consider the proposed proof that all real numbers are equal to 0 below. which is the first line that contains an error?

It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.

Let's consider two consecutive even numbers.

If n = a positive integer

Then the 1st even number would be = 2n

Let the next consecutive even number = 2(n+1)

The consecutive even numbers would be:

2n, 2(n+1)

The square of each consecutive even number is given by -

(2n)² = 2n ×2n = 4n²

[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)

Expanding, we get,

= 4n² +4n +4n+4

[2(n+1)]² = 4n²+8n+4

To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.

Let n = 1, 2, 3

For n= 1,

4n² = 4(1)² = 4×1 = 4

4n²+8n+4 = 4(1)² + 8(1) + 4

= 4+8+4 = 16

Thus, the difference between the squares of consecutive even numbers = 16-4 = 12

For n= 2,

4n² = 4(2)² = 4×4 = 16

4n²+8n+4 = 4(2)² + 8(2) + 4

= 16+16+4 = 36

Thus, the difference between the squares of consecutive even numbers = 36-16 = 20

For n= 3

4n² = 4(3)² = 4×9 = 36

4n²+8n+4 = 4(3)² + 8(3) + 4

= 36+24+4 = 64

Thus, the difference between the squares of consecutive even numbers = 64-36 = 28

Clearly, we can see that 12, 20, and 28 are multiples of 4.

Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

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The average rate of change of the number of chevy car sales from 1990 to 1992 is 1

What is the average change rate?

The average rate of change is the rate at which one value in a function changes in relation to another. Usually, the average rate of change is used to calculate the slope of a graphed function.

The average rate of change of a function is determined by the slope of the line connecting the two endpoints of a specific interval (known as the secant line).

According to the given question:

The average rate of change of the number of chevy car sales from 1990 to 1992 is (total chevy car sold in 1992- total chevy car sold in 1990)/ Total difference in no. of years

That gives (156-154)/2

So, the average rate of change of the number of chevy car sales from 1990 to 1992 is 1

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The quadratic functions given are matched with the parameters as follows

f(x) = -0.3(x - 2)² + 5           f(x) = 0.2(x + 2)² - 5

vertex (-2, 5)                      

axis of symmetry, x = -2    axis of symmetry, x = 2

focus f (-2, 4 1/6)                focus f (2, -3 3/4)

Both the vertex form and the standard form of the quadratic equation are used in the axis of symmetry formula. Any geometric shape is divided into two equal halves by the symmetry.

Parabolic equation in vertex form is written as

f(x) = a (x - h)² + k

the vertex is v (h, k)

f(x) = -0.3(x - 2)² + 5, v (-2, 5)

f(x) = 0.2(x + 2)² - 5, v ( 2, -5)

The axis of symmetry formula is given as, x = h

f(x) = -0.3(x - 2)² + 5, x = -2

f(x) = 0.2(x + 2)² - 5, x = 2

the focus, f (h, k + 1/4a)

f(x) = -0.3(x - 2)² + 5, f (-2, 5 + 1/(4 * -0.3)) = f(-2, 5 - 5/6) = f (-2, 4 1/6)

f(x) = 0.2(x + 2)² - 5, f (2, -5 + 1/(4 * 0.2)) = f(2, -5 + 1/0.8) = f (2, -3 3/4)

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Answer: the right answer is D

Step-by-step explanation:

If you multiply 4 by 2 you get 8. If this goes on the answers are aways the same and it’s going to be proportional

The exact value of the minimum of function  f(x) = x^2 e^−x for x ≥ 0 is f(x) = 0

In this question we have been given a function  f(x) = x^2 e^−x

We need to find the exact value of the minimum of function for x ≥ 0.

Consider the first derivative of the function

f'(x) = x^2 f/dx(e^−x) + e^−xd/dx(x^2)

f'(x) = -x^2 e^(-x) + e^-x (2x)

f'(x) = xe^-x (2 - x)

To find the critical points., consider f'(x) = 0

xe^-x (2 - x) = 0

xe^-x = 0,   (2 - x) = 0

x = 0, x = 2

Substitute the value of critical point into the function.

f(0) =  0^2 e^(0)

f(0) = 0

and f(2) =  2^2 e^-2

f(2) = 0.5413

This means, the minimum of the function occurs at x = 0

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Answer:

360 cm³

Step-by-step explanation:

height of bottom layer = 7 - 2 = 5cm

Volume = 9 · 8 · 5 = 360 cm³

The lines a and b are parallel. The proof is given.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

Statement 1:

∠1 and ∠6 are supplementary.

Justification:

If two angles sum up to 180 degrees, they are referred to as supplementary angles.

That means,

∠1 + ∠6 = 180°  

∠1 = 180°- ∠6

∠1 =∠5, given that the angles are made by intersecting lines.

Statement 2:

∠1 ≅∠4

Justification:

Vertical angles are also congruent angles, meaning they are equal or have the same measurement.

Two crossing lines actually create two sets of opposite angles that, when the measures of their angles, are added all together.

Since, ∠1 ≅∠4

That means, ∠4 and ∠6 are supplementary.

Statement 3:

∠4 and ∠6 are supplementary.

Justification:

If two angles sum up to 180 degrees, they are referred to as supplementary angles.

Statement 4:

a and b are parallel lines.

Justification:

This means that lines a and b make the same angle with the intersecting line, meaning they don't intersect each other at any point.

a and b are parallel lines.

Therefore, the all statements are true.

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Answer:

433 pizzas

Step-by-step explanation:

6062 / 14 = 433

4 quarts in a gallon, 8 quarts in 2 gallons, so 32.40 divided by 8 is $4.05..

each quart cost 4 dollars and 5 cents

Step-by-step explanation:

The price per quart will be $4.05.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that 4 quarts are in a gallon. Therefore, since the 2-gallon container of laundry detergent costs $22.00. The price per quart will be:

= $22.00 / (4 × 2)

= $4.05

The price is $4.05.

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The inequality to represent this situation is 5 + 1.25x < 45.

Rob and Ahab are in Las Vegas for vacation. They get a taxi to drive

them around town. The taxi charges a flat fee of $5.00 plus $1.25 per

mile of traveling. They want to spend less than $45.00 for their taxi

fare. The inequality to represent the situation is as follows:

let

x = number of miles

Therefore, the inequality is as follows:

5 + 1.25x < 45

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Answer:

7.5 joules

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the box is 5 newtons and the distance over which the force is applied is 1.5 meters.

The amount of work done on the box is therefore 5 newtons * 1.5 meters = 7.5 joules. This is the amount of energy that has been transferred to or from the box as a result of the force applied to it.

Answer:

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

The distance traveled in each minute is a speed.

Find the speed per min for each distance:

Since the speed is not same over the total distance, the first choice is correct.

Find the average speed over the given distance:

Find the predicted time to travel 30 km:

Value of x is -6

According to question

(x/2)-6 = 2+(2x+1)

⇒x-12/2 = 3+2x

⇒x-12=2(3+2x)

⇒x-12=6+4x

⇒-3x=18

⇒x=18/-3

∴x=-6

The value of x is -6.

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Answer:

x = - 6

Step-by-step explanation:

(b)

[tex]\frac{1}{2}[/tex] x - 6 = 2 + (2x + 1) ← remove parenthesis

[tex]\frac{1}{2}[/tex] x - 6 = 2 + 2x + 1

[tex]\frac{1}{2}[/tex] x - 6 = 2x + 3 ( add 6 to both sides )

[tex]\frac{1}{2}[/tex] x = 2x + 9 ( multiply through by 2 to clear the fraction )

x = 4x + 18 ( subtract 4x from both sides )

- 3x = 18 ( divide both sides by - 3 )

x = - 6

324 miles can Mario drive with 9 gallons of gas.

The term "proportional" refers to any connection where the ratio and amount fluctuate directly with one another.

As per the details share in the above question we get,

The data are as follow,

Mario has a driving range of 18 miles  ½ gallon of gas.

Here we have to find how many miles can mario drive with 9 gallons of gas.

Thus we know that,

He can travel 18 miles on just half a gallon of fuel.

Let x be the amount of miles that 9 gallons of gas will cover.

Thus, if we use the notion of proportion, we obtain

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Mario can travel 324 miles on 9 gallons of gas.

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(1) We incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

(2) The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

1) Assume you predicted the variable "Number of Promotion Earned" by regressing it against just two other variables, "Income in $s" and "Years of Experience."

When compared to the beta for years of experience, the income beta is quite modest. You incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

But until we standardize the variables, this is incorrect. Then they can be put side by side.

2) As HR, I was questioned about whether employees who earn more money perform better. Do those with higher salaries complete the same task more quickly? I've been given data with two columns: "HIGH" salary people's income, and "LOW" salary people's income.

I conduct an ANOVA method test on two groups of individuals and track their typical completion time. The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

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The complete question is:

First, how can graphics and/or statistics be used to misrepresent data? Where have you seen this done? Second, image that you are a human resources (HR) analyst reporting to a recently hired supervisor. Your supervisor has asked you to provide an example of data processed by HR. Describe one type of data that an HR department may process, and discuss a corresponding statistical method that may be used to summarize the data.

Option A is the correct answer

A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial. A third-degree polynomial is of the form f(x) = ax³ + bx²+ cx + d where is not equal to zero. It is also called a cubic polynomial as it has a degree of 3.

Given here the polynomial as g(x) = f(2x)

                                                         =8ax³ + 4bx²+2cx + d

Both the polynomial have the same constant d and therefore the same y-intercept.

Hence, the correct option is B

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The Density of object is 10,490 kg/m³

What is Density, Mass and Volume ?

Given,

Mass = 73,430 Kg

Volume = 7 m³

We know,

Density = Mass / volume

Now, plug in the values

Density = 73430/7

             = 10, 490 kg/m³

Hence, the Density of object is 10,490 kg/m³

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Answer:

12

Step-by-step explanation:

Yes, the instructor should use linear regression to predict exam scores for a student who studied 10 hours for the final.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Nonlinear regression uses a curve to associate the variables, whereas linear regression uses a straight line.

If a clear linear relationship can be shown on the scatterplot, linear regression may be useful. The use of linear regression is appropriate because there is a high correlation. So, it is concluded that it is beneficial for instructor to use linear regression.

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The number sentence to find how many people are on all the buses is 7 x10 = ?. (Option C)

A number sentence refers to an equation or inequality which expresses using numbers and mathematical symbols. Examples of number sentences include 32 + 57 = ? or 5 x 6 = ?. In the given situation, Jack sees 7 buses and each bus has 10 people on it. In order to determine the total number of buses on all the buses, multiplication operation is used. Multiplication, one of the four basic mathematical operations of arithmetic, refers to an operation that represents the basic idea of repeated addition of the same number. Hence, it is used to combine groups of equal sizes. As in the given case, the group of equal size i.e., the number of people on each bus is seen in 7 buses, the total number of people would be the product of two and would be represented by 7 x10 = ?.

Note: The question is incomplete. The complete question probably is: Jack sees 7 buses. Each bus has 10 people on it. Which number sentence can be used to find how many people are on all the buses? A. 7 + 10 = ? B. 10 – 7 = ? C. 7 x10 = ? D. 10 ÷ 7 = ?

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Answer:

63

Step-by-step explanation:

using the ratio

[tex] \frac{4}{1} = \frac{252}{x} [/tex]

cross multiply

[tex]4x = 252[/tex]

divide both sides by (4)

[tex] \frac{4x}{4} = \frac{252}{4} [/tex]

x = 63

i hope this helps

The correct answer is x = 63

[tex]\boxed{\frac{4}{1}=\frac{252}{x}4x=252\frac{4x}{4} =\frac{252}{4}x=63 }\\\huge\boxed{\underline_ So, \frac{4}{1}=\frac{252}{\bold{63}} }[/tex]

Therefore, the correct answer is x = 63

Answer: 300 miles

Step-by-step explanation:

Let x be the number of miles

We have the equation below

20 + 0.35x = 35 + 0.30x

Subtract 20 from both sides

0.35x = 15 + 0.30x

Then subtract 0.30x from both sides

0.05x = 15

Then divide by 0.05 from both sides

x = 300 miles

The distance between the two given points is 13 units.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagorean theorem is given by the following formula:

h² = a² + b²

Where h is the hypotenuse and a and b are the legs of the right triangle.

In the given image, when you construct a right triangle with the line of the two points as a hypotenuse, you have for a and b:

a = 5

b = 12

Replace the previous values of a and b in the formula for h:

h² = (5)² + (12)²

h² = 25 + 144

h² = 169

h = √169

h = 13

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Answer: A

Step-by-step explanation:

:D

the answer is A. because x² is quardatic function and x³ is cubic function

Answer: 30%

Step-by-step explanation:

First, take 300 divided by 1000, then times 100% = 30% for 6 years

If you want to find the rate for each year

The take 30% divided by 6

You get 5% each year

940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

Given that,

An amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.

We know that,

Formula is

S=a(r+1)ⁿ

Here,

S is initial value

a is 800

r is 5.5%

n is time 30/10

800×(5.5%+1[tex])^{30\div10}[/tex]

=939.3931

Therefore, 940 is the quantity's value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

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Answer:

939.39

Step-by-step explanation:

The researcher can use two categorical variables or two values from a contingency table to perform chi - squared test.

A standard hypothesis test used to analyze contingency tables with large sample sizes is the chi-squared approach. This test is designed to examine if two categorical factors influence the test statistic independently. Pearson's chi-squared test and its variants are true when the test statistic equals chi-squared under the null hypothesis.

Pearson's chi-squared test is used to determine whether there is a statistically significant difference between expected and observed frequencies for one or more contingency table categories. For contingency tables with fewer samples, a Fisher's exact test is employed instead.

In the traditional application of this exam, observations are classified into mutually exclusive kinds. If the null hypothesis is correct and there are no variations in the population between classes, the test statistic generated by the data has a two-frequency distribution.

The test's purpose is to estimate how likely observed observed frequencies are if the null hypothesis is true.

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The slope of the line is 2/3.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Given coordinates of the points are A(1,-9) and (4,-7).

The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

Here x₁ = 1, y₁ = -9, x₂ = 4, and y₂ = -7

m = (-7 - (-9))/(4 - 1)

m = 2/3

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A total discount of $18.6 and 1860 cents is availed by Amadou in buying pair of sunglasses after the final step of processing charge.

Given the intital price as $60 i.e cost price

given he had a coupon code to get discount of 40%

so after apply discount the price of pair of sunglasses is [tex]\frac{100-40}{100} *60[/tex]

=> 0.6 *60

=>36

so the current price of pair of sunglasses is $36

now we need to apply 15% processing fee after the discount so the current price of pair of sunglasses will increase from previous value and is given by:

[tex]36 + \frac{15}{100} *36[/tex]

=>36 + 5.4

=> 41.4

so the final price of pair of sunglasses is $ 41.4

Total discount = initial price - final price

=> 60- 41.4

=> $18.6

$1 = 100 cents

so total discount = 18.6 *100 = 1860 cents

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