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tatuchka [14]
3 years ago
11

Two points on a line are (-10, 1) and (5,-5). If

Mathematics
1 answer:
NeX [460]3 years ago
8 0

Answer:

The x-coordinate is 0

Step-by-step explanation:

step 1

Find the slope  m of the line

we have the points

(-10, 1) and (5,-5)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{-5-1}{5+10}

m=\frac{-6}{15}

Simplify

m=-\frac{2}{5}

step 2

Find the equation of the line in slope intercept form

y=mx+b

where

m is the slope

b is the y-intercept

we have

m=-\frac{2}{5}

point\ (-10,1)

substitute in the equation and solve for b

1=-\frac{2}{5}(-10)+b

1=4+b

b=1-4=-3

The equation of the line is

y=-\frac{2}{5}x-3

step 3

Find the x-coordinate of another point in the line if the y-coordinate is -3

For y=-3

substitute in the equation and solve for x

-3=-\frac{2}{5}x-3

-3+3=-\frac{2}{5}x

0=-\frac{2}{5}x

x=0

The point is (0,-3) -----> the y-intercept

therefore

The x-coordinate is 0

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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
4 years ago
A hat salesman earns a commission of 30% of all hat sales made. Yesterday he sold 3 hats for $90 each and 4 hats for $50 each. H
zalisa [80]
(30/100)(90*3+50*4)

(30/100)(270+200)

(30/100)(470)

$141.00


6 0
3 years ago
Read 2 more answers
Mr. warren has a bag of nails assorted lengths. he asks his sons paul and tim to sort them by length. paul pours 3/4 of the bag
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Answer:

Step-by-step explanation:

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2 years ago
The sum of two consecutive integers is 131. What are the integers?
Dahasolnce [82]
X, x+1
x+x+1=131
2x+1=131
2x=131-1=130
x=130÷2 = 65
the integers are 65 and 66
3 0
3 years ago
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natali 33 [55]
If M <span>is the midpoint of AB then AB = 2AM

8x - 6 = 2(3x + 3)
8x - 6 = 6x + 6
8x - 6x = 6 + 6
2x = 12
x = 12/2
x = 6

AM = 3x + 3 = 3*6 + 3 = 18 + 3 = 21 units
</span>
6 0
3 years ago
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