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2 years ago

When rolling two fair, standard dice, what is the probability that the sum of the numbers rolled is a multiple of 3 or 4?

Mathematics

1 answer:

Dominik [7]2 years ago

8 0

Answer:

The probability that sum of numbers rolled is a multiple of 3 or 4 is: $\frac{7}{12}$ .

Step-by-step explanation:

The sample space for two fair die (dice) is given below:

$\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right]$

From the above table:

Number of occurrence where sum is multiple of 3 = 12

Number of occurrence where sum is multiple of 4 = 9

Total number in the sample space = 36

probability(sum is 3) = 12/36

probability(sum is 4) = 9/36

probability(sum is 3 or 4) $=\frac{12}{36} +\frac{9}{36} \\=\frac{12 + 9}{36} \\=\frac{21}{36}\\=\frac{7}{12}$

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Number 26.

Natasha_Volkova [10]

B.

This is because when you substitute y-2 in for x, you get y=(y-2)+2.
Then the twos would cancel out, leaving you with y=y which would make an infinite number of solutions for y.

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2 years ago

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k0ka [10]

Y = x+5

To find the various values of y, given the respective values of x, you just replace x by its value in the equation y = x +5:
y = x + 5;
for x = -4 → y = (-4) + 5 ; y = 1
for x = -2 → y = (-2) + 5 ; y = 3
for x = 0 → y = (0) + 5 ; y = 5
for x = 2 → y = (2) + 5 ; y = 7

Follow the same logic for te remaining values of x

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3 years ago

How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?

Arturiano [62]

Answer:

$y = \frac{2}{3} x + 2$

Step-by-step explanation:

Start by finding the slope of the given line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of given line

$= \frac{5 - ( - 1)}{ - 2 - 2}$

$= \frac{5 + 1}{ - 4}$

$= \frac{6}{ - 4}$

$= - \frac{3}{2}$

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

$- \frac{3}{2} m = - 1$

$m = - 1 \div ( - \frac{3}{2} )$

$m = - 1 \times ( - \frac{2}{3} )$

$m = \frac{2}{3}$

$y = \frac{2}{3}x + c$ , where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$