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seraphim [82]
3 years ago
14

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience i

s 140. What is the theoretical probability of 4 students from your school being selected as contestants out of 8 possible contestant​ spots?
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

5.3%

Step-by-step explanation:

The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations

Let's start with the specific ones,

First the number of combinations of 4 of the 30 students getting a spot, i.e .:

A combinations are equal to:

nCx = n! / x! * (n-x)!

Replacing:

30C4 = 30! / (4! * 26!) = 27405

Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30

110C4 = 110! / (4! * 106!) = 5773185

Now the total combinations of possible 8 contestants from the audience

140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12

Finally, the probability is equal to:

P = (30C4 * 110C4) / 140C8

replacing:

P = 27405 * 5773185 / 2.98 * 10 ^ 12

P = 0.053

Therefore the probability is 5.3%

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Wittaler [7]

Answer:

The choice that best describes the given sentence above is, it is a complete and correct sentence. What makes this sentence complete is having both the subject and the verb in a simple form, and still expresses a complete thought. The verb and simple predicate "volunteered" is enough to describe the subject "Cassidy".

6 0
3 years ago
Find the distance between two points ( -1,1) and (2,-4)
sladkih [1.3K]

Answer:

The distance between two points ( -1,1) and (2,-4) is:

d=\sqrt{34}  or d = 5.8 units.

Step-by-step explanation:

Given the points

  • (-1, 1)
  • (2, -4)

Finding the distance between (-1, 1) and (2, -4) using the formula

d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

substitute (x₁, y₁) =  (-1, 1)   and  (x₂, y₂) = (2, -4)

   =\sqrt{\left(2-\left(-1\right)\right)^2+\left(-4-1\right)^2}

   =\sqrt{\left(2+1\right)^2+\left(-4-1\right)^2}

   =\sqrt{3^2+5^2}

   =\sqrt{9+25}

   =\sqrt{34}  units

or

d = 5.8 units

Therefore, the distance between two points ( -1,1) and (2,-4) is:

d=\sqrt{34}  or d = 5.8 units.

3 0
2 years ago
Simplify the expression <br> x^2+5x+4/x^2+3x-4*x^2-2x+1/x^2-1
AysviL [449]

Answer:

Simplifying

(2x2 + -3x + 1)(x + -2)

Reorder the terms:

(1 + -3x + 2x2)(x + -2)

Reorder the terms:

(1 + -3x + 2x2)(-2 + x)

Multiply (1 + -3x + 2x2) * (-2 + x)

(1(-2 + x) + -3x * (-2 + x) + 2x2 * (-2 + x))

((-2 * 1 + x * 1) + -3x * (-2 + x) + 2x2 * (-2 + x))

((-2 + 1x) + -3x * (-2 + x) + 2x2 * (-2 + x))

(-2 + 1x + (-2 * -3x + x * -3x) + 2x2 * (-2 + x))

(-2 + 1x + (6x + -3x2) + 2x2 * (-2 + x))

(-2 + 1x + 6x + -3x2 + (-2 * 2x2 + x * 2x2))

(-2 + 1x + 6x + -3x2 + (-4x2 + 2x3))

Combine like terms: 1x + 6x = 7x

(-2 + 7x + -3x2 + -4x2 + 2x3)

Combine like terms: -3x2 + -4x2 = -7x2

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Step-by-step explanation:

3 0
3 years ago
Choose all the expression with accurately written descriptions
Kruka [31]

Answer:

All except 4th and last.

Step-by-step explanation:

The one that says equation is definitely wrong because it doesn't have an equal sign anywhere (there is nothing to solve there).

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They should have said 5 times x^2 there which actually means 5x^2.

So I don't like the way some of these are written but the only two that are really wrong are the 4th one and the last one.

3 0
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statuscvo [17]

Answer:

8 unit ^2   or 8cm^2

Step-by-step explanation:

area 1

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area 2 we split the triangle into half

= 1/2 ( 2 x 2) = 2 unit ^2

we know the other half is also  2 unit ^2 but we add then subtract

1/2 (1 x 1) = 0.5^2

To get

4.5 + 2+ 2 - ( 0.5)  = 8 unit ^2

8 0
3 years ago
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