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d1i1m1o1n [39]
3 years ago
10

What is the equation, in point slope form, of the line

Mathematics
1 answer:
melamori03 [73]3 years ago
5 0

Answer:

y=3/2x+11/2

Step-by-step explanation:

Hello! Sorry  I just saw this

Anyways, let's continue

first, we need to find the equation of the line with the one that is (-2,-4) and (2,2)

first, we need to find the slope

the equation for slope is y2-y1/x2-x1

so let's label the points

x1=-2

y1=-4

x2=2

y2=2

now plug it in

2-(-4)/2-(-2)=6/4=3/2

now, let's turn it into a line

the point-slope form is y-y1=m(x-x1) (m=slope)

now, plug it in

y-(-4)=3/2(x-(-2))

simplify to

y+4=3/2(x+2)

turn into y=mx+b format

y+4=3/2x+3

subtract 4 on both sides

y=3/2x-1

Now for the line that is parallel.

Parallel lines have the same slopes, so you automatically know that the new line will be y=3/2x+b

To make sure (-3,1) is a solution to the point, put 1 as y and -3 as x

1=3/2(-3)+b

1=-9/2+b

add 9/2 on both sides

b=11/2 or 5.5

now, put it into the equation

y=3/2x+11/2

Hope this helps!

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An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservation
miss Akunina [59]

Answer:

a) 0.109375 = 0.109 to 3 d.p

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Step-by-step explanation:

Probability of someone that made a reservation not showing up = 50% = 0.5

Probability of someone that made a reservation showing up = 1 - 0.5 = 0.5

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

For this to happen, 5 or 6 people have to show up since the limousine can accommodate a maximum of 4 people

Let P(X=x) represent x people showing up

probability that at least one individual with a reservation cannot be accommodated on the trip = P(X = 5) + P(X = 6)

P(X = x) can be evaluated using binomial distribution formula

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6

x = Number of successes required = 5 or 6

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 5) = ⁶C₅ (0.5)⁵ (0.5)⁶⁻⁵ = 6(0.5)⁶ = 0.09375

P(X = 6) = ⁶C₆ (0.5)⁶ (0.5)⁶⁻⁶ = 1(0.5)⁶ = 0.015625

P(X=5) + P(X=6) = 0.09375 + 0.015625 = 0.109375

b) If six reservations are made, what is the expected number of available places when the limousine departs?

Probability of one person not showing up after reservation of a seat = 0.5

Expected number of people that do not show up = E(X) = Σ xᵢpᵢ

where xᵢ = each independent person,

pᵢ = probability of each independent person not showing up.

E(X) = 6(1×0.5) = 3

If 3 people do not show up, it means 3 people show up and the number of unoccupied seats in a 4-seater limousine = 4 - 3 = 1

So, expected number of unoccupied seats = 1

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Evgesh-ka [11]

Answer:

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Step-by-step explanation:

Hope this helps

7 0
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