the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that

The amount of money that Margret needs to deposit to reach this amount is $8.

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.

Since Margret has $32.00 in a savings account. Margret wants to have a balance of $40.00 in the account, the amount needed will be:

= $40 - $32

= $8

She'll need $8 more.

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The value of x = 6cm.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object refers to the space occupied by its outer surface.

From the given figure,

Surface area(A) = [tex]192cm^{2}[/tex]

Height = 8cm

a base side = 6 cm

b base side = 10 cm

c base side = x cm

Therefore,  TSA= 2B +Px = [tex]2 \times\frac{1}{2} \times8\times6 +(6+10+8)x[/tex]

                                          =48+24x

Thus, 60+24x=192

                     [tex]x=\frac{192-48}{24}[/tex]

                      x= 6cm

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i) The number of participants that would need to attend the forum for Patricia to break even is of: 30.

ii) The number of participants that would need to attend the forum for Patricia to obtain a profit of Ksh 337,500 is of: 75.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

Hence in the context of this problem, the meaning of each coefficient is given as follows:

Hence the values of each coefficient are given as follows:

Hence the profit function is given as follows:

P(x) = 7500x - 225000.

She breaks even when P(x) = 0, hence:

7500x - 225000 = 0

7500x = 225000

x = 225000/7500

x = 30 participants.

She makes a profit of 337500 when:

7500x - 225000 = 337500

x = (337500 + 225000)/7500

x = 75 participants.

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The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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The slope and y-intercept of this function is

B. The slope is 5/6, The y-intercept is (0, -3

Linear function is a function of the form y = mx + c

m = slope

c = intercept

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculated using the points (0, -3) and  (6, 2)

m = (y₀ - y₁) / (x₀ - x₁)

m = (2 - -3) / (6 - 0)

m = (5) / (6)

m = 5/6

c = y intercept, from the table

c = -3

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The graph line for function d = 0.25t is added as an attachment

The equation of the function is given as

d = 0.25t

The above function is a linear function

One way to create the graph is to make a list of ordered pairs

So, we have

When t = 0, d = 0.25 * 0 = 0

When t = 1, d = 0.25 * 1 = 0.25

When t = 2, d = 0.25 * 2 = 0.5

So, the ordered pairs are (0, 0), (1, 0.25) and (2, 0.5)

We plot these points on a graph and connect them through a line

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The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

Given that,

He makes paths that follow Line segments A and B, X and Y, and Z and Y through the garden.

We have to find which accurately compares the pathways' lengths.

We know that,

The length of the third side in a triangle is proportional to the angle Ф  if the lengths of the two sides that make up the angle Ф are fixed.

XY > YZ because XY's opposing angle (79°) is greater than YZ's (65°).

As before, YZ > AB because the opposing angle of YZ (65°) is greater than that of AB (36°).

Since both sides of the angle are the same length (8 feet),

As a result, assertion A. is accurate. (Answer)

Therefore, The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

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Answer:

It's A

Step-by-step explanation:

I got 100 on the quiz

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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The value of x for the given equation is 1.

What is solving an equation?

A General Rule for Equation Solving

Remove parentheses from each side of the equation and combine similar phrases to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Consider the given expression

0.2(x + 1) + 0.5x = -0.3(x - 4)

Simplifying,

0.2x + 0.2 + 0.5x = -0.3x + 1.2

0.7x + 0.2 = -0.3x + 1.2

Add 0.3x on both sides,

0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x

x + 0.2 = 1.2

Subtract 0.2 from both sides,

x + 0.2 - 0.2 = 1.2 - 0.2

x = 1

Hence, the value of x for the given expression is, 1.

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Answer:

[tex]\huge\boxed{\sf 3 \ baskets}[/tex]

Step-by-step explanation:

Let the baskets missed in game 2 be x.

Says that, the shooting of both the games were accurate.

So,

[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]

The statemet 2, the variable K represent carrying capacity and the variable N represent population size, is correct.

In the given question we have to review the video to determine whether each statement about the following equation is true or false.

The given equation is:

[tex]\frac{dN}{dt}=rN(\frac{K-N}{K})[/tex]

The given equation is used to find the annual growth of population.

In which, dN/dt = the annual increase for the population,

r = the annual growth rate,

N = the population size, and

K = the carrying capacity.

So the statemet two, the variable K represent carrying capacity and the variable N represent population size, is correct.

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Answer: How Weather Exists

Step-by-step explanation:

~I think you mean, how weather exists.

You see, "Weather" exists because of the atmosphere. Evidently, weather  is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.

~Hope this helped :)

The system of equations are

The solution of the equation from the graph is

The system of equations is derived from the statements as interpreted below

If x represents the number of hours lifeguarding and y represents the number of hours tutoring

number of hours lifeguarding = x  

number of hours tutoring = y

she can work no more than 11 total hours

x + y not more than 11 hours

x + y < 11

making $14 per hour lifeguarding and making $25 per hour tutoring and must earn no less than $200

$14x + $25y no less than $200

14x + 25y > 200

The required equations are

14x + 25y > 200

x + y < 11

The graph is attached

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By resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

A formula that describes how two expressions on each side of a sign are connected.

It typically has an equal sign and one variable.

Similar to this: 2x - 4 = 2.

Graphing, substitution, or elimination are the three methods that can be used to solve systems of equations.

To answer a problem by graphing, just plot the given equations on a graph and identify the point(s) where they all intersect.

So, a number of items Uan should sell to earn a profit of $60 or above:
We know that Uan earns $5 for each item he sells.

So, let x be the number of items Uan should sell.

Then, the equation will be:

5x = 60

Now, solve as follows:
5x = 60

x = 60/5

x = 12

Profit of $60: 12 items to sell

Profit more than $60: More than 12 items to sell

So, by resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

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The height of the kite assuming that there is no slack in the string is 86.6 m.

We have given that,

the string of a kite is 100 meters long and it makes an angle of 60°.

and we have to find the height of the kite.

So therefore we know the formula for right angled triangle,

i.e. sinθ = Opposite side/ Hypotenuse

Here θ = 60°

Opposite side = height of the kite = h (say)

Hypotenuse = length of string = 100 m

⇒ sin60° = [tex]\frac{h}{100}[/tex]

           h = 100sin60°

              = 100 × [tex]\frac{\sqrt{3} }{2}[/tex]

              = 50 × 1.732

           h = 86.6 m

Hence the height of the kite is 86.6 m.

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Answer:

Slope-intercept form: y = 3x + 5

Slope: 3

y-intercept: 5

Step-by-step explanation:

When the equation of a line is written in the slope-intercept form, we can easily identify the slope from the coefficient of x and the y-intercept from the constant.

The slope-intercept form is expressed as y = mx + c, where m is the slope and c is the y-intercept. Note that other textbooks might use y = mx + b instead, but both have the same meaning as both m and b or c will be replaced by a certain value.

To rewrite an equation in the slope-intercept form, isolate the y term on the right-hand side of the equation and divide the whole equation by the coefficient of y.

Working

[tex]y - ( - 7) = 3(x - ( - 4))[/tex]

Expand:

[tex]y + 7 = 3(x + 4)[/tex]

[tex]y + 7 = 3x + 12[/tex]

Subtract both sides by 7:

[tex]y = 3x + 12 - 7[/tex]

[tex]\bf{y = 3x + 5}[/tex]

Since the coefficient of y is already 1, we have arrived at our final answer.

When the equation is in the slope-intercept form, the slope can be identified from the coefficient of x. This refers to the number that comes before x which is multiplied to x.

Thus, the slope is 3.

The y-intercept is the value of the constant in the slope-intercept form. This refers to the number that is not attached to any variables.

Hence, the y-intercept is 5.

Note that the y-intercept can also be found by substituting x = 0 into the equation.

The x-intercept occurs at y = 0. Since we have the equation of the line, we can substitute y = 0 into the equation to find the value of x when y = 0.

Working

y = 3x + 5

When y = 0,

0 = 3x + 5

3x = -5

Divide both sides by 3:

[tex]x = - \frac{5}{3} [/tex]

I have attached the graph as an image. If only a sketch is required, there are 3 pieces of information that needs to be labelled on the graph:

Additional resources:

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[tex](\stackrel{x_1}{r}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{r}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{-4} \\\\\\ \cfrac{-4}{10-r}=-4\implies -4=-40+4r\implies 36=4r\implies \cfrac{36}{4}=r\implies 9=r[/tex]

Answer: [tex]x=-1, 2[/tex]

Step-by-step explanation:

If [tex]ab=0[/tex], then [tex]a=0[/tex] and/or [tex]b=0[/tex].

So, [tex]x+1=0[/tex] or [tex]2x-4=0[/tex].

[tex]x+1=0 \implies x=-1\\\\2x-4=0 \implies x=2\\\\\therefore x \in \{-1, 2\}[/tex]

1) The bus took a 30-minute stop in the interval between D and E

2) The bus traveled the fastest in the interval between C and D

3) The bus was traveling at 60 miles per hour during this interval.

4) The average rate of speed of the bus over the entire journey is 35 miles /hr

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here for the first question we have there was no change in the distance in the interval between D and E thus bus must have stopped for 30 minutes.

2) The interval in which the bus travelled the fastest is between C and D

3) The Speed of the bus in this interval is S = 90/1.5

                                                                         = 60 miles/hr

4) The average speed of the bus over the entire trip is Sₐ = 140/4

                                                                                                = 35 miles/hr

Hence the above answers are correct ones.

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By solving a quadratic equation, it can be calculated that

Length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

What is a quadratic equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic  equation.

Here a quadratic equation needs to be solved.

Let the length be l ft. and the width be b ft.

Perimeter = 2(l + b) ft.

By the problem,

2(l + b) = 200

l + b = [tex]\frac{200}{2}[/tex]

l + b = 100

b = (100 - l) ft.

Now,

Area = l [tex]\times[/tex] b sq. ft.

        = [tex]l \times (100 - l)[/tex]

By the problem,

[tex]l \times (100 - l) = 1275\\100l - l^2=1275\\l^2 -100l+1275 = 0\\l^2 - 85l -15l + 1275 = 0\\l(l -85) - 15(l - 85) = 0\\(l -85)(l -15) =0\\l -85 = 0 \ or \ l -15 = 0\\l =85 \ or \ l =15[/tex]

If l = 15 ft.

b = 100 - 15 = 85 ft.

Which is not possible as length is always greater than the width

So, length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

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The length of the other leg of the given right triangle is [tex]\sqrt{70}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The question gives:

Therefore, from the Pythagorean Theorem, you will find the value of the other leg. See below.

[tex]9^2={\sqrt{11}^2 +{leg_2}^2[/tex]

[tex]81=11 +{leg_2}^2[/tex]

[tex]{leg_2}^2=81-11\\ \\ {leg_2}^2=70\\ \\ leg_2=\sqrt{70}[/tex]

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By using the concept of maxima, it can be calculated that

Volume is maximum if the radius of the cone is 40 cm

What is maxima of a function?

Maxima of a function gives the maximum value of the function on a certain interval or on the whole domain.

Let the height of the cylinder be h and radius be r

Sum of height and circumference = h + 2πr

By the problem,

h + 2πr = 60

h = 60 -2πr

Volume(V) = π[tex]r^2[/tex] h

             = π[tex]r^2[/tex](60 - r)

             = 60π[tex]r^2[/tex] - π[tex]r^3[/tex]

[tex]\frac{dV}{dr} = 120\pi r - 3 \pi r^2[/tex]

For maximum volume

[tex]\frac{dV}{dr} = 0[/tex]

[tex]120\pi r - 3 \pi r^2 = 0\\[/tex]

[tex]3 r^2 = 120 r\\3r = 120 [r \neq 0]\\r = \frac{120}{3}\\r = 40 \ cm[/tex]

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi r\\[/tex]

Putting r = 40

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi \times 40\\\frac{d^2V}{dr^2} =120\pi - 240 \pi\\\frac{d^2V}{dr^2} = -120\pi < 0[/tex]

Hence Volume is maximum

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Answer: 2/11

Step-by-step explanation: there are 11 letters and 2 of them are p so the chances of getting p is 2/11

Answer:

2/11

Step-by-step explanation:

The total amount of tiles is 11. There are only 2 tiles that have the letter P on them.

Theoretical probability is the probability that should occur over many, many trials.

Theoretical probability = favorable outcomes / total outcomes.

In this scenario, the favorable outcome is the letter P. which there are two of. The total outcomes would be all the letters that make up the word MISSISSIPPI, or 11.

So your theoretical probability would be 2/11.

A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

The angles ∠BCD and ∠BAD are opposite interior angles of a parallelogram. in which the alternate interior angles  ∠BAC  and  ∠ACD and ∠BCA and ∠DAC are congruent, from which by angle addition property, ∠BCD ≅ ∠BAD

Alternate interior angles are angles formed by the transversal to two parallel lines on the inside of the parallel lines, and on opposite sides of the transversal.

The two column-method used to  prove that ∠BCA is congruent to ∠DAC can be presented as follows;

Step       [tex]{}[/tex]         Statement                                          Reason

1.        [tex]\overline{BC}[/tex]║ [tex]\overline{AD}[/tex],  [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex]   [tex]{}[/tex]       Given

2. [tex]{}[/tex]    ∠BCA ≅ ∠DAC                  ║ lines cut by a trans. form ≅ int.  ∠s

3. [tex]{}[/tex]    [tex]\overline{AC}[/tex]║[tex]\overline{CA}[/tex]     [tex]{}[/tex]                         Reflexive Property

4.     ∠BAC ≅ ∠ACD [tex]{}[/tex]                  Alternate interion angles

5.     ∠BCA = ∠DAC[tex]{}[/tex]                    Definition of congruency

[tex]{}[/tex]        ∠BAC = ∠ACD

6.    ∠BCD = ∠BCA + ∠ACD[tex]{}[/tex]       Angle addition property

      ∠BAD = ∠BAC + ∠DAC

7.    ∠BCD = ∠BCA + ∠ACD  [tex]{}[/tex]       Substitution property

8. [tex]{}[/tex]   ∠BCD = ∠BAD   [tex]{}[/tex]                    Substitution property

9.    ∠BCD ≅ ∠BAD   [tex]{}[/tex]                    Definition of congruency

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On simplifying for variable, we get -

G = - 20

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following equation -

(G-2)/(2-24) = 0

We have -

(G-2)/(2-24) = 0

G - 2 = 2 - 24

G - 2 = - 22

G = - 22 + 2

G = - 20

Therefore, on simplifying for variable, we get -

G = - 20

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Answer:

For the first graph:

Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Range: y [tex]\geq[/tex] 3

For the second graph:

Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4

Range: y [tex]\leq[/tex] 64

Step-by-step explanation:

For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.

The x-intercept of the quadratic inequality is -4 ≥ x and 2 ≥ x.

Let's factor the quadratic inequality to find the x-intercepts. The x-intercept of the quadratic inequality is the value of x when y = 0.

Therefore,

y ≥ x² + 2x - 8

0 ≥ x² + 2x - 8

0 ≥ x² - 2x + 4x - 8

0 ≥ x(x - 2) + 4(x - 2)

0 ≥ (x + 4)(x - 2)

Therefore,

0 ≥ x + 4

-4 ≥ x

0 ≥ x - 2

2 ≥ x

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A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.

What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.

b) 7x+5y-5y = 7x

Here the Additive inverse of 5y is used which is -5y .

c) (x-4)(x+3) = 0

here distributive property of addition over multiplication is used.

d) 4x+5x = 5x+4x

here commutative property is used.

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Answer:

In simple terms, it basically means to select the important parts of the data and take note of them. It's a very helpful technique.

On the cherry - picking mean in the context of data analytics is confirmation bias. The correct option is (B)

Cherry picking is the selective use of evidence to support a claim while ignoring other data that is more likely to challenge that claim.

here, we have,

It's not always done with malicious purpose, but this behavior is extremely widespread. Probably even you have cherry-picked.

now, we know that,

cherry picking looks  like as:  

For instance, someone who cherry picks may only mention a few studies out of the many that have been published on a certain topic in an effort to make it appear as though the scientific consensus supports their position.

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