Answer:
2.5 seconds after the initial ball was struck.
Step-by-step explanation:
The height equations are:
At the point where the balls intersect, both heights are alike, therefore:
-16t² + 56t = -16t² + 156t - 248
-16t² + 56t + 16t² - 156t + 248 = 0
- 100t + 248 = 0
248 = 100t
t = 248/100
t = 2.48 ≈ 2.5
Response
The first diagram displays angles 1 and 2 as vertical angles.
Clarification
In all four diagrams, the initial one illustrates the vertically opposite angles.
Angles 1 and 2 are classified as vertically opposite because they face each other.
These angles maintain equal measurement when two lines intersect, resulting in four angles where two pairs of vertically opposite angles are formed.
In contrast, all other figures depict angles 1 and 2 as adjacent angles.
The cake board’s circumference measures 35π cm. Initially, noting the cake's diameter of 30 cm, the board's diameter is established as an additional 5 cm, leading to circumference determination by applying the formula, yielding 35π cm.
The formula for determining the number of ways to select two pairs of sneakers from three pairs labeled A, B, and C is represented by 3C2 (3 combinations of 2), which calculates as 3! / (2!(3 - 2)!) = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3. Therefore, the sample space is S = {AB, AC, BC}.
The test statistic (Z) is 2.5767, and the p-value of the test is 0.009975. The null hypothesis suggests that the smoking rate among students has not changed, while the alternative indicates otherwise. The z-statistic for the sampled proportion is computed, yielding z ≈ 2.5767. As we investigate whether the smoking percentage has shifted over the preceding five years, the two-tailed p-value is found to be 0.009975. This result is significant at a 99% confidence level, demonstrating substantial evidence that the percentage of smoking students has changed.
