If an arrow is shot upward on Mars with a speed of 68 m/s, its height in meters t seconds later is given by

Response:

Step-by-step breakdown:

For the null hypothesis,

H0: p = 88

For the alternative hypothesis,

Ha: p < 88

In terms of population proportion, where the probability of success is p = 0.88

q represents the probability of failure = 1 - p

q = 1 - 0.88 = 0.12

Considering the sample,

Sample proportion, P = x/n

Where

x = number of successes = 21

n = total samples = 32

P = 21/32 = 0.66

Next, we determine the test statistic, which represents the z-score

z = (P - p)/√pq/n

z = (0.66 - 0.88)/√(0.88 × 0.12)/32 = - 3.83

The relevant p-value corresponds by referencing the normal distribution table for the area falling beneath the z-score. As a result,

P value = 0.00006

The value of x is 12. This can be found using the Pythagorean theorem with c equal to 13 and b equal to 5, where a equals x.

Apply the Pythagorean theorem
x^2 + x^2 = 2x^2
sqrt(2x^2)=x sqrt(2)

Response:

Congruent:  (x, y)→(x+3, y-4); (x, y)→(-x, -y)

Not Congruent:  (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)

Explanation in steps:

Transformations that yield congruent figures include translations, reflections, and rotations. In contrast, dilations result in figures that are not congruent.

The first transformation, (x, y)→(x+3, y-4), represents a translation 3 units right and 4 units down, leading to congruent figures since it merely shifts the figure.

The second transformation, (x, y)→(3x, 3y), indicates a dilation by a factor of 3, which enlarges the figure and therefore makes it non-congruent.

The third transformation, (x, y)→(0.4x, 0.4y), involves a dilation by a factor of 0.4, which shrinks the figure, leading to non-congruence.

The fourth transformation, (x, y)→(x/3, y/3), results in a dilation by a factor of 1/3, also shrinking the figure and rendering it non-congruent.

The fifth transformation, (x, y)→(-x, -y), reflects the figure, maintaining its size while modifying its orientation, thus ensuring congruence.

The linear equation in slope-intercept format representing the population of Jose's town is y = 320x + 2400. The town's population in 1995 was recorded at 2400, increasing to 4000 by 2000. By establishing x as the number of years since 1995, we derive the linear equation from the change in population per year.