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aleksley [76]
3 years ago
12

Kent is cutting a long tree into pieces. He cut the trunk into 3 pieces. Then he cut each of those pieces into 3 smaller pieces.

Finally he cut each of those smaller pieces into 3 still smaller pieces. ​How many pieces did they have then?
Mathematics
1 answer:
VladimirAG [237]3 years ago
6 0

Answer:

27

Step-by-step explanation:

he started by cutting one log into 3

1×3=3

then cutting each of those into 3

3×3=9

then again

9×3=27

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The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take f
Alexeev081 [22]

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}

Where <em>A₀</em> is the initial amount, <em>t</em> is the time that has passes (in this case seconds), <em>d</em> is the half-life, and <em>A</em> is the amount after <em>t</em> seconds.

Since the half-life of the element is 30 seconds, <em>d</em> = 30. Our initial sample has nine grams, so <em>A₀</em> is 9. Substitute:

\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let <em>A</em> = 0.72 and solve for <em>t: </em>

<em />\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}<em />

Divide both sides by 9:

\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}

We can take the natural log of both sides:

\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)

By logarithm properties:

\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)

Solve for <em>t: </em>

<em />\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}<em />

<em />

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

5 0
3 years ago
Sarah, Natasha and Richard share some sweets in the ratio 4:5:3. Sarah gets 36 sweets. How many sweets are there altogether?
strojnjashka [21]

Answer:

40

Step-by-step explanation:

4 0
3 years ago
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is and the equ
Karolina [17]
I think I had think before so 3x-D=10?
4 0
4 years ago
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Lubov Fominskaja [6]

Answer:

5 and 6             Your Answer is (5,8)

Hope It Helped :)

3 0
3 years ago
the table shows the number of students in grade 6-8 who went to local museum.of these between one half and three fourths packed
mojhsa [17]
The total number of students is 45 + 48 +40 = 133 students

1/2 * 133 ------ 3/4 * 133

(66.5 ; 99.75)

So we can say that b<span>etween 65 and 100 students packed their lunch</span>

4 0
4 years ago
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