Before the last school year began, it was estimated that the average discretionary personal expenses each school year for a stud

Answer:

You need to purchase 3 shirts to be able to use your coupon.

Step-by-step explanation:

Each shirt originally costs $17.99.

There is a 20% discount on this specific brand of shirts.

$17.99 × 0.2 = $3.60 (discount per shirt)

Subtracting the discount from the original price:

$17.99 - $3.60 = $14.39 (price per shirt after discount)

To qualify for the $10 off coupon which requires a $40 minimum purchase:

$40 ÷ $14.39 ≈ 2.779, rounded up to 3 shirts

Therefore, you must buy 3 shirts.

3 shirts × $14.39 = $43.17, surpassing the $40 minimum needed to apply the $10 discount.

Solution:

Let x be the distance in miles from the house to the theater.

Total time taken for the trip

Then average speed

Terrence walks at a speed of 2 miles per hour to the theater and returns home at 40 miles per hour.

Thus, Average Speed mi/hr

Both average speeds must be equivalent. Hence, we can express this as:

Consequently, the distance from home is 13.125 miles.

Answer:

The initial goal was $25019.154.

Step by step Explanation:

Assuming the original goal is denoted as x.

As stated

Another Kickstarter initiative for an iPad stylus secured 1,253% of its target, accumulating a total of $313,490.

1253% can be expressed as a decimal.

= 12.53

Thus, the equation is rearranged to

12.53 × x = 313490

12.53x = 313490

x = $ 25019.154

This means the initial goal stands at $25019.154.

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.

To plot the two functions, you need to assign values for x. By selecting various x values, corresponding y values are calculated. You then plot the points as shown. The blue line illustrates the function f(x) = 3x, while the orange line indicates f(x) = -x + 4.

These two lines intersect at the coordinates (1,3). To solve for this analytically, we establish the system of equations:

y = 3x
y = -x + 4

By setting these two equations for y equal to each other:

3x = -x + 4
4x = 4
x = 1

Next, substituting x into one of the original equations gives us: y = 3x = 3(1) = 3. Therefore, the solution is (1,3), meaning at a temperature of 3 units, the number of visitors entering matches those exiting the zoo, indicating a balance of one person entering for each one leaving.