A) Probability is a measure of how likely an event will happen. Here, we calculate the probability of X as:
P(X) = X/N, where X is the successful outcomes, and N is the total outcomes.
P(E) = E/N = 1033/2851 = 0.3623
P(R) = R/N = 854/2851 = 0.2995
P(D) = D/N = 964/2851 = 0.3381
B) Events E and D are mutually exclusive since students accepted early can't be deferred to the regular admission pool, hence, intersection P(E ∩ D) is 0.
C) The count of early accepted students is 1033, and the overall accepted students are 2375.
Thus, the probability is:
P = 1033/2375 = 0.4349
D) Reformulating the question: What’s the probability of being accepted if applying for early admission? Given that 18% of deferred students ultimately got accepted,
0.18 × 964 = 174 was admitted later.
Thus, the probability of being deferred and then accepted becomes:
P(DA) = 174/2831 = 0.0610.
The chance of randomly selecting a student early accepted or deferred then accepted is:
P(E or DA) = 0.0610 + 0.3623 = 0.4233, applying the addition rule.
The interest rate equals 25%
Explanation:
Provided data:
Principal amount, P = $2,000
Total amount, A = $2500
Duration, t = 1 year
Interest rate, r =?
We understand:
Substituting the known values gives:
Thus, the interest rate is 25%
To solve this problem, we need to convert the measurements so we can carry out the necessary calculations. A ton equals 2000 pounds, therefore, 3/4 ton translates to 1500 pounds. Since there are 16 ounces in a pound, 4 pounds and 14 ounces amounts to 4.875 pounds. To find the number of bricks, we divide:
number of bricks = 1500 lbs / 4.875 lbs
= 307.7
Consequently, this is the number of bricks required. The final answer is approximately.
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This represents a finite geometric series where n equals 4, a₁ is -144, and r is ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wish to calculate the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
