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3 years ago

Find an equation of the line that goes through the points (10,34) and (-1,10)

Mathematics

1 answer:

kotykmax [81]3 years ago

3 0

Answer:

Given points are ( 10 ,34 ) and ( -1 , 10)

Step-by-step explanation:

The equation of line is given by 

first we can find slope (m) 

= (y2 - y1) / ( x2 - x1)

= 34-10/10+1

 =24/11

Now the equation is

y - y1 = m ( x - x1) 

y - 10 = 24/11 ( x +11)

11 ( y - 10 ) = 24 (x + 11)

11y - 110 = 24x + 264

24x + 264 +110-11y =0

24x - 11y + 374 = 0

which is the required equation 

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The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago

A square classroom has sides that are 21 feet long. what is the room's perimeter

lutik1710 [3]

The answer is 84 because 21 times 4 equals 84

4 0

3 years ago

Read 2 more answers

Maria has 14 pencils, Ted has 9 pencils, Tom has 12, pencils, Lucinda has 13 pencils, so that they all have the same amount? How

Nina [5.8K]

Answer:

I say 12, but i can be wrong.

Step-by-step explanation:

6 0

3 years ago

Find the interest earned.

SCORPION-xisa [38]

June is 30 days
30-12=18 days
July is 31 days
August is 30 days
Time=18+31+30=79 days
A=2,750×(1+0.035÷365)^(79)
A=2,770.91
Interest earned
I=A-p
I=2770.91-2750
I==20.91

4 0

3 years ago

Write the verbal phrase as a algebraic expression three times the sum of a number and 1

sammy [17]

3 (n + 1) (expression)

3n + 3 (expression simplified)

8 0

3 years ago