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3 years ago

6

translate triangle A by vector (-3,1) to give triangle B. Then roste your triangle B 180 degrees around the origin to give trian

gle C. Describe fully the single transformation that maps triangle A onto triangle C

1 answer:

Strike441 [17]3 years ago

8 0

Answer:

<h3>From A to B.</h3>

The first transformation is a reflection across the x-axis, then a shift one unit down. Finally, a reflection acroos the line x = 1.5. These transformations give figure B.

<h3>From B to C.</h3>

To get figure C, we just need to do a 180° rotation across the origin. Or, you can see this transformation as a reflection acroos the origin, it would be the same result.

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Miguel bought 2 1/4 pounds of hamburgers,1 1/5 pounds of sliced turkey ,and 2 pounds of cheese.what was the total weight of all

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2 years ago

The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth g

Bingel [31]

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

Step-by-step explanation:

This is a problem of the <em>distribution of sample means</em>. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves <em>normally</em> for samples sizes equal or greater than 30 $\\ n \geq 30$ . Mathematically

$\\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a <em>normal standard distribution</em>, i.e., a normal distribution that has a population mean $\\ \mu = 0$ and a population standard deviation $\\ \sigma = 1$ .

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

From the question, we know that

The population mean is $\\ \mu = 88$ WPM
The population standard deviation is $\\ \sigma = 14$ WPM

We also know the size of the sample for this case: $\\ n = 137$ sixth graders.

We need to estimate the probability that a sample mean being greater than $\\ \overline{X} = 89.87$ WPM in the <em>distribution of sample means</em>. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}$

$\\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}$

$\\ Z = 1.5634 \approx 1.56$

This is a <em>standardized value </em> and it tells us that the sample with mean 89.87 is 1.56<em> standard deviations</em> <em>above</em> the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any <em>cumulative</em> <em>standard normal table</em> available in Statistics books or on the Internet. Of course, this probability is the same that $\\ P(\overline{X} < 89.87)$ . Then

$\\ P(z$

However, we are looking for P(z>1.56), which is the <em>complement probability</em> of the previous probability. Therefore

$\\ P(z>1.56) = 1 - P(z$

$\\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594$

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

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3 years ago

Is the product of 3√ and 2.8 is a rational number acquisition?

svetlana [45]

Answer:

It is not rational

Step-by-step explanation:

Given

$\sqrt 3 * 2.8$

Required

Rational or Irrational

$\sqrt 3 * 2.8$

$\sqrt 3 =1.73205$

So, we have:

$\sqrt 3 * 2.8 = 1.73205 * 2.8$

$\sqrt 3 * 2.8 = 4.84974$

<em>The result of the product: 4.84974 is not rational because it can not be represented as a fraction of two integers.</em>

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3 years ago

5/16=n/16 help please

Vsevolod [243]

Both have the same denominator
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5=n

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3 years ago

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