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3 years ago

You roll a 6 sided die 2 times what is the probability of rolling a 6 and then rolling a number greater than 2

Mathematics

1 answer:

jek_recluse [69]3 years ago

7 0

Answer:

1/9 probability of rolling a 6 and then a number greater than 2

Step-by-step explanation:

1. Rolling a six on the first go is 1/6 chance

2. Rolling a number greater than 2, for example 4, is also 1/6 chance

3. So we know that at first, there is a 1/6 chance of rolling a 6, now when the die is rolled again, there needs to be a 3, 4, 5 or 6, each of these has a 1/6 chance again

4. So the chance of rolling a 6 and then a 3 is solved by finding the chance of rolling 6, then multiplying that by the chance of rolling a 3 afterwards

5. We get an equation of 1/6 x 1/6 which = 1/36

6. We apply this to the rest of the possible combinations, 6 and then 4 which is 1/36, 6 and then 5 etc.

7. Once we find all possible combinations, we add them up, this means that 6 then 3 = 1/36, 6 then 4 = 1/36, 6 then 5 = 1/36 and 6 then 6 = 1/36 is added so we get 1/36 + 1/36 + 1/36 + 1/36 = 4/36

8. We simplify this to get 1/9

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The measure is 30° degrees

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3 years ago

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find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

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2 years ago

If you flipped the graph of y=x^2+4x-4 vertically, you would get the graph of y=-x^2+4x-4

bazaltina [42]

True...............................................................

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3 years ago

If US=52, ST=30, UT=40, VW=27, and XW=36, find the perimeter of ΔVWX. Round your answer to the nearest tenth if necessary. Figur

Ierofanga [76]

Answer:

The perimeter is 109.8

Step-by-step explanation:

As we can see here, the angles of the triangles are congruent so we can say that both triangles are congruent

When two triangles are congruent, the ratio of their corresponding sides are equal

So we can get the scale factor here by looking at the sides facing each specific angle in both triangles

In the bigger triangle,

The side facing 34 degrees has a length of 30

In the smaller triangle,

The side facing 34 degree has a length of 27

So the scale factor to get the smaller from the bigger is 27/30 = 9/10 or 0.9

Likewise the side facing 51 degrees in the bigger is 40 while for the smaller, it is 36

So the ratio still stands at 36/40 = 9/10 or 0.9

In essence, the smaller triangle will have a perimeter that is 0.9 times that of the bigger

The perimeter of the bigger is simply the sum of the side lengths

We have this as;

(52 + 30 + 40) = 122

so that of the smaller would be;

122 * 0.9 = 109.8

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2 years ago

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?

DiKsa [7]

Answer:

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2 years ago