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2 months ago

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Explain what it means to have a correlation in a scatterplot.

2 answers:

PIT_PIT [12.4K]2 months ago

3 0

Response:

A correlation is present in a scatter plot when a clear trend is observed in the outputs as the inputs rise. A general increase in the outputs signals a positive correlation, while a general decrease indicates a negative correlation.

tester [12.3K]2 months ago

3 0

Response:Sample Reply/Clarification: Correlation in a scatterplot indicates a discernible trend in outputs as inputs grow. A positive correlation arises when outputs generally increase, while a negative correlation occurs as outputs typically diminish.

This signifies a recognizable trend.

As inputs rise, outputs either increase or decrease predominantly.

Consequently, the trend could be either positive or negative.

Step-by-step clarification:

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Which of these conditions might be true if polygons ABCD and KLMN are similar? The measures of corresponding angles of ABCD and

PIT_PIT [12445]

Answer: The correct choice is

(A) The angles of ABCD and KLMN corresponding to each other are equal, but the sides of ABCD are half the length of those in KLMN.

Step-by-step explanation: It is required to identify which statement reflects the potential truth if the polygons ABCD and KLMN are similar.

Two polygons are considered SIMILAR when their corresponding angles are congruent and the sides are in proportion.

Hence, options (B), (C), (D), and (E) are incorrect since they contradict the principles of similarity.

In option (A), we see

The angles of ABCD and KLMN that correspond are equal. Thus, they must be congruent.

Moreover, the lengths of corresponding sides of ABCD are half those of KLMN.

Thus, we can deduce

$AB=\dfrac{1}{2}KL,~~BC=\dfrac{1}{2}LM,~~CD=\dfrac{1}{2}MN,~~AD=\dfrac{1}{2}KN\\\\\\\Rightarrow \dfrac{AB}{KL}=\dfrac{BC}{LM}=\dfrac{CD}{MN}=\dfrac{AD}{KN}=\dfrac{1}{2}.$

Consequently, the corresponding sides are proportional.

Therefore, option (A) holds true if the two polygons are similar.

3 0

1 month ago

Read 2 more answers

X + y = 4 x - 2y = -5 If the first equation is multiplied by 2 and then the equations are added, the result is _____.

lawyer [12517]

X + y = 4, when multiplied by 2, gives 2x + 2y = 8

x - 2y = -5
Adding 2x + 2y = 8
---------------results in
3x = 3......you are correct <==

8 0

3 months ago

Read 2 more answers

Find the number a such that the line x = a bisects the area under the curve y = 1/x2 for 1 ≤ x ≤ 4. 8 5 (b) find the number b s

Zina [12379]

a. We seek $a$ such that

$\displaystyle\int_1^a\frac{\mathrm dx}{x^2}=\int_a^4\frac{\mathrm dx}{x^2}$

$-\dfrac1x\bigg|_{x=1}^{x=a}=-\dfrac1x\bigg|_{x=a}^{x=4}$

$1-\dfrac1a=\dfrac1a-\dfrac14$

$\dfrac54=\dfrac2a\implies\boxed{a=\dfrac85}$

b. Simplifying the integration concerning $y$ will facilitate the process.

$y=\dfrac1{x^2}\implies x=\dfrac1{\sqrt y}$

(where we consider the positive square root since we know $x>0$ )

Next, we need to determine $b$ such that

$\displaystyle\int_0^b\frac{\mathrm dy}{\sqrt y}=\int_b^1\frac{\mathrm dy}{\sqrt y}$

$2\sqrt y\bigg|_{y=0}^{y=b}=2\sqrt y\bigg|_{y=b}^{b=1}$

$2\sqrt b=2-2\sqrt b$

$4\sqrt b=2\implies\boxed{b=\dfrac14}$

3 0

1 month ago

Working alone, Jack can do a puzzle in 5 hours. With his brother's help, the two can do the same puzzle in 2 hours. How long wou

zzz [12365]

Answer:

3 hours and 20 minutes.

7 0

2 months ago

A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed below:69.40

Zina [12379]

Answer:

The most likely length of the line is 69.4012 meters.

The calculated standard deviation amounts to 0.0032 meters.

Step-by-step explanation:

In the problem, the following values are provided:

69.401, 69.400, 69.402, 69.396, 69.406, 69.401, 69.396, 69.401, 69.405, 69.404

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ represent data points, $\bar{x}$ is the average, and n indicates the count of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{694.012}{10} = 69.4012$

The most likely length of the line is 69.4012 meters.

Sum of squares of differences = 0.0001016

$\sigma = \sqrt{\dfrac{0.0001016}{10}} = 0.0032$

The calculated standard deviation amounts to 0.0032 meters.

3 0

2 months ago