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3 years ago

Which function has an average rate of change of -4 over the interval (-2, 2];

Mathematics

2 answers:

arlik [135]3 years ago

6 0

Answer:

x -2 -1 0 1 2

p(x) 12 5 0 -3 -4

Step-by-step explanation:

Roman55 [17]3 years ago

3 0

Answer: its A for u

Step-by-step explanation: i did the test trust

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The average number of annual trips per family to amusement parks in the UnitedStates is Poisson distributed, with a mean of 0.6

IrinaK [193]

Answer:

a) 0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b) 0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c) 0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d) 0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e) 0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year 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 distributed, with a mean of 0.6 trips per year

This means that $\mu = 0.6n$ , in which n is the number of years.

a.The family did not make a trip to an amusement park last year.

This is P(X = 0) when n = 1, so $\mu = 0.6$ .

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

$P(X = 0) = \frac{e^{-0.6}*(0.6)^{0}}{(0)!} = 0.5488$

0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b.The family took exactly one trip to an amusement park last year.

This is P(X = 1) when n = 1, so $\mu = 0.6$ .

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

$P(X = 1) = \frac{e^{-0.6}*(0.6)^{1}}{(1)!} = 0.3293$

0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c.The family took two or more trips to amusement parks last year.

Either the family took less than two trips, or it took two or more trips. So

$P(X < 2) + P(X \geq 2) = 1$

We want

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1) = 0.5488 + 0.3293 = 0.8781$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.8781 = 0.1219$

0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d.The family took three or fewer trips to amusement parks over a three-year period.

Three years, so $\mu = 0.6(3) = 1.8$ .

This is

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

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

$P(X = 0) = \frac{e^{-1.8}*(1.8)^{0}}{(0)!} = 0.1653$

$P(X = 1) = \frac{e^{-1.8}*(1.8)^{1}}{(1)!} = 0.2975$

$P(X = 2) = \frac{e^{-1.8}*(1.8)^{2}}{(2)!} = 0.2678$

$P(X = 3) = \frac{e^{-1.8}*(1.8)^{3}}{(3)!} = 0.1607$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1653 + 0.2975 + 0.2678 + 0.1607 = 0.8913$

0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e.The family took exactly four trips to amusement parks during a six-year period.

Six years, so $\mu = 0.6(6) = 3.6$ .

This is P(X = 4). So

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

$P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.1912$

0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year period.

4 0

3 years ago

How many acute, obtuse, and right angles are in this figure?

Tanya [424]

Hey!

I hope you don't mind, but before I answer this question I'd like to do a quick review of some general angles and how to tell which is which.

QUICK REVIEW

So, let's first review what an acute angle is. An acute angle is an angle that is smaller than 90°. The word acute basically means having a sharp or pointy end. So this is a helpful way to remember what an acute angle is.

Now, let's review what an obtuse angle is. An obtuse angle is an angle that is more than 90°. If an angle measures over 90° that it is more than likely that it is an obtuse angle.

Last but not least a right angle. A right angle is an angle that has to be exactly 90°. If an angle is 90° than it is most definitely a right

END QUICK REVIEW

Let's start by finding out the angle in the top left hand corner. The angle is clearly no more that 90° and is not 90° exactly. This angle must be an acute angle. We can also tell that it is an acute angle because the angle is sharp.

Now let's look at the angle on the bottom left hand corner. The angle is clearly no less than 90° and more than 90° exactly. This angle must be an obtuse angle.

Since the angles are basically the same on the other side, we won't be reviewing those. Now we'll count all the angles we have.

Acute Angles - 2

Obtuse Angles - 2

Right Angles - 0

So, this means that in the figure shown above, there are 2 acute angles, 2 obtuse angles, and no right angles.

Hope this helps!

- Lindsey Frazier ♥

4 0

3 years ago

Solve the equation below for x. −12(3x−4)=11 A. −1323 B. −813 C. −6 D. 6

geniusboy [140]

-1/2( 3x -4) = 11

Use distributive properties:

-3/2 + 2,= 11

Subtract 2 from both sides:

-3/2x = 9

Divide both sides by -3/2

X = 9/ -3/2

X = -6

The answer is c. -6

3 0

3 years ago

Please please help please!!

netineya [11]

Answer:

The vertex is at (-2,-8)

Step-by-step explanation:

You go left 2, and down 8, and then it's a scale of 1

4 0

3 years ago

Yo whats i lowkey cant think rn 3/4 times 2 ??

Lady_Fox [76]

6/4 or 1 and 2/4 thats a pretty easy question

6 0

3 years ago

Read 2 more answers