The distance, d in meters, that an accelerating object travels is given by

There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r

zhannawk [14.2K]

Answer:

12

Step-by-step explanation:

The first cave has 7 times more bats than the last cave. So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves. So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats. Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end. If cave #45 has b bats, then caves #39-#44 have 77−b bats. And since caves #38-44 have 77 bats, then cave #38 has b bats. Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

x = 12

There are at most 12 bats in the 30th cave.

8 0

3 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

Anastasy [175]

Answer: 19.4

Step-by-step explanation:

Given

Profit is given in terms of the selling price

$y=-5x^2+194x-900$

to get the maximum price, differentiate y w.r.t x

$\frac{\mathrm{d} y}{\mathrm{d} x}=-5\times 2x+194$

Put $\frac{\mathrm{d} y}{\mathrm{d} x}=0$ to get maximum value

$10x=194\\x=19.4$

Thus, the company must sell it at 19.4

8 0

2 years ago

Wood and colleagues (2009) examined the value of self-affirmation. In a typical study, participants either engaged or did not en

maxonik [38]

Answer:

Option A) independent variable – self-affirmations; dependent variable – self-esteem scores

Step-by-step explanation:

We are given the following in the question:

"Wood and colleagues (2009) examined the value of self-affirmation. In a typical study, participants either engaged or did not engage in self-affirmations. Later, their current self-esteem was assessed."

Independent and Dependent Variable: