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3 years ago

The population of bacteria in a culture doubles every 14 hours. How long will it take for

Mathematics

1 answer:

Snezhnost [94]3 years ago

4 0

Answer: 22 hours 11 minutes

Step-by-step explanation:

$P=P_o\cdot e^{(kt)}\\\\\text{Since the initial population is doubled in 14 hours, then:}\\2P_o=P_o\cdot e^{k\cdot 14}\\2=e^{14k}\\ln\ 2=ln\ e^{14k}\\ln\ 2=14k\\\\\dfrac{ln\ 2}{14}=k\\\\0.0495=k\\\\\\\text{Now that the k-value has been determined, we can find the time when the}\\\text{population is tripled:}\\3P_o=P_o\cdot e^{0.0495t}\\3=e^{0.0495t}\\ln\ 3=ln\ e^{0.0495t}\\ln\ 3=0.0495t\\\\\dfrac{ln\ 3}{0.0495}=5\\\\22.19=t\\\\22\ hrs +0.19\ hrs$

$22\ hours + \bigg[\dfrac{19}{100}=\dfrac{x}{60}\bigg]\\\\22\ hours + 11\ minutes$

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3 years ago

Read 2 more answers

Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to

attashe74 [19]

Answer:

0.9726 = 97.26% approximate probability that X is at most 30

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).

This means that $p = 0.11$

Random sample of 200 shafts

This means that $n = 200$

Mean and Standard deviation:

$\mu = E(x) = np = 200*0.11 = 22$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.11*0.89} = 4.42$

(a) What is the (approximate) probability that X is at most 30

Using continuity correction, this is $P(X \leq 30 + 0.5) = P(X \leq 30.5)$ , which is the pvalue of Z when X = 30.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 22}{4.42}$

$Z = 1.92$

$Z = 1.92$ has a pvalue of 0.9726.

0.9726 = 97.26% approximate probability that X is at most 30

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3 years ago

If SQ=11x-26 and PR=5x+28,find PR.

Lisa [10]

Answer:

The full Question is attached in the picture below.

PR = 5(9) +28 = 73

Step-by-step explanation:

Since the figure is a rectangle

SQ = PR

11x-26 = 5x +28

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x = 9

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3 years ago

5x – 2x = 12 How do I solve

FinnZ [79.3K]

Answer:

Step-by-step explanation:

Replace X with 4

(5*4)-(2*4) = 12

6 0

3 years ago

Read 2 more answers

ANSWER QUICKLY PLEWSE FOR BRAINLIEST

photoshop1234 [79]

Angle 3:
62+47=109
All angles in a triangle add to 180 degrees, so 180-109= 71 degrees
Angle 2:
Angles in a straight line always add to 180 degrees too,
so 180-62= 118 degrees
Angle 1:
Again, angles in a triangle add to 180,
so 180-22-118= 40 degrees

Angle 1: 40
Angle 2: 118
Angle 3: 71
Hope that helps :)

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3 years ago