ERROR ANALYSIS Describe and correct the error in finding the difference.
X
(x²+x) - (2x²-3x)
= (x²+x) + (-2²-3r)
= (x^² - 2x²) + (x²-3x)
=-2²-2x

Answer:

Avery can swim 3 laps in 3 minutes.

According to the given rate the incorrect option is Mason can swim 0.5 lap farther than Avery in 2 minutes.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Given that, Avery can swim 3 laps in 2 minutes. Mason can swim 5 laps in 4 minuets.

Their unit rates are =

Avery = 1.5 laps per minute

Manson = 1.25 laps per minute

Now checking the options,

a) Avery can swim 6 laps in 4 minutes :-

6/4 = 1.5 [correct]

b) Mason can swim 2.5 laps in 2 minutes :-

2.5/2 = 1.25 [correct]

c) Avery can swim 2 laps farther than Mason in 8 minutes :-

Avery laps in 8 minutes = 1.5 × 8 = 12 laps

Mason laps in 8 minutes = 1.25 × 8 = 10 laps

Therefore, Avery is 2 laps farther than Mason [correct]

d) Mason can swim 0.5 lap farther than Avery in 2 minutes :-

Mason in 2 minutes = 1.25 × 2 = 2.5 laps

Avery laps in 2 minutes = 1.5 × 2 = 3 laps

Since, Avery laps are 0.5 farther than Mason, so the option is incorrect.

Hence, the incorrect option is Mason can swim 0.5 lap farther than Avery in 2 minutes.

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The complete question is;-

Avery and Mason are both swimming laps in the same swimming pool.

Avery can swim 3 laps in 2 minutes.

Mason can swim 5 laps in 4 minutes.

Based on these rates, which statement is NOT true?

a) Avery can swim 6 laps in 4 minutes.

b) Mason can swim 2.5 laps in 2 minutes.

c) Avery can swim 2 laps farther than Mason in 8 minutes.

d) Mason can swim 0.5 lap farther than Avery in 2 minutes.

(-2, -4) and (2, 4) is the solution to the given system of simultaneous equation

Given the system of equation

f(x) = x^2 + 2x - 4

g(x) = -2x^2 + 2x + 8

When solving graphically, the point of intersection of both curves on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-2, -4) and (2, 4).

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Answer: B

Step-by-step explanation: I took the test

The equation of the linear function is y = -1/2x - 6

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

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 6

From the graph, we have

A unit increment in x gives an decrement of 1/2 in y

This means that

m = -1/2

So, we have

y = -1/2x - 6

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Answer:

7. 45

8. 78

Step-by-step explanation:

In a bimodal histogram, the two highest bars will have the same height.

The above statement is TRUE that is n a bimodal histogram, the two highest bars will have the same height.

A histogram is said to be bimodal if it has two peaks. The only defining characteristic about this distribution is that it has 2 peaks of the same height. Bimodality sometimes occurs when the data set consists of observations from two different group of individuals. If this shape occurs, the two sources should be separated and analysed separately.

A bimodal histogram shape often reflects the presence of two different processes being "mixed" in the displayed data. For example, the data could contain information from two different machines, two shifts, weekdays and weekends, two offices, etc.

In some cases bimodal histogram indicates that the sample can be divided into two sub samples that differ from each other in some way.

Thus in a bimodal histogram, the two highest bars will have the same height.

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The nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions

So the nine principles of inference are logical guidelines that let us draw reasonable conclusions from a set of assertions or propositions. These guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from preexisting ones. These are the nine inference rules:

Modus Ponens (MP) states that if p implies q and p is true, q must also be true.

Modus Tollens (MT) states that if p implies q but q is untrue, then p is untrue.

Hypothetical Syllogism (HS): P implies R if and only if P implies Q and Q implies R.

Disjunctive Syllogism (DS): If p or q and p are both true, then q is true.

When adding (ADD), if p is true, p or q and these guidelines are frequently used in mathematics, philosophy, and computer science to establish the veracity of claims or create new assertions from pre existing ones. These are the nine inference rules.

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The number 46,000 expressed in scientific notation is 4.6 * 10^4

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

The total area of Pennsylvania is about 46,000 square miles

This means that

Area = 46,000 square miles

So, we have

Area = 4.6 * 10000 square miles

Express 10000 as 10^4

Area = 4.6 * 10^4 square miles

Hence, the expression is 4.6 * 10^4 square miles

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The pound is defined as 453.59237 grams. Using the formula to convert pounds to kilograms, you find that 190 pounds equals 86.18 kilograms.

We know that :

1 lb/ Pound = 0.453592 kilogram

therefore,

190 lbs/ Pound =  86.18 kilogram.

Using the formula to convert pounds to kilograms, you find that 190 pounds equals 86.18 kilograms

To convert 190 pounds (pounds) to kilograms (kg), you must use the conversion factor 1 pound = 86.18 kilogram.

Therefore,

we multiply 190 pounds by 86.18 kg/lb to get the equivalent weight in kilograms:

190 pounds x 0.45359237 kg/lb = 86.1825503 kilogram

Therefore,

190 pounds is 86.18 kilogram.

To understand the conversion factor, you need to know that pounds and kilograms are units of mass, but are used in many parts of the world. In the United States and some other countries, the accepted unit of mass is the pound, while most other countries use the kilogram.

A conversion factor connects the number of pounds to the number of kilograms, so you can easily convert from one unit of measure to another. It is important to use the correct conversion factor for accurate conversion.

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No, the sample is random compared to the size of the shipment.

The number of individuals or observations included in a study is referred to as the sample size.

The sample is not large enough to be representative of the entire shipment, and therefore the manufacturer cannot assume the prediction is valid.

A random sample of 13 out of 5,000 MP3 players is too small to accurately predict the proportion of defective MP3 players in the entire shipment.

Additionally, the way the clerk generated the sample by using numbers 1 through 300 to represent defective MP3 players may have introduced a bias into the sample.

To accurately assess the proportion of defective MP3 players, a larger, more representative sample would be necessary.

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There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests:

2.Khan Academy:

3.Ivy Global:

4.PrepScholar

5.CrackSAT

6.Peterson's

There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests: The College Board, the organization that creates and administers the SAT, offers eight official practice tests for free on their website. These tests are the most accurate representation of the real exam.

2.Khan Academy: The College Board has partnered with Khan Academy to provide free SAT practice materials, including full-length practice tests and personalized study plans based on your performance.

3.Ivy Global: Ivy Global offers a free SAT practice test with answer explanations that mimic the actual test.

4.PrepScholar: Prep Scholar offers a free online SAT practice test that closely resembles the real exam.

5.CrackSAT :  CrackSAT offers a wide range of free practice tests, including SAT Subject Tests.

6.Peterson's: Peterson's offers a free online practice test that includes a score report with detailed feedback.

Remember, the more practice you have, the more prepared you'll be for the SAT. So take advantage of these free resources and practice as much as you can.

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In a 45-45-90 triangle, the legs are always equal and the hypotenuse is always [tex]\sqrt{2}[/tex] times either leg.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angles of triangle= 45-45-90

Now,

This is a special case of a right triangle where the two acute angles are equal to 45 degrees each, and it has some unique properties, such as the fact that the two legs are congruent, and the hypotenuse is the square root of 2 times longer than each leg. This relationship can be expressed mathematically as:

If a and b are the lengths of the legs of a 45-45-90 triangle, and c is the length of the hypotenuse, then:

a = b

c = a * sqrt(2) = b * sqrt(2)

Therefore, in this right triangle the answer will be equal and [tex]$\sqrt{2}$[/tex] times.

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Answer:

-2{x+2y=-4}

2x+3y=1

-2x-4y=8

3y-4y=9

-y=9

y=-9

the value of x is

x+2(-9)=-4

x-18=-4

x=14

therefore { 14,-9}

The quadratic equation with x-intercepts of x = -3 and x = 2, with an intercept of y = -6, is given as follows:

y = x² + x - 6.

A quadratic equation with roots x* and x** is defined as follows:

y = a(x - x*)(x - x**).

In which a is the leading coefficient.

Considering the x-intercepts, the roots of the function are given as follows:

x* = -3, x** = 2.

Hence:

y = a(x + 3)(x - 2)

y = a(x² + x - 6).

The y-intercept is of y = -6, meaning that when x = 0, y = -6, hence the leading coefficient a is given as follows:

-6a = -6

6a = 6

a = 6/6

a = 1.

Hence the function is defined as follows:

y = x² + x - 6.

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Using the volume formula, the required volume of the cone is (A) 871in³.

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

Christmas trees, carrots, party hats, ice cream cones, and traffic cones are five instances of cones in everyday life (used as road dividers).

Explanation: A cone is a three-dimensional solid shape with a circular base at one end and one pointy edge serving as a vertex.

So, the volume of a cone is:

πr²h/3

Now, insert values as follows:

πr²h/3

π8²13/3

871.26836

Round off: 871in³

Therefore, using the volume formula, the required volume of the cone is (A) 871in³.

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Complete question:

what is the volume of the cone to the nearest whole unit?

A. 871in.3

B. 1,307in. 3

C. 1,415in. 3

D. 2,614in.3

First option is correct. The volume of the cone to the nearest whole unit is 871 in³

Given data radius r=8in  and height h=13in

Volume denoted by V

Volume can be defined as how much space can hold by the boundaries 3-dimensional figure.

Formula for Volume of the cone is V=[tex]\pi r^{2} \frac{h}{3}[/tex]

Submit the given values in the above formula.

     V=[tex]\pi 8^{2} \frac{13}{3}[/tex]

      V=π*64*(13/3)    

Simplify and calculate the final result

      V=871.20 in³

Therefor, The volume of the cone to the nearest whole unit is 871 in³

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Answer:

Step-by-step explanation:

If two vectors are perpendicular to each other then their scalar(dot) product must be zero.

Therefore,  

A

.

B

=0

(2

i

^

+2

j

^

​

+3

k

^

)⋅(3

i

^

+6

j

^

​

+n

k

^

)=0

6+12+3n=0

3n=−18

n=−6

Converting milliliters (mL) to ounces (oz) involves using a conversion factor. The conversion factor expresses the relationship between the two units of measurement and is given by 1 mL = 0.033814 oz

To convert milliliters (mL) to ounces (oz), you can use the following conversion factor:

1 mL = 0.033814 oz

This means that one milliliter is equivalent to 0.033814 ounces. To convert a given volume in milliliters to ounces, we can multiply that value by the conversion factor of 0.033814.

For example, let's say we want to convert 500 mL to ounces. We can do this by multiplying 500 mL by 0.033814 oz/mL:

500 mL x 0.033814 oz/mL = 16.907 oz

Therefore, 500 mL is equal to approximately 16.907 ounces.

Note that the conversion factor of 0.033814 is exact, meaning that it has an infinite number of decimal places. However, when we round off the final result, we should choose an appropriate number of decimal places based on the level of precision that we need for the particular application.

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The additional information required to prove  that ΔXYZ and ΔFEG are congruent is  ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE. So option 1 and 5 are correct.

Here in the figure it is given that ∠F and ∠X are congruent. To prove the triangle is congruent we have to prove that either two sides including the angles are congruent or another angle and included side is congruent.

When ∠Z ≅ ∠G and XZ ≅ FG, two angles and included sides are congruent, so triangles are congruent.

∠Z ≅ ∠G and ∠Y ≅ ∠E , we can not apply ASA, since three angles are mentioned

XZ ≅ FG  and ZY ≅ GE , Two sides are given, ASA cannot be applied, we need two angles

XY ≅ EF and ZY ≅ FG, is not possible.

∠Z ≅ ∠G and XY ≅ FE, one corresponding side and two angles are equal, so ΔXYZ ≅ ΔFEG according to ASA.

So, the correct answer is option 1 and option 5.

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The complete question is as follows and image is given below

What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and ∠Y ≅ ∠E

XZ ≅ FG and ZY ≅ GE

XY ≅ EF and ZY ≅ FG

∠Z ≅ ∠G and XY ≅ FE

Answer:

1 and 5 are correct

Step-by-step explanation:

Answer:

M = (2500 + 193.25) / 24 = $113.03

We can use the monthly payment to calculate the finance charge over the life of the loan, which is equal to 24 times the monthly payment minus the principal amount:

Finance charge = 24 * M - 2500 = 24 * 113.03 - 2500 = 193.25

Now that we have the finance charge, we can calculate the APR:

APR = (Finance charge / Principal amount) * (12 / Number of months) * 100%

APR = (193.25 / 2500) * (12 / 24) * 100%

APR = 7.73%

So, the APR of this loan is 7.73%.

Answer:

b-15=16

31

Step-by-step explanation:

Because if your sister is 16 and your brother is that age minus 15 that is her sister's age which means      his age (variable); minus how much older: equals her age

The price of the jeans after the markup is equal to $90.

Generally speaking, the markup price of a product can be calculated by multiplying the cost price by the markup value.

Markup price = 20/100 × 75

Markup\; price = 0.2 × 75

Markup price = $15

Now, we can find the new cost of the jeans after the markup is applied as follows:

New cost = Markup price + Cost price

New cost = $15 + $75

New cost = $90.

In conclusion, we can logically deduce that new cost of the jeans after the markup is applied is 90 dollars.

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A' is a dilation can only make the point bigger!

The coordinate plane movement of a point is referred to as dilation. To achieve this, find the horizontal and vertical distances from the center of dilation, multiply them by a scale factor, and then add those results to get the coordinates of the dilated point.

A dilatation is a kind of transformation that increases or decreases the size of a figure (referred to as the preimage) to produce a new figure (called the image). The size of the dilation image relative to the preimage is determined by the scale factor, r. k will always have a value larger than zero.

Therefore, the correct answer is option a) a dilation can only make the point bigger!

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The information which the line of best fit predict about the increase in the minimum wage over the 70 year period is that: C) Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

In Mathematics, a line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.

Based on the scatter plot, an equation which represents the line of best fit include the following:

y = 0.096x - 0.488.

In this context, we can logically deduce that the initial minimum wage is  $0.488 and the average increase in minimum wage is equal to 0.096 dollars each year between 1940 and 2010.

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The total height of the cake and candles is [tex]16\frac{1}{10}[/tex]

A fraction represents a part of a whole.

Ava's birthday cake is [tex]11\frac{7}{10}[/tex]

Her candles stick up from the cake an additional [tex]5\frac{4}{10}[/tex]

We need to find the total height of the  cake and candles

We have to add both the heights.

[tex]11\frac{7}{10}[/tex] +  [tex]5\frac{4}{10}[/tex]

107/10+54/10

161/10

[tex]16\frac{1}{10}[/tex]

Hence, the total height of the cake and candles is [tex]16\frac{1}{10}[/tex]

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The value of each variable include the following:

x = 5 units.

y = 5√2 units.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = 5.

Adjacent side = x.

Hypotenuse = y.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan45 = 5/x

x = 5Tan45

x = 5(1)

x = 5 units.

Next, we would determine the value of y by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

y² = 5² + 5²

y = √50

y = 5√2 units.

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Answer:

81, 144 and 19

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve for the first problem, we can use this equation:

For the second:

And the third:

Therefore, 81, 144 and 19 are the answers.

The area of the shaded portion of the diagram is 218 mm².

The area of the shaded portion of the diagram can be found by subtracting the area of the triangle XYZ from the the area of the circle.

Area of triangle XYZ = 1/2 * YZ * XY

YZ = 16 mm, XZ = 2 * 10 = 20 mm (XZ is the diameter of the circle)

XY = √(20²-16²) = 12 mm      (Pythagoras' theorem)

Area of triangle XYZ = 1/2 * 16 * 12 = 96 mm²

Area of circle = πr²

Area of circle = 3.14 * 10² = 314 mm²

area of the shaded portion = area of circle - Area of triangle XYZ

area of the shaded portion = 314 - 96 = 218 mm²

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Complete Question

The image of the question is attached