Research On effects of poor scale Interpration in maths​

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The origin of the number zero is believed to be ancient India, where it was invented as a placeholder in the decimal system around the 5th century CE. The concept of zero as a number in its own right was a revolutionary idea that greatly advanced mathematical understanding and allowed for much more efficient mathematical calculation. From India, the use of zero spread to the Islamic world and eventually to the West. The modern representation of zero as a circle or a digit was introduced in the 13th century in India.

For k =3, y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].

The differential equation is [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].

Let y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].

So y' = k[tex]x^{k-1}[/tex]

y'' = k(k-1)[tex]x^{k-2}[/tex]

Now putting the value of y, y' and y'' in the differential equation.

[tex]x^2[/tex](k[tex]x^{k-1}[/tex])(k(k-1)[tex]x^{k-2}[/tex]) - 4[tex]x^k[/tex](k[tex]x^{k-1}[/tex]) = 6[tex]x^5[/tex]

Now simplifying the equation.

[tex]k^2(k-1)x^2x^{k-1}x^{k-2} - 4kx^kx^{k-1}[/tex] = 6[tex]x^5[/tex]

As we know that the power gets add in the multiplication so

[tex]k^2(k-1)x^{(2+k-1+k-2)} - 4kx^{(k+k-1)}[/tex] = 6[tex]x^5[/tex]

[tex](k^3-k^2)x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]

[tex]k^3x^{2k-1}-k^2x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]

Taking common [tex]kx^{2k-1}[/tex]

[tex]kx^{2k-1}(k^2-k - 4)[/tex] = 6[tex]x^5[/tex]

On comparing

2k-1 = 5

Add 1 on both side, we get

2k = 6

Divide by 2 on both side, we get

k = 3

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The complete question is:

For what value of k is y = [tex]x^k[/tex] a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex]?

The correct statement about the comparison between Manuel’s and Gretchen’s data is: Gretchen’s data values are more spread out than Manuel’s data values because the mean and median and interquartile range mean and standard deviation and interquartile range are larger for Gretchen's data than for Manuel’s data.

The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics.

The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.

Hence, from the data gotten from both Manuel and Gretchen shows differences in them.

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After solving the statement we get ¬(p → q)→ ¬q = T. So, the conditional statement ¬(p → q)→ ¬q is a tautology.

The conditional statement is ¬(p → q)→ ¬q.

We construct table:

p              q              p → q              ¬q              ¬(p → q)              ¬(p → q)→ ¬q

T              T                 T                   F                     F                           T

T              F                 F                   T                    T                            T

F              T                 T                   F                    F                            T

F              F                 T                   T                    F                            T

As we know that the conditional statement is a tautology. So

¬(p → q)→ ¬q

As p → q = ¬p ∨ q and ¬(¬p) = p. So

¬(¬(p → q)) ∨ ¬q

(p → q) ∨ ¬q

As we know that q ∨ ¬q = T and q ∨ T = T. So

¬p ∨ (q ∨ ¬q)

¬p ∨ T

T

Hence, ¬(p → q)→ ¬q is Tautology.

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The parabola function has a minimum value of -4.

The given parameters are:

Declines through (-5,-2), (-3,-4)

Rises through  (-2, -3), (-1, -2), (0, 0), (0, 2) and (1, 4)

Because the parabola declines before it rises, it means that the function has a minimum

From the point of decline;

-4 is less than -2

Hence, the parabola function has a minimum value of -4.

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Answer:

Step-by-step explanation:

Supplementary angles add up to 180.

49 + 131 = 180  b

114 + 66 = 180  d

71 + 109 = 180  c

87 + 93 = 180   a

Answer:

16.25

Step-by-step explanation:

1% = 5

times 1 by 3.15 so,

5x3.15=16.25

The function is continuous on [−2,2], and its derivative is f′(x)=4 x 3−9 x 2. Because x=9/4 is not in the interval [−2,2], the only critical point occurs at   x = 0 which is (0,−1).

What is meant by function ?

To the complete questions is;    

Find the maximum and minimum values of f(x)= x 4−3 x 3−1 on [−2,2].

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Hello, your answer should be B. I hope this helps. Have a great day! ~Ray

Hello!

If six friends went to a movie and spent $9 per each ticket and also purchased a small bag of popcorn each with them spending a total of $82.50, the cost of each small bag of popcorn costs $4.75.

Step-by-step explanation:

[tex]6[/tex] × [tex]9=54[/tex]

[tex]82.50-54=28.50[/tex]

[tex]28.50[/tex] ÷ [tex]6=4.75[/tex]

Hope this helps!

The numeric value of the expression 5/8 - 5/12 x 3/4 + 2/3 is given as follows:

47/48.

The expression for this problem is defined as follows:

5/8 - 5/12 x 3/4 + 2/3

The multiplication operation has a higher precedence over the addition/subtraction operation, hence it must be solved first.

5/12 x 3/4 = 15/48.

Then the expression is given as follows:

5/8 - 15/48 + 2/3.

Using a common denominator, we have that:

5/8 - 15/48 + 2/3 = 30/48 - 15/48 + 32/48.

Adding the numerators, the result of the expression is given as follows:

(30 - 15 + 32)/48 = 47/48.

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Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

Triangle AFB: A=4 cm, B=5 cm, F=7 cm

Triangle DHG: D=2.8 cm, H=3.5 cm, G=4.9 cm

Scale factor = 7/4.9 = 1.43

Step by explanation

Step 1: Draw triangle AFB on a piece of paper.

Step 2: Measure the side lengths of triangle AFB and record them.

Step 3: Draw a second triangle, DHG, on the paper.

Step 4: Measure the side lengths of triangle DHG and record them.

Step 5: Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.

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The inequality is (a) lt - 10l ≤ 0.75

The range of acceptable weights is t ≥ 9.25 AND t ≤ 10.75.

The range of acceptable weights for a bag of potatoes can be found by writing an absolute value inequality as follows:

|w - 10| ≤ 0.75

Where

Expanding the absolute value:

-0.75 ≤ w - 10 ≤ 0.75

Solving for w:

9.25 ≤ w ≤ 10.75

The range of acceptable weights for a bag of potatoes is 9.25 to 10.75 pounds.

The number line is attached

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Atomic vectors typically come in four different types: logical, integer, double, and character. Complex and raw are the two less common varieties.

An atomic vector can have any properties, with the exception of a dimension attribute, and is either logical, integer, numeric, complex, character, or raw (like matrices). For example, a matrix or NULL are not atomic vectors, but a factor is. This is, in essence, the same as is. atomic. Using the built-in int function, one can transform texts in Python into integers. Any Python data type can be sent to the int() function to be transformed into an integer.

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The required inequality that shows the possible value of x is x < 404/3

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Let's call the number we're trying to find "x". Then, the inequality can be written as:

11 + (3/4)x < 112

To solve for x, we'll isolate x on one side of the inequality. First, we'll subtract 11 from both sides.

(3/4)x < 101

Next, we'll divide both sides by (3/4).

x < (4/3) * 101 = 404/3

So, all values of x that are less than 404/3 satisfy the inequality. The possible values of x are all numbers less than 404/3.

x < 404/3

or written as an interval:

x ∈ (-∞, 404/3)

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Answer:

is equal to the number minus six.

For f(x) = x5 + x3 + x, the value of f1(3) is 1. Because of the inverse function feature, the value of f(f1(2)) is 2.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

f(x)=x^5 + x^3 + x

f(1)=3

f^-1(3)=1

f[f −1 (x)]=f −1 [f(x)]=x

f(f^(-1)2)=2

The value of f−1(3) is 1 for f(x) = x^5 + x^3 + x. The value of f(f−1(2)) is 2 by property of inverse function.

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The exact surface area of the cone having height 3 unit and radius 4 unit,  113.09734 unit²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Given that,

A Cone having,

Radius  r = 4 unit

Height  h = 3 unit

Surface Area = ?

Formula for the Cone,

Surface Area of Cone = πrl  + πr²

where, l = [tex]\sqrt{h^{2}+r^{2} }[/tex]

Surface Area of Cone = πr([tex]\sqrt{h^{2}+r^{2} }[/tex]) + πr²

                                     =  πr([tex]\sqrt{h^{2}+r^{2} }[/tex]  + r)

                                     =  4π([tex]\sqrt{3^{2}+4^{2} }[/tex]  + 4)

                                     =  4π(5 + 4)

                                     =   20π

                                     ≈   113.09734

Thus, the surface area of cone is  113.09734 unit²

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The white paint did she use to paint her bedroom walls will be 6.975 pints.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls 25% of this amount is blue paint.

The amount of white paint will be calculated as:-

Amount = [ 9.3 x ( 100 - 25 )%]

Amount = [ ( 9.3 x 0.75 ) ]

Amount = 6.975 pints.

Hence, the amount of white paint used for painting is 6.975 pints.

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An increase in consumer incomes would lead to a decrease in the demand and price of potatoes, and an increase in supply and quantity.

When consumer incomes increase, the demand for inferior goods such as potatoes usually decreases. This is because as people's incomes rise, they tend to switch to buying more superior goods, which are generally more expensive than inferior goods.

At the same time, the supply of potatoes may also increase as farmers respond to the potential for higher prices by growing more potatoes.

With both a decrease in demand and an increase in supply, the market price for potatoes is likely to fall. The quantity of potatoes supplied will likely increase as well, as the lower price attracts both consumers and producers.

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The value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.

The given function is:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex]

Substituting the value of limit we can see that the function is of the indeterminate form 0/0.

Using the L'Hospital rule we have:

[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}\\\\\lim_{x \to 5} \frac{2x - 5}{2x}\\[/tex]

Substitute the value of limits:

[tex]=\frac{2(5) - 5}{2(5)}\\ \\=\frac{1}{2}[/tex]

Hence, the value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.

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The simplified form after simplifying we get 43z+1

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The expression (56z+5)+(−13z−4)

simplifying the expression we get

(56z+5)+(−13z−4)

56z+5-13z-4

Arranging the like terms and combining we get

56z-13z+5-4

43z+1

Hence, The simplified form after simplifying we get 43z+1

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The words ‘of’ and ‘more than’ are often used in conjunction with percentages. The word ‘of’ is usually used to refer to a portion or part of a whole. For example, ‘50% of the population’ means that half of the population is being referred to.

In comparison, ‘more than’ is used to refer to a number that is higher than the one that is being referred to. For instance, ‘more than 50% of the population’ means that more than half of the population is being referred to.

The two words are related in that they both refer to a number or percentage, but their meanings differ. The word ‘of’ is used to refer to a portion of a number or percentage, while ‘more than’ is used to refer to a number or percentage that is higher than the one being referred to.

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Answer: A. 2/5 or 0.4 and B. 5/2 or 2.5 or 2 1/2

Step-by-step explanation: I'm a personal math calculator

Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.

Hooke aimed to show how a spring's elasticity and the forces acting on it are related.

According to Hooke's Law, a spring's extension is proportional to the load placed on it.

As long as the load does not exceed the material's elastic limit, a variety of materials will adhere to this rule.

F = k(x - x0), where x represents the spring's displacement from equilibrium and k is the spring constant.

The negative sign indicates that the force represented by the spring is a restorative force and operates in the opposite direction.

According to Hooke's Law, when a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length.

The formula k = -F/x, where k is the spring constant, can be used to get the spring constant. F stands for force, and x is for the variation in spring length.

Therefore, Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.

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Answer:

(21, 4)

Step-by-step explanation:

x+y=25

3x-2y=55

3x+3y=75

3x-2y=55

5y=20

y=4

x+4=25

x=21

The option that will give you the most money after 2 years is option (a)

Option (a)

Here, we have

Principal, P = $1000

Rate, r = 12% = 0.12

Number of times, n = 4

Time, t = 2

The formula of amount is

A = P * (1 + r/n)^(nt)

So, we have

A = 1000 * (1 + (0.12/4))^(4 *2)

A = 1266.77

Option (b)

Here, we have

Principal, P = $1000

Rate, r = 6% = 0.06

Time, t = 2

The formula of amount is

A = P * e^(rt)

So, we have

A = 1000 * e^(0.06 * 2)

A = 1127.50

1266.77 is greater than 1127.50

Hence, the option is option (a)

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Deep Learning (DL) is a type of Artificial Intelligence (AI) that uses a set of algorithms to simulate the functioning of the human brain.

It is a form of machine learning that is based on the concept of neural networks. DL uses a set of algorithms to process large volumes of data and identify patterns in the data. DL can be used to identify patterns and relationships in data that are not easily visible to the human eye.

DL works by using a series of layers of neurons, each of which is connected to the next layer by a set of weights and biases. During the training process, these weights and biases are adjusted so that the output of the neural network is adjusted to match the desired output. This is done by using an optimization algorithm such as gradient descent. At each step, the weights and biases are adjusted until the output of the neural network matches the desired output.

Once the DL model has been trained, it can be used to make predictions from new data. It does this by taking inputs and passing them through the layers of neurons to generate an output. This output is then compared to the desired output and an error is calculated. This error is then used to adjust the weights and biases in order to minimize the error. This process of adjusting the weights and biases is repeated until the error is minimized and the model can make accurate predictions from new data.

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Complete question .

What is Deep Learning (DL)?

Yes, w is in col(a) since w can be written as a linear equationof the columns in a. No, w is not in nul(a) since w cannot be written as a linear combination of the columns in a with all scalar coefficients being zero.

Yes, w is in col(a) since w can be written as a linear combination of the columns in a. A linear combination of two or more vectors is a vector that can be expressed as a sum of those vectors, with each vector scaled by a scalar (or coefficient). By expressing w as a linear combination of the columns in a, we are saying that w can be expressed as a sum of those columns, with each column scaled by a scalar.

No, w is not in nul(a) since w cannot be written as a linear combination of the columns in a with all scalar coefficients being zero. In other words, w cannot be expressed as a sum of the columns in a such that all coefficients are zero. This is the definition of nul(a): a subspace in which all linear combinations of the columns in a have a coefficient of zero. Since w cannot meet this requirement, then it is not in nul(a).

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The function is best represented by f (x) = x² + 2x.

option C is the correct answer.

The values of x in the given function can be determined as follows;

From one of the solution of x = - 2 and the second solution = 0

Now, we already know that the function has no y intercept, so we will eliminate option A,  and B because they have values for y intercept.

Since one of the solutions of x, is negative 2, we will consider a function with positive equation.

f (x) = x² + 2x

solve for x;

x ( x + 2 ) = 0

x = 0  or  x + 2 = 0

x = 0 or - 2

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