A restaurant uses 3 pounds of pasta for a party of 14 people. If they are cooking pasta for a party of 56 people, what should they do?

Answer:

Both bottles holds same amount of juice.

Step-by-step explanation:

We have been given that a bottle of orange juice holds quart of juice. A bottle of pineapple juice holds quart of juice. We are asked to which bottle has more juice.

First of all, we will reduce the fraction representing orange juice to lowest terms as shown below:

Since both fractions are equivalent, therefore, both bottles hold same amount of juice.

Final answer:

Using the binomial probability formula, the probability that exactly 1 out of 6 seeds doesn't grow is approximately 0.119 or 11.9%.

Explanation:

This question revolves around the concept of binomial probability. The binomial distribution model is an appropriate statistical model here since there are a fixed number of trials (6 seed plantings), each trial (seed planting) is independent, and each trial results in one of two outcomes: success (plant grows) or failure (plant doesn’t grow).

The binomial probability formula is P(X=k) = C(n, k)*(p^k)*(q^(n-k)), where 'n' is the number of trials (6 in this case), 'k' is the number of 'successes' we're interested in (5 in this case, since we want only 1 seed - out of 6 - not to grow), 'p' is the probability of success, and 'q' is the probability of failure.

Here, to calculate the probability, p (probability of successful growth) is 0.75 and q (probability of not growing) is 0.25 (= 1 - 0.75).

So, P(5 plants grow and 1 doesn’t) = C(6, 5) * (0.75^5) * (0.25^1) = 0.119.

So, the probability that exactly 1 out of 6 seeds does not grow is approximately 0.119 or 11.9%. This scenario is also known as binomial distribution scenario.

Learn more about Binomial Probability here:

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Answer:

9.72405%

Step-by-step explanation:

Binomial Probability

(N choose k) p^k (1-p)^(n-k)

N=7  seeds planted

p= 100% - 70% = 30% = 0.3 <--- we are interested in the plant NOT growing

(1-p) = 70% = 0.7  <--- 70% chance the plant will survive and grow

k=4  <--- we want four of them to fail

The probability is:

 (7 choose 4) * (0.3)^4  (0.7)^3 =

 7!/(4!3!) (0.3)^4 (0.7)^3  =

 (7*6*5/3*2) (0.3)^4 (0.7)^3 =

 7*5 (0.3)^4 (0.7)^3 =

 35 * 0.0081 * 0.343 = 0.0972405 = 9.72405%