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andrey2020 [161]
2 years ago
12

Help please and thank you

Mathematics
1 answer:
gulaghasi [49]2 years ago
3 0

Answer:

56

Step-by-step explanation:

Missing length = x + 21

Based on the Three Parallel Lines Theorem, we have:

x/21 = 20/12

Cross multiply

x*12 = 20*21

12x = 420

12x/12 = 420/12

x = 35

✅Missing length = x + 21

Plug in the value of x

= 35 + 21

= 56

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Read 2 more answers
A city council consists of seven Democrats and five Republicans. If a committee of four people is selected, find the probability
Hoochie [10]

Answer:

The probability  of selecting two Democrats and two Republicans is 0.4242.

Step-by-step explanation:

The information provided is as follows:

  • A city council consists of seven Democrats and five Republicans.
  • A committee of four people is selected.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!\times (n-k)!}

Compute the number of ways to select four people as follows:

{12\choose 4}=\frac{12!}{4!\times (12-4)!}=495

Compute the number of ways to selected two Democrats as follows:

{7\choose 2}=\frac{7!}{2!\times (7-2)!}=21

Compute the number of ways to selected two Republicans as follows:

{5\choose 2}=\frac{5!}{2!\times (5-2)!}=10

Then the probability  of selecting two Democrats and two Republicans as follows:

P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242

Thus, the probability  of selecting two Democrats and two Republicans is 0.4242.

6 0
2 years ago
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