A survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it

(a) The likelihood that all 5 eggs chosen are unspoiled is 0.0531. (b) The probability that 2 or fewer out of the 5 eggs are unspoiled is 0.3959. (c) The probability that more than 1 of the selected 5 eggs are unspoiled is 0.8747. Step-by-step explanation: The complete query is: A subpar carton of 18 eggs has 8 that are spoiled. An unsuspecting chef selects 5 eggs at random for his “Mega-Omelet Surprise.” Calculate the probability of receiving (a) exactly 5 unspoiled eggs, (b) 2 or fewer, and (c) more than 1 unspoiled egg. Define X = number of unspoiled eggs. In the faulty carton, 8 eggs are spoiled. The probability of selecting an unspoiled egg is independent of others. Provided that a chef randomly picks 5 eggs, the variable X follows a Binomial distribution with parameters n = 5 and p = 0.556. Success is defined as selecting an unspoiled egg. The probability mass function of X is as follows: (a) Calculate the probability of selecting all unspoiled eggs. Thus, this probability is found to be 0.0531. (b) For 2 or less unspoiled eggs, the probability is computed: P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2), resulting in a probability of 0.3959. (c) For more than 1 unspoiled egg: P (X > 1) = 1 - P (X ≤ 1), yields a final probability of 0.8747.

Answer: Distance between parent and coach is 24.05m

Step-by-step explanation:

The angle of sight from coach to the ground (θ) = 38°

The angle of sight from the parent to the ground (θ) = 30°

The diving platform height = 10m

Calculating the horizontal distance (x) from coach to Melanie:

Tanθ = opposite / adjacent

Tan 38° = 10 / x

x = 10 / 0.7812856

x = 12.79m

Horizontal distance (y) from parent to Melanie:

Tanθ = opposite / adjacent

Tan 30° = 10 / y

y = 10 / 0.5773502

y = 17.32m

Angle at the diving platform base between coach and parent = 105°

To find the distance (a) from coach to parent, we use the cosine law.

a^2 = x^2 + y^2 - 2bcCosA

Here, a, b, and c denote side lengths, and A is the angle between them

Thus,

a^2 = 12.79^2 + 17.32^2 - 2(12.79)(17.32)Cos105°

a^2 = 163.5841 + 299.9824 − (-114.6686)

a^2 = 163.5841 + 299.9824 + 114.6686

a^2 = 578.2351

a = √578.2351

a = 24.046519

a = 24.05m

500 = 2.5x + 200, x denotes the number of desserts. Rearranging gives 500 - 200 = 2.5x, leading to 300 = 2.5x. Consequently, x = 120. Therefore, the answer is C.

The proportion of defective items bypassing both inspectors is =

Step-by-step explanation:

Step 1; Let's say the likelihood of the first inspector not spotting a defective item is P(A), while P(B) is the chance that the second inspector overlooks those that have passed the first inspector. Step 2; Given that P(A) equals 0.1, we convert it into a fraction to ensure our final probability is a fraction as well.P(A) = 0.1 =

.

Since the second inspector fails to detect 5 out of 10 that go past the first inspector, thus P(B) =

.

Step 3; To determine the probability of both inspectors missing a defective item, we multiply the two probabilities together.P(A and B happening)

= P(A) × P(B) =

× = = =

0.05%

. Thus, the chance of both inspectors missing a defective part is a mere 0.05% chance.