The sum of 6 even integers is 130 what is the 2nd number in the sequence
2 answers:
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Answer: The distribution of the data set is positively skewed.
<u>Explanation: </u>
In order to see whether the given data set is symmetric, positively skewed or negatively skewed, we will find the mean, median and mode of the given data set.
For symmetric distribution,
For positively skewed distribution,
For negatively skewed distribution,
The mean of the given data set is given below:
Now, the Median is:
To find the median we need to sort the data in ascending order as:
The mode is the most frequently occurring observation. Therefore the mode is:
Since the , therefore the distribution of the given data set is positively skewed.
Answer:
y = 116°
Step-by-step explanation:
Given that <em>L₁ </em>|| <em>L</em>₂:
The <u>exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.
Also, ∠y° and ∠2x° are <u>same-side interior angles</u> formed by the intersection of the <em>hypotenuse</em> of the triangle that acts as a transversal to the parallel lines, <em>L₁ </em>and <em>L</em>₂. Given that ∠y° and ∠2x° are <u>same-side interior angles</u>, then it means that they are the supplements of each other, such that the sum of their measures is 180°.
Now that we have established these definitions, we can proceed with the solution.
<u>Equation 1</u>: ∠y° + ∠2x° = 180° ⇒ Same-side interior angles
<u>Equation 2</u>: ∠y° = ∠x° + ∠84° ⇒ exterior angle theorem
Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:
∠y° + ∠2x° = 180°
∠x° + ∠84° + 2x° = 180°
Combine like terms:
∠3x° + ∠84° = 180°
Subtract ∠84° from both sides:
∠3x° + ∠84° - ∠84° = 180° -∠84°
∠3x° = 180° - ∠84°
∠3x° = 96°
Divide both sides by 3 to solve for x:
∠x° = 32°
Substitute the value of x into Equation 2 to solve for y:
∠y° = ∠x° + ∠84°
∠y° = ∠32° + ∠84°
∠y° = 116°
Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:
<h3>Equation 1:</h3>∠y° + ∠2x° = 180°
116° + 2(32)° = 180°
116° + 64° = 180°
180° = 180° (True statement).
<h3>Equation 2:</h3>∠y° = ∠x° + ∠84°
116° = 32° + 84°
116° = 116° (True statement)
Therefore, the correct answer is: y = 116°.