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The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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a. The equation of the tangent at (1,3) is y = -x/3 + 10/3

b. The equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

Since x² + y² = 10, we differentiate the equation with respect to x to find dy/dx which the the equation of the tangent.

So, x² + y² = 10

d(x² + y²)/dx = d10/dx

dx²/dx + dy²/dx = 0

2x + 2ydy/dx = 0

2ydy/dx = -2x

dy/dx = -2x/2y

dy/dx = -x/y

At (1,3), dy/dx = -1/3

Using the equation of a straight line in slope-point form, we have

m = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

-1/3 = (y - 3)/(x - 1)

-(x - 1) = 3(y - 3)

-x + 1 = 3y - 9

3y = -x + 1 + 9

3y = -x + 10

3y + x = 10

y = -x/3 + 10/3

So, the equation of the tangent at (1,3) is y = -x/3 + 10/3

Since the tangent and normal line are perpendicular at the point, for two perpendicular line,

mm' = -1 where

So, m' = -1/m

= -1/(-1/3)

= 3

Using the equation of a straight line in slope-point form, we have

m' = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

3 = (y - 3)/(x - 1)

3(x - 1) = (y - 3)

3x - 3 = y - 3

y = 3x - 3 + 3

y = 3x + 0

y = 3x

So, the equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

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The Sample space for three cards is

[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right),\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex]

There are two cards red(R) and black(B) and a six-sided die.

The event is one card is picked randomly and then rolls the die.

So, the Sample space is as follows.

[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(B,2\right),\left(R,2\right),\left(B,3\right),\left(R,3\right),\left(B,4\right),\left(R,4\right),\left(B,5\right),\left(R,5\right),\left(B,6\right),\left(R,6\right) \right \}[/tex]

Consider there were three cards red(R), black(B) and green(G) a six-sided die.

The event is one card is picked randomly and then rolls the die.

So, the sample space will be as follows,

[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right)\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex].

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The number of possible committees from the given list is; 120 committees

From the given list, we can say that;

Number of faculty members = 4

Number of male students = 2

Number of female students = 3

Number of parents = 5

Thus, the number of ways to fill the 4 member committee is calculated from probability combination as;

Number of committees = 4 * 2 * 3 * 5 = 120 possible committees

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The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).

The term 'foci' is known to be the point at which there is the coming together of light or any other kinds of electromagnetic radiation, particles, etc.

It is also seen as the point from which they seems to go apart.

[tex]\frac{x^{2} }{144} + \frac{y^{2} }{169} = 1[/tex]

[tex]\frac{x^{2} }{12^{2} } + \frac{y^{2} }{13^{2} }[/tex]

Hence, major axis is = (0, ± 13)

e = [tex]\sqrt{1 -\frac{12^{2} }{13^{2} } }[/tex]

= 5/13

Foci is: (0± 13 x [tex]\frac{5}{13}[/tex])

Foci is: (0, ±5)

Therefore, The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).

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Using it's concept, the probability that you flip heads and roll a number greater than 5 is: [tex]\frac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Hence the probability of both events is:

[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex].

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Step-by-step explanation:

Find the slope between the two points given. Then, use the slope and point ONE to write the

equation of the

Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]

Using proportions, it is found that the length of AC is of 15 units.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratios in this problem are given as follows:

The entire length is of 18 units, AB is half of that, hence:

AB = 0.5 x 18 = 9 units.

BC is two thirds of the length from 6 to 15, hence:

BC = 2/3 x (15 - 6) = 6

Thus, the length of AC is:

AC = 9 + 6 = 15 units.

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Answer:

C

Step-by-step explanation:

Equation 1:

[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]

Equation 2:

[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]

[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]

[tex]1 - 4x {}^{2} \geqslant 0[/tex]

[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]

[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]

[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]

[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]

Answer:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

[tex]\textsf{Range}: \quad [0, 1][/tex]

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

Given function:

[tex]f(x)=\sqrt{1-4x^2}[/tex]

As negative numbers don't have real square roots:

[tex]\implies 1-4x^2\geq 0[/tex]

Therefore, to find the domain, solve the inequality.

Subtract 1 from both sides:

[tex]\implies -4x^2\geq -1[/tex]

Divide both sides by -1 (reverse the inequality):

[tex]\implies 4x^2 \leq 1[/tex]

Divide both sides by 4:

[tex]\implies x^2\leq \dfrac{1}{4}[/tex]

[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]

[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]

[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]

Therefore:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

To find the range, input the endpoints of the domain into the function:

[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]

[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]

To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.

[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]

[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]

[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]

Setting it to zero and solving for x:

[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]

[tex]\implies -4x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the function:

[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]

Therefore, the range is [0, 1]

i think this is the answer

cancel by 3

Answer:

[tex]\sf \dfrac{8}{21}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]

When multiplying fractions, simply multiply the numerators and multiply the denominators:

[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]

Cancel the common factor x:

[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]

Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:

[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]

Cancel the common factor 3:

[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]

The net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

A net is a two-dimensional representation of a three dimensional solid object showing its faces.

Examples of material which can have nets are

Now, for a pyramid, we know that a pyramid is a three dimensional solid object that has one square base and four triangular sides.

So, when a pyramid is split into its net, it will have one square at the center and four triangles on the sides of the squares.

So, the net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

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Answer:

B

Step-by-step explanation:

You need to use the net that only have 1 square because a pyramid only has 1 square, it also has all the triangle sides needed which is 4. You can use a model to make a pyramid out of this net

Answer:

The balance in Bank B will be greater.

Step-by-step explanation:

Because simple interest is just interest on the principle only which is 50 every year doesn't change but with compound interest you will get 2% Interest every year.  principle+interest

El valor del número A es 692.31.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{50}{100} =0.5*100=50%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks  etc.

The exercise asks you the value of A and it gives you the value (900) that represents 130%A. Thus, you should write an equality between the division the percentage and the variable A by 100 with the value 900.

You should follow the steps below.

[tex]\frac{130*A}{100}=900\\ \\ 130A=90000\\ \\ A=\frac{90000}{130} =692.31[/tex]

You can check the result : [tex]\frac{692.31*130}{100} =\frac{90000.3}{100} =900.003=900[/tex]

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Answer:

There is only 1 solution, and it is ½

Step-by-step explanation:

-46x - 23 = 46x + 23

46x + 46x = 23 + 23

92x = 46

x = 46 / 92

x = ½

The correct statement regarding the probabilities is given as follows:

P(Male or Type B) > P(Male | Type B)

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 200 people, of which 103 are males and 12 are Type B females, hence:

P(Male or Type B) = 115/200 = 0.575

Of the 103 males, 38 are Type B, hence:

P(Male|Type B) = 38/103 = 0.3683.

Hence:

P(Male or Type B) > P(Male | Type B).

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The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.

The standard equation of a line is ax + by + c = 0.

Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.

In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.

It is given that,

The equation of the given line is 3x + 4y = 24

Rewriting the given equation into the general form,

3x + 4y - 24 =0

On comparing with ax + by + c = 0,

a = 3, b = 4 and c = -24

So,

The x-intercept of the line (-c/a) = -(-24)/3 = 8 and

The y-intercept of the line (-c/b) = -(-24)/4 = 6

Therefore, the required x and y intercepts are 8 and 6 respectively.

(The graph showing the intercepts of the given line is shown below)

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The main difference between the two nets is the top face.

The net of a box with a closed top is a 3-dimensional figure that is made up of 6 faces. The faces are all rectangles, and they are connected to each other by flaps. The flaps are the parts of the net that fold over to create the closed top.

The net of a box with an open top is a 3-dimensional figure that is made up of 5 faces. The faces are all rectangles, and they are connected to each other by flaps. However, the top face of the net is not a rectangle. Instead, it is a trapezoid. The trapezoid is created by the flaps that fold over to create the open top.

As you can see, the main difference between the two nets is the top face. The top face of the net of a box with a closed top is a rectangle, while the top face of the net of a box with an open top is a trapezoid.

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Answer:

2.5

Step-by-step explanation:

2.5 is the only positive number amongst the options, so it must be the greatest.

A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.

B.  Using the formula above, the value of R(10, 3) is $197.

A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.

Functions are used to define physical relationships between variables.

Cost monthly subscription = $28.20 per box

Number of normal potatoes in each box = 16

Cost of additional luxury potatoes = $5 per potato

If the monthly revenue function, R, is given as R(s, n) where:

s = number of monthly subscribers

n = total number of luxury potatoes ordered

The monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.

The value of R(10, 3) is $197 ($18.20 x 10 + $5 x 3)

Thus, using the formula above, the value of R(10, 3) is $197.

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The value of n in the permutation equation P(n, 5) = 2520 is 7

The expression is given as:

P(n, 5) = 2520

The above expression is a permutation expression.

The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula

P(n,r) = n!/(n - r)!

Substitute 5 for r in the above equation

P(n,5) = n!/(n - 5)!

Substitute the given values in the above equation

n!/(n - 5)! = 2520

Expand the above equation

n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520

Evaluate the quotient in the above equation

n(n-1)(n - 2)(n - 3)(n - 4) = 2520

Express 2520 as 7 * 6 * 5 * 4 * 3

n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3

By comparing the equation, we have

n = 7

Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7

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Answer:

True

Number of people is dependent

Answer:

true because it's hots and people cool of by getting by getting the water

Answer:

27.53

Step-by-step explanation:

The apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.

Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides

Given,

A hot tub is in the shape of a regular pentagon.

The side of polygon is 4ft.

We need to find the apothem of the pentagon, area and perimeter.

In the middle we will have 360 degrees.

If we divide the polygon to five triangles, then one of the verte will have 36 degree measure.

h=2/tan 36=2.7528

Perimeter of polygon=5 a

a is side of polygon

Perimeter=5×4=20 ft.

Area=1/2 perimeter ×apothem

=1/2×20×2.7528

=27.528 ft²

Hence the apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.

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1a.The mean is 8.

b. The median is 8.

c. The mode is 8.

2. The shape of the data is: perfectly symmetrical distribution.

To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.

Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12

Mean = (96)/12

Mean = 8

The median is the center of the data when it is ordered.

Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15

The center (median) is the average of the two center values = (8 + 8)/2 = 16/2

Median = 8

The mode of the data is 8, because 8 appeared most in the data set.

The mean is 8.

The median is 8.

The mode is 8.

Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.

Therefore the shape of the data is: perfectly symmetrical distribution.

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Answer:

116

Step-by-step explanation:

zinc : copper

4      :     11

11 = 319

zinc = 4 / 11 * 319

Zinc = 116