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4 years ago

X+y+z=5 -2x-3y+2z=8 3x-y-2z=3

Mathematics

1 answer:

Luba_88 [7]4 years ago

7 0

Answer:

x = 3, y = -2, and z = 4

Step-by-step explanation:

x + y + z = 5 -2x - 3y + 2z = 8

3x - y - 2z = 3 x + y + z = 5....multiply by 3

---------------------add ----------------------------

4x - z = 8 -2x - 3y + 2z = 8

3x + 3y + 3z = 15

--------------------------- add

x + 5z = 23

4x - z = 8

x + 5z = 23....multiply by -4

---------------------

4x - z = 8

-4x - 20z = - 92 (result of multiplying by -4)

------------------------add

-21z = - 84

z = -84/-21

z = 4 <=====

4x - z = 8 x + y + z = 5

4x - 4 = 8 3 + y + 4 = 5

4x = 8 + 4 y + 7 = 5

4x = 12 y = 5 - 7

x = 12/4 y = -2 <====

x = 3 <====

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Let represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of is as follows.

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a) $P(X=3) = 0.1$

b) $P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

c) $P(X=4) = 0.3$

d) $P(X=0) = 0.2$

e) $E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

f) $E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

Step-by-step explanation:

We have the following distribution

x 0 1 2 3 4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

$P(X=3) = 0.1$

Part b

We want this probability:

$P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

Part c

For this case we want this probability:

$P(X=4) = 0.3$

Part d

$P(X=0) = 0.2$

Part e

We can find the mean with this formula:

$E(X)= \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

Part f

We can find the second moment with this formula

$E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

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4 years ago