You earned $62,715 this year and your Income tax calculator says you owe $8,818 in taxes. But you neglected to deduct $1,000 for

We need to specify the interval for numbers ranging from -5 to 4.

Moreover, we must exclude the values -1 and 4 from this range.

First, let’s note some crucial guidelines regarding interval notation.

It’s essential to identify which values are included and which ones are not in the specified range.

An open interval (or) indicates excluded numbers, while a closed interval [or] shows included numbers.

In this scenario, we notice three key numbers: -5, -1, and 4.

It is explicit that -1 and 4 are excluded, though -5 is not indicated as excluded, hence it remains included.

-1 lies between -5 and 4 on the number line.

Consequently, we can represent the interval notation from -5 to -1. (Note: -5 is included and -1 is not).

Thus, we write a closed interval " [ " on the left side of -5 and an open interval " ( " on the right side of -1. This gives us,

[-5, -1 ).

Next, we represent the interval from -1 to 4.

Since both endpoints are excluded, we will use open intervals ( ) on both sides of -1 and 4.

This results in the interval being

(-1,4).

We combine the two interval notations using the union symbol. So, the final interval representation is

[-5, -1 ) ∪ (-1,4).

To find the percent change over time, use the following formula: PR = Percent Rate, VPresent = Present or Future Value, VPast = Past or Present Value. The annual percentage growth rate is calculated by dividing the percent growth by N, which is the number of years. The calculation (415.79 - 200) / 200 * 100 results in 107.89. The annual percentage growth rate is then 107.89 divided by 15, which equals 7.193.

Answer:

(B) There is a single solution: x = 0.

Step-by-step explanation:

The equation that Kate is attempting to solve is:

Consequently, this equation results in one solution: x = 0.

Multiply 0.001 by 26 to arrive at the answer of 0.026.

Utilize the details to create inequalities that reflect each limitation or requirement.

2) Label the variables. 

c: count of color copies
b: count of black-and-white copies

3) Define each constraint:

i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>

3c + b ≤ 12
<span />

4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)

5) Here’s how to illustrate that:

i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.

ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.

iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.

iv) The concluding area is the overlap of the previously mentioned shaded regions.

v) The graph can be viewed in the attached figure.