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ANEK [815]
3 years ago
12

Select all that are measures of angles coterminal with a –60° angle.

Mathematics
2 answers:
miss Akunina [59]3 years ago
6 0

Answer:

Co-terminal angles from given options are <u>300° , - 420°,  660°,   - 780°.</u>

Step-by-step explanation:

Co-terminal angles are angles that have same terminal and initial sides.

We can find co-terminal angles by simply adding or subtracting k ×360° (where k = 1,2,3...)  to the given angle.

So, co-terminal angle to -60° angles

- 60° + 360° = 300°

- 60° - 360° = - 420°    

- 60° + 2×360° =  - 60° + 720° = 660°

- 60° -2×360° = - 60° - 720° = - 780°

- 60° + 3×360° =  - 60° + 1080° = 1020°

- 60° -2×360° = - 60° - 1080° = - 1140°

Thus, Co-terminal angles from given options are <u>300° , - 420°,  660°,   - 780°.</u>

 

monitta3 years ago
4 0
-60

-60 + 360 = 360 -60 = 300

-60 + 360 + 360 = -60 +720 = 720 - 60 = 660

Also for the negative.

-60 -360 = -420

-60 -360 -360 = -780

-780°, -420°, 300°, 660°
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Given two dependent random samples with the following results:
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Answer:

We Fail to reject Null Hypothesis.

Step-by-step explanation:

We are given two dependent random samples;

Population 1   Population 2   d = Population 1 entry-Population 2 entry    d^{2}

      52                       61                                52 - 61 = -9                                 81

      81                        71                                 81 - 71 = 10                                 100

      72                        82                                72 - 82 = -10                             100

      67                        62                                67 - 62 = 5                                25

      73                        79                                 73 - 79 = -6                               36

      73                        77                                 73 - 77 = -4                                16

      76                        71                                  76 - 71 = 5                                 25

      83                        85                                 83 - 85 = -2                          <u>     4    </u>

                                                                                                              ∑d^{2} <u>= 387                                  </u>

Now,  Null Hypothesis, H_0 : \mu_1 = \mu_2    or   \mu_d = 0

 Alternate Hypothesis, H_1 : \mu_1 \neq  \mu_2     or   \mu_d \neq  0

The test statistics for paired data is given by;

                   \frac{dbar - \mu_d}{\frac{s_d}{\sqrt{n} } } follows t_n_-_1

 where, dbar = Mean of Population 2 data - Mean of Population 1 data

Mean of Population 1 data = \frac{52+81+72+67+73+73+76+83}{8} = 72.125

Mean of Population 2 data = \frac{61+71+82+62+79+77+71+85}{8} = 73.5

 Hence, dbar = 73.5 - 72.125 = 1.375

s_d = Standard Deviation of paired data = \sqrt{\frac{\sum d^{2} - n*(dbar)^{2}  }{n-1} } = \sqrt{\frac{387 - 8*(1.375)^{2}  }{8-1} }

                                                                 = 7.3

n = no. of observations = 8

 So, <em>Test Statistics = </em>\frac{1.375 - 0}{\frac{7.3}{\sqrt{8} } }<em> follows </em>t_7<em> </em>

<em>                          = 0.533</em>

Now, if the critical value of t at 7 degree of freedom is less than the test statistics then we will reject null hypothesis.

At 0.01 level of significance, the t table gives a critical value of 3.499. Since our test statistics is less than the critical value we will not reject null hypothesis and conclude that there is no significant difference between the two population means.

                                                                                                       

                                                                                                     

                                                                                                 

                                                                                                       

                                                                                                 

                                                                                                       

                                                                                                   

                                                                                               

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