Tickets to a musical cost $15 for adults and $6 for students. Mr. James and Mrs. Reagan are taking their classes to the musical. If 8 adults, including the teachers, went along as chaperones and the total cost for the combined classes to attend the musical was $480, how many students attended the musical?

Answers

Answer 1

Answer: The answer to your question is 9

Answer 2

Answer: that is not the answer, the answer is 60 students... what I did was 8x15 to get 120, then I subtracted 480-120 to get 360. 360 is the amount of money the kids cost. Finally I divided 360 by 6 to get 60 because each student was 6$

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Consider an experiment where two 6-sided dice are rolled. We can describe the ordered sample space as below where the first coordinate of the ordered pair represents the first die and the second coordinate represents the second die. If the dice are ‘fair’, then all 36 of these possible outcomes are equally likely. 28. Describe the event E that the sum of the two dice is 5. 29. Find P(E). 30. Let F be the event that the number of the first die is exactly 1 more than the number on the second die. Find P(F|E)

Answers

Answer:

$E$ = { (4,1) , (3,2) , (2,3) , (1,4) }

$P(E)=(1)/(9)$

$P(F|E)=(1)/(4)$

Step-by-step explanation:

Let's start writing the sample space for this experiment :

$S=$ { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6) , (5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6) }

Let's also define the event $E$ ⇒

$E$ : '' The sum of the two dice is 5 ''

We can describe the event by listing all the favorables cases from $S$ ⇒

$E$ = { (4,1) , (3,2) , (2,3) , (1,4) }

In order to calculate $P(E)$ we are going to divide all the cases favorables to $E$ over the total cases from $S$ . We can do this because all 36 of these possible outcomes from $S$ are equally likely. ⇒

$P(E)=(4)/(36)=(1)/(9)$ ⇒

$P(E)=(1)/(9)$

Finally we are going to define the event $F$ ⇒

$F$ : '' The number of the first die is exactly 1 more than the number on the second die ''

⇒

$F$ = { (2,1) , (3,2) , (4,3) , (5,4) , (6,5) }

Now given two events A and B ⇒

P ( A ∩ B ) = $P(A,B)$

We define the conditional probability as

$P(A|B)=(P(A,B))/(P(B))$ with $P(B)>0$

We need to find $P(F|E)$ therefore we can apply the conditional probability equation :

$P(F|E)=(P(F,E))/(P(E))$ (I)

We calculate $P(E)=(1)/(9)$ at the beginning of the question. We only need $P(F,E)$ .

Looking at the sets $E$ and $F$ we find that (3,2) is the unique result which is in both sets. Therefore is 1 result over the 36 possible results. ⇒

$P(F,E)=(1)/(36)$

Replacing both probabilities calculated in (I) :

$P(F|E)=(P(F,E))/(P(E))=((1)/(36))/((1)/(9))=(1)/(4)=0.25$

We find out that $P(F|E)=(1)/(4)=0.25$

Final answer:

When rolling two dice, there are 4 combinations that sum to 5. Hence, probability P(E) is 1/9. If considering the event F where the roll on the first die is 1 more than on the second die, it has 5 possible outcomes. So P(F) is 5/36. However, if event E has already happened, P(F|E) is 1/4.

Explanation:

The subject of this question is probability, which is part of Mathematics, specifically, it is a high school-level question. The event E described here is the scenario in which the sum of the numbers rolled on the two dice equals 5. There are 4 possibilities for this event: (1,4), (2,3), (3,2), and (4,1). As there are 36 possible outcomes when rolling two dice, the probability P(E) is 4/36 = 1/9.

Now considering event F where the number on the first die is exactly 1 more than the number on the second die, we have five possible pairs: (2,1), (3,2), (4,3), (5,4), (6,5). So the P(F) is 5/36. However, we're asked to find P(F|E), the probability of event F given that event E has occurred. Looking at the pairs that fit both conditions, we see that there is only one pair: (3,2). Therefore, P(F|E) is 1/4.

Learn more about Probability here:

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Find the product: -5(-3)(-3)

Answers

Answer:

-45

Step-by-step explanation:

Answer:

((−5)(−3))(−3)

=−45

hope this was helpful!

Pls help me with these equations 2x-7/3 = 5
4 (x - 5) = 3 (x - 7) + x + 1
5x + 2x - 9 = 7x + 11
6x - 12 + 4 (x - 7) = 5 (2x - 4) - 1
5x - 1/3 = 8

Answers

The answers to the questions

Last one is 3/4 hope this helps

Find the slope of the line passing through each of the following pairs of points. (−3, 9), (−3, −5

Answers

The formula of a slope:

$m=(y_2-y_1)/(x_2-x_1)$

We have the points (-3, 9) and (-3, -5). Substitute:

$m=(-5-9)/(-3-(-3))=(-14)/(-3+3)=(-14)/(0)\qquad\large{!!!!}\n\n\large\boxed{\text{Division by 0}}!!!$

Conclusion: The slope is not exist.

Given line is a horizontal line. Horizontal line has not a slope.

Answer:

Undefined Slope

Step-by-step explanation:

Well, we can first do (-5-9)÷[-3-(-3)].

We get -14/0.

We know anythingn divided by zero is impossible or undefined, so the answer to this is just undefined. If you can't enter it in your homework portal, then ask your teacher. Please don't report this, as I'm correct. Thank you!

DJ Davon is making a playlist for work; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 14 blues, 25 country, and 21 disco songs, and he wants to play an equal number of blues, country, and disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answers

Answer:

1.80 * 10^19

Step-by-step explanation:

If he has narrowed down his choices to 14blues, 25 country and 21 disco songs and he has to make a list of 12 songs with equal representation of each genre of song, the it means there will be 4 songs from each genre of music.

We select this 4 different songs using the combination formula for selection and multiply our results.

This means we have:

12C4 for blues,

25C4 for country

21C4 for disco.

This gives:

=12C4 * 25C4 * 21C4

= 495 * 12650 * 5985

And the order they can be played = 12!.

We then multiply the number of ways to get these songs by the order they can come in.

That is:

=495 * 12650 * 5985 * 12!

= 1.7951 * 10^19

= 1.80 * 10^19 (nearest hundredth).

Final answer:

DJ Davon can make approximately 3.57 x 10^21 different playlists, if he includes an equal number of blues, country, and disco songs. This calculation utilizes combination and permutation formulas.

Explanation:

DJ Davon wants to play an equal number of blues, country, and disco songs, which means he will play 4 songs from each genre. The number of ways to select 4 songs out of each genre is represented by the combination formula C(n,r) = n! / [r!(n-r)!].

So, for each genre, the number of ways to select 4 songs is:
Blues: C(14,4) = 1001
Country: C(25,4) = 12,650
Disco: C(21,4) = 5985.

After the songs are selected, the order of the playlist matters, so we use the permutation formula. Given 12 slots for the songs, the number of ways to order them is P(n) = n!, which for 12 is 479,001,600. The total number of different playlists is product of blues, country and disco song combinations and the permutations, which gives 3.57 x 10^21. This rounded to the hundredths place in scientific notation is 3.57 x 10^21.