Answer:
Step-by-step explanation:
At this price, the store sells 100 men's hats per week. The owner estimates that for every $1 increase in price, one fewer men's hat is sold per week
Answer:
3 x 6 = 18
6 x 3 = 18
18/6=3
18/3=6
Step-by-step explanation:
Use distributive property:
16. 5k(3 - 4k)
15k - 20k^2
18. 6g^2(g - 8)
6g^3 - 48g^2
20. -2n^2 (5n - 9 + 4n^2)
-10n^3 + 18n^2 - 8n^4
Using the combination formula, it is found that:
a) 180 different starting lineups can be created.
b) The probability that mary and alice will get on the lineup is
.
The order in which the players are chosen is not important, hence the <em>combination formula </em>is used to solve this question.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
Item a:
The lineup is composed by:
- 2 guards from a set of 5.
- 2 forwards from a set of 4.
- 1 center from a set of 3.
Hence the number of lineups is given by:
![N = C_{5,2}C_{4,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{4!}{2!2!} \times \frac{3!}{1!2!} = 180](https://tex.z-dn.net/?f=N%20%3D%20C_%7B5%2C2%7DC_%7B4%2C2%7DC_%7B3%2C1%7D%20%3D%20%5Cfrac%7B5%21%7D%7B2%213%21%7D%20%5Ctimes%20%5Cfrac%7B4%21%7D%7B2%212%21%7D%20%5Ctimes%20%5Cfrac%7B3%21%7D%7B1%212%21%7D%20%20%3D%20180)
Item b:
The number of lineups with Mary and Alice are given as follows:
- 2 guards from a set of 5.
- Mary and 1 other forward from a set of 3.
Hence:
![n = C_{5,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{3!}{1!2!} = 30](https://tex.z-dn.net/?f=n%20%3D%20C_%7B5%2C2%7DC_%7B3%2C1%7D%20%3D%20%5Cfrac%7B5%21%7D%7B2%213%21%7D%20%5Ctimes%20%5Cfrac%7B3%21%7D%7B1%212%21%7D%20%3D%2030)
Hence the probability is given by:
![p = \frac{30}{180} = \frac{1}{6}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B30%7D%7B180%7D%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
The probability that mary and alice will get on the lineup is
.
More can be learned about the combination formula at brainly.com/question/25821700
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Answer:
b= (m)(-150)
Step-by-step explanation:
1800-1350 = 450
450/3 = 150
b= m*-150