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vodka [1.7K]
2 years ago
14

Find the mass at time t=0. ANSWER HAS TO BE IN GRAMS

Mathematics
1 answer:
777dan777 [17]2 years ago
3 0

For part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c)  20 years.

<h3>What is exponential decay?</h3>

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an equation for radioactive decay:

\rm m(t) = 400e^{-0.035t}

a) Plug t = 0

\rm m(0) = 400e^{-0.035\times 0}

m(0) = 400 grams

b) plug t = 20 years

\rm m(20) = 400e^{-0.035\times 20}

After solving:

m(20) = 198.63 grams

c) Plug m(t) = m(0)/2 = 400/2 = 200 grams

\rm 200 = 400e^{-0.035t}

x = 19.80 years ≈ 20 years

Thus, for part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c)  20 years.

Learn more about the exponential decay here:

brainly.com/question/14355665

#SPJ1

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its b. AC=DF

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3 0
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Bottles of purified water are assumed to contain 250 milliliters of water. There is some variation from bottle to bottle because
marshall27 [118]

Answer:

We accept H₀ we don´t have evidence of differences between the information from the sample and the population mean

Step-by-step explanation:

From data and excel (or any statistics calculator) we get:

X = 249,6 ml         and       s  1,26 ml

Sample mean and sample standard deviation respectively.

Population mean  μ₀  = 250 ml

We have a normal distribution but we dont know the standard deviation of the population. Furthermore we have a two tails test since we are finding if the sample give us evidence of differences ( in both senses ) when we compare them with the amount of water spec ( 250 ml )

Our test hypothesis are: null hypothesis       H₀    X = μ₀

Alternative Hypothesis                                 Hₐ     X ≠ μ₀

We also know that sample size is 8  therefore df  =  8 - 1   df = 7 , with this value and the fact that we are required to test at α = 0,05 ( two tails test)

t = 2,365

Then we evaluate our interval:

X ± t* (s/√n)   ⇒   249,6 ±  2,365 * ( 1,26/√8 )

 249,6 ±  2,365 * (1,26/2,83)  ⇒ 249,6 ±  2,365 *0,45

249,6 ± 1,052

P [ 250,652 ; 248,548]

Then the population mean 250 is inside the interval, therefore we must accept that the bottles have being  fill withing the spec. We accept H₀

7 0
3 years ago
A college sends a survey to members of the class of 2012. Of the 1254 people who graduated that year, 672 are women, of whom 124
Svetllana [295]

Answer:

a) P(F) = \frac{672}{1254}=\frac{112}{209}=0.536

b) P(M) = \frac{582}{1254}= \frac{97}{209}=0.464

c) P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815

Step-by-step explanation:

For this case we have a total of 1254 people. 672 are women and 582 are female.

We know that 124 women wnat on to graduate school.

And 198 male want on to graduate school

We can define the following events:

F = The alumnus selected is female

M= The alumnus selected is male

A= Female and attend graduate school

And we can find the probabilities required using the empirical definition of probability like this:

Part a

P(F) = \frac{672}{1254}=\frac{112}{209}=0.536

Part b

P(M) = \frac{582}{1254}= \frac{97}{209}=0.464

Part c

For this case we find the probability for the event A: The student selected is female and did attend graduate school

P(A) =\frac{124}{672}=\frac{31}{168}=0.185

And using the complement rule we find P(A') representing the probability that the female selected did not attend graduate school like this:

P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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