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baherus [9]
3 years ago
12

Consider rolling two fair dice one 3-sided the other 5-sided

Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

1\leq x\leq 3,\quad 1\leq y \leq 5

We have P(X=x)=\frac{1}{3} and P(Y=y)=\frac{1}{5}, because the dice are fair.

Now we use the assumption of independence to claim that

P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

  • 2 in a unique way (1+1)
  • 3 in two possible ways (1+2, 2+1)
  • 4 in three possible ways
  • 5 in three possible ways
  • 6 in three possible ways
  • 7 in two possible ways
  • 8 in a unique way

This implies that the probabilities of the outcomes of W=X+Y are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5

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You need to determine how much paper you need to cover the lateral side of the cylinder shown in the picture. For this, you have to calculate the surface area of the cylinder, which you can do using the following formula:

A=2\pi rh

Where

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π is the number pi, for the calculations we usually use up to the first two decimal values of this number, 3.14

r is the radius

h is the height of the cylinder

The given cylinder has a height of h=15m and a diameter of d=6m

To calculate the lateral area you need to use the radius. The diameter is twice the radius, so to determine the radius of the cylinder you have to divide the diameter by 2

\begin{gathered} r=\frac{d}{2} \\ r=\frac{6}{2} \\ r=3 \end{gathered}

Now you can calculate the lateral area as follows:

\begin{gathered} A=2\pi rh \\ A=2\cdot3.14\cdot3\cdot15 \\ A=282.6m^2 \end{gathered}

Charlie will need 282.6 m² to cover the lateral side of the cylinder.

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Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b,
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Answer:

-9

Step-by-step explanation:

What b represents here is the y intercept.

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3 years ago
Read 2 more answers
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