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Bad White [126]
3 years ago
6

NIne times ten to the negative power of three

Mathematics
1 answer:
Ivanshal [37]3 years ago
3 0

   9 x 10⁻³  is the same amount as  0.009
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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
What is the value of x?<br> A.3<br> B.4<br> C.5<br> D.4.5
Phantasy [73]

Happy Valentines Day!

Answer:

C. 5

Step-by-step explanation:

32 / 4 = 8

40 / 8 = 5

Both triangles represent a translation where the triangle on the left is bigger than the one on the left which means the one on the left has to have something similar which in this case there is a side on both triangles that have a measurement which lets us start on solving the question.

Hope This Helps :)

8 0
3 years ago
Solve 2^10 + 2^10 = 2^n.
Lina20 [59]

Answer: n = 11

Step-by-step explanation:

2^10 = 1,024

1,025 + 1,025 = 2,048

2^11 = 2,048

8 0
3 years ago
Read 2 more answers
Find the circumference
My name is Ann [436]

Answer:

circumference:

2 × 3.14 × 5.8m = the circumference ** (use your calculator here, ill die if I in do this)

3 0
3 years ago
Line segment XY has endpoints X(5,7) and Y(-3,3)
dem82 [27]

y=-2x+7

Step-by-step explanation:

line segment xy has endpoints x(5 7) and y(-3 3)

for the equation of the perpendicular bisector of line segment xy

slope of line segment xy = 7-3 / 5+3

= 4/8

=1/2

so slope of perpendicular bisector is -2

as m1m2= -1 or m1= -1/m2

As perpendicular bisector goes through midpoint of xy , let's find midpoint of xy

midpoint(x,y) = (5-3 / 2 , 7+3 / 2)

=(2/2, 10/2)

=(1,5)

find the equation of line(perpendicular bisector) passing through (1,5) and the slope -2

y-5 = -2(x-1)

y-5 =-2x+2

y=-2x+7

6 0
2 years ago
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