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2 years ago

Help with translations!

Mathematics

1 answer:

Vadim26 [7]2 years ago

3 0

Given:

The figure of a trapezoid.

The figure is translated down 5 units and then rotated 180 degrees clockwise.

To find:

The coordinates of the image of point W after these transformation.

Solution:

From the given figure it is clear that the coordinates of point W are (-6,3).

The figure is translated down 5 units. So,

$(x,y)\to (x,y-5)$

$W(-6,3)\to W'(-6,3-5)$

$W(-6,3)\to W'(-6,-2)$

After that the figure is rotated 180 degrees clockwise.

$(x,y)\to (-x,-y)$

$W'(-6,-2)\to W''(6,2)$

Therefore, the coordinates of point W after the given transformations are (6,2).

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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following p

drek231 [11]

Answer:

$P(X=14)=(18C14)(0.8)^{14} (1-0.8)^{18-14}=0.2153$

$P(X=15)=(18C15)(0.8)^{15} (1-0.8)^{18-15}=0.2297$

$P(X=16)=(18C16)(0.8)^{16} (1-0.8)^{18-16}=0.1722$

$P(X=17)=(18C17)(0.8)^{17} (1-0.8)^{18-17}=0.0811$

$P(X=18)=(18C18)(0.8)^{18} (1-0.8)^{18-18}=0.0180$

And adding the values we got:

$P(X \geq 14)= 0.2153 +0.2297+0.1722+0.0811+0.0180=0.7164$

Step-by-step explanation:

Assuming this question: P(X≥14), n=18, p=0.8

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=18, p=0.8)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X \geq 14) = P(X=14) +P(X=15) +P(X=16)+P(X=17)+P(X=18)$

And we can find the individual proabilities using the probability mass function:

$P(X=14)=(18C14)(0.8)^{14} (1-0.8)^{18-14}=0.2153$

$P(X=15)=(18C15)(0.8)^{15} (1-0.8)^{18-15}=0.2297$

$P(X=16)=(18C16)(0.8)^{16} (1-0.8)^{18-16}=0.1722$

$P(X=17)=(18C17)(0.8)^{17} (1-0.8)^{18-17}=0.0811$

$P(X=18)=(18C18)(0.8)^{18} (1-0.8)^{18-18}=0.0180$

And adding the values we got:

$P(X \geq 14)= 0.2153 +0.2297+0.1722+0.0811+0.0180=0.7164$

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3 years ago

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The answer will be $-11w^6.$

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2 years ago

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7 0

2 years ago

Hank has large of trail mid weighs 7.8 pounds. He uses the mix in the large bag to make bags each containing 0.6 pounds of mix.

KonstantinChe [14]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

5. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swam to the boat

frosja888 [35]

Answer:

hello your question is incomplete attached below is the complete question

answer :

Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.

Step-by-step explanation:

First determine the time it will take Daniel to reach the Boat and the jogging time

time = distance / rate

where distance can be calculated using this equation: sin 53° = 400 / x

hence x ( distance ) = 500 ft

rate = 150

therefore Time ( t ) to reach boat = 500 / 150 = 3.33 minutes

Time for jogging ( as calculated ) = 3.69 minutes

therefore total time taken by Daniel = 3.33 + 3.69 = 7.02 minutes

Finally determine if Daniel's sister is correct that he should have swam to the boat ramp and then jogged

lets assume Distance to swim = x ( according his sister )

determine the value of x = $\sqrt{400^2 + 1400^2 }$ therefore X = 1456.02 feet

∴

Total time to be taken if Daniel follows his sister's instruction = 1456.02 / 150 = 9.71 minutes

Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.

6 0

2 years ago