The winner of a raffle will receive a​ 21-foot outboard boat. If 6000 raffle tickets were sold and you purchased 30 ​tickets, what are the odds against your winning the​ boat?

To find the volume of the solid that lies between the paraboloid z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2 using cylindrical coordinates, set up the integral for the volume by rewriting the sphere equation in cylindrical coordinates, determining the limits for r and z, and evaluating the integral.

To find the volume of the solid that lies between the paraboloid z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2

We can rewrite the sphere equation in cylindrical coordinates as r^2 + z^2 = 2. The limits for r are from 0 to √(2-z^2), and for z, they are from 0 to √(2-r^2).

The volume can be found by integrating the constant 1 over the limits of r and z: V = ∭1 dz dr dθ. Evaluate this integral to find the volume of the solid.

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Final answer:

The equation of a circle with a center at (-7, -7) and a radius of 7 is  [tex](x + 7)^2 + (y + 7)^2 = 49.[/tex]

Explanation:

The equation of a circle is typically expressed in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with a center at (–7, –7) and a radius of 7, the equation would be (x + 7)² + (y + 7)² = 7². Here, we squared the radius to get 49, which gives us the final equation (x + 7)² + (y + 7)² = 49.

Answer:

[tex]1.5\times 10^{-18}[/tex]

Step-by-step explanation:

We have been given that the quotient of [tex]8.4\times 10^9[/tex] and a number n results in [tex]5.6\times 10^{27}[/tex]

To find the value of n we will write our given information in an equation as:

[tex]\frac{8.4\times 10^9}{n}=5.6\times 10^{27}[/tex]

[tex]\frac{8.4\times 10^9}{5.6\times 10^{27}}=n[/tex]

Using quotient rule of exponents [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] we will get,

[tex]\frac{8.4\times 10^{9-27}}{5.6}=n[/tex]

[tex]\frac{8.4\times 10^{-18}}{5.6}=n[/tex]

[tex]1.5\times 10^{-18}=n[/tex]

Therefore, the value of n is [tex]1.5\times 10^{-18}[/tex].

Final answer:

The probability that a bridge hand chosen at random contains at least 3 kings is 0.0000244.

Explanation:

To find the probability that a bridge hand chosen at random contains at least 3 kings, we need to first determine the total number of possible bridge hands and then calculate the number of favorable outcomes.

The total number of bridge hands is calculated using the combination formula: C(52, 13) = 52! / (13! * (52-13)!) = 635,013,559,600.

To calculate the number of favorable outcomes, we count the number of ways we can select 3 kings and then fill the remaining 10 positions with the remaining 39 cards. The number of ways to select 3 kings is C(4, 3) = 4 and the number of ways to fill the remaining 10 positions is C(48, 10) = 17,259,390.

Therefore, the probability is given by: P(At least 3 kings) = favorable outcomes / total outcomes = (4 * 17,259,390) / 635,013,559,600 = 0.0000244.

An algebraic expression to denote the quotient obtained when the product of the two numbers is divided by their sum is (xy)/(x+y).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that let x and y represent two real numbers. The expression to denote the quotient obtained when the product of the two numbers is divided by their sum is written as,

E = (xy)/(x+y).

To know more about an expression follow

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the upper left on TTM                                                                                  Trust

Answer:

46.15

Step-by-step explanation:

I do RSM :)

Answer:

 0.07 -The probability that a randomly chosen team has 3 girls and 7 boys.

0.12 -The probability that a randomly chosen team includes all 6 girls in the class.

0.44 -The probability that a randomly chosen team has 5 girls and 5 boys.

0.49-The probability that a randomly chosen team has either 4 or 6 boys.

GANGGGGG  #Plutolivesmatter

When a team of 10 players is to be selected from a class of 6 girls and 7 boys the probability of each scenario occurring is:

0.07 = The probability that a randomly chosen team has 3 girls and 7 boys.

0.12 = The probability that a randomly chosen team includes all 6 girls in the class.

0.44 = The probability that a randomly chosen team has 5 girls and 5 boys.

0.49 = The probability that a randomly chosen team has either 4 or 6 boys.

What is probability?

In simple words, it refers to a numerical guess of how likely an event is to occur. Hence, when it comes to probability we believe there is no guarantee the event would occur.

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Final answer:

To find the two numbers, we created a system of equations with the sum being 70 and the larger number as five less than twice the smaller number. Solving the equations, we found that the smaller number is 25 and the larger number is 45.

Explanation:

The question asks us to find two numbers where the sum is 70, and the larger number is five less than twice the smaller number. To solve this, we'll set up a system of equations with two variables, which we'll call x and y. The first equation would be x + y = 70, since their sum is 70. The second equation is derived from the statement that the larger number is five less than twice the smaller number, which can be expressed as y = 2x - 5. Now we substitute the second equation into the first to solve for x. We get x + (2x - 5) = 70. Simplifying, we have 3x - 5 = 70, thus 3x = 75, and therefore x = 25. With the smaller number found, we can determine the larger number using the second equation y = 2(25) - 5, resulting in y = 45. Hence, the two numbers are 25 and 45.

Answer:

Step-by-step explanation:

Let the American Population = x

1/10 x = 32,000,000  Multiply by sides by 10

x = 320,000,000 Thirty two followed by 7 zeros is the population of America.

Answer:

the quotient of this problem is 3x^3+6x^+8x+24+47/x-2

The provided table outlines the probability distribution for drawing varying numbers of aces in a random draw of 4 cards from a standard 52-card deck, using combinatorial probability calculations.

To answer your question, we need to consider the different possibilities for pulling aces in a draw of four cards. There are 4 aces in a standard deck of 52 cards, and here's a table showing the probability distribution for each outcome:

Please note that 'comb(a, b)' in this case represents 'a choose b', which is a way to compute combinations in probability.

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The width of the photograph is 8 inches

let

width of the photograph = x

length of the photograph = 6 + x

Area  = x(6 + x)

112 =  x(6 + x)

112 = 6x + x²

x² + 6x - 112 = 0

x² - 8x + 14x - 112 = 0

x(x - 8) + 14(x - 8) = 0

(x + 14)(x - 8)

x = -14 or 8

x = 8

x cannot be negative so we use only 8.

width of the photograph = 8 inches

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Final answer:

The amount in the savings account increased by 3%. This was calculated by determining the amount of the increase ($9), dividing by the original amount ($300), and then multiplying by 100 to get the percent increase.

Explanation:

The question is asking to calculate the percent of increase in the amount of money in a savings account that went from $300 to $309. To determine the percent increase, you subtract the original amount ($300) from the new amount ($309) to find the amount of the increase, which is $9. Then, you divide the increase ($9) by the original amount ($300) and multiply by 100 to get the percentage:

Percent Increase = (Increase ÷ Original Amount) × 100%

Percentage Increase = ($9 ÷ $300) × 100% = 0.03 × 100% = 3%

Therefore, the percent of increase is 3%.

To find the slope of a line perpendicular to the line defined by the equation 0.5x−5y=9, first convert the equation into slope-intercept form to determine the slope of the original line. The slope of the line perpendicular to this is its negative reciprocal. For this specific problem, the slope of the line perpendicular to the given line is -10.

Firstly, rearrange the given equation, 0.5x−5y=9, into the slope-intercept format, i.e. y=mx+b. Here, 'm' is the slope of the line. To illustrate this rearrangement: 5y = 0.5x - 9, then divide through by 5 to get y = 0.1x - 1.8. Thus, the slope of the given line is 0.1.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. In this case, the slope of the given line is 0.1, so the negative reciprocal (which represents the slope of the line perpendicular to this line) is -1/0.1, which equals -10. This is the slope of the line perpendicular to the given line.

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90% = 9,750

9750/90 = 1%

1% = 108.3

100% = 10,833.3

original retail price = $10,833.30

Answer:

Option C is the correct answer.

Step-by-step explanation:

Volume of box = Length x width x height.

Volume of box = 36 cubic centimetres.

Option A:

Length = 12 cm

Width = 12 cm

Height = 12 cm

Volume = 12 x 12 x 12 = 1728 cubic centimetres.

Option A is wrong.

Option B:

Length = 4 cm

Width = 4 cm

Height = 2 cm

Volume = 4 x 4 x 2 = 32 cubic centimetres.

Option B is wrong.

Option C:

Length = 3 cm

Width = 4 cm

Height = 3 cm

Volume = 3 x 4 x 3 = 36 cubic centimetres.

Option C is correct.

Option C is the correct answer.