Answer:
do you have a picture of this
We are given with three lengths of a triangle expressed in terms and variables: (3x – 4) feet, (x^2 – 1) feet, and (2x^2 – 15) feet. The perimeter of the triangle is equal to the sum of the three sides of the triangle. In this case, the sum is 3x^2 + 3x -20. When x is equal to 4, we substitute <span>3*16 + 3*4 -20 equal to 40 feet.</span>
Probability =
(number of ways it can come out the way you want)
divided by
(total number of ways it can come out).
Total number of ways to draw a marble = 30 (marbles in the bag).
Number of ways it can succeed = 15 (number of red or green ones)
Probability = 15/30 = 1/2 = 50% .
Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.
<h3>The condition for two parallel lines.</h3>
In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:
m₁ = m₂
<u>Note:</u> m is the slope.
<h3>What is the alternate interior angles theorem?</h3>
The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):
For angle BDF, we have:
<BDF = <BDH + <HDF
<BDF = 38° + 62°
<BDF = 100°.
Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:
∠BDF + <DFC = 180°
<DFC = 180 - ∠BDF
<DFC = 180 - 100
<DFC = 80°.
For angle CFG, we have:
∠DFE + <DFC + <CFG= 180°
<CFG = 180° - ∠DFE - <DFC
<CFG = 180° - 62° - 80°
<CFG = 38°.
Read more on parallel lines here: brainly.com/question/3851016
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Using the Empirical Rule, it is found that her finishing time will be between 70 and 82 seconds in 95% of her races.
<h3>What does the Empirical Rule state?</h3>
It 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, the mean is of 76 seconds and the standard deviation is of 3 seconds, then:
76 - 2 x 3 = 70.
76 + 2 x 3 = 82.
Which means that values between 70 and 82 seconds are within 2 standard deviations of the mean, hence the percentage is of 95%.
More can be learned about the Empirical Rule at brainly.com/question/24537145
