100 POINTS!!!

Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are

True [87]

Answer:

The number of balls in the box at 2010th step is 6 balls

Explanation:

Since the boxes are arranged from left to right, and since the empty boxes are capable of holding 4 balls at once.

Therefore, her steps would follow this pattern ;

00001 - 1st Step

0002 - 2nd Step

0003 - 3rd Step

0004 -4th Step

0010 - 5th Step

0011 - 6th Step

0021 - 7th step

0031 - 8th step

0041 - 9th step

Looking at this pattern, it is obvious this digits are in base 5 because once we count to 4 in a unit, we move to the next at 1.

Thus,at Mady's 2010th step, we'll convert to base 5,thus 2010 in base 5 is calculated as;

2010 ÷ 5 = 402 r 0, so Base 5 is now: _ _ _ _ 0.

402 ÷ 5 = 80 r 2, so Base 5 is now: _ _ _ 2 0.

80 ÷ 5 = 16 r 0, so Base 5 is now:

_ _ 0 2 0.

16 ÷ 5 = 3 r 1, so Base 5 is now: _ 1 0 2 0.

3 ÷ 5 = 0 r 3, so Base 5 is now: 3 1 0 2 0.

So 2010 in base 10 is 31020 in base 5. Thus,the number of balls in the box at 2010th step is equal to 3 + 1 + 0 + 2 + 0 = 6balls

3 0

3 years ago

______ clouds are formed when air masses rise vertically in the atmosphere.

zhannawk [14.2K]

a) Cumulus is 100% the correct answer

6 0

3 years ago

Read 2 more answers

Which kind of force do you exert on an object when you pull it toward you?

Vilka [71]

It's gravity I believe? I'm not entirely sure.

7 0

4 years ago

Read 2 more answers

Jill applies a force of 250 N to a machine. The machine applies a force of 25 N to an object. What is the mechanical advantage o

Vinvika [58]

Mechanical advantage is defined as the ratio of output load to the input load. The mechanical advantage of the machine will be 0.1.

<h3>What is mechanical advantage?</h3>

Mechanical advantage is a measure of the ratio of output force to input force in a system,

It is used to obtain the efficiency of forces in levers and pulleys. It is an effective way of amplifying the force in simple machines like levers.

The theoretical mechanical advantage is defined as the ratio of the force responsible for the useful work in the system to the applied force.

Given

applied force = 250 N

Output force = 25

Mechanical advantage = work output / work input

$\rm{Mechanical advantage}=\frac{F_O}{F_I}$

$\rm{Mechanical advantage}=\frac{25}{250}$

$\rm{Mechanical advantage}=0.1$

Hence the mechanical advantage of the machine will be 0.1

To learn more about the mechanical advantage refer to the link;

brainly.com/question/7638820

3 0

2 years ago

A tree falls in a forest. How many years must pass before the 14C activity in 1.03 g of the tree's carbon drops to 1.02 decay pe

Illusion [34]

Answer:

t = 5.59x10⁴ y

Explanation:

To calculate the time for the ¹⁴C drops to 1.02 decays/h, we need to use the next equation:

$A_{t} = A_{0}\cdot e^{- \lambda t}$ (1)

<em>where $A_{t}$ : is the number of decays with time, A₀: is the initial activity, λ: is the decay constant and t: is the time.</em>

To find A₀ we can use the following equation:

$A_{0} = N_{0} \lambda$ (2)

<em>where N₀: is the initial number of particles of ¹⁴C in the 1.03g of the trees carbon </em>

From equation (2), the N₀ of the ¹⁴C in the trees carbon can be calculated as follows:

$N_{0} = \frac{m_{T} \cdot N_{A} \cdot abundance}{m_{^{12}C}}$

<em>where $m_{T}$ : is the tree's carbon mass, $N_{A}$ : is the Avogadro's number and $m_{^{12}C}$ : is the ¹²C mass. </em>

$N_{0} = \frac{1.03g \cdot 6.022\cdot 10^{23} \cdot 1.3\cdot 10^{-12}}{12} = 6.72 \cdot 10^{10} atoms ^{14}C$

Similarly, from equation (2) λ is:

$\lambda = \frac{Ln(2)}{t_{1/2}}$

<em>where t 1/2: is the half-life of ¹⁴C= 5700 years </em>

$\lambda = \frac{Ln(2)}{5700y} = 1.22 \cdot 10^{-4} y^{-1}$

So, the initial activity A₀ is:

$A_{0} = 6.72 \cdot 10^{10} \cdot 1.22 \cdot 10^{-4} = 8.20 \cdot 10^{6} decays/y$

Finally, we can calculate the time from equation (1):

$t = - \frac{Ln(A_{t}/A_{0})}{\lambda} = - \frac {Ln(\frac{1.02decays \cdot 24h \cdot 365d}{1h\cdot 1d \cdot 1y \cdot 8.20 \cdot 10^{6} decays/y})}{1.22 \cdot 10^{-4} y^{-1}} = 5.59 \cdot 10^{4} y$

I hope it helps you!

4 0

3 years ago