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Margaret [11]
3 years ago
5

Find the expected value of the winnings

Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

The expected value is $3.95

Step-by-step explanation:

Here, we want to get the expected value

Mathematically, what we have to do here is to multiply each of the probabilities by the pay out value, before we proceed to add up

We have this as;

0(0.5) + 0.2(5) + 0.15(8) + 10(0.1) + 15(0.05)

= 0 + 1 + 1.2 + 1 + 0.75 = 3.95

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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
  • Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

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3 years ago
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Which statement correctly identifies the line of reflection?
Alchen [17]

Answer:

the triangles are reflected across the line y= -x

hope this helps

Step-by-step explanation:

4 0
3 years ago
–8(n + 7) >-96??????????????
mihalych1998 [28]

Answer:

D) n<5

Step-by-step explanation:

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3 years ago
A polygon has an interior angle sum of 3060° how many sides must the polygon have?
AVprozaik [17]
Sum of interior angles=(n-2)180
3060=(n-2)180
3060/180=n-2
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n=19..
5 0
3 years ago
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In the given figure, find ∠PQS, if∠PQR = 5x + 25 and∠SQR = 2x + 10.
kramer

Answer:

∠PQS= 3(x +5)

Step-by-step explanation:

∠PQR = 5x + 25

∠SQR+∠PQS= 5x+25

∠PQS = ∠PQR-∠SQR

∠PQS= (5x + 25 )-(2x + 10)

∠PQS = 5x+25 -2x-10

∠PQS= 3x +15

∠PQS= 3(x +5)

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3 years ago
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