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juin [17]
2 years ago
5

Calculate the number of subsets and the number of proper subsets for the set.

Mathematics
1 answer:
arlik [135]2 years ago
6 0

A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 <em>proper</em> subsets.

The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.

Just to illustrate the claim, we have

• subsets of size 0 (1 of these):

{ } (empty set)

• subsets of size 1 (4 of these):

{1/6}, {1/7}, {1/8}, {1/9}

• subsets of size 2 (6 of these):

{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}

• subsets of size 3 (4 of these):

{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}

• subsets of size 4 (1 of these):

{1/6, 1/7, 1/8, 1/9}

and the last one is the only subset that is not a proper subset, because that subset = the set.

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You can rewrite that as:

a^2-4ab+6ab-24b^2  then factor 1st and 2nd pair of terms.

a(a-4b)+6b(a-4b) so you have

(a+6b)(a-4b)
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Simify
Harlamova29_29 [7]

Step-by-step explanation:

1. -9x - 3 - 3 + 2x

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2 years ago
Heather makes $6.50 per hour. Every three months, she is eligible for a 2% raise. How much will she make after 2 years if she ge
sammy [17]

Answer:

$7.62 per hour


Step-by-step explanation:

Since, Heather gets a raise every 3 months, in 2 years, she will get a raise 8 times (2years = 24 months, 24 divided by 3 is 8).

Now it becomes a compound growth problem. We can use the formula shown below to solve these type of problems.

F=P(1+r)^t

Where,

  • F is the future value (what we want to find)
  • P is the present rate ($6.5)
  • r is the rate of growth, in decimal (2% growth means 0.02)
  • t is the time frame, number of times compounding occurs (for our case we have figured it to be 8)

<u>Now plugging in all the info, we get the value of F:</u>

F=P(1+r)^t\\F=6.5(1+0.02)^8\\F=6.5(1.02)^8\\F=7.62


Thus, after 2 years, Heather's hourly rate will be $7.62


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vesna_86 [32]

Answer:

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Step-by-step explanation:

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