40PT! - Mathematical Proofs: Practice Save and Exit
Select the correct answer from each drop-down menu.

Options for first box - transitive property, subtraction property of equality,
segment addition, substitution property of equality

Options for second box - AC does not equal XZ, AC equals XZ, AB equals YZ,
AB does not equal YZ

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The coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Additionally, if we are aware of the ratio that the line segment connecting two places has produced, we can locate the point of division. The two can be accomplished using a section formula from coordinate geometry.

The coordinates of the points on the line are:

M = (-3, -3)

N = (4, 2)

m= 3

n = 2

Using the section formula we have:

M(x, y) = (mx2 + nx1 / m+n , my2 + ny1 /m + n)

M(x, y) = ((3)(4) + (2)(-3)) / (3 + 2) , (3)(2) + (2)(-3) / (3 + 2))

M (x, y) = (12 - 6 / 5 , 6. -6 / 5)

M (x, y) = (6/ 5 , 0)

Hence, the coordinates of point P that lies along the directed line segment from M to N and partitions the deferment in the ratio 3 to 2 is (6/ 5 , 0).

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The power of a study refers to the ability of a statistical test to correctly detect a difference or association in the population when it actually exists. Decreasing the overall alpha level from 0.10 to 0.05 would increase the power of the study.

The alpha level, also known as the significance level, is the probability of making a Type I error in a statistical test, which is rejecting the null hypothesis when it is actually true. By decreasing the alpha level, the statistical test becomes more stringent, and the likelihood of making a Type I error decreases.

For example, if the alpha level is 0.10, a statistically significant result would be achieved if the p-value (the probability of observing the test statistic under the null hypothesis) is less than or equal to 0.10. If the alpha level is decreased to 0.05, the p-value must now be less than or equal to 0.05 for the result to be considered statistically significant.

In general, decreasing the alpha level makes the test more conservative and increases the power of the study. However, this comes at the cost of increased likelihood of Type II error, which is failing to reject the null hypothesis when it is actually false.

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Answer: en fait je ne sais pas désolé

Step-by-step explanation: désole.

Yes, when the length of the paper strip doubles, so will the number of dots on it.

Yes, when the length of the paper strip doubles, so will the number of dots on it. This is the case because the dots are uniformly spaced apart, and the total number of spaces between the dots doubles as the length of the strip does. As a result, to occupy the same number of spaces as the strip's length, the number of dots must also double. The same rule holds true for every paper strip of any length; increasing the strip's length will result in doubling the number of dots on it. The quantity of dots on the paper strip is therefore directly proportional to the length.

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The cost of broccoli per ounce is $0.06.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

Given  2 pound bag of broccoli costs $1.92,

to find the cost per ounce

we know,

1 pound = 16 ounces

2 pound = 2*16 ounces

2 pound = 32 ounces

cost of 32 ounces = $1.92

cost per ounce = $1.92/32

cost per ounce = $0.06 per ounce

Hence per ounce, the cost is $0.06.

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The Price per ounce is $0.06.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A 2 pound bag of broccoli costs $1.92.

As, 1 pound = 16 ounce

So, the cost of 32 ounce of broccoli is 1.92.

Then, the price per ounce

= 1.92/ 32

= 0.06

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Answer:

⅘

Step-by-step explanation:

We start by subtracting 11 from both sides of the equation:

√5x + 11 - 11 = 9 - 11

√5x = -2

Next, we square both sides of the equation:

(√5x)² = (-2)²

5x = 4

Finally, we divide both sides by 5:

x = 4/5.

The perimeter of the circle is 395.64 m, and the length of wire needed to fence it with 5 rounds is 1,978m

We kow that for a circle, the perimeter is equal to its circumference, and the circumference of a circle of radius R is:

C = 2*pi*R

Where pi = 3.14

Then the perimeter of a circle of radius of 63m is:

Perimeter = 2*3.14*63m = 395.64 m

And the length of wire needed to fence it with 5 rounds is 5 times that, so we will get:

total length = 5*395.64 m = 1,978m

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The tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.

Tax refers to a compulsory financial charge or some other type of levy imposed upon a taxpayer (an individual or legal entity) by a governmental organization in order to fund various public expenditures. The tax amount is typically determined by the taxpayer's income or wealth and is used to fund various public services such as national defense, infrastructure, social services, and other government operations. Taxes can be direct, such as income tax, or indirect, such as sales tax. They are typically collected by the government through various tax collection agencies, and failing to pay taxes can result in penalties and legal consequences.

From the tax table, for a taxable income of $27,811 (which is greater than $27,450 and less than $27,500), the tax for a head-of-household taxpayer is $3,103.

Therefore, the tax for a head-of-household taxpayer with a taxable income of $27,811 is $3,103.

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Answer:

a=4

b=18

c=30

d=46

e=60

Step-by-step explanation:

you first write the 4 and then add 14 i.e the next number on the frequency row. then you add the next number to the answer you get and so on

Step-by-step explanation:

The first term is, 3a2 its coefficient is 3 .

The middle term is, -10a its coefficient is -10 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 3 • 7 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -10 .

-21 + -1 = -22

-7 + -3 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -3

3a2 - 7a - 3a - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (3a-7)

Add up the last 2 terms, pulling out common factors :

1 • (3a-7)

Step-5 : Add up the four terms of step 4 :

(a-1) • (3a-7)

Which is the desired factorization

Equation at the end of step

2

:

(3a - 7) • (a - 1) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : 3a-7 = 0

Add 7 to both sides of the equation :

3a = 7

Divide both sides of the equation by 3:

a = 7/3 = 2.333

Solving a Single Variable Equation:

3.3 Solve : a-1 = 0

Add 1 to both sides of the equation :

a = 1

Supplement : Solving Quadratic Equation Directly

Solving 3a2-10a+7 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

4.1 Find the Vertex of y = 3a2-10a+7

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aa2+Ba+C,the a -coordinate of the vertex is given by -B/(2A) . In our case the a coordinate is 1.6667

Plugging into the parabola formula 1.6667 for a we can calculate the y -coordinate :

y = 3.0 * 1.67 * 1.67 - 10.0 * 1.67 + 7.0

4.2 Solving 3a2-10a+7 = 0 by Completing The Square .

Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :

a2-(10/3)a+(7/3) = 0

Subtract 7/3 from both side of the equation :

a2-(10/3)a = -7/3

Now the clever bit: Take the coefficient of a , which is 10/3 , divide by two, giving 5/3 , and finally square it giving 25/9

Add 25/9 to both sides of the equation :

On the right hand side we have :

-7/3 + 25/9 The common denominator of the two fractions is 9 Adding (-21/9)+(25/9) gives 4/9

So adding to both sides we finally get :

a2-(10/3)a+(25/9) = 4/9

Adding 25/9 has completed the left hand side into a perfect square :

a2-(10/3)a+(25/9) =

(a-(5/3)) • (a-(5/3)) =

(a-(5/3))2

Things which are equal to the same thing are also equal to one another. Since

a2-(10/3)a+(25/9) = 4/9 and

a2-(10/3)a+(25/9) = (a-(5/3))2

then, according to the law of transitivity,

(a-(5/3))2 = 4/9

We'll refer to this Equation as Eq. #4.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(a-(5/3))2 is

(a-(5/3))2/2 =

(a-(5/3))1 =

a-(5/3)

Now, applying the Square Root Principle to Eq. #4.2.1 we get:

a-(5/3) = √ 4/9

Add 5/3 to both sides to obtain:

a = 5/3 + √ 4/9

Since a square root has two values, one positive and the other negative

a2 - (10/3)a + (7/3) = 0

has two solutions:

a = 5/3 + √ 4/9

or

a = 5/3 - √ 4/9

Note that √ 4/9 can be written as

√ 4 / √ 9 which is 2 / 3

HOPE IT HELPS.

PLEASE MARKE AS BRAINLEST.

NOTE:IF THIS IS NOT WHAT YOU WANT,INFORM ME AND I WILL GOVE BETTER ANSWERS

The appropriate test to see if neck size and number of teeth have a linear relationship in 18 randomly selected puppies is the t-test for slope of regression line.

A regression line is a line that best fits the data by minimizing the sum of the squared differences between the observed and predicted values. A t-test for slope of regression line tests the null hypothesis that the slope of the regression line is equal to zero, which would indicate that there is no linear relationship between the variables.

In this case, neck size and number of teeth are two continuous variables and we want to test if there is a linear relationship between them. A t-test for slope of regression line would provide information on the significance of the relationship and the direction of the relationship (positive or negative).

It is important to note that the test conditions such as independence, normality, and homoscedasticity must be met before conducting the test. If these conditions are not met, the results of the test may be biased and should be interpreted with caution.

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Complete Question: Comparing the neck circumference (in inches) and tooth count of 18 puppies chosen at random. Which statistical analysis should be performed to determine whether there is a linear relationship between neck size and tooth count? Assume that every test requirement is satisfied.

a. Z-test with two samples

b. T-test with two samples

c. Test of two proportions

d. T-Test for Regression Line Slope

e. Z-test for one proportion

The distance between the golf balls is determined to be 14 feet.

Let's call the distance between the two golf balls "d".

Using the law of cosines, we can find the value of d by using the angles and the two distances to the hole:

d² = 8² + 13² - 2 * 8 * 13 * cos(64)

d² = 64 + 169 - 104 * cos(64)

d² = 233 - 104 * cos(64)

Next, we'll use a calculator to find the value of cos(64):

cos(64) = 0.37

So,

d² = 233 - 104 * 0.37 = 233 - 38.48

d² = 194.52

Finally, we'll take the square root of both sides to find the value of d:

d = √(194.52) = 14.0

So the distance between the golf balls is 14 feet.

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Answer:

Step-by-step explanation:

The answer is x + 14. If just adding 2 to (x + 12), the parenthesis can be disregarded.

Answer:

(x + 6)(x + 4)

Step-by-step explanation:

x² + 10x + 24

= x²+ 6x + 4x + 24=0

= x(x + 6)+4(x + 6)

= (x + 6)(x + 4)

Answer:

(x + 6)(x +4)

Step-by-step explanation:

x² + 10x + 24

    Sum = 10

Product = 24

Factors = 6 , 4        

{When we multiply 6 and 4, we get 24  & when we add 6 and 4, we get 10}

x² + 10x + 24 = x² + 6x + 4x + 24    {Rewrite the middle term using the factors}

                    = x(x + 6) + 4 (x + 6)

{Group the first two terms and third & fourth term together. Then take out the common factors}

                   = (x + 6)(x + 4)

The required radical form of the given expression [tex](x^2)^{4/3}[/tex] is ∛x⁸.

Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.

To rewrite [tex](x^2)^{4/3}[/tex]in radical form, you can simplify it by dividing the fractional part by the same number which will turn the fraction into a whole number. In this case, that number is 3.

So, you can simplify [tex](x^2)^{4/3}[/tex] as follows:

[tex](x^2)^{4/3}[/tex]

[tex]x^{2\times4/3}[/tex]

[tex]x^{8/3}[/tex]

[tex](x^8)^{1/3}[/tex]

∛x⁸

This is the radical form of [tex](x^2)^{4/3}[/tex].

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Answer:

Step-by-step explanation:

0.267

No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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The solution is, x= 50  &  y= 19.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

1.5x−y3=18

2x−3y=43

solving the equations in graph , we get,

x= 50

y= 19

Hence, The solution is, x= 50  &  y= 19.

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The slope formula to calculate the slope of the ocean floor would be

[tex]slope = \frac{y}{x}[/tex].

What is slope?

The slope of a line characterizes its direction.

To find the slope of the ocean floor, we need to calculate the rise (change in depth) and the run (distance along the ocean floor) between the edge of the continental shelf and the beginning of the oceanic crust.

Let's call the depth of the water at the edge of the continental shelf "d1" and the depth of the water at the beginning of the oceanic crust "d2". Then, the rise is:

rise = d2 - d1

We don't have the actual values for d1 and d2, so let's call the rise "y" and the run "x". Then, the slope of the ocean floor is given by:

[tex]slope =\frac{rise}{run} \\\\slope = \frac{y}{x}[/tex]

So, we can use the slope formula to calculate the slope of the ocean floor.

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Answer:

D 588 miles

Step-by-step explanation:

We know

Leo is training for a marathon later this summer. He has run 42 miles over the last 3 days.

42 divided by 3 = 14 miles per day

So, he runs at a rate of 14 miles per day.

If he continues to run at the same rate, how many miles will he run over the next 6 weeks?

1 week = 7 days

1 week = 14 x 7 = 98 miles

6 weeks = 98 x 6 = 588 miles

So, he will run 588 miles over the next 6 weeks.

Answer: 12.2

Step-by-step explanation: I did 8 times 6.3= 50.4

Then 8 times 4.4=35.2.

50.4-35.2=15.2 then minus the 3 is 12.2

Step-by-step explanation:

The circle as a whole is one.

So to find the shaded area find a common denominators for both first

1/4 = 7/28

2/7= 8/28

Add the two together

7/28 + 8/28 = 15/28

This is the area taken up the the white fractions areas

Now because the circle is one

28/28 - 15/28 = 13/28

So the area of the blue is

13/28

Hope this helped :)

Answer:

[tex]-\frac{3}{2} , -\frac{4}{9} , \frac{2}{11}, 0.7[/tex]

Step-by-step explanation:

Negative numbers are obviously smaller than positive numbers, hence, we have -4/9 and -3/2.

-3/2 is obviously have a smaller value than -4/9 as the mixed number for it is -1  1/2.    [In negative numbers, the larger the number, the smaller the value it holds.]

[tex]0.7= \frac{7}{10}[/tex]

We can turn the denominator of 2/11 and 7/10 to the same number, 110.

[tex]\frac{2}{11} = \frac{20}{110}[/tex]

[tex]\frac{7}{10} = \frac{77}{110}[/tex]

Hence, we know that 77 is larger than 20, so, the largest number is 0.7.

The two amount of numbers are 11 and 135. 11 is a multiple of 11 and 135 is a multiple of 17. The sum of the two numbers is 146.

Step 1: One of the numbers is a multiple of 11

Let the number be 11x, where x is an integer

Step 2: The total of the two numbers is 146

Therefore, 11x + 17y = 146, where y is an integer

Step 3: Solve the equation

11x + 17y = 146

11x = 146 - 17y

x = (146 - 17y) / 11

Step 4: Find the two numbers

x = (146 - 17y) / 11

For y = 1, x = 11

Therefore, the two numbers are 11 and 17.

The two numbers that add up to 146 are 11 and 135. 11 is a multiple of 11, which means it is divisible by 11 without any remainder. 135 is a multiple of 17, which means it is divisible by 17 without any remainder. When these two numbers are added together, the sum is 146. This means that 11 and 135 are the two numbers that add up to 146. 11 is a multiple of 11 and 135 is a multiple of 17, which explains why the sum of the two numbers is 146. The two numbers together can be used to represent a variety of different mathematical equations, such as the addition of two integers or the multiplication of two fractions. Knowing the two numbers that add up to 146 can be useful in a variety of different scenarios, such as solving math problems or accounting for the total of two items.

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The value of x is obtained as follows:

x = 9.

Similar triangles are triangles that share these two features presented as follows:

Considering the equivalent side lengths, the proportional relationship for this problem is given as follows:

8/6 = 12/x.

Applying cross multiplication, the value of x is obtained as follows:

8x = 72

x = 72/8

x = 9.

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The air conditioner is being sold for $673.20. The discount price is lower than the initial price of $680 because this is less. The air conditioner is therefore being sold for less than what it originally cost.

A singular tax known as GST is applied to the supply of products and services from the customer to the manufacturer. GST is basically a tax only on productivity improvement at each stage because credits of supply taxes paid at each step will be accessible in the following stage of value addition.

The first step is to calculate the GST that is added to the original price of the air conditioner:

GST = 10% of $680 = 0.1 x $680 = $68

So the total cost of the air conditioner including GST is:

Total cost = $680 + $68 = $748

Now, the air conditioner is sold at a 10% discount. To find the sale price, we need to subtract 10% of the total cost from the total cost:

Sale price = Total cost - 10% of Total cost

= $748 - 0.1 x $748

= $748 - $74.80

= $673.20

The sale price of the air conditioner is $673.20.

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ABCD is a parallelogram and ∠ BID is equal to ∠ BAI, which means that IA is a bisector of ∠BID.

An angle's bisector divides the angle into two identical segments. We must demonstrate that ∠BID equals ∠ BAI in order to demonstrate that IA is a bisector of ∠BID.

Since ABCD is a parallelogram, we have:

AB || CD, which means that ∠ABD is equal to ∠ADC.

BC || AD, which means that ∠ ABC is equal to ∠ DAC.

Adding these equal angles, we have:

∠ABD + ∠ ABC = ∠ ADC + ∠ DAC

∠BDA = ∠CDA

Also, since BM = DN, we have:

∠DBM = ∠ DNM (by vertical angles)

Adding these equal angles, we have:

∠ BDA + ∠ DBM = ∠CDA + ∠ DNM

∠ BID = ∠ BAI

Therefore, we have shown that ∠ BID is equal to ∠BAI, which means that IA is a bisector of ∠BID.

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Answer: Let's use "x" to represent the number of electoral votes in Florida. Then, we can write the equation for North Carolina's number of electoral votes as "x - 12".

The equation can then be written as:

x + (x - 12) = total number of electoral votes

Solving for x, we get:

2x - 12 = total number of electoral votes

2x =total number of electoral votes + 12

2x = total number of electoral votes + 12

x = (total number of electoral votes + 12)/2

So, the number of electoral votes for Florida is (total number of electoral votes + 12)/2.

Note: The total number of electoral votes for both states needs to be known in order to solve for the number of electoral votes in Florida.

Step-by-step explanation:

The area of the base of the triangular prism is 3 inches square.

The figure above is a triangular prism. Therefore, the base of the triangular prism is a triangle.

Therefore, let's find the area of the base.

Hence,

area of the base = 1 / 2 bh

where

Therefore,

b = 5 inches

height = 1.2 inches

Hence,

area of the base = 1 / 2 × 5 × 1.2

area of the base = 6 / 2

Therefore,

area of the base = 3 inches²

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