Answer:
i) A total of 40320 different arrangements
ii) For the initial 3 spots, there are 336 different combinations.
Step-by-step explanation:
Given: The total finalists = 8
The count of boys = 3
The count of girls = 5
To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!
The number of possible arrangements equals 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.
nPr =
Here n = 8 and r = 3
Substituting n = 8 and r = 3 into the formula, we arrive at
8P3 = 
= 
= 6.7.8
= 336
Thus, there are 336 different arrangements for the first 3 spots.
Greetings:
<span>x² + y² + 8x + 22y + 37 = 0
(x² +8x) +(y² +22y) +37 = 0
</span>(x² +8x+4²)-4² +(y² +22y+11²) -11²+37 = 0
(x+4)² +(y+11)²-16-121+37 =0
(x+4)² +(y+11)² =10²...(<span>standard form )
</span><span>The circle's center is located at (-4, -11) and has a radius of 10</span>
Lacking information on the proportion, we will assume the sample proportion is 0.50
thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)
The calculation for the margin of error when estimating population proportions follows:
Consequently, 271 students need to be part of the sample.
36 divided by 6
which results in 6
then multiply 6 x 5
which gives 30
your final answer is: 30
*HOPE I HELPED!*
