help!!!!!!!!!!!!!!!!

Statement 1, BD ≅ SD and ED ≅ TD would not be sufficient to prove quadrilateral BEST is a parallelogram.

A quadrilateral is a parallelogram if it satisfies any of the following conditions: Opposite sides are parallel and congruent, Opposite angles are congruent, Diagonals bisect each other. If a quadrilateral satisfies any of these conditions, it is a parallelogram.

Although BD ≅ SD and ED ≅ TD indicate that the diagonals bisect each other, it does not necessarily mean that the opposite sides are parallel. For example, a kite has diagonals that bisect each other but its opposite sides are not parallel.

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Answer:

#7
AB = 4.1

CB = 4.1

#10
AC = 21.21

CB = 15

#11
AC = 2.828
CB =2

#12
AB =  2.616
CB = 2.616

#13

AC = 6
CB = 3√2

#14

AC = 5.94

CB = 4.2

Step-by-step explanation:

The triangle is a right isosceles triangle with AB = AC

This means
AC² = AB² + CB²
= AB² + AB²
= 2AB²
AC =  AB√2

and

AC = CB√2                (since CB= AB)

#7
Given  AC = 5.8

We know AC = AB√2
[tex]AB= \dfrac{AC}{\sqrt{2}} = \dfrac{5.8}{\sqrt{2}} = 4.1[/tex]

CB = AB  is also  4.1

#10
Given AB = 15

AC = AB√2 =  15√2 =
CB= AB = 15

#11

Given CB = 2

AB = CB= 2

AC = CB√2 = 2√2 = 2.828

#12

Given AC = 3.7

We know AC = AB√2
AB= AC/√2 = 3.7 ÷ √2 = 2.616

CB = AB  is also  2.616

#13

Given AB = 3√2

AC = AB√2 = 3 x √2 x √2 = 3 x 2 =6   (√2 x √2 = 2)
CB = 3√2

#14

Given AB= 4.2

AC = 4.2 x √2 = 5.94

CB = AB = 4.2

The coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

The transition matrix from B to B' can be found by first finding the inverse of matrix B, then multiplying it by matrix B'. The transition matrix from B' to B can be found by first finding the inverse of matrix B', then multiplying it by matrix B. To verify that the two transition matrices are inverses of each other, we can multiply them together and see if the result is the identity matrix. Finally, to find the coordinate matrix [x]B, given the coordinate matrix [x]B', we can multiply the transition matrix from B' to B by the coordinate matrix [x]B'.

(a) Find the transition matrix from B to B'.
P−1 = B^(-1) * B' =
[(-0.04, 0.04, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(0, −1, 8), (1, 1, −8), (2, 2, −12)] =
[(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)]

(b) Find the transition matrix from B' to B.
P = B'^(-1) * B =
[(-0.33, 0.17, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(14, −2, −6), (−6, 1, 3), (12, −2, −5)] =
[(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)]

(c) Verify that the two transition matrices are inverses of each other.
PP−1 = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)] =
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]

(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

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Answer:

To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.

In this case, the base is a square with side length 11.5 inches. Therefore, its area is:

Area of base = 11.5^2 = 132.25 square inches

Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:

c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)

The area of each triangular face can be found using the formula:

Area of triangle = (1/2) * base * height

where the base is 11.5 inches and the height is 8.121 inches.

Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)

So, the total surface area of the square pyramid is:

Total surface area = Area of base + 4 * Area of each triangular face

Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)

Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.

The solution to the logarithmic equation log_(3x - 2)(125) = 3 is given as follows:

x = 7/3.

The logarithmic equation for this problem is defined as follows:

log_(3x - 2)(125) = 3

The definition of the logarithm can be applied, which means that if we elevate the base of 3x - 2 to the power of 3, we obtain the result of 125.

With the application of the definition, the expression is given as follows:

(3x - 2)³ = 125.

125 is the third power of 5, hence:

(3x - 2)³ = 5³.

The third power function is one-to-one function, meaning that each output is related to a single input, hence the value of x is obtained as follows:

3x - 2 = 5

3x = 7

x = 7/3.

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Answer: 1/3

Step-by-step explanation: so there is six cards total and only two of them are even so 2/6 and that can go to 1/3

1/3

There are 2 even numbers, and the total is 6. So 2/6 in the simplest form is 1/3.

Answer:

If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:

t = kc

We can find the value of k by using the given information that 5 climbs cost $52.50:

52.50 = k(5)

Solving for k, we get:

k = 10.50

Therefore, the equation that represents the total cost, t, of c climbs is:

t = 10.50c

The value of x in the function 4x+6=8x-22 is 7.

The slope is equal to -10.

The slope-intercept form of the function 4x+5y=24 is y = -4x/5 + 24/5.

The value of f(-5) is equal to -36.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m = (-12 - 8)/(-4 + 6)

Slope, m = -20/2

Slope, m = -10.

4x+6=8x-22

8x - 4x = 22 + 6

4x = 28

x = 7.

4x + 5y = 24

5y = -4x + 24

y = -4x/5 + 24/5

For f(-5), we have:

f(x)=7x-1

f(-5)=7(-5)-1

f(-5) = -36.

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The measured unknown sides are -

GH = 4.6

QR = 1.3

AB = 15

UW = 41

Two triangles are similar if the ratio of their corresponding sides is same and their corresponding angles are equal.

Given are the triangles as shown in the image.

{ 1 } -

We can write -

GH/HJ = GK/KJ

GH/4.6 = 3.6/3.6

GH = 4.6

{ 2 } -

QT/TS = QR/RS

4.7/4.7 = QR/1.3

QR = 1.3

{ 3 } -

AD/DC = AB/BC

AD/AD = AB/BC

AB/BC = 1

5x/4x + 3 = 1

5x = 4x + 3

x = 3

AB = 15

{ 4 } -

UW/UV = DW/DV

7x + 13 = 9x + 1

3x = 12

x = 4

UW = 41

Therefore, the measured unknown sides are -

GH = 4.6

QR = 1.3

AB = 15

UW = 41

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The total materials purchase usage variance is -P122.50.

The total materials cost variance is calculated by subtracting the total standard cost from the total actual cost. The total standard cost is P675.00 per batch and there were 14 batches produced during the month, so the total standard cost is P675.00 x 14 = P9,450.00. The total actual cost is calculated by multiplying the quantity purchased by the purchase price for each fruit and then adding them all together. The total actual cost is (300 x P9.50) + (150 x P22.00) + (350 x P7.20) + (80 x P15.40) = P2,850.00 + P3,300.00 + P2,520.00 + P1,232.00 = P9,902.00. The total materials cost variance is P9,902.00 - P9,450.00 = P452.00.

The materials yield variance is calculated by subtracting the standard quantity of materials from the actual quantity of materials used and then multiplying by the standard cost per liter. The standard quantity of materials is 60 liters per batch and there were 14 batches produced during the month, so the standard quantity of materials is 60 x 14 = 840 liters. The actual quantity of materials used is 290 + 130 + 350 + 75 = 845 liters. The materials yield variance is (840 - 845) x P10.00 = -P50.00.

The materials purchase usage variance is calculated by subtracting the standard cost per liter from the actual cost per liter and then multiplying by the actual quantity of materials used. The materials purchase usage variance for each fruit is (P9.50 - P10.00) x 290 + (P22.00 - P21.25) x 130 + (P7.20 - P7.50) x 350 + (P15.40 - P15.00) x 75 = -P145.00 + P97.50 - P105.00 + P30.00 = -P122.50. The total materials purchase usage variance is -P122.50.

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The European company will earn 128,750 Euros in profit for selling 1,500 headphones.

To find the profit for selling 1,500 headphones, we need to plug in the value of h into the profit function E(h) and simplify.

Since h is measured in thousands of headphones, we need to divide 1,500 by 1,000 to get h = 1.5.

Now we can plug in h = 1.5 into the profit function and simplify:

E(1.5) = -4(1.5)^(4) + 7(1.5)^(3) - 7(1.5) + 20

E(1.5) = -4(5.0625) + 7(3.375) - 10.5 + 20

E(1.5) = -20.25 + 23.625 - 10.5 + 20

E(1.5) = 12.875

So the profit for selling 1,500 headphones is 12.875 ten thousands of Euros, or 128,750 Euros.

Therefore, the European company will earn 128,750 Euros in profit for selling 1,500 headphones.

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The value of x and y in the line segment are 6 and 6.5 units repsectively.

The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .

Using the information in the diagram let's find the value of x and y in the diagram.

Therefore,

2x + 1 = x + 7

2x - x = 7 - 1

x = 6 units

Therefore,

3y - 8 = y + 5

3y - y = 5 + 8

2y = 13

divide both sides by 2

y = 13 / 2

y = 6.5 units

Therefore,

x = 6 units

y = 6.5 units

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The table can be filled up accordingly:

1.  5 years compounded semi-annually:

b = (1 + 0.06/2)

y= 1800 (1 + 0.03)^10

x = 2

2. For the 5 years compounded quarterly:

b =  (1 + 0.06/4)

y =  1800 (1 + 0.015)^20

x =4

3. For the 5 years compounded monthly:

b = (1 + 0.06/12)

y = 1800 (1.005)^60

x = 12

4. For 10 years compounded annually:

b = (1 + 0.06/1)

x =  1800 (1.06)^10

y = 1

5. For 10 years compounded quarterly:

b =  (1 + 0.06/4)

y =1800 (1 + 0.005)^60

x = 4

6. For 10 years compounded monthly:

b = (1 + 0.06/12)

y = 1800 (1 + 0.005)^120

x = 12

To solve the compound interest we use the formula:

P(1+r/n)^(n*t).

For the 5 years compounded semi-annually:

A = 1800 (1 + 0.06/2)^2*5

A = 1800 (1 + 0.03)^10

A = 1800 (1.03)^10

A = 1800 (1.344)

A = 2419

For the 5 years compounded quarterly:

A = 1800 (1 + 0.06/4)^4*5

A = 1800 (1 + 0.015)^20

A = 1800 (1.015)^20

A= 1800 (1.3468)

A= 2424.24

For the 5 years compounded monthly:

A = 1800 (1 + 0.06/12)^12*5

A = 1800 (1 + 0.005)^60

A = 1800 (1.005)^60

A = 1800 (1.34885)

A = 2427.93

For 10 years compounded annually:

A= 1800 (1 + 0.06/1)^10

A = 1800 (1.06)^10

A = 1800 (1.7908)

A = 3223.53

For 10 years compounded semi-annually:

A = 1800 (1 + 0.06/2)^20

A = 1800 (1 + 0.03)^20

A = 1800 (1.03)^20

A =1800 (1.806)

A = 3251

For 10 years compounded quarterly:

A= 1800 (1 + 0.06/4)^4*10

A = 1800 (1 + 0.015)^40

A= 1800 (1.015)^40

A = 1800 (1.814)

A = 3265.23

For 10 years compounded monthly:

A= 1800 (1 + 0.06/12)^120

A = 1800 (1 + 0.005)^120

A = 1800 (1.005)^20

A= 1800 (1.8194)

A = 3274.9

The best pay period is that with the highest returns which is 10 years compounded monthly.

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Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.

Let's start by setting up an inequality to represent the mileage for which Company A charges less than Company B:

Cost of Company A < Cost of Company B

The cost of Company A is a constant $101, regardless of how many miles are driven. The cost of Company B, on the other hand, depends on the number of miles driven. If m represents the number of miles driven, then the cost of Company B can be expressed as:

Cost of Company B = $65 + $0.80m

Now we can substitute these expressions into the inequality we set up earlier:

$101 < $65 + $0.80m

Simplifying and solving for m:

$36 < $0.80m

$45 < m

Therefore, Company A will charge less than Company B for mileage greater than $45.

To summarize, Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.

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Answer: 22

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

(36 x8-204)

multiply first

36(8)=288

then subtract

288-204=84

8+84 ÷6

divide first

84 ÷6=14

8+14=22

What is rhombus ?

A rhombus is a special type of parallelogram in which two pairs of opposite sides are congruent. That means all the sides of a rhombus are equal.

What is the Area of a Rhombus?

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

Using Diagonals                A = ½ × d1 × d2

Using Base and Height        A = b × h

Using Trigonometry        A = b2 × Sin(a)

the correct answer is the option (C) 340 cm^2

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Answer:

2g) Letty cannot use the factors 4 and 12 to simplify the square root of 48 using the Product Property of Square Roots because 4 is a perfect square, but 12 is not. The Product Property of Square Roots only applies to factors that are both perfect squares.

2h) A better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is a perfect square and is a factor of 48, which means it can be taken out of the radical completely. The remaining factor is 3, which cannot be simplified any further since it is not a perfect square. Therefore, the square root of 48 can be simplified to 4 times the square root of 3. It is important to choose 16 and 3 as the factors and not any other pair because 16 is the largest perfect square factor of 48, and 3 is the remaining factor after taking out 16 that cannot be simplified any further.

2g) These factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.

2h) a better choice to simplify the square root of 48 would be to use the factors 16 and 3. This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.

Now, Using the Product Property of Square Roots, we can simplify the square root of 48 as :

√48 = √(4 x 12)

However, these factors (4 and 12) are not the best choice to simplify the square root of 48 because 4 is a perfect square, but 12 is not.

Hence, We want to simplify the radical by finding the largest perfect square that is a factor of 48.

For this, we can break down 48 into its prime factors:

48 = 2 x 2 x 2 x 2 x 3

Then, we group the prime factors into pairs of the same number:

48 = (2 x 2) x (2 x 2) x 3

This gives us two perfect squares, 4 and 16.

Hence, We can simplify the square root of 48 by using the largest perfect square factor, which is 16:

√48 = √(16 x 3)

√48 = √16 x √3

√48 = 4√3

Therefore, a better choice to simplify the square root of 48 would be to use the factors 16 and 3.

This is because 16 is the largest perfect square factor of 48, which simplifies the radical the most.

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We round up to the nearest whole number because we are unable to have half a player. As a result, the softball team is allowed to send 7 players to the competition.

The equal sign joins two expressions to create a mathematical formula called an equation. An illustration formula could be 3x - 5 = 16. By resolving this equation, we find that the value of the variable x is 7.

To begin, let's define a few variables:

x: The softball team's total roster size

y: the sum of the players' meal expenses

We can construct the equation shown below:

$1353 - $943.50 - $31.50x = y

Simplifying this equation, we get:

$409.50 - $31.50x = y

we can set up another equation:

y = $31.50x

Now we can substitute the second equation into the first equation to eliminate y:

$409.50 - $31.50x = $31.50x

Simplifying this equation, we get:

$409.50 = $63x

Dividing both sides by 63, we get:

x = 6.5

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The decimal fοrm οf the mixed fractiοn 33 2/3, apprοximated tο the nearest tenth, is 33.67.

A mixed fractiοn is οne that is represented by bοth its quοtient and remainder. Sο, a mixed fractiοn is a cοmbinatiοn οf a whοle number and a prοper fractiοn. A fractiοn represents a piece οf a larger tοtal. Tο learn hοw tο determine the precise values οf mixed numbers, it is crucial tο cοnvert a mixed number tο a decimal. A mixed number can be cοnverted tο decimal fοrm using οne οf twο techniques:

the mixed number is changed intο an imprοper fractiοn.

by first changing the given mixed number's fractiοnal pοrtiοn tο decimal, then adding the whοle number pοrtiοn tο it.

Nοw the given fractiοn is 33 2/3.

This is a mixed fractiοn because it has a whοle number οf 33 and a fractiοn οf 2/3.

This mixed fractiοn can be cοnverted tο a decimal number by finding the value οf the fractiοn part οf the number and adding it tο the whοle number.

Sοlving fractiοnal parts,

2/3 = 0.66666 = 0.67 (Rοunding tο the nearest tenth)

Nοw add tο the whοle number.

33 + 0.67 = 33.67

Therefοre the decimal fοrm οf the mixed fractiοn 33 2/3 is 33.67.

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Uncle Moneybags can withdrawal approximately $583.67 per month.

To find out how much Uncle Moneybags can withdraw each month, we can use the formula for the future value of an annuity:

FV = PMT × [(1 + i)ⁿ - 1] / i

Where:
FV = future value
PMT = payment amount
i = interest rate per period
n = number of periods

In this case, we want to solve for PMT, so we can rearrange the formula to:

PMT = FV × i / [(1 + i)ⁿ - 1]

We know that FV = $500,000, i = 8% / 12 = 0.00667, and n = 25 × 12 = 300. Plugging these values into the formula, we get:

PMT = $500,000 × 0.00667 / [(1 + 0.00667)³⁰⁰ - 1]

PMT = $500,000 × 0.00667 / 5.7435

PMT = $583.67

Therefore, Uncle Moneybags can withdraw $583.67 each month for 25 years.

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The measure of line KR is 8 inches

It is important that we know the properties of an isosceles trapezoid.

From the information given, we have that;

KR = 1/2x + 5

DH = 2x - 4

Since the non- parallel sides of an isosceles trapezoid are equal, then, we have;

KR = DH

1/2x + 5 = 2x - 4

collect the like terns, we have

1/2x - 2x = -4 - 5

x - 4x  /2 = - 9

cross multiply

-3x = -18

x = 6

KR =  1/2(6) + 5 = 8 inches

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The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.

Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.

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Answer:

277 milliliters

Step-by-step explanation:

945-668= 277

The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.

Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.

Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:

y - 5 = -6(x - 3)

Simplifying the equation, we get:

y - 5 = -6x + 18

y = -6x + 23

Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.

Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

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Answer:

4-2-5

Step-by-step explanation:

16, 8, and 20 can all be divided by 4

Leaving you with 4 2 and 5.

The ratio is 4 to 2 to 5

The roots of equation A are  2 and 0.25.

The roots of equation B are 3.14 and -0.64.

To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation.

For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:

x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8

This gives us two possible values for x:

x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25

Therefore, the roots of equation A are 2 and 0.25.

For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:

x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4

This gives us two possible values for x:

x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64

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Answer: 25

Step-by-step explanation:

4x - 25 = -125
4x = -125 + 25
4x = -100

Divide both sides by 4
x = -25

The probability distribution function of Y = |X| is given by:
P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y) = P(X ≤ y) - P(X < -y)

Since X ~ N(0, 2), we can use the standard normal distribution to find the probabilities:
P(X ≤ y) = Φ(y/√2)
P(X < -y) = Φ(-y/√2)

Therefore, the probability distribution function of Y is:
P(Y ≤ y) = Φ(y/√2) - Φ(-y/√2)

To find E(|X|) and Var(|X|), we can use the properties of the absolute value function:
E(|X|) = ∫_(-∞)^(∞) |x| f(x) dx = 2 ∫_(0)^(∞) x f(x) dx
Var(|X|) = E(|X|^2) - (E(|X|))^2 = 2 ∫_(0)^(∞) x^2 f(x) dx - (2 ∫_(0)^(∞) x f(x) dx)^2

Since f(x) is the probability density function of X, we can substitute it with the standard normal distribution:
f(x) = (1/√(2π)) e^(-(x^2)/4)

Therefore, E(|X|) and Var(|X|) can be found by evaluating the integrals:
E(|X|) = 2 ∫_(0)^(∞) x (1/√(2π)) e^(-(x^2)/4) dx = √(2/π)
Var(|X|) = 2 ∫_(0)^(∞) x^2 (1/√(2π)) e^(-(x^2)/4) dx - (√(2/π))^2 = 2 - (2/π)

So the final answers are:
1. E(|X|) = √(2/π)
2. Var(|X|) = 2 - (2/π)

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The answer to the quadratic equation -9d^(2)+6=-6d is 11/20 and -11/20. To solve the given quadratic equation f -9d^(2)+6=-6d, we need to rearrange the terms and use the quadratic formula.

Step 1: Rearrange the terms to get the equation in the standard form of ax^(2) + bx + c = 0
-9d^(2) + 6d + 6 = 0

Step 2: Identify the values of a, b, and c.
a = -9
b = 6
c = 6

Step 3: Use the quadratic formula to find the solutions for d.
The quadratic formula is given by:

d = (-b ± √(b^(2) - 4ac))/(2a)

Substitute the values of a, b, and c into the formula:

d = (-(6) ± √((6)^(2) - 4(-9)(6)))/(2(-9))

Step 4: Simplify the expression inside the square root:

d = (-(6) ± √(36 + 216))/(-18)

d = (-(6) ± √(252))/(-18)

Step 5: Simplify the expression further:

d = (-(6) ± 15.87)/(-18)

Step 6: Solve for d using both the positive and negative values inside the square root:

d = (-(6) + 15.87)/(-18) = 0.55

d = (-(6) - 15.87)/(-18) = -0.55

So, the solutions for d are 0.55 and -0.55 or 11/20 and -11/20 using the quadratic formula to solve the given quadratic equation.

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