6/12<br> is that equivalent to<br> 1/12

A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacte

kotykmax [81]

Answer:

P(t) = 400×2^(t/2)
6400
5.0

Step-by-step explanation:

The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.

1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.

population = (initial population) × (growth factor)^(t/(growth period))

where the "growth period" is the period of time in which the population is multiplied by the "growth factor".

Here, we're given ...

(initial population) = 400

(growth factor) = 800/400 = 2

(growth period) = 2 . . . . hours

So, our population function can be written as ...

P(t) = 400×2^(t/2)

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2) Putting t=8 into the formula, we get ...

P(8) = 400×2^(8/2) = 400×16 = 6400

After 8 hours, the population will be 6400.

__

3) Fill in the given number and solve for t.

2270 = 400×2^(t/2)

2270/400 = 2^(t/2)

Taking logs, we have ...

log(227/40) = (t/2)log(2)

t = 2×log(227/40)/log(2) ≈ 5.009

After 5.0 hours, the population will reach 2270.

7 0

3 years ago

Need help ASAP

diamong [38]

Answer:

b. {-9, 3}.

Step-by-step explanation:

x^2 + 6x - 27 = 0

We need 2 numbers whose product is -27 and whose sum is + 6.

These are + 9 and - 3. So the factors are:

(x - 3)(x + 9) = 0

(x - 3) = 0 or (x + 9) = 0

x = 3 or -9.

7 0

3 years ago

Read 2 more answers

A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to d

kenny6666 [7]

Answer:

$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

$p_v =2*P(Z>2)=0.0455$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X=25$ represent the sample mean

$\sigma=2$ represent the sample population deviation for the sample

$n=16$ sample size

$\mu_o =24$ represent the value that we want to test

$\alpha=0.05$ 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 true mean is different from 24, the system of hypothesis would be:

Null hypothesis: $\mu = 24$

Alternative hypothesis: $\mu \neq 24$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(Z>2)=0.0455$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

6 0

3 years ago

Find the total amount in the compound interest account. $1510 is compounded daily at a rate of 8% for 7 years. Let 1 year 365

OLga [1]

Answer:

120.8

Step-by-step explanation:

1510divide15.10x8%=120.8

8 0

3 years ago

If f(x) = 3x + 5 and g(x) = –2x2 – 5x + 3, find (f + g)(x).

vazorg [7]

(f + g)(x) is equal to f(x) + g(x).

So (f + g)(x) = (3x + 5) + (-2x^2 - 5x + 3) = -2x^2 - 2x + 8
which is choice C.

8 0

3 years ago

6/12 is that equivalent to 1/12