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Anuta_ua [19.1K]
3 years ago
9

Given the triangle below, what is the length of the third side, rounded to the nearest whole number?

Mathematics
1 answer:
Leno4ka [110]3 years ago
7 0

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

x^2=21^2+14^2-2(21)(14)cos58 where x is the missing side.

x^2=441+196-311.5925 and

x^2=325.4075 so

x = 18.0 or just 18

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The ages of students enrolled in two math classes at the local community college, Class A and Class B, are listed in order below
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The true statement about Class B is that Class B has a smaller median and the same inter quartile range.

Step-by-step explanation:

We are given the ages of students enrolled in two math classes at the local community college, Class A and Class B, below;

Class A: 20, 20, 20, 21, 22, 23, 23, 25, 27, 29, 30, 31, 34, 35, 36, 39, 40

Class B: 16, 17, 18, 18, 20, 22, 22, 24, 26, 26, 28, 29, 30, 34, 37, 40, 42

1) <u>Firstly, we will calculate Median for Class A;</u>

For calculating median, first we have to observe that number of observations (n) in our data is even or odd, that is;

  • If n is odd, then the formula for calculating median is given by;

                     Median  =  (\frac{n+1}{2})^{th} \text{ obs.}

  • If n is even, then the formula for calculating median is given by;

                     Median  =  \frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.}}{2}

Here, number of observation is odd, i.e. n = 17.

So,  Median  =  (\frac{n+1}{2})^{th} \text{ obs.}

                     =  (\frac{17+1}{2})^{th} \text{ obs.}

                     =  (\frac{18}{2})^{th} \text{ obs.}

                     =  9^{th} \text { obs.} = 27

Hence, the median of class A is 27.

2) <u>Now, we will calculate Median for Class B;</u>

For calculating median, first we have to observe that number of observations (n) in our data is even or odd, that is;

  • If n is odd, then the formula for calculating median is given by;

                     Median  =  (\frac{n+1}{2})^{th} \text{ obs.}

  • If n is even, then the formula for calculating median is given by;

                     Median  =  \frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.}}{2}

Here, number of observation is odd, i.e. n = 17.

So,  Median  =  (\frac{n+1}{2})^{th} \text{ obs.}

                     =  (\frac{17+1}{2})^{th} \text{ obs.}

                     =  (\frac{18}{2})^{th} \text{ obs.}

                     =  9^{th} \text { obs.} = 26

Hence, the median of class B is 26.

3) Now, we will calculate the Inter quartile range for Class A;

Inter quartile range = Upper quartile - Lower quartile

                                = Q_3-Q_1

SO,  Q_1 = (\frac{n+1}{4})^{th} \text{ obs.}

             =  (\frac{17+1}{4})^{th} \text{ obs.}

             =  (\frac{18}{4})^{th} \text{ obs.}

             =  4.5^{th} \text{ obs.}

             =  4^{th}  \text{ obs.} + 0.5[5^{th} \text{ obs.} -  4^{th} \text{ obs.}]

             =  21+ 0.5[22-  21]

             =  21.5

Similarly,  Q_3 = 3(\frac{n+1}{4})^{th} \text{ obs.}

             =  3(\frac{17+1}{4})^{th} \text{ obs.}

             =  (\frac{54}{4})^{th} \text{ obs.}

             =  13.5^{th} \text{ obs.}

             =  13^{th}  \text{ obs.} + 0.5[14^{th} \text{ obs.} -  13^{th} \text{ obs.}]

             =  34+ 0.5[35-  34]

             =  34.5

Therefore, Inter quartile range for Class A = 34.5 - 21.5 = 13.

4) Now, we will calculate the Inter quartile range for Class B;

Inter quartile range = Upper quartile - Lower quartile

                                = Q_3-Q_1

SO,  Q_1 = (\frac{n+1}{4})^{th} \text{ obs.}

             =  (\frac{17+1}{4})^{th} \text{ obs.}

             =  (\frac{18}{4})^{th} \text{ obs.}

             =  4.5^{th} \text{ obs.}

             =  4^{th}  \text{ obs.} + 0.5[5^{th} \text{ obs.} -  4^{th} \text{ obs.}]

             =  18+ 0.5[20-  18]

             =  19

Similarly,  Q_3 = 3(\frac{n+1}{4})^{th} \text{ obs.}

             =  3(\frac{17+1}{4})^{th} \text{ obs.}

             =  (\frac{54}{4})^{th} \text{ obs.}

             =  13.5^{th} \text{ obs.}

             =  13^{th}  \text{ obs.} + 0.5[14^{th} \text{ obs.} -  13^{th} \text{ obs.}]

             =  30+ 0.5[34-  30]

             =  32

Therefore, Inter quartile range for Class B = 32 - 19 = 13.

Hence, the true statement about Class B is that Class B has a smaller median and the same inter quartile range.

4 0
4 years ago
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