Aperson is using a new tennis ball launching machine that is 15 inches by 15 inches by 14. assuming the machine uses tennis balls that are spherical and 2.7 inches in diameter, how many tennis should fit in one of the top of the machine.

305 tennis balls should fit

Step-by-step explanation:

The volume of the machine is length * width * height

So Volume of Machine = 15 * 15 * 14 = 3150

Volume of Sphere is  

Where

V is volume and r is radius (half of diameter)

Since 2.7 is diameter, 2.7/2 = 1.35 inches is radius

Volume of 1 tennis ball = (rounded to 1 decimal)

We simply divide the volume of the machine by volume of 1 tennis ball to get number of tennis balls:

3150/10.3 = 305.82

the fractional amount (.82) won't be possible so the max number of balls possible is 305 balls

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: