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abruzzese [7]
2 years ago
12

In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and 7 of them are drawn at random. If the 7

numbers drawn match the 7 numbers a player has chosen, in any order, she or he win $2,500,000. Alternatively, if 6 of the numbers drawn match 6 of the 7 numbers a player has chosen, in any order, the player wins $40,000, and if 5 of the numbers drawn match 5 of the 7 numbers a player has chosen, in any order, the player wins $10,000.
Required:
a. What is the probability a player who buys one ticket will win the $2,500,000 prize?
b. What is the probability a player who buys one ticket will win the $10,000 prize?
Mathematics
1 answer:
DENIUS [597]2 years ago
8 0

Answer:

Step-by-step explanation:

From the given information;

The total number of ways to choose 7 number = ^{40}C_7

Number of ways to choose 7 correct numbers = ^{7}C_7

∴

The probability P( win $2500000) is;

= \dfrac{^{7}C_7}{^{40}C_7}

= \dfrac{\dfrac{7!}{7!(7-7)!} }{\dfrac{40!}{7!(40-7)!}}

= \dfrac{1 }{\dfrac{40!}{7!(40-7)!}}

= \dfrac{1 }{\dfrac{40!}{7!(33)!}}

= \dfrac{1 }{18643560}

= 5.36 × 10⁻⁸

The probability P( win $10000) is:

= \dfrac{^7C_5 \times ^{33} C_2}{^{40}C_7}

= \dfrac{ \dfrac{7!}{5!(7-5)!} \times  \dfrac{33!}{2!(33-2)!} }{ \dfrac{40!}{7!(40-7)!}}

= \dfrac{ \dfrac{7!}{5!(2)!} \times  \dfrac{33!}{2!(31)!} }{ \dfrac{40!}{7!(33)!}}

= \dfrac{ 21 \times 528 }{ 18643560}

= \dfrac{ 11088 }{ 18643560}

=\dfrac{462}{776815}

= 5.95 × 10⁻⁴

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Step-by-step explanation:

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What is the slope of the line parallel to y=2/5x-1?<br> I really need help with this fast please
lana66690 [7]

Answer:

The slope will be 2/5.

Step-by-step explanation:

y = 2/5x -1 is written in slope-intercept form.

This formula looks like:

y=mx+b

where:

  • M = Slope
  • x = independent variable
  • b = y-intercept

So:

  • 2/5 is our slope
  • x remains our independent variable
  • -1 is our y-intercept.

1 ). For two lines to be parallel they must have the same slope.

  • Slope would remain 2/5

2 ). For two line to be perpendicular they must have slopes that are opposite reciprocals.

  • .  Slope would become -5/2

As the question states, we must find the slope of a line parallel to the equation given. This means that the slope will remain 2/5.

Lets check our work!

Choose a random ordered pair. I will choose (5, 6).

Now, using point slope-form we can find out if what was said above is true!

This formula looks like:

y - y1 = m (x-x1)

Let us substitute:

y - 6 = 2/5(x-5)

Distribute:

y-6=2/5x-2

Add 6 to both sides:

y= 2/5x+4

Now using both equations I will plot them on a graph to see if they a parallel.

As you can see from the graph below, these lines are parallel. Where the equation you were given is in blue and the equation I made is in red.

Based on all of the evidence, the slope will be 2/5.

Hope this helped! :)

4 0
3 years ago
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