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Law Incorporation [45]

3 years ago

5

A taxicab starts at (1, -2) on the grid. It goes 3 blocks east and 1 block south to pick up a passenger. Then it goes 6 blocks w

est and 5 blocks north and drops off the passenger. What are the coordinates of the point where the passenger was dropped off?

1 answer:

elena-14-01-66 [18.8K]3 years ago

8 0

(x,y)
east is an increase in x
west is a decrease in x
north is an increase in y
south is a decrease in y

so
3 east (x+3)
1 block south (y-1)
6 blocks west (x-6)
5 blocks north (y+5)

so in total, x+3-6 and y-1+5
basically x-3 and y+4
minus 3 from and add 4 to y
(1,-2)
(1-3,-2+4)
(-2,2) is the dropoff point

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The number of people arriving for treatment at an emergency room can be modeled by a Poisson Distribution with a rate parameter

AlekseyPX

Answer:

a) 0.052 = 5.2% probability that exactly three arrivals occur during a particular hour

b) 0.971 = 97.1% probability that at least three people arrive during a particular hour

c) 5.25 people are expected to arrive during a 45-min period

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Poisson Distribution with a rate parameter of seven per hour.

This means that $\mu = 7$

(a) What is the probability that exactly three arrivals occur during a particular hour?

This is P(X = 3).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 3) = \frac{e^{-7}*7^{3}}{(3)!} = 0.052$

0.052 = 5.2% probability that exactly three arrivals occur during a particular hour.

(b) What is the probability that at least three people arrive during a particular hour? (Round your answer to three decimal places.)

Either less than three people arrive, or at least three does. The sum of the probabilities of these events is 1. So

$P(X < 3) + P(X \geq 3) = 1$

We want $P(X \geq 3)$ , which is

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-7}*7^{0}}{(0)!} = 0.001$

$P(X = 1) = \frac{e^{-7}*7^{1}}{(1)!} = 0.006$

$P(X = 2) = \frac{e^{-7}*7^{2}}{(2)!} = 0.022$

So

$P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.001 + 0.006 + 0.022 + 0.029$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.029 = 0.971$

0.971 = 97.1% probability that at least three people arrive during a particular hour

(c) How many people do you expect to arrive during a 45-min period?

During an hour(60 minutes), 7 people are expected to arrive. So, using proportions:

$\frac{45*7}{60} = \frac{3*7}{4} = \frac{21}{4} = 5.25$

5.25 people are expected to arrive during a 45-min period

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3 years ago

Naoya read a book cover to cover in a single session, at a rate of 555555 pages per hour. After 444 hours, he had 350350350 page

natali 33 [55]

Answer:

$y=-55x+570$

Step-by-step explanation:

The correct question is

Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read.

Let y represent the number of pages left to read after x hours.

Complete the equation for the relationship between the number of pages left and number of hours.

Let

x -----> the time in hours

y ----> the number of pages left to read

we know that

The linear equation in point-slope form is equal to

$y-y1=m(x-x1)$

In this problem we have

$m=-55\frac{pages}{hour}$ ----> is negative because the linear function is decreasing

$point\ (4,350)$

substitute

$y-350=-55(x-4)$

$y-350=-55x+220$

$y=-55x+220+350$

$y=-55x+570$

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4 years ago

A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall

timurjin [86]

Think of it like a triangle.

The flagpole is vertical and is at 90° to the ground. This makes a right-angle to the ground, which is flat.

Since we have two sides of the triangle already, and they are in a ratio of ?? : 16 : 20 = ?? : 4 : 5, that means that because the triangle is a right-angled triangle, the third and last side must be 3 to complete the ratio! (This is called 'Pythagoras')

Since the other sides were divided by 4 to get the simple ratio, we must multiply 3 to get the actual ratio! 3 × 4 = 12 ft tall flagpole.

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4 years ago

find two consecutive integers such that ten more than twice the smaller is seven less than three times the larger

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This is how I would work it out:

1st no. = x+1 2x+10=3(x+1)-7
2nd no. = x 2x+10=3x-4
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1st no. is 15; 2nd no. is 14

To check: 28+10=38; three times the larger is 45; and 38 is 7 less than 45.

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3 years ago

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Salsk061 [2.6K]

Answer:

$\Large \boxed{\sf 136 \ m^2}$

Step-by-step explanation:

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$(6 \times 4 \times 0.5 \times 2 )+(7 \times 5 \times 2+7 \times 6)=136$

7 0

3 years ago