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Travka [436]
3 years ago
9

Yulet rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 7.

Mathematics
1 answer:
Pie3 years ago
6 0

Answer:

the answer is 1/6

Step-by-step explanation:

Let (a,b) denote a possible outcome of rolling the two die, with a the number on the top of the first die and b the number on the top of the second die. Note that each of a and b can be any of the integers from 1 through 6. Here is a listing of all the joint possibilities for (a,b):  

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

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

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

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

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

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

With the above declaration, the outcomes where the sum of the two dice is equal to 7 form an event. If we call this event E, we have

E={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}.

so Possibilities(P) of having Event (E)

P(E)=6/36

= 1/6

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1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n
Andrew [12]
Part 1
We are given x^2-21x=-4x. This can be rewritten as x^2-18x=0.
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
     x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}
     x=\frac{18\pm 18}{2}

The values of x are
     x_1=\frac{18-18}{2}=0
     x_2=\frac{18+18}{2}=18

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function. 

Part 3.
The first equation is y=x^2+2.
The second equation is y=3x+20.

We have 
     x^2+2=3x+20
     x^2-3x-18=0
Factoring, we have 
     \left(x-6\right)\left(x+3\right)=0
Equating both factors to zero.
     x_1-6=0\rightarrow x_1=6
     x_2+3=0\rightarrow x_2=-3

When the value of x is 6, the value of y is 
     y=3\left(6\right)+20=38

When the value of x is -3, the value of y is 
     y=3\left(-3\right)+20=11

Therefore, the solutions are (6,38) or (-3,11)
7 0
2 years ago
Name the lengths of the side of three rectangles that have perimeters of 14 units
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5,5.2,2
6,6,1,1
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2,2,55
8 0
3 years ago
A family needs to cross a river in a small raft.
serg [7]

Answer:

so basically you can take more than one trip you can take the mother and the bag at the same time

Step-by-step explanation:

and then you can get the daughter in the son at the same time and then for the final trip you take the father by himself

8 0
2 years ago
PLEASE PEOPLE, HELP ME!! Geometry
Oksanka [162]
I use the sin rule to find the area

A=(1/2)a*b*sin(∡ab)

1) A=(1/2)*(AB)*(BC)*sin(∡B)
sin(∡B)=[2*A]/[(AB)*(BC)]

we know that
A=5√3
BC=4
AB=5
then

sin(∡B)=[2*5√3]/[(5)*(4)]=10√3/20=√3/2
(∡B)=arc sin (√3/2)= 60°

 now i use the the Law of Cosines 

c2 = a2 + b2 − 2ab cos(C)

AC²=AB²+BC²-2AB*BC*cos (∡B)

AC²=5²+4²-2*(5)*(4)*cos (60)----------- > 25+16-40*(1/2)=21

AC=√21= 4.58 cms

the answer part 1) is 4.58 cms

2) we know that

a/sinA=b/sin B=c/sinC

and

∡K=α

∡M=β

ME=b

then

b/sin(α)=KE/sin(β)=KM/sin(180-(α+β))

KE=b*sin(β)/sin(α)

A=(1/2)*(ME)*(KE)*sin(180-(α+β))

sin(180-(α+β))=sin(α+β)

A=(1/2)*(b)*(b*sin(β)/sin(α))*sin(α+β)=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

KE/sin(β)=KM/sin(180-(α+β))

KM=(KE/sin(β))*sin(180-(α+β))--------- > KM=(KE/sin(β))*sin(α+β)

the answers part 2) are

side KE=b*sin(β)/sin(α)
side KM=(KE/sin(β))*sin(α+β)
Area A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

5 0
3 years ago
Fill in the blanks in questions 8 through 10.
SVEN [57.7K]

Answer:

45

Step-by-step explanation:

1 minute = 8 revolutions

x minutes= 360 revolutions

Divide 360 by 8

45

The wheel will make 360 revolutions in 45 minutes

Check your work:

If 45 minutes = 360 revolutions, and the wheel revolves 8 times per 1 minute, 8 revolutions x 45 minutes should equal 360 revolutions.

(it does)

6 0
2 years ago
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