[tex] \rm \int_{0}^{1} \sqrt{ \frac{2 - {x}^{2} }{1 - {x}^{2} } } dx \\ [/tex]​

The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs). The answer will be 0.9+0.06+0.004= 0.964

Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. The set that the values created are contained in is known as the codomain, while the set that the operation really produced is known as the codomain of definition, active codomain, image, or range. For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.

A scalar can be multiplied by a vector to create another vector (a process known as scalar multiplication), and two vectors can be combined to make a scalar quantity in an inner product operation. An operation may or may not have specific characteristics, such as being idempotent, associative, commutative, or anticommutative.

The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs).

9x1/10+6x1/100+4x1/1000

0.9+0.06+0.004= 0.964

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After simplifying the expression we get: 12√6

Given, √864

Take the LCM of the given number:

864 = 2×2×2×2×2×3×3×3

Minimize the terms:

= √4×4×2×9×3

Reduce the terms:

= √16×9×2×3

multiply the terms:

= √144×2×3

= 12√6

Hence after simplifying we get the answer as 12√6

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To fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.

As given in the question,

To fence in a portion of Amitie Park for an inclusive play space for children

Diameter of the section = 90 feet

Let r be the radius

r = diameter/2

⇒ r = 90 / 2

⇒r = 45 feet

Total fencing required to fence a play space

= 2πr

= 2 × 3.14 × 45

= 282.6 feet

Therefore, to fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.

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The most appropriapriate choice for factorization will be given by-

[tex](x^2+12+4x)(x^2+12-4x)[/tex] is the required factorization.

What is factorization?

The process of breaking an algebraic expression into product of different factors is called factorization.

Here,

The factorization of [tex]x^4+8x^2+144[/tex] has been shown below-

[tex]x^4+8x^2+144[/tex]

[tex](x^{2} )^2 + 24x^2 +144 -16x^2\\(x^{2} )^2 + 2\times x^2\times 12+ 12^2-16x^2\\(x^2+12)^2 - (4x)^2\\(x^2 + 12+4x)(x^2+12-4x)[/tex]

This is the required factorization

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Step-by-step explanation:

Your slope and your x and y intercept.

x + 2y =7

Divide through by 2, we have:

x/2 + 2y/2 = 7/2

x/2 + y = 7/2

y = 7/2 - x/2

In the form y = mx + c gives.

Where m is the slope.

.: The slope = -1

EXPLANATION

Let's see the facts:

Length = 4*longer leg

Shorter leg of the base= 1/2 longer leg

We know that Volume = 5832 = 1/2* length* longer leg* shorter leg

Let's call x to the longer leg, the variables are:

length= 4*longer leg= 4x --> x is the longer leg

Shorter leg= 1/2longer leg= 1/2x --> x is the longer leg

Substituting terms, the equation would be:

Multiplying like terms:

Simplifying:

Switching sides:

Isolating x:

Solving the cubic root:

So, x is the value of the longer leg.

Now, we need to find the length, we know that length=4*longer leg

So, the length of the carton is 4*18= 72

The answer is 72

The location of the image of point S is the midpoint of the line segment RS. A representation of the geometric system and the rigid transformation is shown in the image attached below.

Herein we know the center of dilation and the location of point S, which must be dilated by a rigid transformation, that is, a transformation applied on the point such that its Euclidean distance is conserved. The operation is defined by the following equation:

RS' = k · RS

S'(x) - R(x) = k · S(x) - k · R(x)

Where k is the scale factor.

If we know that R(x) = 0, S(x) = 6 and k = 1 / 2, then the location of the point S' is:

S'(x) - 0 = (1 / 2) · 6 - 0

S'(x) = 3

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The equation for the linear function f(x) is f(x) = 2 / 7 x - 10 / 7

The linear function is f(x)

f(-2) = - 2 and f(5) = 0

Therefore, let's find the equation for the linear function f(x):

A linear function is a function that represents a straight line on the coordinate plane.

Therefore, linear function is represented as follows:

y = mx + b

where

Hence,

-2 = m(-2) + b

0 = 5m + b

b = -5m

Therefore,

m(-2) + - 5m = -2

-2m - 5m = -2

-7m = -2

m = 2 / 7

Therefore,

b = - 5 (2 / 7)

b = - 10 / 7

Hence,

f(x) = 2 / 7 x - 10 / 7

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The correct option for Negative abscissa, positive ordinate is -

• Quadrant 2

For the given question;

The other names for x and y axis are;

x -axis - abscissa

y- axis - ordinate

Thus, Negative abscissa means negative x axis.

And, positive ordinate means positive y axis.

This, lines in second quadrant.

Thus, Negative abscissa, positive ordinate will give the point is second quadrant.

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A. The absolute maximum of the function f(x) is : f(-8) = 4.

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Answer: Using the pythaorean theoream we have to det

Answer:

Outline 4 factors to the conside.

Two triangles cannot be proven to be congruent using the method: A. Prove all sets of corresponding angles are congruent.

Two triangles are congruent to each other if they have the same shape and the same size, that is, all three sets of corresponding sides and all three sets of corresponding angles of the two triangles are congruent to each other.

Also, the following condition or criteria can be used to determine if two triangles are congruent to each other:

Thus, the method that cannot be used is: A. Prove all sets of corresponding angles are congruent.

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Answer:

This video provides an example of how to determine the original price of an item given the discounted price and the percent mark

Step-by-step explanation:

Answer:

Steps to find the equation of a line from two points:

Find the slope using the slope formula. ...

Use the slope and one of the points to solve for the y-intercept (b). ...

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Step-by-step explanation:

Answer:

[tex]y=-2x+30[/tex]

where y is the weight of the cat (in pounds) and x is the number of months.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The y-intercept is the y-value when x is zero, so the initial value.

If the cat initially weighs 30 pounds, the y-intercept is 30.

The slope is the rate of change.

If the cat lost 2 pounds per month, then the rate of change is -2.

Therefore, the equation the models the given word problem is:

[tex]\boxed{\begin{minipage}{7 cm}\phantom{ww}\\$y=-2x+30$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is the weight of the cat (in pounds). \\ \phantom{ww}$\bullet$ $x$ is the number of months.\\\end{minipage}}[/tex]

The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards ,  

or length = 40 yards and width = 70 yards .

In the question ,

it is given that

the total length of the fence = 150 yards

let L be the length of the area to be fenced

let B be the width of the house

Given that one side of the area is fenced using the back side of the house

So, the perimeter of the area to be fenced is 2L+B

equating both the perimeter we get

2L+B=150

B=150-2L       ....(i)

Given the area fenced-in portion = 2800 yards

also the fenced-in portion area = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , The dimensions of the fenced-in area is

either length = 35 yards and width = 80 yards   ,

or length = 40 yards and width = 70 yards   .

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The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways

The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways

We are given that In a soccer match;

A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.

Each kick must be taken by a different player

Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;

11C5 = 11!/(5! * (11 - 5)!)

= 11!/(5! * 6!)

= 462 ways

Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;

5P5 = 5!/(5 - 5)

= 120 Ways

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Dragon needs 2.16 seconds to eat 90 kilograms of human beings.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that,

If a dragon can eat an entire cow weighing 500 kilograms in 12 seconds,

500 kilograms = 12 seconds

By unitary method

1 kilogram = 12 / 500

1 kilogram = 0.024 second

For 90 kilograms

90 kilogram=90 × 0.024 second

90 kilogram = 2.16 second

Thus, a dragon needs 2.16 seconds to eat 90 kilograms of human beings.

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This is a problem with a non-linear equation. The data is the temperature of water and the time. But we have to fit a line anyway.

We can the Least Squares Method, the best line fit is:

Now, we apply the formula above:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x² + y² = 16[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The distance between the centre and the point through which the circle is passing is equal to the radius of the circle.

so, let's use distance formula here :

[tex]\qquad \tt \rightarrow \: \sqrt{(y2 - y1) {}^{2} + (x2 - x1) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(0 - 0) {}^{2} + (4 - 0) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{0 + (4) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{ {4}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: 4 \: \: units[/tex]

Now, let's write the equation of circle in standard form :

[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {4}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 16 [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Mean=54.1 Median=55 Mode=1 Midrange=53 are the correct values of mean, median, mode and midrange.

(a) Mean= sum of data/ number of data

=(55+64+45+77+88+51+41+54+35+67+18)/11

=595/11

=54.09 or 54.1

(b) Median is the middle value, which in this case is 51.

(c)  Mode is the count of the number stating how many time it has been repeated in the data.

For instance in the given data :-

55 64 45 77 88 51 41 54 35 67 18

mode of 55 is 1, since it appears only one time.

No numbers in the given data repeats, i.e. all the values are unique. Thus the mode of the given data is 1.

(d) Mid-range is (highest value in the data + lowest value in the data)/2

in this case, the highest value is 88 and the lowest value is 18. Substituting these values in the formula:

(88+18)/2

=106/2

=53

What is mean median mode and midrange?

Mean is the sum of data divided by number of data, Median is the middle value of the data when arranged in ascending or descending order, Mode is the count of the number stating how many time it has been repeated in the data and Mid-range is highest value in the data plus lowest value in the data whole divided by 2.

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The quadratic equation with roots 4 and -2 and leading coefficient 4 is;

⇒ 4x² - 8x - 32

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree of x.

Given that;

Roots of a quadratic equation = 4 and -2

Leading coefficient = 4

Now, The quadratic equation whose roots 4 and -2 with leading coefficient is calculated as;

⇒ 4 ( x - 4) (x + 2)

Solve as;

= 4 (x - 4) (x + 2)

= 4 (x² + 2x - 4x - 8)

= 4 (x² - 2x - 8)

= 4x² - 8x - 32

Thus, The quadratic equation with roots 4 and -2 and leading coefficient 4 is;

⇒ 4x² - 8x - 32

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Answer:

Equation = 1/4 x + 25 = 70

Solution = $180

Explanation:

Let the original amount she had before she went shopping be x

If she spent one-fourth on sloth, then the amount spent on cloth will be;

1/4 x

If she receives another $25 a week later totalling her money $70, then the equation that represents the situation will be;

1/4 x + 25 = 70

Find the solution

1/4 x + 25 = 70

1/4 x = 70 - 25

1/4 x = 45

x = 45 * 4

x = 180

Hence the amount she had before going for shoppind was $180

Part a: Cost of downloading album B = 13.3 euros

Part b: Cost of downloading album B = 12.6 euros

Number of tracks in album A = 11 tracks

The total cost of downloading album A = 10.45 euro

Cost of each track on album A = Total cost of album/Number of tracks in the album

= 10.45/11

= 0.95 euro

Part a:

Number of tracks in album B = 14 tracks

Cost of album B = Number of tracks in album B * Cost of each track

= 0.95*14

= 13.3 euros

Part b:

The cost of 5 tracks on album B is 5p less therefore, the cost of 5 tracks will be 0.90*5 = 3.60 euros

The cost of 9 tracks on album B is 5p more therefore, the cost of 9 tracks will be = 1*9 = 9 euros

The total cost of downloading album B = 9+3.6 = 12.6 euros

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The answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.

In the question ,

the expression is given as

=[2−||−23−2(−15)||]÷(−13)

Solving the terms inside [ ] , we have

2*(-15) = -30

Substituting the value of 2*(-15) in the expression , we get

=[2-||-23-(-30)||]÷(−13)

=[2−||−23+30||]÷(−13)   ....as -(-30) = 30

Solving the terms inside the modulus ||  || , we get

=[2−||+7||]÷(−13)      ...as ||-23+30|| represents the modulus(norm) value ..

So ,Simplifying further , we get

=[2−7]÷(−13)                ....as 2-7 = -5

=[-5]÷(−13)       ...as a÷b can be written as a/b

= -5/-13

writing the answer in the simplified form .

= 5/13

Therefore , the answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.

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The total number of dots tells us the total number of observations of the values. the dot plot of the information are attached below.

A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale.  Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line.

If a value occurs more than once, then the dots are placed one above the other thus, that the height of the column of dots represents the frequency for that value.

Given data set:

{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}

First we need to Label the increments on the given line to include the range of data.

Then Label them order -2 to 16 increasing in 1 unit.

Now Label the dot plot with a suitable describing the dot plot.

Then Count the number of data points for each discrete category.

The dot plot of the information are attached below.

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First, we will start by converting 607,200 feet to miles

1 mile= 5280 foot

607, 200 feet can be changed to mile by dividing it by 5280

That is;

607,200 feet to mile = 607, 200 / 5280 = 115 miles

Hence; speed

= distance over t/

= 115 /1

=115 miles per hour