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katrin [286]
3 years ago
5

The newly elected president needs to decide the remaining 6 spots available in the cabinet he/she is appointing. If there are 10

eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer: There are 151,200 ways the members can be appointed.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 10

Number of remaining spots available = 6

Here, rank matters.

so, we will use "Fundamental theorem of counting or by Permutation":

So, Number of different ways the members can be selected is given by

^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200

Hence, there are 151,200 ways the members can be appointed.

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A movie studio surveyed married couples about the types of movies they prefer. In the survey, the husband and wife were each ask
Aleksandr [31]

Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:

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Out of the next 75 couples, the amount is:

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I need help with pre calculus.
fiasKO [112]

Answer:

  a) a = 7.37, b = 15.13, C = 67°

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Step-by-step explanation:

<h3>a)</h3>

Two angles and one side are given. That means the triangle is uniquely determined, and the remaining sides can be found from the Law of Sines.

The third angle is ...

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Then the Law of Sines tells you ...

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__

<h3>b)</h3>

Ordinarily, when the given angle (B = 30°) is opposite the shorter of the given sides (b = 10 < a = 20), it means there are two possible solutions to the triangle.

However, when the sine of the angle is exactly equal to the ratio of the given sides: sin(30°) = 10/20 = 1/2, the larger angle can only be 90°. That is, the one triangle that can be formed is a right triangle.

The Law of Sines tells you this.

  sin(A)/a = sin(B)/b

  sin(A) = (a/b)sin(B) . . . . . . multiply by 'a'

  A = arcsin(a/b·sin(B)) = arcsin(20/10·sin(π/6)) = arcsin(1)

  A = 90°

 

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2 years ago
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