"A gumball machine is in the shape of a sphere with a radius of 6 inches. A store manager wants to fill up the machine with mini

Answer:

Translate the circles so they align at a common center and subsequently enlarge circle Y using a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Let's describe how to approach this problem

- To establish that all circles are similar, a translation and a dilation factor are necessary to align one circle with another

- We can reposition the circles to coincide at the center and then expand one of the circles by the defined scale factor, with the center of dilation being the common point for all circles.

* Let's resolve the issue

∵ Circle X displays a radius of 6 units

∵ Circle Y has a radius of 2 units

- Initially, we shift the circles so they coalesce at a central point

∴ We utilize translation to place the centers of both circles at the same location

- Determine the dilation factor based on the different radii of the circles

∵ The radius of circle X measures 6 units

∵ The radius of circle Y measures 2 units

∴ Therefore, the scale factor is calculated as 6/2 = 3

∴ Enlarge circle Y by a scale factor of 3

* The actions that affirm the circles are similar are as follows;

  Translate the circles so they share a common center point, and

  enlarge circle Y by a factor of 3.

A vacuous proof has been employed. The proposition p(n) states: "if n is a positive integer greater than 1, then n² > n." To prove p(0), it translates to "if 0 is a positive integer greater than 1, then 0² > 0." Since the premise stating that "0 is a positive integer greater than 1" is false, the overall implication holds true. This exemplifies that in vacuous proof, if a statement's premise is false, the implication remains trivially true.

To determine how many cans of paint Paula requires, first find out the coverage area for one can. After that, divide 24 square feet by the coverage area of the paint can to calculate the number of cans needed.

Answer:

Step-by-step explanation:

Let’s consider that the amount deposited, C dollars, generates r% simple interest each year.

After a span of t years, the value of the deposited C dollars reaches D dollars; our task now is to formulate a relationship using these variables to find t.

We can express this relationship through the simple interest formula:

⇒

⇒

⇒

Thus, this yields the formula for t. (Answer)