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Of the students attending a school party, 60% of the students are girls, and 40% of the students like to dance. After these stud

elena-s [515]

Answer:

252 students at the party like to dance

Step-by-step explanation:

Given:

60% of the students are girls

40% of the students like to dance

20 more boy students

Percentage of the girls in the party = 58%

To Find:

How many students now at the party like to dance=?

Solution:

Let the number of girls be g.

Let the number of total people originally be t.

We know that

$\frac{g}{t}=\frac{60}{100}$

$\frac{g}{t}=\frac{3}{5}$ ----------------------------------(1)

We also know that

$\frac{g}{t+20}=\frac{58}{100}$

$\frac{g}{t+20}=\frac{29}{50}$ -----------------------------(2)

We now have a system of equation from (1) and (2)

3t=5g

$g = \frac{3t}{5}$ ------------------------(3)

50g=29t+580------------------------(4)

Substituting 3 in 4, we get

$50(\frac{3t}{5})=29t+580$

$(\frac{150t}{5})=29t+580$

$30t =29t+580$

$30t -29t = 580$

t =589

So originally there was 580 students

In this 580 students 40% liked to dance

Then the number of students liked to dance =

=> $40\% \text{of} 580$

=> $\frac{40}{100} \times 580$

=> $0.4 \times 580$

=> 232

We also know that with these people, 20 boys joined, all of whom like to dance.

Now the number of students like to dance = 232+20 = 252 students

7 0

3 years ago

At Sally's Hair Salon there are three hair stylists. 36% of the hair cuts are done by Chris, 26% are done by Karine, and the res

Marina86 [1]

Answer:

Probability that their hair was done by Amy is 0.475.

Step-by-step explanation:

We are given that Sally's Hair Salon there are three hair stylists. 36% of the hair cuts are done by Chris, 26% are done by Karine, and the rest are done by Amy.

Let the Probability of hair cutting done by Chris = P(C) = 0.36

Probability of hair cutting done by Karine = P(K) = 0.26

Probability of hair cutting done by Amy = P(A) = 0.368

Also, let NS = event that customer is not satisfied with his cutting

So, Probability that customers are not satisfied given that their hair cutting is done by Chris = P(NS/C) = 0.05

Probability that customers are not satisfied given that their hair cutting is done by Karine = P(NS/K) = 0.06

Probability that customers are not satisfied given that their hair cutting is done by Amy = P(NS/A) = 0.08

Now, a customer leaving the salon is selected at random. If the customer is not satisfied, the probability that their hair was done by Amy is given by = P(A/NS)

For finding the above probability we will use the concept of Bayes' Theorem;

SO, P(A/NS) = $\frac{\text{P(A) \times P(NS/A)}}{\text{P(C) \times P(NS/C) + P(K) \times P(NS/K) +P(A) \times P(NS/A) }}$ $\frac{P(A) \times P(NS/A) }{P(C) \times P(NS/C) +P(K) \times P(NS/K) +P(A) \times P(NS/A) }$