Part A:
Given that a<span>t a gymnastics meet, twenty gymnasts compete for first, second, and third place. The number of ways </span><span>first, second, and third place can be assigned</span><span> is given by
![^{20}P_3= \frac{20!}{(20-3)!} \\ \\ = \frac{20!}{17!} =20\times19\times18 \\ \\ =6,840\ ways](https://tex.z-dn.net/?f=%20%5E%7B20%7DP_3%3D%20%5Cfrac%7B20%21%7D%7B%2820-3%29%21%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B20%21%7D%7B17%21%7D%20%3D20%5Ctimes19%5Ctimes18%20%5C%5C%20%20%5C%5C%20%3D6%2C840%5C%20ways)
Part B:
</span>Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the t<span>hird place has been announced the number of ways that the remaining two places can be assigned</span> is given by :
<span>
![^{19}P_2= \frac{19!}{(19-2)!} \\ \\ = \frac{19!}{17!} =19\times18 \\ \\ =342\ ways](https://tex.z-dn.net/?f=%20%5E%7B19%7DP_2%3D%20%5Cfrac%7B19%21%7D%7B%2819-2%29%21%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B19%21%7D%7B17%21%7D%20%3D19%5Ctimes18%20%5C%5C%20%20%5C%5C%20%3D342%5C%20ways)
</span>
Part C:
Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the third and second places have been announced the number of ways that the <span>first place</span> can be assigned is given by :
Answer: 8x=-2
The steps are in the photo below
ANSWER:
$9.0.
Each person will owe $9.0.
STEP-BY-STEP SOLUTION:
Total amount of people:
= 3
Total bill:
= $31.84
Discount off total bill:
= 15%
Total bill after discount:
= 31.84 × ( 100% - 15% )
= 31.84 × 85%
= 27.064
Total bill after discount split evenly / Amount each person will owe:
= 27.064 ÷ 3
= 9.0213 ( 3 repeater )
= $9.0 ( rounded to the nearest tenth )
Answer:
Lines stay parallel or overlap
Step-by-step explanation:
AB and CD are parallel lines
Rotation around a point 90 degrees clockwise will make these lines perpendicular to their initial position but AB and CD will still be parallel to each other
They will overlap if the distance between them and point E is equal
Their initial slope is same and equal to m
Their final slope will be -1/m as a result of 90 degrees rotation