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scoundrel [369]
2 years ago
6

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

Mathematics
1 answer:
Nastasia [14]2 years ago
8 0

Answer:

B.Between 2 and 3

Step-by-step explanation:

60÷40

=3/2

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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:

  • Dependent variable is the variable whose value depends on the independent variable.
  • Independent variable is the free variable.

For the given scenario, self esteem is assessed based on the fact that participants either engaged or did not engage in self-affirmations.

Thus, the dependent variable is self esteem and the independent variable is engagement in self affirmation.

Thus, the correct answer is

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

8 0
3 years ago
Write an equation of each line in standard form with integer coefficients.<br> 4. y = 2.4x + 1.8
Nadusha1986 [10]

Answer:

<h2>12x - 20y = -9</h2>

Step-by-step explanation:

The standard form of an equation of a line:

Ax+By=C

We have

4y=2.4x+1.8

Convert

4y=2.4x+1.8          <em>multiply both sides by 10</em>

40y=24x+18          <em>subtract 24x from both sides</em>

-24x+40y=18            <em>change the signs</em>

24x-40y=-18          <em>divide both sides by 2</em>

12x-20y=-9

3 0
2 years ago
Can someone help me? ​
zimovet [89]

Answer:

61.538

Step-by-step explanation:

5 0
2 years ago
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