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gayaneshka [121]
3 years ago
12

What does it mean to say​ "correlation does not imply​ causation"? Choose the correct answer below. A. Two variables can only be

strongly correlated if there existed a​ cause-and-effect relationship between the variables. B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables. C. The fact that two variables are strongly correlated implies a​ cause-and-effect relationship between the variables. D. Two variables that have a​ cause-and-effect relationship are never correlated.
Mathematics
1 answer:
pav-90 [236]3 years ago
6 0

Answer:

B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.

While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.

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What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)
zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

  • Integrals
  • Definite Integrals
  • Integration Constant C

Arc Length Formula [Parametric]:                                                                         \displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.

Interval [0, π]

<u>Step 2: Find Arc Length</u>

  1. [Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]:         \displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.
  2. Substitute in variables [Arc Length Formula - Parametric]:                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx
  3. [Integrand] Simplify:                                                                                       \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx
  4. [Integral] Evaluate:                                                                                         \displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

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3 years ago
Tell whether the lines through the given points are parallel, perpendicular, or neither. (-3,1), (1,9), (-2-9), (-1,-7)​
Brrunno [24]

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parallel

Step-by-step explanation:

all the details are in the attached picture.

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In Mrs. Trach’s class, 18 students prefer to do their homework before dinner. In Ms. Love-Benson's class, 20 students prefer to
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Exponents and roots are what operations
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3 years ago
Points A,M and P are collinear with M in between A and P. If AP=29, AM =5x-3 and MP=8x+6, what does MP=?
charle [14.2K]

The length of MP is 22 units.

<h3>What is a Line Segment?</h3>

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure is given below shows a line segment AP, where the length of line segment AP refers to the distance between its endpoints, A and P.

Given that Points A, M and P are collinear with M in between A and P.

AP=29, AM =5x-3 and MP=8x+6,

A______________M______________P

⇒ AP = AM + MP

Substitute the values of AP = 29, AM =5x-3 and MP=8x+6,

⇒ 29 = 5x - 3 + 8x+6,

Rearranging the terms in the above equation,

⇒ 5x + 8x = 29 + 3 - 6

⇒ 13x = 26,

⇒ x = 26/13,

⇒ x = 2

So MP = 8x+6

Substitute the value of x = 2 in the above equation,

⇒ MP = 8(2) + 6

⇒ MP = 22

Hence, the length of MP is 22 units.

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