Can someone please answer this math problem and show your working

Mathematics

1 answer:

schepotkina [342]3 years ago

3 0

378 because 49*3 and then add 35

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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.

Yanka [14]

Answer: 0.025

Step-by-step explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between the interval [48.0 minutes, 58.0 minutes].

The probability density function :-

$f(x)=\dfrac{1}{58-48}=\dfrac{1}{10}$

Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-

$\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}|x|^{50.5}_{50.25}\\\\=\dfrac{1}{10}\ [50.5-50.25]=\dfrac{1}{10}\times(0.25)=0.025$

Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025

Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025

5 0

2 years ago

In a lab, a scientist is growing bacteria for a study. The scientist begins with a bacteria

Diano4ka-milaya [45]

Answer:

The answer is below

Step-by-step explanation:

The growth of the bacteria is in the form of an exponential growth. It is given by the formula:

$P(t)=ae^{rt}\\\\where\ t\ is\ the\ number\ of \ hours, P(t)\ is\ the \ population\ at\ t\ hours\\\and\ a=population\ at\ start$

At 2 hours, the population is 62 cells, hence:

$P(2)=ae^{2r}\\\\62=ae^{2r}\ \ .\ \ .\ \ .\ (1)$

After another 2 hours (4 hours), the population is 1 million:

$P(4)=ae^{4r}\\\\1000000=ae^{4r}\ \ .\ \ .\ \ .\ (2)\\\\Divide \ equation\ 2\ by\ equation\ 1:\\\\\frac{1000000}{62}=\frac{ae^{4r}}{ae^{2r}} \\\\16129=e^{2r}\\\\ln(e^{2r})=ln(16129)\\\\2r=9.688\\\\r=4.844$