Answer:
The are a is 6
The length of h = 2.4
Step-by-step explanation:
This is a 3 4 5 special triangle so the length of the hypotenuse is 5
The area for a triangle is calculated by multiplying height to the base and that divided by two
Since it's a right triangle we can take any side length as the height and the result wouldn't change
4×3÷2 = 6 is the area for this triangle now we can use thus information to find the length of h :
h × 5 ÷ 2 = 6
5h = 12
h = 2.4
Answer:
Approximately 68%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 1, standard deviation = 0.05.
Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.
0.95 = 1 - 0.05
1.05 = 1 + 0.05
So within 1 standard deviation of the mean, which by the Empirical Rule, is approximately 68% of values.
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature.
To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, a
diagram showing the lines and their common transversal is attached.
The completed two column proof is presented as follows;
Statement 
Reason
1. ∠1 and ∠2 are supplementary angles 1. Given
2. m∠1 + m∠2 = 180° 2. <u>Definition of supplementary ∠s</u>
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. <u>m∠1 + m∠3 = 180° </u> 4. <u>Definition of supplementary ∠s</u>
5. m∠1 + m∠2 = m∠1 + m∠3 5. <u>Transitive property of equality</u>
6. <u>m∠2 = m∠3 </u> 6. <u>Subtraction property of equality</u>
7. l ║ m 7. <u>Converse of alternate interior </u>
<u>angles postulate</u>
Reasons:
- Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°
- Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)
- Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles
- Reason for statement 5: Transitive property of equality describes the property that if a number <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.
- Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality
- Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.
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