You are climbing a mountain by the steepest route at a slope of 10∘ when you come upon a trail branching off at a 45∘ angle from
yours. What is the angle of ascent of the branch trail?
2 answers:
Envision yourself starting at the origin, noticing another path deviating 45 degrees from your current one.
Thus, the correct solution would be given by arctan(cos(45)tan(10)).
Thus, the correct solution would be given by arctan(cos(45)tan(10)).
Answer:
The angle of ascent for the branch trail is 55°.
Step-by-step explanation:
Given:
- The steepest ascent has a slope of 10°.
- When we reach the branch trail, the angle measures 45°.
To find the angle of ascent, we need to compute the angle from the horizontal. This involves adding the two angles together.
Thus, the angle of ascent for the branch trail totals 55°.
It's important to note that this angle is measured from the horizontal plane.
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Answer:
(a) The data point that is considered an outlier is $810.
(b) The distribution regarding expenditures on textbooks among the 34 students is right skewed.
Step-by-step explanation:
The provided data regarding how much 34 college students spent on textbooks is:
S = {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280, 290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}
(a)
An outlier is defined as a value significantly different from the rest of the dataset, being either excessively high or low.
A widely-used approach for identifying outliers involves:
- Identifying values that fall below Q₁ - 1.5 IQR as outliers.
- Identifying values that exceed Q₃ + 1.5 IQR as outliers.
In our case,
Q₁ = first quartile
Q₃ = third quartile
IQR = Interquartile range = Q₃ - Q₁.
The first quartile value corresponds to more than 25% of the data points. It can be found by examining the median of the first half of the data.
Calculate the first quartile with the set below:
Initial half of data: {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280}
This subset contains 17 values.
The median in an odd-sized dataset is the central point.
The central value here is: 180
Thus, the first quartile is Q₁ = 180.
The third quartile value corresponds to more than 75% of the data points.
We determine the third quartile from the second half of the data:
Final half of data: {290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}
<pthis subset="" also="" consists="" of="" values.="">The median of an odd dataset serves as the middle value.
The central point is: 390
Hence, the third quartile is Q₃ = 390.
Calculate the interquartile range as follows:
IQR = Q₃ - Q₁
= 390 - 180
= 210
Next, we compute the value of [Q₁ - 1.5 IQR]:
And then we compute [Q₃ + 1.5 IQR]:
There are no values below [Q₁ - 1.5 IQR]. However, one value exceeds [Q₃ + 1.5 IQR].
X = 810 > [Q₃ + 1.5 IQR] = 705
Consequently, the outlier identified within the dataset is $810.
(b)
A distribution is classified as positively skewed or right-skewed when the majority of the data congregates on the lower end of the spectrum.
The stem plot indicates that most of the data values are concentrated on the left side, confirming that the distribution is indeed right skewed.
</pthis>Answer:
Step-by-step explanation:
Ang exponential function ay karaniwang ginagamit para ilarawan ang natural na pagtaas o pagbaba ng mga proseso, kung saan ang pagbabago ay proporsyonal sa kasalukuyang halaga.
Ang isang exponential decaying function ay ipinapahayag bilang:
Saan:
C(t) ang aktwal na halaga ng function sa oras na t
Co ang paunang halaga ng C sa t=0
r ang rate ng pag-alis, na ipinahayag sa decimal
Ang konsentrasyon ng pollutants ay nagsisimula sa Co=5 mg/lt. Alam din natin na ang pollutant ay bumababa ng 10% ng konsentrasyon nito bawat oras. Kaya't ito ay nagbibigay ng r = 10% / 100 = 0.1
Pagpapalit sa pangkalahatang equation:
Pagsasagawa: