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3 years ago

Given: m arc AB = 4x, m arc BC = 3x m arc CD = 2x, m arc DA = 3x Find: m∠APB

Mathematics

2 answers:

Svetradugi [14.3K]3 years ago

5 0

Answer:

m<APB = 30 degrees

Step-by-step explanation:

The sum of angles in a circle is 360 degrees. Add up all the arcs to get the equation : 4x+3x+2x+3x=360 degrees.

x is equal to 30 degrees

m arc AB = 4x = 120 degrees

m arc DC = 2x = 60 degrees

By secants exterior angles, m<APB = 1/2(m arc AB - m arc DC) = 1/2(120-60) = 30 degrees.

The answer is m<APB = 30 degrees

Vitek1552 [10]3 years ago

3 0

Answer:

a > m/bp

Step-by-step explanation:

flip the equation

abp > m

divide both sides with bp

abp/bp > m/bp

a > m/bp

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Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.

bonufazy [111]

Answer:

The ratio of Tan B is

$\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}$

$\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}$

Step-by-step explanation:

In Right Angle Triangle ABC

angle C = 90°

AB = Ramp = 17 feet

BC =Horizontal distance = 15 feet

AC = Height from floor = 8 feet

To Find:

Ratio of Tan B = ?

Solution:

In Right Angle Triangle ABC By Tangent Identity we have

$\tan B= \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}$

Substituting the given values we get

$\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}$

$\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}$

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3 years ago

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below

mafiozo [28]

Answer:

a) $\bar X = 369.62$

b) $Median=175$

c) $Mode =450$

With a frequency of 4

d) $MidR= \frac{Max +Min}{2}= \frac{49+3000}{2}= 1524.5$

<u>e)</u> $s = 621.76$

And we can find the limits without any outliers using two deviations from the mean and we got:

$\bar X+2\sigma = 369.62 +2*621.76 = 1361$

And for this case we have two values above the upper limit so then we can conclude that 1500 and 3000 are potential outliers for this case

Step-by-step explanation:

We have the following data set given:

49 70 70 70 75 75 85 95 100 125 150 150 175 184 225 225 275 350 400 450 450 450 450 1500 3000

Part a

The mean can be calculated with this formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

Replacing we got:

$\bar X = 369.62$

Part b

Since the sample size is n =25 we can calculate the median from the dataset ordered on increasing way. And for this case the median would be the value in the 13th position and we got:

$Median=175$

Part c

The mode is the most repeated value in the sample and for this case is:

$Mode =450$

With a frequency of 4

Part d

The midrange for this case is defined as:

$MidR= \frac{Max +Min}{2}= \frac{49+3000}{2}= 1524.5$

Part e

For this case we can calculate the deviation given by:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s = 621.76$

And we can find the limits without any outliers using two deviations from the mean and we got:

$\bar X+2\sigma = 369.62 +2*621.76 = 1361$

And for this case we have two values above the upper limit so then we can conclude that 1500 and 3000 are potential outliers for this case

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