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Salsk061 [2.6K]
3 years ago
13

Every ninth person in line at a movie theater gets free popcorn. Every sixth person gets free apple juice. Shani says that the t

hirty-sixth customer will be the first customer to get both free popcorn and free apple juice. Is she right? If not,describe her mistake.
Mathematics
1 answer:
tresset_1 [31]3 years ago
8 0

We are told that every 9th person gets free popcorn and every 6th person gets free apple juice at the movie theater. We want to show if the 36th person is the first to get both free popcorn and apple juice.

Since every 9th gets free popcorn, then the 9th and 18th and 27th and 36th people get it. We can use numbers and show this as multiples of 9.

9, 18, 27, 36, 45, 54, ...

And we repeat it for every 6th and the free juice.

6, 12, 18, 24, 30, 36,....

Shani thinks 36 comes first, and she's wrong. 18 appears on the list before 36 as something that's common. What are we finding is the lowest common muliple of 6 and 9.

6 = 2 x 3

9 = 3 x 3

The lowest common multiple will have a 2, a 3, and a second 3 (because we don't double count). 2 x 3 x 3 = 18. This matches up to the list of multiples.


Thus, Shani is wrong that the 36th person gets both free items, as she did not account for the 18th person gettting both free items.

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LUAHLILULL-----
Ann [662]

x+y=19 and 6.5x+3y=74.5 can be used to determine the number of gifts wrapped and number of giftbags prepared where x represents the wrapped gifts and y represents giftbags.

Step-by-step explanation:

Let,

x be the gift wrapped with wrapping paper.

y be the gifts in gift bag.

Time for wrapping one gift = 6.5 minutes

Time for doing 1 gift bag = 3 minutes

Total gifts = 19

Total time = 74.5 minutes

According to given statement;

x+y=19

6.5x+3y=74.5

x+y=19 and 6.5x+3y=74.5 can be used to determine the number of gifts wrapped and number of giftbags prepared where x represents the wrapped gifts and y represents giftbags.

Keywords: linear equation, addition

Learn more about linear equations at:

  • brainly.com/question/788903
  • brainly.com/question/774670

#LearnwithBrainly

3 0
3 years ago
X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y
andriy [413]

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

<h3>What is normal random variables?</h3>

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}

Part b.

Consider V(3X + 2Y)

\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

3 X+2 Y \sim N(18,77)

Thus,

P(3 X+2 Y < 18)=0.5

Part d.

Consider P(3X + 2Y < 28)

Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}

\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

brainly.com/question/23836881

#SPJ4

The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

8 0
2 years ago
Write to explain 44 - 9
timama [110]
44 - 9 = 35

If we have 44 apples and we take away 9, we have 35 left.
5 0
3 years ago
Read 2 more answers
Which expression is equivalent to 4(3n-5)?​
iren2701 [21]

Answer: 12n - 20

Step-by-step explanation:

3 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs.
Aliun [14]

Answer:

i think its 24

Step-by-step explanation:

2=2

8 0
2 years ago
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