In the context of the disc assessment, Belinda would most likely score high in conscientiousness
- Conscientiousness is one of the five big personality of people. It is the extent an individual is focused especially on a few goals, making the person to behave in ways that are responsible, highly dependable, consistent, and is focused on achieving something and not being a failure.
Conclusively we can therefore say that in the context of the disc assessment, Belinda would most likely score high in conscientiousness
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1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
<em />
Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
Answer:
The following data represents a random sample of 35 online purchases (in $) on
Cyber Monday:
152
158
158
162
163
164
165
166
171
171
176
180
180
184
185
188
189
190
191
197
200
213
213
214
222
222
224
227
The premium that the insurance company should charge each year to realize an average profit of $500 is $6,900.
First step is to calculated the expected amount to pay
Expected amount=Total loss +50% loss+25% loss
Expected amount=$200,000(0.002)(1)+$200,000(0.01)(0.5)+$200,000(0.1)(0.25)
Expected amount=$400+$1,000+$5,000
Expected amount=$6,400
Second step is to calculate the premium
Premium=Expected amount+ Average profit
Premium=$6,400+$500
Premium=$6,900
Inconclusion the premium that the insurance company should charge each year to realize an average profit of $500 is $6,900.
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