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zysi [14]
3 years ago
9

Which algebraic property does this statement show?

Mathematics
2 answers:
Rudik [331]3 years ago
7 0
D commutative property

Hope it helps
Umnica [9.8K]3 years ago
4 0
C) associative property

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Memory module consists of 9 chips. The device is designed with redundancy so that it works even if one of its chips is defective
soldier1979 [14.2K]

Answer:

a) P[C]=p^n

b) P[M]=p^{8n}(9-8p^n)

c) n=62

d) n=138

Step-by-step explanation:

Note: "Each chip contains n transistors"

a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:

P[C]=p^n

b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.

We can calculate this as a binomial distribution problem, with n=9 and k≥8:

P[M]=P[C_9]+P[C_8]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)\\\\P[M]=p^{8n}(p^{n}+9(1-p^n))\\\\P[M]=p^{8n}(9-8p^n)

c)

P[M]=(0.999)^{8n}(9-8(0.999)^n)=0.9

This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.

d) If the memoty module tolerates 2 defective chips:

P[M]=P[C_9]+P[C_8]+P[C_7]\\\\P[M]=\binom{9}{9}P[C]^9(1-P[C])^0+\binom{9}{8}P[C]^8(1-P[C])^1+\binom{9}{7}P[C]^7(1-P[C])^2\\\\P[M]=P[C]^9+9P[C]^8(1-P[C])+36P[C]^7(1-P[C])^2\\\\P[M]=p^{9n}+9p^{8n}(1-p^n)+36p^{7n}(1-p^n)^2

We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.

6 0
3 years ago
Provided<br> What is the value of 2 in the equation 60x = 360x
WARRIOR [948]
It would be 6 I hope I helped
6 0
3 years ago
A pool company is trying out several new drains. Drai n A empties a pool at a rate of 2 gal/min. Drain B empties a pool at a rat
shtirl [24]
108 ÷ 2 = 54 minutes
108 ÷ 5 = 21.6 minutes
8 0
3 years ago
Which graph represents the solution to this inequality? 16x - 80x &lt; 37 + 27
AlladinOne [14]

Answer: ​107

Step-by-step explanation:

1 Remove parentheses.

16x-80<2716x−80<27

2 Add 8080 to both sides.

16x<27+8016x<27+80

3 Simplify  27+8027+80  to  107107.

16x<10716x<107

4 Divide both sides by 1616.

x<\frac{107}{16}x<

​16

​

​107

​​  

Done

3 0
3 years ago
Use inverse operation to solve the question <br><br> 2/3z = -4<br><br><br> Z= ?
sweet [91]

Answer:

z=(-6)

Step-by-step explanation:

(2/3)*z=(-4)

2*z=3*(-4) --> We move the 3 from the left to the right part of the equation. It was dividing, so we move it multiplying.

2*z=(-12)

z=(-12)/2 --> It's the inverse case of before. 2 was multiplying, so we move it to the right by dividing it.

z=(-6)

7 0
3 years ago
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