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guapka [62]
3 years ago
8

After 3 days a sample of radon-222 has decayed to 58% of its original amount.

Mathematics
1 answer:
Rina8888 [55]3 years ago
6 0
The half-life of the radioactive substance can be determined through teh equation ln 2 = k (t 1/2) where k is equal to ln (1/(1-0.58)) / 3. Hence t 1/2 is equal to 2.40 days. To decay to 10% of the original amount, ln (1/0.90) / ( ln2) / 2.40, time is equal to 0.37 days.
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10d - 22 + 6d = 12d + 10
ryzh [129]

Answer:

8

Step-by-step explanation:

10d - 22 + 6d = 12d + 10

16d - 22 = 12d +10

4d = 32

d = 8

4 0
3 years ago
The manufacturer of an airport baggage scanning machine claims it can handle an average of530 bags per hour.(a-1) At α = .05 in
-Dominant- [34]

Answer:

b. H0: μ < 530. Reject H0 if tcalc > -1.753

Step-by-step explanation:

1) Data given and notation  

\bar X=507 represent the sample mean

s=47 represent the sample standard deviation  

n=16 sample size  

\mu_o =530 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is less than 530 (left tailed tes), the system of hypothesis would be:  

Null hypothesis:\mu \geq 530  

Alternative hypothesis:\mu < 530  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{507-530}{\frac{47}{\sqrt{16}}}=-1.957

Critical value

Since we are conducting a left tailed test we need to first find the degrees of freedom for the statistic given by:

df=n-1=16-1=15

Now we need to look on the t distribution with 15 degrees of freedom that accumulates 0.05 of the area on the left area. And on this case the critical value would be t_{\alpha}=-1/753.

And we can use the following excel code to find it: "=T.INV(0.05,15)"  

So then the correct rejection zone for H0 would be: Reject H0 if t_{calc}

P-value  

Since is a one side left tailed test the p value would be:  

p_v =P(t_{(15)}  

Conclusion  

If we compare the p value and the significance level for example \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean is significantly lower than 530 at 5% of significance.  

6 0
3 years ago
What is the exact decimal equivalent for 1/9
pantera1 [17]

\underline{\ \ 0.111...=0.\overline{1}}\\9|1\\\underline{\ \ 0}\\.\ \ 10\\\underline{\ \ \ \ 9}\\.\ \ \ \ 10\\\underline{\ \ \ \ \ \ 9}\\.\ \ \ \ \ 10\\\underline{\ \ \ \ \ \ \ 9}\\.\ \ \ \ \ \ 1\\\\\dfrac{1}{9}=0.111...=0.\overline{1}\\\\REMEMBER:\\\\\dfrac{1}{9}=0.111...=0.\overline{1}\\\\\dfrac{2}{9}=0.222...=0.\overline{2}\\\\\dfrac{3}{9}=0.333...=0.\overline{3}\\\vdots\\\\\dfrac{8}{9}=0.888...=0.\overline{8}

5 0
3 years ago
What is the logarithmic function modeled by the following table?
cupoosta [38]
Answer: option 1.

log_{4} x

x      f(x)

4      log (4) 4 = 1 ... because 4^1 = 4

16    log(4) 16 = 2 .... because 4^2 = 16

64    log (4) 64 = 3 .... because 4^3 = 64


3 0
3 years ago
Read 2 more answers
PLZ HeLP
eimsori [14]
112.5...............
5 0
2 years ago
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