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olganol [36]
3 years ago
15

In the half-life function Q(t)=28550⋅((34)h)(th) Q ( t ) = 28550 ⋅ ( ( 3 4 ) h ) ( t h ) , what is the half-life, h h , if (34)h

=12 ( 3 4 ) h = 1 2 ?
Mathematics
1 answer:
just olya [345]3 years ago
4 0

Answer:

h=2.4 hours \: 2hours\:24'

Step-by-step explanation:

1)Rewriting it properly:

Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}

2) Let's calculate the time (in hours), based on this relation:

\left ( \frac{3}{4} \right )^{h}=\frac{1}{2} \Rightarrow log_{\frac{3}{4}}\frac{1}{2} \Rightarrow h \approx 2.4\: hours

3) Testing it. We must find something around the half of 28850, due to some rounding in logarithms.

Q(t)=28850*\left ( \left ( \frac{3}{4}\right )^{h} \right )^{\frac{t}{h}}\, if \left ( \frac{3}{4} \right )^{h}=\frac{1}{2}\Rightarrow h=\\Q(t)=28850(\frac{1}{2})^{\frac{t}{h}}\Rightarrow Q(t)=28850(\frac{1}{2})^{\frac{t}{2.4}}\\28850(\frac{1}{2})^{\frac{t}{2.4}}=14425 \Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{14425}{28850}\Rightarrow (\frac{1}{2})^{\frac{t}{2.4}}=\frac{1}{2}\Rightarrow t=2.4\\Q(2.4)=28850*\left ( \left ( \frac{3}{4}\right )^{2.4} \right )^{\frac{2.4}{2.4}}\Rightarrow Q\approx14464

4) So, h≈ 2.40 hours or 2 hours 24'

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almond37 [142]

Answer:

\$16,990.62  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4  

substitute in the formula above

A=15,000(1+\frac{0.025}{4})^{4*5}  

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5 0
3 years ago
Coach Smith went to the sporting goods store to get ready for tennis season. He bought 25 containers of tennis balls and 12 pack
sesenic [268]

Answer:

C

Step-by-step explanation:

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150.9375+31.5= 182.4375

This can be rounded up to 182.44 (which is your final answer)

5 0
3 years ago
Find the population variance of: 4 6 8 9 9 <br><br> round to the nearest hundredth
soldi70 [24.7K]

Answer:

Step-by-step explanation:

To find the population variance, we first need the mean:

\bar{x}=\frac{4+6+8+9+9}{5}=\frac{36}{5}=7.2 so the mean is 7.2. To find the population variance (which is almost exactly the same as the sample variance except for a small difference in the denominators of the formula) we have to take each number minus the mean, and then square the difference. Add together all these squared numbers and then divide by the number of numbers. Like this:

(4-7.2)^2=10.24\\(6-7.2)^2=1.44\\(8-7.2)^2=.64\\(9-7.2)^2=3.24\\(9-7.2)^2=3.24

Add together those numbers and divide them by 5:

\sigma=\frac{10.24+1.44+.64+3.24+3.24}{5}=\frac{18.8}{5}=3.76

5 0
3 years ago
(PLEASE HELP) The table below - does it represent an exponential function?
Aliun [14]
Short answer: I don't know, but that doesn't mean I can't give you something that you can decide for yourself.
y = 4*2^(2n - 2) is the pattern.
Go for broke. Try n = 4. You should get 256. Let's try it.
y = 4 * 2^(2*4 - 2)
y = 4 * 2^(8 - 2)
y = 4 * 2^6
y = 4 * 64
y = 256 yup it works.

The other end is just as important. Suppose n = 1
Then y = 4 * 2^(2*1 - 2) = 4 * 2^0 = 4*1 = 4 Both work.

If this formula is correct, we can abbreviate it to make your task easier.
y = 4 * 2^(2n - 2)
y = 2^2 * 2^(2n - 2)
y = 2^(2n - 2 + 2)
y = 2^(2n) Now try the two end points again.

n = 4
y = 2^(2*4)
y  =  2^8
y = 256

n = 1
y = 2^(2*1)
y = 2^2
y = 4 which again checks.

so y = 2^(2n) I think is an exponential function.
Sorry my explanation is so long.

6 0
4 years ago
Sam brought brushes for $8,a palette for $5,and oil paints for $15.He paid 29.82 in all.What sale-tax rate did Sam pay?
sertanlavr [38]
8+5+15=28 
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5 0
3 years ago
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