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almond37 [142]
3 years ago
5

Solve the system of linear equations x + y = 4 and 2x + 3y = 0

Mathematics
1 answer:
forsale [732]3 years ago
8 0

solve this answer by using substitution. set the first equation to x=-y+4 then substitute -y+4 for x in the second equation.

2(-y+4) + 3y=0

-2y+8 + 3y=0

y+8=0

y=-8

now use -8 and solve for x

x+(-8)=4

x=12

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What is 4:6 as a percentage ​
MaRussiya [10]
66.6667%

Now we can see that our fraction is 66.666666666667/100, which means that 4:6 as a percentage is 66.6667%.
5 0
3 years ago
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Consider an experiment where two 6-sided dice are rolled. We can describe the ordered sample space as below where the first coor
agasfer [191]

Answer:

  • E = { (4,1) , (3,2) , (2,3) , (1,4) }
  • P(E)=\frac{1}{9}
  • P(F|E)=\frac{1}{4}

Step-by-step explanation:

Let's start writing the sample space for this experiment :

S= { (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) }

Let's also define the event E ⇒

E : '' The sum of the two dice is 5 ''

We can describe the event by listing all the favorables cases from S ⇒

E = { (4,1) , (3,2) , (2,3) , (1,4) }

In order to calculate P(E) we are going to divide all the cases favorables to E over the total cases from S. We can do this because all 36 of these possible outcomes from S are equally likely. ⇒

P(E)=\frac{4}{36}=\frac{1}{9} ⇒

P(E)=\frac{1}{9}

Finally we are going to define the event F ⇒

F : '' The number of the first die is exactly 1 more than the number on the second die ''

⇒

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

Now given two events A and B ⇒

P ( A ∩ B ) = P(A,B)

We define the conditional probability as

P(A|B)=\frac{P(A,B)}{P(B)} with P(B)>0

We need to find P(F|E) therefore we can apply the conditional probability equation :

P(F|E)=\frac{P(F,E)}{P(E)}   (I)

We calculate P(E)=\frac{1}{9} at the beginning of the question. We only need P(F,E).

Looking at the sets E and F we find that (3,2) is the unique result which is in both sets. Therefore is 1 result over the 36 possible results. ⇒

P(F,E)=\frac{1}{36}

Replacing both probabilities calculated in (I) :

P(F|E)=\frac{P(F,E)}{P(E)}=\frac{\frac{1}{36}}{\frac{1}{9}}=\frac{1}{4}=0.25

We find out that P(F|E)=\frac{1}{4}=0.25

6 0
3 years ago
If you roll a six-sided die, what is P (not a 5)?​
Setler79 [48]

Answer:

5/6

Explanation:

5 of the sides of the die are not the number 5,

<em>Hence, </em><em>the answer is...</em>

<em>5/6</em>

7 0
3 years ago
please help i will mark brainliest, no spam answers i will report.
vovikov84 [41]

9514 1404 393

Answer:

  (c)  (3, 3)

Step-by-step explanation:

Point E partitions both the x-distance and the y-distance in the ratio 2 : 1. That is, for either the x-coordinates or the y-coordinates, ...

  CE : ED = 2 : 1

Try the answers with the x-coordinates.

  CE : ED = (1 -(-1)) : (5 - 1) = 2 : 4 . . . . incorrect

  CE : ED = (-3 -(-1)) : (5 -(-3)) = -2 : 8 . . . . incorrect

  CE : ED = (3 -(-1)) : (5 -3) = 4 : 2 = 2 : 1 . . . . correct

  CE : ED = (-1 -(-1)) : (5 -(-1)) = 0 : 6 . . . . incorrect

The only viable choice is (3, 3).

_____

<em>Alternate solution</em>

For a partitioning of m : n, the desired point is ...

  E = (n×C +m×D)/(m+n)

For partitioning of 2 : 1, the desired point is ...

  E = (1×(-1, -3) + 2×(5, 6))/(2+1) = (-1+10, -3 +12)/3

  E = (3, 3)

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2 years ago
Three eights of Mrs Stevens ride the bus. If there are 24 students in the class how manh students ride the bus?
tia_tia [17]
There would be 9 students riding the bus.
5 0
3 years ago
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