What is the variance of 2 4 6 8 10?

Answer:

To express the quadratic expression x^2 - 5x + 8 in the form of (x - a)^2 + b, we need to complete the square. To do this, we can add and subtract the square of half the coefficient of the x term. In this case, that would be (1/2)(-5) = -5/2. Therefore, we add and subtract (1/2)(-5)^2 = (-5/2)^2 = 25/4 to get:

x^2 - 5x + 8 = (x^2 - 5x + (25/4)) + (8 - (25/4))

Next, we need to add and subtract 25/4 in such a way that we can factor the quadratic expression as the square of a binomial. To do this, we add 25/4 to the first term and subtract 25/4 from the second term to get:

x^2 - 5x + (25/4) + (8 - (25/4)) = (x^2 - 5x + 25/4) + (8 - 25/4)

Now we can factor the quadratic expression as the square of a binomial:

(x^2 - 5x + 25/4) + (8 - 25/4) = (x - 5/2)^2 + (8 - 25/4)

Therefore, we can express x^2 - 5x + 8 in the form of (x - a)^2 + b where a is -5/2 and b is 8 - 25/4.

Note that the values of a and b are not whole numbers because we added and subtracted a fraction when completing the square.

The  probability of the card being an ace, given that it is a non-face card is option A: 8% .

To find the probability of an event occurring, we can use the formula:

Probability = number of ways the event can occur / total number of outcomes.

In this case, we are trying to see the probability of drawing an ace from a standard deck of 52 cards, given that the card is a non-face card. There are 4 aces in a standard deck of 52 cards, so the number of ways the event (drawing an ace) can occur is 4. There are 52 total cards in the deck, and 48 of them are non-face cards. So, the total number of outcomes is 48.

Therefore, the probability of the card being an ace, given that it is a non-face card, is 4/48.

4/48 = 0.083

When converted to percentage, it is  approximately 8.3%.

Therefore,  This means that the probability of the card being an ace, given that it is a non-face card, is approximately 8%, which is seen as the closest to the answer choice "8%".

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The surface area of the cuboid is given as follows:

147.68 cm².

A cuboid is equivalent to a rectangular prism, having dimensions given as follows:

The volume of the cuboid is given by the multiplication of the base area and the height, as follows:

V = Ab x h.

In which:

Ab = l x w.

Considering the base area and the volume of the cuboid, the height is obtained as follows:

120 = 30 x h

h = 120/30

h = 4 cm.

A cuboid has a square base, hence the length = width are obtained as follows:

l² = 30

l = square root of 30

l = w = 5.48 cm

Hence the surface area of the cuboid is obtained as follows:

S = 2(lw + wh + lh)

S = 2(30 + 4 x 5.48 + 4 x 5.48)

S = 147.68 cm².

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The probability of both sprouts blooming under the best conditions is 16 percent.

The probability that two sprouts will both bloom under the best conditions can be calculated using the formula P(A and B) = P(A) * P(B), where P(A) and P(B) are the probabilities of each sprout blooming. Assuming that each sprout has an independent probability of blooming of 0.5, then the probability of both sprouts blooming is 0.5 * 0.5 = 0.25, or 25%. This can also be expressed as a proportion of 1/4, or a percentage of 25%.

In other words, if two sprouts are selected at random, then the probability that both will bloom, under the best conditions, is 25%. This can also be expressed as a probability of 1 in 4, or 16%. This means that out of 4 sprouts, on average, one will bloom, and the other three will not. Therefore, the probability of both sprouts blooming under the best conditions is 16 percent.

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The figure of Pumpkin according to the transformation is shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The Transformation rule are as follow:

1. T(-4 , -18) reflect across x = -4.

2. T(-3, 4) (R0, 180)

3. [tex]R_0[/tex] , 180 ( [tex]r_y[/tex] = x+ 11)

4. [tex]r_y[/tex] = 11 ( [tex]R_0[/tex] , 90)  T(6, -10)

5. T(-12, 0),  [tex]r_y[/tex] = -10, ( [tex]R_0[/tex] , 270)

6. T(0, -3),  [tex]r_y[/tex] = x

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10.5 is the mean of 20 .

What are the mean, median, and example?

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

 x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + ................. + 20/20

  x = 210/20

  x = 10.5

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The complete question is -

How do you find the mean of 20 natural numbers?

a) The equation has a root between x = 0 because there is a change in the sign of the output value.

b) The arrangement is given in the answer.

c) The estimate of the root is given as follows: 0.7469.

The polynomial function is defined as follows:

x³ + 6x - 5 = 0.

The numeric values at x = 0 and x = 1 are given as follows:

Change in the sign, hence necessarily there is a root, as the function is continuous.

The function can be arranged as follows:

x³ + 6x - 5 = 0.

x³ + 6x = 5

x(x² + 6) = 5

x = 5/(x² + 6).

Considering an initial estimate of x = 0, the first estimate of the solution is of:

x = 5/(0² + 6) = 0.8333.

Then the second estimate for the root is of:

x = 5/(0.8333² + 6) = 0.7469.

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Since, a prime number is whole number higher than one that cannot be divided exactly by any other whole number than itself and one. No, there are many prime numbers.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.

Prime number 2,5,7,13, ......

so there are multiple prime numbers.

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Let x represent the precursor to 3. Preimages of 3 are 13 and 15, respectively. the collection of all domain components that correspond to a certain subset of the codomain;

Mages and pre-images: what are they?

On geometry, new shapes can be produced by shifting, scaling, and other geometrical transformations of figures in a plane. Images are the new (modified) forms, whereas preimages are the old, unchanged ones.

What in geometry is a pre-image?

The pre-image of a figure in a transformation process is that figure's original look.

Let x represent a 3 picture. Preimages of 3 are 13 and 15, respectively.

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Answer:

6.6 in

Step-by-step explanation:

[tex]\angle P=180^{\circ}-37^{\circ}-89^{\circ}=54^{\circ} \\ \\ \frac{p}{\sin P}=\frac{q}{\sin Q} \\ \\ \frac{p}{\sin 54^{\circ}}=\frac{4.9}{\sin 37^{\circ}} \\ \\ p=\frac{4.9\sin 54^{\circ}}{\sin 37^{\circ}} \\ \\ p \approx 6.6[/tex]

Answer:

Step-by-step explanation:

6.6

As opposed to last year when 113 pies were prepared for the bake sale, 219+ d  expression pies have been prepared throughout the past two years.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Since we have given that

Number of pies baked for bake sale last year = 219

Number of pies baked for bake sale this year = d

So, total number of pies baked in two years is given by

219 +d

Hence, there are 219+d pies baked in two years.

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Answer:

[tex]V=(3W^{3} + 12W^{2} ) units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a rectangular prism is equal to

[tex]V=LBH-- >[/tex][tex]EquationA[/tex]

where

L is the length

W is the width

H is the height

we know that

[tex]L=3W--- > EquationB[/tex]

[tex]H = W + 4----- > EquationC[/tex]

substitute equation B and equation C in equation A

[tex]V=(3W)(W)(W+4)[/tex]

Apply distributive property

[tex]V=(3W^{3} + 12W^{2} ) units^{3}[/tex]

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E(z),the expected value of z in which at least one member has a birthday in 12 months is (11/12)^10

Define the random variable Zi’s as

[tex]Z_{i}[/tex]= 1 : if no member of the club has a birthday in the month

   = 0: otherwise   for, i =1,2, ......,12 .

Now, we have,

= P ([tex]Z_{i}[/tex] =1) .

=p( no member of the club has a birthday in month i).

= p, say.

Now, there are a total of 10 members in the club and their birthdays are assumed to be independently and uniformly distributed over the 12 months of the year. So, there are 12 possible choices of months for each of the 10 members for their birthday. Thus, the total no. of exhaustive mutually exclusive and equally likely no. of ways of birthdays 12^10.

Again, if no member of the club has a birthday in month 'i'; then, all of their birthdays should be on the remaining (12 - 1) = 11 months of the year. So, there are possible choices of birthday months for each of the 10 members of the club. So, the no. of cases for the event (Zi=1) is 11^10.

So, p([tex]Z_{i}[/tex]=1) = Favorable no. of cases for Zi=1) / Total no. of all possible cases

= 11^10 / 12^10

By the classical definition of probability.

= (11/12)^10

p([tex]Z_{i}[/tex] = 1) = (11/12)^10

E(Zi).= (11/12)^10

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Answer:

5 1/3 books

Step-by-step explanation:

1 1/3 = 4/3

So, she read

4/3 book = 1/2 day

8/3 book = 1 day

16/3 book = 2 days

16/3 = 5 1/3 books

So, he read 5 1/3 books in two days at this rate

Answer:

y = -3x + 6

Step-by-step explanation:

According to the information given, your two points are (2, 0) and (4, -6).

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-6 - 0) / (4 - 2)

Simplify the parentheses.

= (-6) / (2)

Simplify the fraction.

-6/2

= -3

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (4, -6). Plug in the x and y values into the x and y of the standard equation.

-6 = -3(4) + b

To find b, multiply the slope and the input of x(4)

-6 = -12 + b

Now, add 12 to both sides to isolate b.

6 = b

Plug this into your standard equation.

y = -3x + 6

This is your equation.

Check this by plugging in the other point you have not checked yet (2, 0).

y = -3x + 6

0 = -3(2) + 6

0 = -6 + 6

0 = 0

Your equation is correct.

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

The inverse calculator is a function calculator which finds the inverse of the given function.

Any function can have its inverse value computed using an inverse function calculator. Recall that an inverse function is one that can make another function do the opposite. Another name for it is an anti-function.

It is denoted as:

f(x) = y ⇔ f⁻¹(y) = x

Any function's inverse can be found by first substituting the other variable for the function and then solving for the other variable by substituting each other.

This online calculator for finding the inverse function is very simple to use. To find the inverse of any function, follow the directions below.

Step 1: Type any function into the input field, which is located across the sentence "The inverse function of."

Step 2: Press the "Submit" button located at the calculator's base.

Step 3: A different window will open in which the supplied function's inverse will be calculated.

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We also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the vertically opposite angles Therefore, angle 1 is-congruent-to angle 8 by the substitution property.

How to find angles when parallel lines are cut by a transversal?

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line e and f are parallel lines cut by the the transversal g.

∠1 ≅ ∠4(vertically opposite angles)

Hence,

∠4 ≅ ∠8(corresponding angles)

Since, ∠1 ≅ ∠4

Then, by substitution,

∠1 ≅ ∠8 (transitive property)

∠5 ≅ ∠8 (vertically opposite angles)

Therefore, ∠1 ≅ ∠8 by the transitive property.

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The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. The roots are irrational numbers and can only be approximated.

The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. To find the roots, the quadratic formula can be used. The formula requires the coefficients of the equation, which in this case are a=5, b=4, and c=3. When the quadratic formula is applied, the results are two complex roots, which are expressed as x1 = -1/5 + (√16)/5i and x2 = -1/5 - (√16)/5i. These roots are irrational numbers and can only be approximated. Complex roots are often found when the discriminant, which is b²-4ac, is negative. In this case, the discriminant is -64, which is negative, indicating that the equation has complex roots.

Discriminant = b²-4ac = 4²-4(5)(3) = -64

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The SSS postulate states that "if all the three sides of a triangle are equal to the sides of another triangle then the given triangles are congruent" is proved.

Assume that the lengths of all three sides of the triangles ABC and DEF are known.

The diagram is attached at the end of the solution.

Pick a side from triangle ABC. Find the side with the same length as triangle DEF. For example, we pick [tex]\overline{AB}[/tex] and find that [tex]\overline{D E}[/tex] is equivalent in length to [tex]\overline{AB}[/tex].

Next, write a proof statement about our conclusion and the reason for it. For the reason clause, we state that the two sides are given, since no other work was involved besides reading the lengths of the sides of the diagram. The three dots in the upside-down triangle means "because".

[tex]$$\overline{AB} \cong \overline{DE}$$[/tex]

Choose the other side from triangle ABC. Find the side with the same length as triangle DEF.

We choose the second side [tex]\overline {BC}[/tex] and find from the diagram that [tex]\overline{EF}[/tex] has the same length. The proof statement for this step is:

[tex]$$\overline{BC} \cong \overline{EF}$$[/tex].

Step 3: Pick the last side from triangle ABC.  From triangle DEF, identify the side that is the same length. [tex]\overline{AC}[/tex] and [tex]\overline{DF}[/tex] have the same length. We add another proof statement.

[tex]$$\overline{AC} \cong \overline{DF}$$[/tex]

Step 4: We've discovered that the two triangles have three pairs of congruent sides. That means, by the SSS congruence theorem, triangles ABC and DEF are congruent.

Add a proof statement for this conclusion. The list of the proof statements looks like this.

[tex]$\overline{AB} \cong \overline{DE}[/tex] because [tex]\overline{AB}$[/tex] and [tex]$\overline{DE}$[/tex] are given.

[tex]$\overline{BC} \cong \overline{EF}[/tex] because [tex]$\overline{BC}$[/tex] and [tex]$\overline{EF}$[/tex] are given.

[tex]$\overline{AC} \cong \overline{DF}[/tex] because [tex]$\overline{AC}$[/tex] and [tex]$\overline{DF}$[/tex] are given.

[tex]$\triangle A B C \cong \triangle D E F$[/tex] by SSS congruence theorem.

We have proved that the SSS congruence theorem holds for triangles ABC and DEF.

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Two triangles with three congruent sides are referred to as side-side-side (SSS) triangles. The measures are identical, or congruent, which means they are precisely the same. All three sides of SSS triangles will be equal to their corresponding sides in the second triangle, however individual triangle sides are not always equal to one another.

Theorems of Triangle Congruence

One of four triangle congruence theorems, the SSS theorem is unique in that it excludes the need of an angle. The following three are listed:

Two sides and the angle separating them are congruent, or side angle side (SAS).

Angle Side Angle (ASA): Congruence of two angles and the side joining them.

The three angles are all congruent (AAA).

The 3 benefits of SSS theorem are as follow,

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The iron shark has a top speed of 2.4 miles per hour faster than the regression line prediction.

ŷ = 0.2143 (100) + 28.17

ŷ = 49.6

Now, we have to subtract y from ŷ

That is,

52 - 49.6 = 2.4

Hence, 2.4 miles per hour

One or more independent (predictor) variables and one or more dependent (criterion) variables are related in regression analysis, a statistical method. A predicted value for the criterion is obtained from the analysis as a result of a linear combination of the predictors. Your independent variable and your dependent variable are related, as seen by the regression line.

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The rectangle's length and width can be replaced by variables. and can make use of the area. The area of the garden under consideration can be expressed as x^2-11x+28 square feet.

What mathematical expressions can be created using the above description?

Variables can be used to represent the unknowable amounts. Follow the description and mathematically convert each item one by one. For instance, if you are instructed to multiply an item by 4, you can do so by adding 4. You can multiply anything by two, for instance, if it is doubled, and so on to translate a description into a mathematical expression.

How can you describe the size of the garden in words?

Let the garden's length be y feet.

Since the garden's length is one foot longer than its breadth, which is specified as being (x-7) feet, y=3+ (x-7)

y=3+(x-7)

y=x-4 feet

Since the length and breadth of the rectangle under consideration are multiplied to determine the area of the rectangle, the following results are obtained:

A= length * width

A= (x-4)(x-7)

A= x^2-7x-4x+28

A= x^2-11x+28

Consequently, one phrase for the size of the garden under consideration is x^2-11x+28 square feet.

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Answer:

[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, x=-11

Step-by-step explanation:

y = x^2 - 8x + 5, x<=4

x = y^2 - 8y + 5, y<=4  ==> switch the x and y variables to find the inverse

x = y^2 - 8y + 5  ==> solve for y

x + 16 = y^2 - 8y + 16 + 5  ==> add 16 to get a perfect polynomial square

x + 16 = (y - 8/2)^2 + 5  ==> simplify

x + 16 = (y - 4)^2 + 5

x + 16 - 5 = (y - 4)^2 + 5 - 5  ==> isolate y by subtracting 5 on both sides

x + 11 = (y - 4)^2  ==> simplify

[tex]\sqrt{x+11}[/tex] = [tex]\sqrt{(y - 4)^2}[/tex]  ==> take the square root of both sides to remove the

                                        square

[tex]\sqrt{x+11}[/tex] = y - 4

y = [tex]\sqrt{x+11}[/tex] + 4  ==> add 4 on both sides to isolate y

[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4  ==> substitute [tex]f^{-1}[/tex](x) for y

[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, [tex]f^{-1}[/tex](x)<=4  ==> add in the domain restriction

4 = [tex]\sqrt{x+11}[/tex] + 4  ==> plugin the domain restriction for [tex]f^{-1}[/tex](x)

0 = [tex]\sqrt{x+11}[/tex] ==> subtract 4 on both sides

x + 11 = 0  ==> the square root of 0 is 0

x = -11  ==> subtract 11 on both sides

Hence, answer is: [tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, x=-11

Your instrument's pads, finish, springs, and other metal components can all be damaged if you let dirt, moisture, and other debris build up inside of it. It can also corrode strings and other metal components. These faults might cause expensive long-term consequences and are not easily fixed.

Clean the body, head stock, tuners, and fret board using a damp cloth dipped in vinegar, making careful to follow up with a dry towel. Keep in mind that too much moisture ruins wooden instruments. To keep your case odor-free, wait 30 minutes before storing it.

Due to the fact that these solutions often offer the best material compatibility profile and effective filth removal, neutral or detergent solutions with a pH close to neutral are frequently employed for instrument cleaning. Sometimes neutral pH solutions with proteases added to them help remove organic debris.

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Answer:

5 - [tex]\sqrt{5}[/tex]

Step-by-step explanation:

a polynomial of degree 3 has 3 roots

radical roots occur in conjugate pairs.

given 5 + [tex]\sqrt{5}[/tex] is a root then 5 - [tex]\sqrt{5}[/tex] is also a root.

the 3 roots are therefore

x = 5 and x = 5 ± [tex]\sqrt{5}[/tex]

A quadratic inequality of the form

y>a[tex]x^{2}[/tex]+bx+c

(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola

A quadratic inequality of the form

y>a[tex]x^{2}[/tex]+bx+c

(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola .

To graph a quadratic inequality, start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality.

If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary.

Example:

Graph the quadratic inequality.

y≤[tex]x^{2}[/tex]−x−12

The related equation is:

y=[tex]x^{2}[/tex]−x−12

First we notice that a , the coefficient of the [tex]x^{2}[/tex] term, is equal to 1 . Since a is positive, the parabola points upward.

The right side can be factored as:

y=(x+3)(x−4)

So the parabola has x -intercepts at −3 and 4 . The vertex must lie midway between these, so the x -coordinate of the vertex is 0.5 .

Plugging in this x -value, we get:

y=(0.5+3)(0.5−4)

y=(3.5)(−3.5)

y=−12.25

So, the vertex is at (0.5,−12.25) .

We now have enough information to graph the parabola. Remember to graph it with a solid line, since the inequality is "less than or equal to".

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Square root of 1, √1 is a real number as it is a rational number.

√  is a symbol that means square root in mathematics.

Real number is a set of all rational and irrational numbers. It can be plotted on a number line.

A rational number is a number that can be expressed in the form of p/q, where p and q are integers and denominator, q not equal to 0.

Numbers that cannot be plotted on number line, numbers that are not real number are called imaginary numbers.

√1 = 1

1 is a rational number as it can be written as 1/1. All integers are rational numbers in the similar way.

Therefore square root of 1 is a rational number and hence it is a real number.

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