Mathematics : asked on hamzaha
 05.04.2023

10
Find the indicated measure in CABCD.

. 4

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Mathematics
Step-by-step answer
P Answered by PhD

RS = 12.2 in ⇒ answer (a)

Step-by-step explanation:

∵ m∠R = 78° , m∠T = 39° , TS = 19

∵ By using sin Rule:

∵ ST/sin∠R = RS/sin∠T

∴ 19/sin78 = RS/sin39

∴ RS = (19 × sin39) ÷ sin 78 = 12.2 in ⇒ answer (a)

Mathematics
Step-by-step answer
P Answered by PhD

RS = 12.2 in ⇒ answer (a)

Step-by-step explanation:

∵ m∠R = 78° , m∠T = 39° , TS = 19

∵ By using sin Rule:

∵ ST/sin∠R = RS/sin∠T

∴ 19/sin78 = RS/sin39

∴ RS = (19 × sin39) ÷ sin 78 = 12.2 in ⇒ answer (a)

Mathematics
Step-by-step answer
P Answered by PhD

for Derek's collection :

Mean= 1929

Median= 1930

Range= 54

IQR = 48

MAD= 23.75

for Paul's collection:

Mean= 1929

Median= 1929.5

Range= 15

IQR = 6

MAD= 3.5

Step-by-step explanation:

Derek's collection:

1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

Mean is given by:

Mean=\dfrac{1950+1952+1908+1902+1955+1954+1901+1910}{8}\\\\\\Mean=\dfrac{15432}{8}\\\\\\Mean=1929

Now absolute deviation from mean is:

|1950-1929|= 21

|1952-1929|= 23

|1908-1929|= 21

|1902-1929|= 27

|1955-1929|= 26

|1954-1929|= 25

|1901-1929|= 28

|1910-1929|= 19

and the mean of these absolute deviation gives the MAD of the data i.e.

  MAD=\dfrac{21+23+21+27+26+25+28+19}{8}\\\\\\MAD=23.75

Now, on arranging the data in increasing order we get:

    1901   1902    1908   1910    1950  1952    1954   1955

The least value is: 1901

Maximum value is: 1955

Range is: Maximum value-Least value

          Range=1955-1901

          Range= 54

Also, the median lie between 1910 and 1950 and is calculated as:

       Median=\dfrac{1910+1950}{2}\\\\\\Median=\dfrac{3860}{2}\\\\\\Median=1930

Also, the lower set of data is:

   1901   1902    1908   1910

and the median of lower set of data also known as first quartile or lower quartile is:

Q_1=\dfrac{1902+1908}{2}\\\\\\Q_1=\dfrac{3810}{2}\\\\\\Q_1=1905

and upper set of data is:

1950  1952    1954   1955

and the median of upper set of data i.e. upper quartile or third quartile is:

Q_3=\dfrac{1952+1954}{2}\\\\\\Q_3=\dfrac{3906}{2}\\\\\\Q_3=1953

Hence, IQR is calculated as:

  IQR=Q_3-Q_1\\\\\\i.e.\\\\\\IQR=1953-1905\\\\\\IQR=48

Paul's collection:

1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

Mean is given by:

Mean=\dfrac{1929+1935+1928+1930+1925+1932+1933+1920}{8}\\\\\\Mean=1929

Now absolute deviation from mean is:

|1929-1929|=0

|1935-1929|= 6

|1928-1929|= 1

|1930-1929|= 1

|1925-1929|= 4

|1932-1929|= 3

|1933-1929|= 4

|1920-1929|= 9

Hence, we get:

MAD=\dfrac{6+1+1+4+3+4+9}{8}\\\\\\MAD=\dfrac{28}{8}\\\\\\MAD=3.5

Now, on arranging the data in increasing order we get:

1920   1925   1928   1929   1930   1932   1933   1935  

Least value= 1920

Maximum value= 1935

Range=  15 ( Since, 1935-1920=15 )

The median lie between 1929 and 1930

Hence, Median= 1929.5

Also, lower set of data is:

1920   1925   1928   1929  

and median of lower set of data is the first quartile or upper quartile and is calculated as:

Q_1=\dfrac{1925+1928}{2}\\\\\\Q_1=1926.5

and the upper set of data is:

1930   1932   1933   1935  

Hence, we get:

Q_3=\dfrac{1932+1933}{2}\\\\\\Q_3=1932.5

Hence, IQR is calculated as:

IQR=Q_3-Q_1\\\\\\IQR=1932.5-1926.5\\\\\\IQR=6

Mathematics
Step-by-step answer
P Answered by PhD

for Derek's collection :

Mean= 1929

Median= 1930

Range= 54

IQR = 48

MAD= 23.75

for Paul's collection:

Mean= 1929

Median= 1929.5

Range= 15

IQR = 6

MAD= 3.5

Step-by-step explanation:

Derek's collection:

1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910

Mean is given by:

Mean=\dfrac{1950+1952+1908+1902+1955+1954+1901+1910}{8}\\\\\\Mean=\dfrac{15432}{8}\\\\\\Mean=1929

Now absolute deviation from mean is:

|1950-1929|= 21

|1952-1929|= 23

|1908-1929|= 21

|1902-1929|= 27

|1955-1929|= 26

|1954-1929|= 25

|1901-1929|= 28

|1910-1929|= 19

and the mean of these absolute deviation gives the MAD of the data i.e.

  MAD=\dfrac{21+23+21+27+26+25+28+19}{8}\\\\\\MAD=23.75

Now, on arranging the data in increasing order we get:

    1901   1902    1908   1910    1950  1952    1954   1955

The least value is: 1901

Maximum value is: 1955

Range is: Maximum value-Least value

          Range=1955-1901

          Range= 54

Also, the median lie between 1910 and 1950 and is calculated as:

       Median=\dfrac{1910+1950}{2}\\\\\\Median=\dfrac{3860}{2}\\\\\\Median=1930

Also, the lower set of data is:

   1901   1902    1908   1910

and the median of lower set of data also known as first quartile or lower quartile is:

Q_1=\dfrac{1902+1908}{2}\\\\\\Q_1=\dfrac{3810}{2}\\\\\\Q_1=1905

and upper set of data is:

1950  1952    1954   1955

and the median of upper set of data i.e. upper quartile or third quartile is:

Q_3=\dfrac{1952+1954}{2}\\\\\\Q_3=\dfrac{3906}{2}\\\\\\Q_3=1953

Hence, IQR is calculated as:

  IQR=Q_3-Q_1\\\\\\i.e.\\\\\\IQR=1953-1905\\\\\\IQR=48

Paul's collection:

1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920

Mean is given by:

Mean=\dfrac{1929+1935+1928+1930+1925+1932+1933+1920}{8}\\\\\\Mean=1929

Now absolute deviation from mean is:

|1929-1929|=0

|1935-1929|= 6

|1928-1929|= 1

|1930-1929|= 1

|1925-1929|= 4

|1932-1929|= 3

|1933-1929|= 4

|1920-1929|= 9

Hence, we get:

MAD=\dfrac{6+1+1+4+3+4+9}{8}\\\\\\MAD=\dfrac{28}{8}\\\\\\MAD=3.5

Now, on arranging the data in increasing order we get:

1920   1925   1928   1929   1930   1932   1933   1935  

Least value= 1920

Maximum value= 1935

Range=  15 ( Since, 1935-1920=15 )

The median lie between 1929 and 1930

Hence, Median= 1929.5

Also, lower set of data is:

1920   1925   1928   1929  

and median of lower set of data is the first quartile or upper quartile and is calculated as:

Q_1=\dfrac{1925+1928}{2}\\\\\\Q_1=1926.5

and the upper set of data is:

1930   1932   1933   1935  

Hence, we get:

Q_3=\dfrac{1932+1933}{2}\\\\\\Q_3=1932.5

Hence, IQR is calculated as:

IQR=Q_3-Q_1\\\\\\IQR=1932.5-1926.5\\\\\\IQR=6

Chemistry
Step-by-step answer
P Answered by PhD

Al(NO₃)₃ >  KI > HF > CH₃OH

Explanation:

The electrical conductivities of the solutions will depend on the concentration of ions in solution.

Al(NO₃)₃ solution contains 0.1 M of Al³⁺ ions and 0.3 M of NO₃⁻ ions

KI solution contains 0.1 M of K⁺ ions and 0.1 M of I⁻ ions

HF solution contains less than 0.1 M of H⁺ ions and less then 0.1 M of F⁻ ions, because the HF acid will not dissociate completely

CH₃OH practically it does not dissociate, so in the solution will not be electrical conductive (comparative with the other solutions)

The solutions in order of decreasing intensity of the bulb are ranked as following:

Al(NO₃)₃ >  KI > HF > CH₃OH

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