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serious [3.7K]
3 years ago
6

Damian filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every ho

ur driven, and after driving for 3 hours, there were 6 gallons of gas left in the tank. Write an equation for the function G(t),G(t), representing the number of gallons of gas remaining in Damian's gas tank after tt hours of driving.
Mathematics
1 answer:
vesna_86 [32]3 years ago
7 0

Answer:

G(t)=12-2t

Step-by-step explanation:

Okay, first we need to find out how many gallons he lost, so we multiply 2 by 3 and get 6 gallons used.

Next, now knowing 6 gallons are left and 6 have been used we now add to get 12 gallons originally.

Then, now that we have the rate of change and the starting number we put together the equation to the way that best suits the question

Last, to check our work plug six into t next to the two and solve to get six gallons used,

I hope this helps you

If i am right a thanks would be appreciated if i am wrong please leave a comment

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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.

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3 years ago
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