Figures R, S, and T are all scaled copies of one another. Figure S is a scaled copy of R using a scale factor of 3. Figure T is

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.

In this scenario, we'll define the following variables:

x: total volume of potting soil in liters.

y: quantity of potting soil allocated to each pot in liters.

To determine the number of pots, we can use the expression:

Substituting in the respective values yields:

Reformatting gives us:

When rounding down to the nearest whole number, we find:

The conclusion is:

Yao Xin is capable of filling 18 pots.

Answer:

final equation: 55,000 + 3,700n = 63,000 + 2,900n

Step-by-step explanation:

Blanca's current salary: 55,000

With an annual increase of $3,700, her salary after n years is 55,000 + 3,700n

Isabel's current salary: 63,000

With an annual increase of $2,900, her salary after n years is 63,000 + 2,900n

Setting the two salary equations equal gives:

55,000 + 3,700n = 63,000 + 2,900n

Answer:

We conclude that less than or equal to 50% of the student body supports him significantly.

Step-by-step explanation:

Mike, while campaigning for the student government presidency, is keen to determine if more than 50% of the student body supports him.

A random sample of 100 students was surveyed, with 55 expressing support for Mike.

Let p = the proportion of students backing Mike.

Thus, Null Hypothesis, : p 50% {indicating that the proportion of supporters among the student body is significantly less than or equal to 50%}

Alternate Hypothesis, : p > 50% {indicating that the proportion of supporters among the student body is significantly more than 50%}

The test statistics to be utilized here One-sample z proportion statistics;

T.S. = ~ N(0,1)

where, = the sampled proportion in favor of Mike = = 0.55

n = number of sampled students = 100

Therefore, test statistics =

= 1.01

The z test statistic is 1.01.

At a significance level of 0.05, the z table provides a critical value of 1.645 for a right-tailed test.

Given that our test statistic falls below the critical value of z (1.01 < 1.645), we lack sufficient evidence to reject the null hypothesis as it remains outside the rejection region, leading to failure to reject our null hypothesis.

As a result, we conclude that less than or equal to 50% of the student body is in favor of him or the proportion supporting Mike is not significantly greater than 50%.