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rosijanka [135]

3 years ago

7

Kali has a 20 foot ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 5 feet away from t

he base of the tree. How high into the tree will the ladder reach? Round your answer to the nearest tenth of a foot.

1 answer:

Musya8 [376]3 years ago

3 0

A^2 + b^2 = c^2
5^2 + b^2 = 20^2
25 + b^2 = 400
b^2 = 375
b = 19.4 feet

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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

The complement of an angle is 25. What is the measure of an angle

Inessa [10]

The complement of an acute angle A in degrees is 90 - A. So if the complement is 25 degrees, the angle would be 90 - 25 = 65 degrees.

8 0

2 years ago

Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Dale drove h

Yuliya22 [10]

Use a system of equations:

For his trip on the way there:
D = 7*s

For his trip on the way home you have:
D = 5*(s+18)

use substitution to solve

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2 years ago

Sam's father bought a cat for $26,304. He expects to pay for it in 24 equal monthly payments. How much will Sam's father have to

podryga [215]

Price of the car= $26304
Monthly payments= 24
Just divide
26304/24 which equals $1096

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2 years ago

The number of seats in each row of an auditorium increases by 2 from one row to the next. if there are 48 seats in the first row

Sveta_85 [38]

Let's see if we can find a pattern:

Row number 1 has $48 = 48 + 2\cdot 0$ seats

Row number 2 has $50 = 48 + 2\cdot 1$ seats

Row number 3 has $52 = 48 + 2\cdot 2$ seats

Row number 4 has $54 = 48 + 2\cdot 3$ seats

Can you see the pattern? After $n$ rows, we have added $2(n-1)$ seats.

So, the 60th row will have

$48 + 2\cdot 59 = 48 + 118 = 166$

7 0

3 years ago