In the trapezoid at the right, BE= 2x-8, DE= x-4, and AC= x+2

Answer:

The answer is option (A).

Step-by-step explanation:

Let X represent the count of orange milk chocolate M&M’s.

The proportion of orange milk chocolate M&M’s is defined as p = 0.20.

In a small bag containing milk chocolate M&M’s, n is established at 55.The occurrence of an orange milk chocolate M&M is independent of the remaining candies.

The random variable X conforms to a Binomial distribution characterized by parameters n = 55 and p = 0.20.

Calculating the average number of orange milk chocolate M&M’s in a package of 55 candies proceeds as follows:

It is noted that in a randomly selected pack of milk chocolate M&M's there were 14 orange M&M's, indicating that the ratio of orange milk chocolate M&M's in that selection was 25.5%.

This ratio is not unexpected.

This is due to the expected count of orange milk chocolate M&M’s in a 55 candy bag being estimated at 11. Therefore, encountering 14 orange milk chocolate M&M’s does not seem unusual.

Unusual instances typically have exceedingly low probabilities, specifically below 0.05.

To calculate the probability of having P (X ≥ 14), follow the subsequent calculation:

The likelihood of obtaining 14 or more orange candies in a milk chocolate M&M’s bag is 0.1968.

This probability is considerably higher than 0.05.

Thus, the correct answer is option (A).

Given that the salt concentration in a 125 ml salt solution is at 20%, it indicates a salt to water ratio of 20:80, which simplifies to 1:4.

Consequently, the salt quantity in the 125 ml 20% solution can be calculated as 20% of 125, yielding 0.2 x 125 = 25 ml, and therefore, the water content amounts to 125 - 25 = 100 ml.

When adding 25 ml of water to this 20% salt solution, the total water becomes 100 + 25 = 125 ml while the salt quantity remains at 25 ml.

Thus, the new total volume of the solution is 125 + 25 = 150 ml, leading to a salt proportion in the updated mixture of 25/150 = 0.1667.

As a result, the concentration of the new solution <span>after mixing 25 ml of water with 125 ml of a 20% salt solution is 16.67%</span>