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1 year ago

On my 30th birthday, I plan to light 30 candles on my cake and blow 30% of them. How many candles will stay lit after I'm done?

Mathematics

2 answers:

zloy xaker [14]1 year ago

8 0

30 candles=100%

30% of 100%= 9 candles out of 100 candles

after blowing out 30% of the candles, 9 should be left lit.

SashulF [63]1 year ago

6 0

You can set up an proportion like this:

———- = ————
You can use this way for future questions.

On the left denominator/bottom, place 100, as for percents it will always be 100. On the right denominator, place 30/ the whole. On the right numerator/top, place an x, as the part is unknown. On the right numerator, place 30%/The percent.
You multiply across, then divide what’s left over.
1) multiply: 30 candles x 30 = 900
2) divide: 900/100= 9

After you blow 30% of your 39 candles, you will have 9 candles that are still lit.

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1 year ago

Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small

Greeley [361]

Answer:

(a) $\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}$

P(1) = $\text{0.74} \times \text{(1 - 0.74)}^{1-1}$ = 0.74

P(2) = $\text{0.74} \times \text{(1 - 0.74)}^{2-1}$ = 0.192

P(3) = $\text{0.74} \times \text{(1 - 0.74)}^{3-1}$ = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

= 1 - 0.74 - 0.192 - 0.050

= 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

Mean = $\dfrac{p}{1-p}$ = $\dfrac{0.74}{1-0.74}$

= $\dfrac{0.74}{0.26}$ = 2.85 or 3 (approx).

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