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SOVA2 [1]
2 years ago
8

What is the probability you roll doubles on two 6 sides dice please show work

Mathematics
1 answer:
Mars2501 [29]2 years ago
8 0

Answer:

1/6

Step-by-step explanation:

We can start by determining all the different combinations we can get.

We are using 6 sided dices, so we have a chance of getting 6 different numbers for each dice.

If we only have 1 dice, the our possible values would be:

1, 2, 3, 4, 5, 6

However, we have 2 dices. As such, our combinations have been multiplied, and now our possibilities are:

(1 , 1) , (1 , 2) , (1 , 3) , (1 , 4) , (1 , 5) , (1 , 6) , (2 , 1) , (2 , 2) , (2 , 3) , (2 , 4) , (2 , 5) , (2 ,6), and so on for 3, 4, 5, and 6

We can find the number of combinations by simply multiplying the amount of possible values for each dice.

Since both dices have 6 possible values, we multiply 6 by 6, and the amount of possible combinations is 36.

Now, let's determine the possibility for getting a double.

First, let's determine how many doubles we can get:

(1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) , (5 , 5) , (6 ,6)

There are 6 different combinations for rolling a double.

So, our probability of rolling a double on two 6 sided dices is 6 out of 36

We can simplify that to 1 out of 6.

So the probability of rolling a double on two 6 sided dices is 1/6

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The Ironman endurance race has a 2.4 miles swim. Javier can swim 0.5 miles in 20 minutes. If he can continue this pace, it will
Dafna1 [17]

Given :

The Ironman endurance race has a 2.4 miles swim.

Javier can swim 0.5 miles in 20 minutes.

To Find :

How much time in hours it takes to complete the race.

Solution :

Speed of Javier :

s=\dfrac{2.4}{\dfrac{20}{60}}\ mph\\\\s= 7.2\ mph

Let, time taken to cover 2.4 miles is t .

So,

t = \dfrac{2.4}{7.2}\ hours\\\\t = 0.33\ hours

Hence, this is the required solution.

7 0
3 years ago
Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0
3 years ago
Please help simplify this...
juin [17]
Answer is 36.
First use the negative exponent rule. When a number is put to the negative power it becomes a fraction
4/3^2

Now 3 to the second power is 9
4/1/9 (4 over 1/9)
Now multiply 4 x 9 (dividing by 1/9 is the same as multiplying by 9)

4 x 9= 36
5 0
3 years ago
Use the value of the first integral I to evaluate the two given integrals. I = integral^3_0 (x^3 - 4x)dx = 9/4 A. integral^3_0 (
Troyanec [42]

Answer:

A) -9/2

B) 9/4

C) -9/2, same as A)

Step-by-step explanation:

We are given that I=\int_0^3 x^3-4x dx=9/4. We use the properties of integrals to write the new integrals in terms of I.

A) \int_0^3 8x-2x^3 dx=\int_0^3 -2(x^3-4x) dx=-2\int_0^3 x^3-4x dx=-2I=-9/2. We have used that ∫cf dx=c∫f dx.

B) \int_3^0 4x - x^3 dx=-\int_0^3 (4x-x^3) dx=\int_0^3-(4x-x^3) dx=\int_0^3 x^3-4x dx=I=9/4. Here we used that reversing the limits of integration changes the sign of the integral.

C) It's the same integral in A)

4 0
3 years ago
What is the answer?!
Brut [27]
The answer is 445363.571429!
3 0
2 years ago
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