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Ivenika [448]
3 years ago
5

There are four volume of “Humor in Accounting” sitting on a bookshelf. Each book is exactly eight centimeters thick. The pages o

f each book constitute seven centimeters and the covers are each half a centimeter thick. A starving beetle starts eating at page one of volume one and eats straight through to the last page of volume four. How far does the beetle travel?
Mathematics
1 answer:
zhenek [66]3 years ago
8 0
The beetle ate everything except the front cover of volume one and the back cover of volume four.
The thickness of the front cover of volume one and the back cover of volume four = 0.5 cm + 0.5 cm = 1 cm.
Total distance covered by the books = 4 x 8cm = 32 cm.
Therefore, total distance travelled by the beetle is 32 - 1 = 31 cm.
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Ben had knee surgery and was given a prescription with instructions to take 4 tablets twice a day for pain on day 1, then take 3
azamat

Answer:40

Step-by-step explanation:4 tablets twice a day is 8 (4*2=8). 3 tablets twice a day (3*2=6) for days 2-6 which is 5 days (6*5=30) is 30. The 7th day is 1 tablet twice a day (1*2=2). You’re multiplying the tablets Ben has to take times 2. Add them all together and you have 40.

7 0
3 years ago
The ​half-life of a radioactive element is 130​ days, but your sample will not be useful to you after​ 80% of the radioactive nu
gtnhenbr [62]

Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

\frac{dN}{dt}\propto -N

\Rightarrow \frac{dN}{dt} =-\lambda N

\Rightarrow \frac{dN}{N} =-\lambda dt

Integrating both sides

\int \frac{dN}{N} =\int\lambda dt

\Rightarrow ln|N|=-\lambda t+c

When t=0, N=N_0 = initial amount

\Rightarrow ln|N_0|=-\lambda .0+c

\Rightarrow c= ln|N_0|

\therefore ln|N|=-\lambda t+ln|N_0|

\Rightarrow ln|N|-ln|N_0|=-\lambda t

\Rightarrow ln|\frac{N}{N_0}|=-\lambda t.......(1)

                            \frac{N}{N_0}=e^{-\lambda t}.........(2)

Logarithm:

  • ln|\frac mn|= ln|m|-ln|n|
  • ln|ab|=ln|a|+ln|b|
  • ln|e^a|=a
  • ln|a|=b \Rightarrow a=e^b
  • ln|1|=0

130 days is the half-life of the given radioactive element.

For half life,

N=\frac12 N_0,  t=t_\frac12=130 days.

we plug all values in equation (1)

ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130

\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130

\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130

\rightarrow -ln|2|=-\lambda \times 130

\rightarrow \lambda= \frac{-ln|2|}{-130}

\rightarrow \lambda= \frac{ln|2|}{130}

We need to find the time when the sample remains 80% of its original.

N=\frac{80}{100}N_0

\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t

\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t

\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t

\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}

\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}

\Rightarrow t\approx 42

We can use the sample about 42 days.

7 0
3 years ago
Sandra runs at a rate of 8 miles in
Harman [31]
She runs 8/45 miles per min
3 0
3 years ago
Karrine hit 4 more home runs than half the number of home runs Lu hit. Together they hit 10 home runs. Let x represent the numbe
Andreas93 [3]

Answer:

The number of home runs that Lu hit is 4 and the number of home runs that Karrine hit is 6

Step-by-step explanation:

Let

x ----> represent the number of home runs Lu hit

y ---> represent the number of home runs Karrine hit

we know that

Together they hit 10 home runs

so

x+y=10 ----> equation A

Karrine hit 4 more home runs than half the number of home runs Lu hit

so

y=\frac{1}{2}x+4 ---> equation B

substitute equation B in equation A

x+\frac{1}{2}x+4=10

solve for x

\frac{3}{2}x=10-4

\frac{3}{2}x=6\\x=4

Find the value of y

y=\frac{1}{2}(4)+4=6

therefore

The number of home runs that Lu hit is 4 and the number of home runs that Karrine hit is 6

5 0
2 years ago
Simplify. (–8x) ÷ (–4)
vovikov84 [41]
(-8x)<span> ÷ (-4)=0
First you have to divide both sides by -4:
2x</span><span> ÷ 1=0
Now divide both sides by 1 so that the left side can be eliminated:
2x=0
</span>Now divide both sides by 2 so that the left side only has x:
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7 0
3 years ago
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