error or a typo.

Assuming that the correct effect size is a positive value, the magnitude of the effect size can be described as follows based on Cohen's convention:

A small effect size is around d = 0.2A medium effect size is around d = 0.5A large effect size is around d = 0.8 or higher

However, it's important to note that the interpretation of effect sizes also depends on the context and the specific field of study.

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During a sale, a store offered a 15% discount on a TV that originally sold for $370. After the sale, the discounted price of the TV was marked up by 15%. What was the price of the TV after the markup?

Answers

Answer:

$361.675 dollars

Step-by-step explanation:

Multiply by .85 then take new number multiply by 1.15

Which is a solution of the inequality 7 ≤ −2x + 3 ?
A.) 1
B.) 2
C.) −2
D.) −1

Answers

Answer: x ≤ -2

Option C is correct

Answer:

x ≤ -2 then it is C) -2

Step-by-step explanation:

7 ≤ −2x + 3

2x+7 ≤ + 3

2x ≤ 3-7

2x ≤ -4

x ≤ -4/2

x ≤ -2

use the method of elimination to determine whether the given linear system is consistent or inconsistent. For each consistent system, find the solution if it is unique; otherwise, describe the infinite solution set in terms of an arbitrary parameter t (as in Examples 5 and 7). 3. 2x+3y=1 3x+5y=3 5. x+2y=4 2x+4y=9 7. x−4y=−10 −2x+8y=20

Answers

The given system of linear equations is checked to be consistent or inconsistent.

Given system of linear equations are:

2x+3y=1 3x+5y=3and x+2y=4 2x+4y=9 and x−4y=−10 −2x+8y=20

To determine whether the given linear system is consistent or inconsistent, we use the method of elimination.

Method of Elimination: Add or subtract equations to eliminate a variable. Once a variable is eliminated, the other variable can be solved for, and then the value substituted into one of the original equations to find the remaining variable.

Considering the first equation, 2x+3y=1, and the second equation, 3x+5y=3, we can eliminate x by multiplying the first equation by 3 and the second equation by -2, then add both equations (3 times the first equation plus -2 times the second equation) to obtain:

6x+9y=33-6x-10y=-6

Simplifying this system results in:

y = 1

Substituting y=1 into either of the original equations gives:

x = -1

Therefore, the solution of the system is (-1, 1). The system is consistent and the solution is unique.

Considering the third equation, x-4y = -10, and the fourth equation, -2x+8y=20, we can eliminate x by multiplying the third equation by 2 and the fourth equation by 1, then add both equations (2 times the third equation plus 1 times the fourth equation) to obtain:

0x+0y=0

The last equation is always true, which implies that there are infinitely many solutions in this system of linear equations.

Considering the fifth equation, x+2y = 4, and the sixth equation, 2x+4y=9, we can eliminate x by multiplying the fifth equation by -2 and the sixth equation by 1, then add both equations (-2 times the fifth equation plus 1 times the sixth equation) to obtain:

0x+0y=1

This equation is always false, which implies that there are no solutions in this system of linear equations. Therefore, the given system of linear equations is inconsistent.

Learn more about linear equations here:

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Evaluate to function for the given value of X

Evaluate to function for the given value of X

Answers

\(\text{Given that,}\\\\\\f(x) = 9x^3 -x^2 +2 \\\\f(2) = 9(2^3) - 2^2 +2\\\\~~~~~~~ = 9(8) -4 +2 \\\\~~~~~~~= 72 -2 \\\\~~~~~~~=70\)

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