Answer:
Volume of the shaded area = (600 - 36π) units³
Step-by-step explanation:
Volume of the shaded area = Volume of pyramid - Volume of cone
Volume of pyramid = ⅓*l*w*h
Where,
l = length of the base of the pyramid = 15 units
w = width of the base of the pyramid = 10 units
h = height of pyramid = 12 units
Substituting the values helps find the volume of the pyramid
Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³
Volume of Cone = ⅓πr²h,
Where,
r = radius = ½ of diameter = ½ of 9 = 3 units
h = height = 12 units
Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12
= π*3*12 = 36π units³
Volume of shaded area = (600 - 36π) units³
Answer:
$110.
Step-by-step explanation:
Let x represent the cost of the item that Carmen bought from the department store.
Carmen possesses $30 in store bucks along with a 25% discount coupon for a local department store. Our goal is to determine the maximum cost for Carmen's purchase such that after applying her store bucks and discount, her total remains at or below $60 before sales tax.
Since the $30 in store bucks is deducted prior to applying the 25% discount, we need to find x such that x - 30 minus 25% of (x - 30) must be less than or equal to 60. This can be set up as an equation:
Thus, Carmen's purchases should total no more than $110 before sales tax.
Answer:
StartFraction negative 1 Over k cubed EndFraction
Detailed breakdown:
3k / (k + 1) × (k² - 1) / 3k³
= 3k(k² - 1) / (k + 1)(3k³)
= 3k³ - 3k / 3k⁴ + 3k³
= -3k / 3k⁴
= -1/k³
StartFraction k + 1 Over k squared EndFraction
(k + 1) / k²
StartFraction k minus 1 Over k squared EndFraction
(k - 1)/k²
StartFraction negative 1 Over k cubed EndFraction
= -1/k³
StartFraction 1 Over k EndFraction
= 1/k
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Answer: Acquire a systematic sample by selecting every 20th vehicle that travels past (irrespective of the lane or direction).
Step-by-step explanation:
