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torisob [31]
2 years ago
13

Figure M and it’s congruent image, figure N, are graphed on the coordinate plane below.

Mathematics
1 answer:
mixer [17]2 years ago
7 0

The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we can see in the graph there are two shapes are shown.

Figure M and Figure N

The sequence of transformations that will take figure M onto its congruent image, figure N is:

First, we need to draw a line that passes through (3, 0) and (0, -3)

The equation of the line is:

\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)

y + 3 = x

y = x - 3

The reflection over the above line will take figure M onto its congruent image, figure N.

Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

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slavikrds [6]

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3 years ago
Use the definition of a derivative to find f’(x).
tatyana61 [14]

Answer:

f'(x) = -\frac{9}{x^2}

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x)  = $\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $  \hspace{0.2cm}

        = $\lim_{h\to 0} \frac{\frac{9}{x+h}  - \frac{9}{x} }{h}  =  \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} =  \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)}  =  $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$

7 0
3 years ago
As part of the Pew Internet and American Life Project, researchers conducted two surveys in late 2009. The first survey asked a
REY [17]

Answer:

The 95% confidence interval for the difference between the proportion of all U.S. teens and adults who use social networking sites is (0.223, 0.297). This means that we are 95% sure that the true difference of the proportion is in this interval, between 0.223 and 0.297.

Step-by-step explanation:

Before building the confidence interval we need to understand the central limit theorem and the subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Sample of 800 teens. 73% said that they use social networking sites.

This means that:

p_T = 0.73, s_T = \sqrt{\frac{0.73*0.27}{800}} = 0.0157

Sample of 2253 adults. 47% said that they use social networking sites.

This means that:

p_A = 0.47,s_A = \sqrt{\frac{0.47*0.53}{2253}} = 0.0105

Distribution of the difference:

p = p_T - p_A = 0.73 - 0.47 = 0.26

s = \sqrt{s_T^2+s_A^2} = \sqrt{0.0157^2+0.0105^2} = 0.019

Confidence interval:

Is given by:

p \pm zs

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Lower bound:

p - 1.96s = 0.26 - 1.96*0.019 = 0.223

Upper bound:

p + 1.96s = 0.26 + 1.96*0.019 = 0.297

The 95% confidence interval for the difference between the proportion of all U.S. teens and adults who use social networking sites is (0.223, 0.297). This means that we are 95% sure that the true difference of the proportion is in this interval, between 0.223 and 0.297.

3 0
2 years ago
Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using
AlladinOne [14]

Answer:

<u></u>

  • <u>a) P(X=1) = 0.302526</u>
  • <u>b) P(X=5) = 0.010206</u>
  • <u>c) P(X=3) = 0.18522</u>
  • <u>d) P(X≤3) = 0.92953</u>
  • <u>e) P(X≥5) = 0.010935</u>
  • <u>f) P(X≤4) = 0.989065</u>

Explanation:

Binomial experiments are modeled by the formula:

       P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}

Where

  • P(X=x) is the probability of exactly x successes

  • C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}

  • p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.
  • n is the number of trials
  • 1 - p is the probability of fail
  • there are only two possible outcomes for each trial: success or fail.

<u>a.) P (x=1)</u>

<u></u>

       P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526

<u>b.) P (x=5)</u>

     P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206

<u>c.) P (x=3)</u>

Using the same formula:

    P(X=3)=0.18522

<u>d.) P (x less than or equal to 3)</u>

  • P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

  • P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

  • P(X=4) = 0.059335
  • P(X=5) = 0.010206
  • P(X=6) = 0.000729

  • P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

<u>e.) P(x greather than or equal to 5)</u>

  • P(X≥5) = P(X=5) + P(X=6)
  • P(X≥5) = 0.010206 + 0.000729 =  0.010935

<u>f.) P(x less than or equal 4)</u>

  • P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)
  • P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
5 0
3 years ago
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