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Oksi-84 [34.3K]

3 years ago

11

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 apple juice. Is she right? If not, describe her mistake

1 answer:

uysha [10]3 years ago

8 0

No, Shani is not right.
The 1st customer to get popcorn and apple juice is the 18th customer.
She missed that 18 is a common multiple of 6 & 9

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lions [1.4K]

Answer:

$1 \to 22 \to 0.176$

$2 \to 13 \to 0.104$

$3 \to 18 \to 0.144$

$4 \to 29 \to 0.232$

$5 \to 37 \to 0.296$

$6 \to 6 \to 0.048$

Step-by-step explanation:

Given

$n = 125$

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

$Pr = \frac{Frequency}{n}$

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

$Pr(2) = \frac{13}{125} = 0.104$

$Pr(4) = \frac{29}{125} = 0.232$

$Pr(6) = \frac{6}{125} = 0.048$

When the frequency is to be calculated, we use:

$Pr = \frac{Frequency}{n}$

$Frequency = n * Pr$

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

$Frequency(3) = 125 * 0.144 = 18$

$Frequency(5) = 125 * 0.296 = 37$

For roll of 1 where the frequency and the probability are not known, we use:

$Total \ Frequency = 125$

So:

Frequency(1) added to others must equal 125

This gives:

$Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125$

$Frequency(1) + 103 = 125$

Collect like terms

$Frequency(1) =- 103 + 125$

$Frequency(1) =22$

The probability is then calculated as:

$Pr(1) = \frac{22}{125}$

$Pr(1) = 0.176$

So, the complete table is:

$1 \to 22 \to 0.176$

$2 \to 13 \to 0.104$

$3 \to 18 \to 0.144$

$4 \to 29 \to 0.232$

$5 \to 37 \to 0.296$

$6 \to 6 \to 0.048$

5 0

2 years ago

1. Find the probability of this set of independent events. rolling a six on the first roll of a 1-6 number cube and rolling an o

jeyben [28]

For the first question, the chance of rolling a six is a 1/6 chance because there is one six and six different sides that could be rolled. As a percent, it would be 16.6 %. The probability of rolling an odd number on the second roll would be a 3/6 chance, which as a percent is 50 %. For the second question, both probabilities are 33 % because in both instances you are drawing three cards from nine total, so it would be 3/9. For the third question, the probability of drawing a blue marble is 3/5, because there are three blue marbles and five total marbles. As a percent, this is 60 %. Following this up with a green marble would be 2/4, because there are now 2 green marbles and four total marbles. One of the marbles was not replaced, so we have one less marble. 2/4 as a percent is 50%.

7 0

2 years ago

Which of the following statements describes one part of completing the square for x 2 + 4x = 32?

Westkost [7]

SOS:

Answer:

Take the square root of 36 and subtract 2.

Step-by-step explanation:

$x^2+4x=32\\(\frac{1}{2}*4=2; 2^2=4) : x^2+4x+4=36\\\sqrt{(x+2)^2}=\sqrt{36}\\ x+2=±6: -2+6=4, -2-6=-8$

<em>Hope this helps!!</em>

7 0

2 years ago

23% of 75 is what number?

Nonamiya [84]

Answer:

17.25 or 69/4 as a fraction

Step-by-step explanation:

use the desmos scientific calculator :) hope this helped

5 0

2 years ago

The areas of two similar octagons are 9 m² and 25 m². What is the scale factor of their side lengths? PLZ HELP PLZ PLZ PLZ

torisob [31]

Answer:

$\frac{3}{5}$

Step-by-step explanation:

Let the side length for the octagon having 9m² as area = x

Side length for the octagon having area of 25m² = y.

Thus:

$\frac{9}{25} = (\frac{x}{y})^2$ (area of similar polygons theorem)

The scale factor of their sides would be $\frac{x}{y}$ . Which is:

$\sqrt{\frac{9}{25}} = \frac{x}{y}$

$\frac{\sqrt{9}}{\sqrt{25}} = \frac{x}{y}$

$\frac{3}{5} = \frac{x}{y}$

Scale factor of their sides = $\frac{3}{5}$

6 0

2 years ago