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The probability that a randomly selected point in space (x, y, z) satisfies the condition $x^2 + y^2 + z^2 \leq 1$ can be found by calculating the volume of the region in the given space that satisfies this condition, and then dividing it by the total volume of the given space.

The given space is defined by the constraints -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, and -1 ≤ z ≤ 1. It forms a cube with sides of length 2 centered at the origin.

The condition $x^2 + y^2 + z^2 \leq 1$ represents a sphere with a radius of 1 centered at the origin.

To find the volume of the region that satisfies the condition, we need to calculate the volume of the sphere and divide it by the volume of the cube.

The volume of the sphere is given by the formula: V_sphere = (4/3) * π * r^3, where r is the radius of the sphere.

In this case, r = 1, so V_sphere = (4/3) * π * 1^3 = (4/3) * π.

The volume of the cube is given by the formula: V_cube = length^3 = 2^3 = 8.

Therefore, the probability that a randomly selected point satisfies the condition is:

P = V_sphere / V_cube = [(4/3) * π] / 8

Simplifying, we have:

P = (π/6) / 8 = π/48

Hence, the probability that a randomly selected point (x, y, z) in the given space satisfies the condition x^2 + y^2 + z^2 ≤ 1 is π/48.

Hello! Angle BCD = 80º, I'm working to make a solution soon.

A small agro-industrial company has a rectangular cistern 2m above the ground, with a base of 2m by 3m and a height of 2m, which is filled with water. This water tank is used for irrigation of 4 plots of avocado plants. Determine the work necessary to pump the water up to the ground level and the size of the pump to be used. Consider the specific weight of water 9800N/m^3

Volume of the water in cistern=2m x 3m x 2m=12 m^3

The mass of the water in the cistern =9800 * 12 / 9.81 =11,987.77 kg

The amount of Work needed to pump the water up to ground level:

W = m * g * h
W = 11,987.77 kg * 9.81 m/s² * 2m
W = 235,200 J (Joules)

The size of the pump depends on how fast you want to pump out the water. Let us assume, you want to finish the job in 1 hour, or 3600 seconds:

235,200 J / 3,600 s =65 + 1/3 Watts - the size of the pump.

right!

wrong

The angle bisector from P bisects QR in X.

\(sin\ 60 ^{\circ}=\dfrac{\overline{XY}}{0.5\cdot \overline{QR}}\\ \overline{XY}=0.5\cdot \overline{QR}\cdot sin\ 60^{\circ}=0.5\cdot 9\cdot sin\ 60^{\circ}\\ \color{blue}\overline{XY}=3.897\)

  !

k = 8, m = -4.

[10   +  3  -  1]  C  [10] ==12 C 10 ==66 ways of distributing 10 stickers to 3 friends.

To find the coordinates of the two points on the circle where x = 7, we need to substitute x = 7 into the equation of the circle and solve for the corresponding y-coordinates.

The equation of a circle centered at the origin with radius sqrt{130} is given by x^2 + y^2 = 130^2 = 16900.

Substituting x = 7 into the equation, we have:

49 + y^2 = 16900.

Then y^2 = 16900 - 49 = 16851, so y = +/- sqrt(16851).

The coordinates of the two points on the circle are then (7,sqrt(16851)) and (7,-sqrt(16851)).

16 ==F *  R^22,             

24 ==F *  R^27, solve for F, R

F==2.687314174158 - this is the first term

R ==1.0844717711977 - this is the common ratio.

The 43rd term ==2.687314174158  x  1.0844717711977^(43 - 1)==81 - the 43rd term

Your sequence looks like this:

2.687314174 , 2.914316362 , 3.160493827 , 3.427466339 , 3.716990491 , 4.030971261 , 4.371474543 , 4.740740741 , 5.141199508 , 5.575485736 , 6.046456892 , 6.557211815 , 7.111111111 , 7.711799262 , 8.363228605 , 9.069685338 , 9.835817722 , 10.66666667 , 11.56769889 , 12.54484291 , 13.60452801 , 14.75372658 , 16 , 17.35154834 , 18.81726436 , 20.40679201 , 22.13058988 , 24 , 26.02732251 , 28.22589654 , 30.61018802 , 33.19588481 , 36 , 39.04098376 , 42.33884481 , 45.91528202 , 49.79382722 , 54 , 58.56147564 , 63.50826722 , 68.87292303 , 74.69074083 , 81 , >>Number of terms = 43>>Total Sum == 1008.087058

[1 + 2 + 3 +4 +5 +...........+ 25]  +  [4 + 8 + 12 + 16 + 20 +..........+100]=

          [25  x  26] / 2 ==325         +        [100 - 4==96 / 4 + 1==25 terms=

                        325                          +       [4 + 100] / 2  x  25     ==1,300

                        325                          +                  1,300                  ==1,625

Let r be the common ratio of the geometric sequence. Then, we have g23​=g1​r23−1=16 and g28​=g1​r28−1=24. Dividing these two equations, we get r5=2, so r=21/5. Therefore, g43​ = g1​r43−1 = 16r42 = 16(21/5)42 = 16*(2^4) = 128​.

There are 10 ways to choose which friend gets the first sticker, 9 ways to choose which friend gets the second sticker, and 8 ways to choose which friend gets the third sticker. However, we have overcounted the number of ways, since we have counted each possible distribution of stickers three times. Therefore, the number of ways to give out 10 stickers to 3 friends is 10×9×8​/3! = 168​.

why.

We know that the sum of the roots of a quadratic equation is equal to -b/a and the product of the roots is equal to c/a. In this case, the sum of the roots is b + 1 + 8b2 + 1 = 8b2 + b + 2 and the product of the roots is (b + 1)(8b2 + 1) = 8b3 + b + 1. We are given that the sum of the roots is equal to -a/1 and the product of the roots is equal to 2023. Therefore, we have the following equations:

8b2 + b + 2 = -a/1 8b3 + b + 1 = 2023

Solving for a and b, we get a = -8b2 and b = 3. Therefore, a + b = -8b2 + b = -7b2 = -7(3) = -21.

There is one combination only as follows:

111125 ==6! / 4! ==30 different sequences of rolls.

780 different sequence of rolls

1. The expression is equal to \(\sqrt[3]{12} - \sqrt[3]{2}\)

1. Find the area of triangle ABC if AB = 6, BC = 8, and angle ABC = 90 degrees.  

In a right triangle, either leg can be the base, and the other leg the altitude.  

The area is half the base times the height,and so (1/2)(6)(8) =  24 sq units  

2. If angle ABC = 135 degrees, and angle ACB = 30 degrees, what is angle BAC?  

For this I'm assuming we're talking about a triangle, which was not specified.  

The sum of all three angles of a triangle is 180^o so 180^o – (135^o + 30^o)  =  15^o  

_.

Please just post one question at a time! You posted 13 questions! We are not here to do your homework.

Assembly: 2x + 3y <= 120

Finishing: 3x + 2y <= 120

Total Number of Gadgets: x + y <= 190

We have 7^4x+10=7^2x=(7x)2, so 4x+10=2x, and x=5​.

c. P = (2/3, 1, 2/3).