According to the calculations made, 410 gumballs will be needed to fill the box.
Since you are trying to figure out how many gumballs you need to fill a 7.3 x 5.0 x 9.4 rectangular box for Halloween, and each gumball has a radius of 1/2 in, if the packing density for spheres is 5/8 of the volume will be filled with gumballs while the rest will be air how many gumballs will be needed, to determine this amount the following calculation must be performed:
- (Volume of box x 5/8) / volume of gumballs = Amount of gumballs
- Volume of a sphere = 4/3 x 3.14 x (radius x radius x radius)
- Volume of a gumball = 4/3 x 3.14 x (0.5 x 0.5 x 0.5) = 0.5235 inches
- ((7.3 x 5 x 9.4) x 5/8) / 0.523 = X
- (343.1 x 5/8) / 0.523 = X
- 214.4375 / 0.523 = X
- 410 = X
Therefore, 410 gumballs will be needed to fill the box.
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Answer:
A. 8.3
B.18.7
C. 10.4
D. 1.04
Step-by-step explanation:
p(x) = 0.03x² + 0.56x + 6.35
A. Determination of p(3)
p(x) = 0.03x² + 0.56x + 6.35
x = 3
p(3) = 0.03(3)² + 0.56(3) + 6.35
p(3) = 0.03(9) + 1.68 + 6.35
p(3) = 0.27 + 1.68 + 6.35
p(3) = 8.3
B. Determination of p(13)
p(x) = 0.03x² + 0.56x + 6.35
x = 13
p(13) = 0.03(13)² + 0.56(13) + 6.35
p(13) = 0.03(169) + 7.28 + 6.35
p(13) = 5.07 + 7.28 + 6.35
p(13) = 18.7
C. Determination of p(13) – p(3)
From A and B above,
p(13) = 18.7
p(3) = 8.3
p(13) – p(3) = 18.7 – 8.3
p(13) – p(3) = 10.4
D. Determination of p(13) – p(3) / 13 – 3
From C above,
p(13) – p(3) = 10.4
p(13) – p(3) / 13 – 3 = 10.4/ 13 – 3
= 10.4 / 10
= 1.04
Answer:
(1/2,7/4)
Step-by-step explanation:
x=-b/2a
x=1/2
y=(1/2)^2-(1/2)+2
y=1/4-2/4+8/4
y=7/4
Since we are given with the three sides of the triangle and asked to determine the angle, we can use the cosine law.
Answer:y=6x
Step-by-step explanation: a proportional equation is y=kx
