1
2
3
Step-by-step explanation: Generally, during the roll of two fair 6-sided dice, the doubles result in (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6). Therefore, the total for doubles is N = 6. The outcome of rolling two fair 6-sided dice yields n = 36. Thus, the probability of rolling doubles (matching numbers on both dice) is calculated mathematically. When rolling two fair dice, outcomes that sum to 4 or less are (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1). Observing this, we see two doubles present. Consequently, the conditional probability of rolling doubles is represented mathematically. Lastly, when rolling the two fair dice, outcomes that show different numbers result in L = 30, while outcomes where at least one die shows a 1 give W = 10. Hence, the conditional probability of having at least one die show a 1 is presented mathematically.
1. Angle DEF
2. Definition of congruent angles
3. Measure of angle GHI
Answer:
The correct answer is;
A. 0.17
Step-by-step explanation:
Here are the provided details;
The average time taken for a cashier to handle an order, μ = 276 seconds
The deviation from the average, σ = 38 seconds
The z-score for an order processing time of x = 240 seconds can be calculated as follows;

Thus;

The resulting probability
P(z = -0.9474) = 0.17361
Hence, the estimated proportion of orders processed in under 240 seconds is roughly 0.17361 or 0.17 when rounded to two decimal places.
C. -31m⁴n - 8m²Step-by-step explanation:Given:(9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)Required:Identify an equivalent expression for itSolution:Distributing the negative sign across the parentheses results in:9mn - 19m⁴n - 8m² - 12m⁴n - 9mnNext, we combine like terms:9mn - 9mn - 19m⁴n - 12m⁴n - 8m²This simplifies to -31m⁴n - 8m²Thus, -31m⁴n - 8m² is the equivalent expression for (9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn).
Lacking information on the proportion, we will assume the sample proportion is 0.50
thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)
The calculation for the margin of error when estimating population proportions follows:
Consequently, 271 students need to be part of the sample.