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spayn [35]
3 years ago
9

In a state lottery game you select six numbers from 1 to 44. the state selects six numbers at random from 1 to 44 without replac

ement. you must match four out of the state's six to win third prize. the order of the numbers is irrelevant. find the probability of winning third prize.
Mathematics
1 answer:
LiRa [457]3 years ago
6 0
We need to correctly choose exactly 4 out of the 6 drawn numbers.

Apply hypergeometric distribution:
a=number of correctly chosen numbers = 4
A=number of correct (drawn) numbers = 6
b=number of incorrectly chosen numbers = 2 
B=number of undrawn numbers = 44-6 = 38

Then by the hypergeometric distribution
P(a,b,A,B)
=C(A,a)C(B,b)/C(A+B,a+b)  [C(n,r)=combination of r objects taken out of n]
=C(6,4)C(38,2)/C(44,6)
=15*703/7059052
= 10545/7059052
= 0.001494 (to the nearest millionth)
Answer: probability of winning third prize is 10545/7059052=0.001494

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Find the area of the shaded region to the nearest tenth. See picture for full problem. Please and thank you so much!
Anestetic [448]

Answer:

Step-by-step explanation:

Radius =6 ft

Area of circle = πr²

                      = 3.14 * 6 * 6

                      = 113.04 ft²

base = 10.39 ft

height = 6+3 = 9 ft

Area \ of \ triangle = \dfrac{1}{2}*base * height\\\\\\=\dfrac{1}{2}*10.39*9\\

= 46.76 ft²

Area of the shaded region = area of circle - area of triangle

             = 113.04 - 46.76

            = 66.28

             = 66.3 ft²

8 0
2 years ago
In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is
zheka24 [161]

Answer:

f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

Step-by-step explanation:

Let:

M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y

This is and exact equation, because:

\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}

So, define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)

The solution will be given by:

f(x,y)=C_1

Where C1 is an arbitrary constant

Integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y):

f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}

Substitute into \frac{\partial f(x,y)}{\partial y} =N(x,y)

2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y

Integrate \frac{dg(y)}{dy} with respect to y:

g(y)=\int\ {8y} \, dy =4y^2

Substitute g(y) into f(x,y):

f(x,y)=2x^2+4y^2+2xy

The solution is f(x,y)=C1

f(x,y)=2x^2+4y^2+2xy=C_1

Solving y using quadratic formula:

y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

4 0
3 years ago
Please assist me<br><br>NO LINKS!!<br>​
Nana76 [90]

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today, I hope you are having a nice day!

We can solve this in two steps, Comprehension and Solving. I'll go ahead and start with Comprehension.

If you have any questions feel free to ask away!!

Comprehension

We know according to the laws of geometry that all angles in a triangle add up to 180 degrees.

We also know that in an isosceles angle, the base angles are equation to each other.

Now that we know what we need to know, we can setup an equation.

2x-6+(2x)=180

We can do this because first of all, we know that 2x-6 is one of the angles and as per the base angles of an isosceles triangle we know that both base angles are x, therefore we can add 2x to get 180 degrees.

I'll start solving now.

Solving

We can solve this by using the equation we made above and solving it with algebra.

2x-6+2x=180\\4x-6=180\\4x=186\\x=46.5

We know that x is equal to 46.5 degrees. We can check that by inputting it into the equation.

2(46.5)-6+2(46.5)=180?\\4(46.5)=186?\\46.5=46.5

We've proven that our answer is correct by double checking,

Therefore the answer is 46.5!

Cheers!

4 0
2 years ago
Lucy's fish tank has 14 liters of water in it. She plans to add 5 liters per minute until the tank has at least 49 liters. What
Vikentia [17]

Answer:

Step-by-step explanation:

14 + 5t > = 49 (thats a greater then or equal sign)

5t > = 49 - 14

5t > = 35

t > = 35/5

t > = 7 <===

3 0
3 years ago
HELP
Inga [223]

Answer:

3.75 quarts, rounded to 3.8 quarts

Step-by-step explanation:

3 quarts of solution is 10% antifreeze, so 0.3 quarts are already antifreeze, and 2.7 quarts are not.

a(the antifreeze we already have)+x(what we're going to add)= 1.5*2.7

Let me explain. If we have 60% antifreeze, 40% is not. 60/40=1.5

Substitute a for 0.3

0.3+x=4.05  Subtract 0.3 from both sides

x=3.75

7 0
2 years ago
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