A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = Correct: Your answer is correct. (b) Find an expression for the number of cells after t hours. P(t) = Correct: Your answer is correct. (c) Find the number of cells after 8 hours. 973078528 Correct: Your answer is correct. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. hr

Answer: there are 4 solutions

x = -2

x = -1/2 = -0.500

x =(3-√5)/2= 0.382

x =(3+√5)/2= 2.618

Step-by-step explanation:

Answer:

m = -2/3

Step-by-step explanation:

Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]

So,

[tex]m = \frac{-1-1}{9-6}[/tex]

m = -2/3

Answer:

5 out of 9

Step-by-step explanation:

You have 5 blue marbles and for red marbles which makes a total of 9 marbles in a bag. If you take one marble out and put it back in another marble out and put it back at random the probability of getting a blue marble is 5 out of 9.

The probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

There is a bag filled with 5 blue and 4 red marbles. Thus, the total number of marble in the bag are,

[tex]5+4=9[/tex]

One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,

[tex]P(B)=\dfrac{5}{9}[/tex]

The probability of getting red marble is,

[tex]P(R)=\dfrac{4}{9}[/tex]

The Probability of getting red marble in first pick and  probability of getting blue marble in second pick is,

[tex]P_1=\dfrac{4}{9}\times\dfrac{5}{9}=\dfrac{20}{81}[/tex]

The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,

[tex]P_2=\dfrac{5}{9}\times\dfrac{4}{9}=\dfrac{20}{81}[/tex]

The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,

[tex]P=P_1+P_2\\P=\dfrac{20}{81}+\dfrac{20}{81}\\P=\dfrac{40}{81}[/tex]

Thus, the probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

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Answer:

The probability that 35 or more from this sample used Google Chrome as their browser is 0.9838.

Step-by-step explanation:

We are given that according to Statcounter, the Google Chrome browser controls 62.8% of the market share worldwide.

A random sample of 70 users was selected.

Let [tex]\hat p[/tex] = sample proportion of users who used Google Chrome as their browser.

The z-score probability distribution for the sample proportion is given by;

                              Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{35}{70}[/tex] = 0.50

            p = population proportion = 62.8%

            n = sample of users = 70

Now, the probability that 35 or more from this sample used Google Chrome as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50)

       P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.50) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.50-0.628}{\sqrt{\frac{0.50(1-0.50)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.14)

                           = P(Z [tex]\leq[/tex] 2.14)  = 0.9838

The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.9838.

Answer:

2580 ft-lb

Step-by-step explanation:

Water leaks out of the bucket at a rate of [tex]\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}[/tex]

Work done required to pull the bucket to the top of the well is given by integral

[tex]W=\int_{a}^{b} F(x) dx[/tex]

Here, function [tex]F(x)[/tex] is the total weight of the bucket and water [tex]x[/tex] feet above the bottom of the well. That is,

[tex]F(x)=4+(42-0.1 x)[/tex]

[tex]=46-0.1x[/tex]

[tex]a[/tex] is the initial height and [tex]b[/tex] is the maximum height of well. That is,

[tex]a=0 \text { and } b=60[/tex]

Find the work done as,

[tex]W=\int_{a}^{b} F(x) d x[/tex]

[tex]=\int_{0}^{60}(46-0.1 x) dx[/tex]

[tex]&\left.=46x-0.05 x^{2}\right]_{0}^{60}[/tex]

[tex]=(2760-180)-0[[/tex]

[tex]=2580 \mathrm{ft}-\mathrm{lb} [/tex]

Hence, the work done required to pull the bucket to the top of the well is [tex]2580 \mathrm{ft}- \mathrm{lb}[/tex]

Answer:

d = 234.6 m

Step-by-step explanation:

You can consider a system of coordinates with its origin at the beginning of the walk of the student.

When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:

[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]

she is at the coordinates (52.97 , 28.16)m.

Next, when she walks 180m to the east, her coordinates are:

(52.97+180 , 28.16)m = (232.97 , 28.16)m

To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:

[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]

The displacement of the student on her complete trajectory was of 234.6m

Answer:

Step-by-step explanation:

Add the two equations together:

  (x -y) +(x +y) = (34) +(212)

  2x = 246

  x = 123

  y = x-34 = 89

Malik has 89 foreign stamps and 123 domestic stamps.

Answer:

89 and 123

Step-by-step explanation:

Answer:

y≤4

Step-by-step explanation:

y≤4

try to graph it on a parabola and u will find the answer above :D hope this helped

Answer:

60

Step-by-step explanation:

x=60 .

The triangle is equilateral and x=60 cause the two lines are ||

a. x=60°

b. Alternate interior angles

Solution,

Given,

All sides of triangle are equal.

AB=BC=AC

<ABC=<ACB=<BAC=y

By angle sum property of triangle,

<ABC+<BCA+<CAB=180

or y+y+y=180

or 3y=180

or y=180/3

y=60

Now,

<ACB=<CAD

<CAD(x)=60( Alternate interior angles)

Hope this helps ..

Good luck on your assignment..

Answer:

180

Step-by-step explanation:

2(24)-3=45

24-8=√16=4

45*4=180

Answer:

it it the highest or lowest point of a parabola

Answer:

0.1905 = 19.05%

Step-by-step explanation:

We have a total of 106 containers of oxygen, from which:

20 have oxygen not ionized, 86 have oxygen ionized.

If the first one selected is ionized, now we have 20 not ionized and 85 ionized.

So the probability of the second one selected being not ionized is the number of not ionized (20) over the total number of containers (20 + 85):

P = 20 / (20 + 85) = 0.1905 = 19.05%

Answer:

ge

Step-by-step explanation:

ge

Answer:

its 2pi/3

Step-by-step explanation:

because the full radian measure of a circle is 2pi radians, the smaller circle is a third of the size of the larger one. Multiply straight across for (2pi/1)(1/3)  

The circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (radius)[/tex]

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (OB)[/tex]

[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (x)[/tex]

Circumference of the Larger circle = 3 x Circumference of the smaller circle

[tex]2\times \pi \times x = 3\times Circumference\ of\ the\ smaller\ circle\\\\3\times Circumference\ of\ the\ smaller\ circle = 2\times \pi \times x \\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi \times x }{3}\\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi}{3}( x )\ units[/tex]

Hence, the circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].

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Answer:

a) The p-value obtained from the one-proportion applet is more valid because a z-test statistic shouldn't have been used for the other obtained p-value. Check Explanation for more Explanation.

b) No, there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.

Step-by-step explanation:

The p-value for this problem was obtained from a one proportion simulation applet and another obtained using a one proportion z-test p-value.

But one of the conditions for the use of the z-test or the z-distribution in obtaining the p-value is that information on the population mean and standard deviation should be known or the sample size should be large enough such that the properties of the sample should approximate the properties of the the population distribution.

But for this question and hypothesis test, the sample that the we are working with is only of sample size 12 with no information on the population standard deviation provided, hence, the p-value obtained from the z-test statistic one proportion test is not a valid enough one due to this reason.

Plus, on calculating this p-value manually, it was obtained to be 0.078, to justify this explanation as it is very close to.the value obtained using the simulation applet.

Manual way of calculating

t = (x - μ)/σₓ

x = 5/12 = 0.41667

μ = p₀ = 0.20

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 12

σₓ = √[0.4167×0.5833/12] = 0.1423

t = (0.4167 - 0.20) ÷ 0.1423

t = 1.52

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 12 - 1 = 11

Significance level = 0.05 (This is used when no significance level is provided in the question)

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 1.52, at 0.05 significance level, df = 11, with a one tailed condition) = 0.07836

b) To know which conclusion to draw, we need to first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.

And the alternative hypothesis is that there is enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.

Mathematically, if p is the proportion of times the spun penny will turn up heads in the long run,

The null hypothesis is represented as

H₀: p ≤ 0.20

The alternative hypothesis is represented as

Hₐ: p > 0.20

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05 (usually used when the significance level for the test isn't specified)

p-value = 0.0770

0.0770 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say there isn't enough evidence to suggest that a spun penny will land heads more that 20% of the time in the long run.

Hope this Helps!!!

Answer:

0.637

Step-by-step explanation:

The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out

Answer:

[tex](\frac{-1}{2} , \frac{-\sqrt{3} }{2} )[/tex]

Step-by-step explanation:

Memorize your unit circle.

Step 1: Subtract 360 from 600 degrees to find rotation

600° - 360° = 240°

Step 2: Either find coordinates from unit circle or convert to radians

240° = 4π/3

Step 3: Find coordinates

Answer:

The type of observational study describer here is retrospective study.

Step-by-step explanation:

The complete question is:

Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were matched - in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. Determine what type of observational study is described. Explain.

Solution:

In retrospective study design, the concerned outcome has previously taken place in each participant by the phase he or she is signed up for the study, and the information are gathered either from past data or by requesting the participants to recall exposures.

It is also known as a historic cohort study.

A retrospective study is completed as posterior experiment, using data on events that have already taken place in the history. In most cases some or most of the data has already been collected and stowed in the archive.

In the provided scenario, the researcher collect the past data for the exposure to sunshine over the previous twenty years for 250 women. And estimated the  total number of hours that each woman had been exposed to sunshine in the previous twenty years.

Then the researcher compares the amount of exposure to sunshine for the two groups.

Thus, the type of observational study describer here is retrospective study.

Answer

its -1

Step-by-step explanation:

ED 2020 boiiiii

The residual value of the line of the best fit when x = 2 is -1

The equation of the line is given as:

y = 0.5x + 1

When x = 2, we have:

y = 0.5 * 2 + 1

Evaluate

y = 2

The residual is the difference between the actual value and the predicted value.

From the complete graph, the actual value is 1.

So, we have:

Residual = 1 - 2

Evaluate

Residual = -1

Hence, the residual value when x = 2 is -1

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Answer:

C. Between 175 and 295 dollars.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 235

Standard deviation = 20

According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:

Within 3 standard deviations of the mean.

235 - 3*20 = 175

235 + 3*20 = 295

So the correct answer is C.

Answer:

Type II error.

Step-by-step explanation:

We have a hypothesis test for the claim that placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales.

The null hypothesis will state that there is no difference, while the alternative hypothesis will state that there is significant positive difference.

The result is a P-value of 0.1288 and the null hypothesis failing to be rejected.

As the null hypothesis failed to be rejected, if an error has been made in the conclusion, is that we erroneusly accept a false null hypothesis.

This is a Type II error, where the null hypothesis is accepted although the alternative hypothesis is true.

Answer:

The average population growth per year is 102.

Step-by-step explanation:

From the given data, we can find the slope which will give us the average rate of change. Our points are:

[tex](2003, 903)\quad and \quad (2007, 1311)[/tex]

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{1311-903}{2007-2003}\\\\m=102[/tex]

Best Regards!

Answer:

[tex]18\sqrt{10}$ units[/tex]

Step-by-step explanation:

We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.

We want to find the point on the line y=3x which is closest to Q.

Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.

If x=a, y=3a, so the point P has the coordinates (a,3a).

Distance between point Q and P

[tex]=\sqrt{(60-a)^2+(0-3a)^2}\\D =\sqrt{10a^2-120a+3600}[/tex]

To minimize D, we find its derivative

[tex]\dfrac{dD}{da}=\dfrac{10a-60}{\sqrt{10a^2-120a+3600} }\\$Setting \dfrac{dD}{da}=0\\10a-60=0\\10a=60\\a=6[/tex]

Therefore, the y-coordinate for P is 3*6=18.

The point P=(6,18).

Next, we calculate the distance between P(6,18) and (60,0).

[tex]D =\sqrt{10(6)^2-120(6)+3600}\\=\sqrt{3240}\\=18\sqrt{10}$ units[/tex]

Answer:

670 Cans of fruit will be left

Step-by-step explanation:

First you multiply 155 by the 6 weeks.

That equals 930 and then you subtract 930 from 1,600 and that gives you 670.

There are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week.

First term a = 1600

Common difference d = -155

After 6 weeks means on week 7.

n = 7

a(7) = 1600 + (7-1)(-155)

a(7) = 1600 - 930

a(7) = 670

Thus, there are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.

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Answer:

7:1

Step-by-step explanation:

28:4=

7(4):1(4)=

7:1

Hope this helps!

Answer:

[tex]7:1[/tex]

Step-by-step explanation:

[tex]28:4[/tex]

Common highest factor is 4.

Simplify the ratio.

[tex]28 \div 4 : 4 \div 4[/tex]

[tex]7:1[/tex]

Answer:

Not sure 3/10?

Step-by-step explanation:

numbers are 0-9...that's 10 choices.

he chooses 3 numbers

I would think 3/10?

Answer:

27.11% probability that 2 of them have blue eyes

Step-by-step explanation:

For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

8% of all people have blue eyes.

This means that [tex]p = 0.08[/tex]

Random sample of 20 people:

This means that [tex]n = 20[/tex]

What is the probability that 2 of them have blue eyes?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]

27.11% probability that 2 of them have blue eyes

The probability that 2 of them have blue eyes is 27.11%.

Given that,

Approximately 8% of all people have blue eyes.

Out of a random sample of 20 people,

We have to determine,

What is the probability that 2 of them have blue eyes?

According to the question,

People having blue eyes p = 8% = 0.08

Sample of people n = 20

For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.

The probability of a person having blue eyes is independent of any other person.

The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.

[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]

Therefore,

The probability that 2 of them have blue eyes is,

[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]

Substitute all the values in the formula,

[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]

Hence, The required probability that 2 of them have blue eyes is 27.11%.

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Answer:

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159

Step-by-step explanation:

According to the given data we have the following:

mean = μ= 22

standard deviation = σ = 2

n = 100

μx = 22

σx=σ/√n=2/√100=0.2

Therefore, P( x < 21.8)=P(x-μx)/σx<(21.8-22)/0.2

=P(z<-1)

= 0.159

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159