A board 120 inches long is divided into 2 sections. If the ratio of the 2 sections is 3:5, what are the lengths of the sections?
1 answer:
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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.
Answer:
$110.
Step-by-step explanation:
Let x represent the cost of the item that Carmen bought from the department store.
Carmen possesses $30 in store bucks along with a 25% discount coupon for a local department store. Our goal is to determine the maximum cost for Carmen's purchase such that after applying her store bucks and discount, her total remains at or below $60 before sales tax.
Since the $30 in store bucks is deducted prior to applying the 25% discount, we need to find x such that x - 30 minus 25% of (x - 30) must be less than or equal to 60. This can be set up as an equation:
Thus, Carmen's purchases should total no more than $110 before sales tax.