Prove or disprove that the product of two irrational numbers is irrational

We are given here that a blackjack hand consists of:

1 of the 4 aces = 4 / 52

1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52

So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:

P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace

P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)

P = 0.04827 = 4.83%

Therefore there is a 4.83% probability to get a blackjack hand.

Final answer:

The probability of being dealt a blackjack hand with a single deck is approximately 0.0483, which translates to about 4.83% of the hands.

Explanation:

To find the probability of being dealt a blackjack hand in a single-deck game, we need to calculate the chances of drawing an ace and a 10-point card (10, Jack, Queen, or King) in any order. There are 4 aces and 16 cards worth 10 points in a deck of 52 cards. The probability of drawing an ace first is 4/52, and then drawing a 10-point card is 16/51, giving us (4/52)*(16/51). Conversely, if a 10-point card is drawn first (16/52) followed by an ace (4/51), the probability is (16/52)*(4/51). Adding the two probabilities gives us the chance of a blackjack in either order:

P(Blackjack) = (4/52)*(16/51) + (16/52)*(4/51) = (64/2652) + (64/2652) = 128/2652 ≈ 0.0483

The approximate percentage of hands that are winning blackjack hands is about 4.83%.

The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).

In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).

The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.

The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.

In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).

https://brainly.com/question/31745830

#SPJ12

The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.

To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.

Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.

As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).

Therefore, the solid can be described using the following inequalities in spherical coordinates:

https://brainly.com/question/31850328

#SPJ11

Thomas = x

Julian = x-10

x +x-10 = 74

2x-10 = 74

2x = 84

x = 84/2 = 42

Thomas is 42

Julian is 32

multiply 152 by 15%

152 * 0.15 = 22.80 ( amount of discount

152 - 22.80 = 129.20 ( sale price)

By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.

To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.

The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.

Solving this system of equations will give us the number of each type of sweet sold.

To solve the system of equations, we can use substitution or elimination. I'll use substitution:

Tiffany and Adele sold 11 cookies and 14 brownies.

Answer:

-16         81       19

Step-by-step explanation:

To calculate the perimeter of the rectangular sandbox, use the formula P = 2l + 2w, where l is the length and w is the width. For the given dimensions, 31.7 meters in length and 24.5 meters in width, the perimeter is 112.4 meters.

The question asks us to calculate the perimeter of a rectangular sandbox. The formula to calculate the perimeter of a rectangle is 2 times the length plus 2 times the width, often written as P = 2l + 2w.

Given the dimensions of the sandbox, the length (l) is 31.7 meters, and the width (w) is 24.5 meters.

We calculate the perimeter as follows:

Therefore, the perimeter of the rectangular sandbox is 112.4 meters.

Answer: A

Step-by-step explanation:

to convert feet to miles you would use a ratio of feet over miles

 so the answer would be B

A wheel turn 60π radians per second.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A wheel turns 1,800 revolutions per minute.

Now,

Since, A wheel turns 1,800 revolutions per minute.

Hence, Number of revolution in one seconds = 1800 / 60

                                                                       = 30

We know that;

⇒ 1 revolution = 2π radian

So, Number of revolution in radian per second = 30 × 2π

                                                                         = 60π

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

Answer:

x = -2/3; x = 5/2.

Step-by-step explanation:

6x 2 - 11x - 10 = 0

Use the 'ac' method:

6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.

That would be -15 and +4.  So we write:

6x^2 - 15x + 4x - 10 = 0      Factor by grouping:

3x(2x - 5) + 2(2x - 5) = 0

(3x + 2)(2x - 5) = 0

x = -2/3; x = 5/2.

The simplification of 1/4 (-12+4/3) first involves simplifying the operation in the parentheses which gives -10.67. Multiplying this by 1/4 we get -2.67.

To simplify the expression 1/4 (-12+4/3), first simplify the operation in the parentheses.

-12 + 4/3 equals -12 + 1.33 (approx.), which simplifies to -10.67.

Then, multiply this result by 1/4. So, 1/4 of -10.67 equals -2.67 (approx.).

So, 1/4 (-12+4/3) simplifies to -2.67.

https://brainly.com/question/33857870

#SPJ2

Is It A Fraction If So Then The Answer Is [tex]\frac{9}{16}[/tex]

If Not Then The Other Guy Is Right

              HoPe It HeLpS PlEaSe MaRk Me ThE BRAINlYEST!!!!!!!!!!!!

Answer:

its a

Step-by-step explanation:

Answer:

19 1/2 ft

Step-by-step explanation:

hope this helped

Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.

---------------------

The volume of a cube of edge e is given by:

[tex]V = e^3[/tex]

In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.

[tex]V = e^3[/tex]

[tex]125 = e^3[/tex]

[tex]e = \sqrt[3]{125}[/tex]

[tex]e = 5[/tex]

Now, for the rate of change, we need to apply the implicit differentiation, thus:

[tex]V = e^3[/tex]

[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]

Volume decreases at a rate of 4 cubic meters per minute, thus:

[tex]\frac{dV}{dt} = -4[/tex]

The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:

[tex]-4 = 75\frac{de}{dt}[/tex]

[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]

[tex]\frac{de}{dt} = -0.0533[/tex]

The rate of change is of -0.0533 cubic meters per minute.

A similar problem is given at https://brainly.com/question/24158553