10 boxes of paper at 6 lbs each = (10 * 6) = 60 lbs
36 boxes of pens at 12 oz each = (36 * 12) = 432 oz.
there are 16 oz in 1 lb....so 432 oz = (432/16) = 27 lbs.
so we have a total weight of (60 + 27) = 87 lbs
shipping charges : $ 12 for first 20 lbs, $ 10 for the next 30 lbs....so thats 50 lbs...leaving 37 lbs at 0.50 per lb = 37(0.50) = $ 18.50
for a total of : 12 + 10 + 18.50 = $ 40.50 <==
Using it's concept, the range of the given exponential function is:
C. 0 < y ≤ 46638.
<h3>What is the range of a function?</h3>
The range of a function is the set that contains all possible output values for the function.
In this problem, the function is:
y = 46,638(0.78)^x.
It is an exponential function with initial value 46,638 and rate of change 0.78. Exponential functions that are not shifted down, such as this one, are never negative nor zero, hence the range also has the restriction y > 0, and is given by:
C. 0 < y ≤ 46638.
More can be learned about the range of a function at brainly.com/question/28388172
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a) Parallel for both line segments have the same slope = -5/4
b) 55º
Step-by-step explanation:
a) To verify the parallelism of these line segments, It's necessary to find the slope of each one. Parallel lines share the same slope value:

b) If ∠DAB = 125°, what is the measure of ∠CBA? Justify your reasoning.
Those beams do not form a parallelogram because:
Using the formula of distance between those points

So this is a trapezoid. And two adjacent angles within a trapezoid are supplementary, so If ∠DAB = 125º then 180 - ∠CBA=55º
An isosceles triangle is a special triangle having at least 2 equal sides equal. But in this case, since all sides are equal having a length of 15 inches, this is actually an equilateral triangle.
When you create a perpendicular bisector from the top vertex to the midpoint of the base, you get a right triangle with the hypotenuse equal to 15 inches, a base equal to half of 15 because it was bisected, and the height. Therefore, we use the pythagorean theorem. The solution would be
h = √(15)^2 +(15/2)^
h = 13.0 meters