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Andreyy89
3 years ago
8

For a given event, what is the result of dividing the number of successful outcomes by the number of possible outcomes?

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
5 0
Dividing the number of successful outcomes by the number of possible outcomes is the definition of the probability of the given event.

P(E)=n(E)/n(S)

example. let the Experiment be throwing a dice. The sample space, all the possible outcomes, is the set S={1, 2, 3, 4, 5, 6 }  and n(S)=6

Let the even E be: getting an even number. The successful outcomes set is  E {2, 4, 6 } and n(E)=3

So probability of getting an even number is P(E)=n(E)/n(S)=3/6=0.5


Answer: Probability of the given Event
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Find a fraction equivalent to 5/7 whose squared terms add up to 1184.
bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y  } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}

                                                              \large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \  \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28  } \end{gathered}$}

                                                                  \large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20  } \end{gathered}$}

The fraction that satisfies the request is \bf{\dfrac{20}{28}} , since in \bf{\dfrac{-20}{-28}} the negative signs are canceled and the first fraction is obtained.

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2 years ago
Evaluate each expression express the result in scientific notation PLSSS I NEED THIS QUICK AND INCLUDE THE EXPLANATION
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Answer:

3.1 × 10^5

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6 0
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3 years ago
What is the total surface area of the solid?
mash [69]

Answer:

Step-by-step explanation:

The formula for determining the total surface area of a rectangular prism is expressed as

Total surface area = 2lw + 2wh + 2lh

Where

l represents the length = 16

w represents the width = 11

h represents the height = 10

Total surface area = (2 × 16 × 11) + (2 × 11 × 10) + (2 × 16 × 10) = 352 + 220 + 320 = 892 mm²

The formula for determining the total surface area of a triangular prism is expressed as

Total surface area = ph + 2b

p represents perimeter of base

h represents height of prism

b represents base area

From the information given,

h = 16

b = 1/2base × height = 1/2 × 11 × 8 = 44 mm²

to determine the perimeter of the base, we would determine the slant height, l by applying Pythagoras theorem.

Hypotenuse² = opposite side² + adjacent side²

l² = 11² + 8² = 185

l = √185 = 13.6

p = 13.6 + 11 + 8 = 32.6 mm

Total surface area = (32.6 × 16) + (2 × 44) = 521.6 + 88 = 609.6 mm²

6 0
3 years ago
Read 2 more answers
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