0
Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
Mesoamerica is a geographical region that includes Mexico and Central America. In this areas, different civilizations flourished, such as the Maya and Aztec empires. The word 'Mesoamerica' means 'Middle America', which is from the Latin.
When is the next geomagnetic reversals?
It is difficult to predict when the next geomagnetic reversal will occur as they are irregular and can happen every few hundred thousand years. However, there is currently no evidence to suggest that a reversal is imminent.
What is the probabililty of at least 2 people same birthday from a group of 12 people?
The probability of at least 2 people in a group of npeople sharing a common birthday can be expressed more easily (mathematically) as 1 minus the probability that nobody in the group shares a birthday. Consider two people. The probability that they don't have a common birthday is 365/365 x 364/365. So the probability that they do share a birthday is 1-(365/365 x 364/365) = 1-365x364/3652 Now consider 3 people. The probability that at least 2 share a common birthday is 1-365x364x363/3653 And so on so that the probability that at least 2 people in a group of n people having the same birthday = 1-(365x363x363x...x365-n+1)/365n = 1-365!/[ (365-n)! x 365n ]
In the case of 12 people this equates to 0.16702 (or 16.7%).
Triamterene-h is a medication that contains a combination of triamterene and hydrochlorothiazide. It is used to treat high blood pressure and reduce excess fluid retention in the body. Triamterene is a diuretic that helps the body get rid of excess salt and water, while hydrochlorothiazide helps prevent the body from absorbing too much salt.
Z-score calculation formula with examples?
In a certain city the mean price of a quart of milk is 63 cents and the standard deviation is 8 cents. The average price of a package of bacon is $1.80 and the standard deviation is 15 cents. If we pay $0.89 for a quart of milk and $2.19 for a package of bacon at a 24-hour convenience store, which is relatively more expensive? To answer this, we compute Z-scores for each:
If Pu239 emits alpha particles of energy 5.4Mev calculate the decay probability?
It is possible to relate a decay constant of some α emitting nucleus to an energy of α particle in the framework of the Gamow theory (see Related links) that is based on the quantum mechanics description of the tunneling through the potential barriers.
Previous view (by Quirkyquantummechanic)The fact that 239Pu decays by alpha particle emission (with the α particle coming away at 5.245 Mev) has nothing to do with this isotope of plutonium's decay probability. The decay probability of 239Pu (or anything else) can be expressed as a distribution function. That's math speak. What that means is that any nuclear decay event has "odds" that it may happen. Let's look at that a bit.All unstable radionuclides will eventually decay. But when? Well, they all have some, um, "quirks" about them. Some take a long time to eventually fall apart, but some don't take that long. All we can do is "average out" the decay of a given material. Got that idea? It's important. And one of the ways we talk about the decay probability is in terms of something called the half life of a material. In the case of 239Pu, for example, the half life is 2.41 x 104 years. That's 24,100 years. What that means is that if we have a kilogram of the stuff, in 24,100 years, only half of the plutonium we started with will be left. Make sense? Mmhmm. But check this out. If we have two atoms of the stuff, does that mean that in 24,100 years only one will be here? No, it does not. They could both decay in the next week or the next month. Or the next century. Half life is a "probability thing" with unstable materials. And it is calculated across a "curve" of probability (that distribution function we mentioned) based on measurements of a quantity of the material being considered. It's that simple.
As an aside, but on a related note, if you guessed that the artificial elements (we call them synthetic, because they must be synthesized or made) that we know of by only a few atoms don't have very accurate measurements of their half lives, you'd be absolutely right. It's really difficult to (with accuracy) "guestimate" the half life of something, of some element, that is known from only a dozen atoms of the material....
What two ports share the same estuaries as Felixstowe?
Harwich on the River Stour & Ipswich on the River Orwell ... and you could add Manningtree on the River Deben since Felixstowe is a peninsula
First of all, you need to clarify your question. 4-pentylmethyl ketone, unfortunately, does not exist. You have made a mistake in the nomenclature.
I am assuming that you are talking about /\/\/*\, which is the carbon skeleton of pentylmethyl ketone, with the * representing C=O. The molecular formula is C7H14O, and it is also known as 2-heptanone. I don't know why you added in the "4-", unless you mean that the methyl is coming off the fourth carbon of the pentyl group. If that is the case, and you have moved methyl off to be a substituent on the pentyl, then the compound should be named an aldehyde and not a ketone.
UV spec gives you a graph with absorbance on the y-axis and wavelength (in nanometers) on the x-axis.
Conjugated systems are where double bonds occur, and are separated by exactly one single bond. In other words C=C-C=C is conjugated. C=C-C-C=C is not.
Conjugation reduces the energy gap between the "excited" state of electrons and the normal state. In other words, it takes less energy (and is easier) to excite electrons in compounds that have conjugated double bonds, such as 3-Methyl-2-cyclohexen-1-one. When these compounds return to their normal state, they emit a photon (light).
This light can have different wavelengths, which is why molecules with conjugated double bonds are often very colorful.
The energy that a photon is:
E = hf
Since f = c/(wavelength)
E = hc/(wavelength)
h is a constant, f stands for frequency, c is the speed of light, and the wavelength is measured in nanometers.
High energy light has high frequency and low wavelength (to make this more intuitive: think of short and fast pulsing ultraviolet radiation from the sun...it is powerful/energetic enough to cause sunburn.)
Therefore, the more conjugated bonds you have, the LESS energy it will take to excite your electrons. This means that if you have more conjugated bonds you have, the compound can give a high signal at higher the wavelength (and lower energies).
Red is very low energy. This is why beta-carotene, which is basically C=C-C=C-C=C-C=C-C=C-C=C-C=C-C=C-C=C-C=C-C=C, etc is orange. That's why carrots are orange.
Anyways, this is a lot of detail. Basically, it means that 3-Methyl-2-cyclohexen-1-one will give a peak in your absorbance graph, whereas you other compound probably will not (assuming that I have interpreted its incorrect name).
If you see a compound, the more CONJUGATED double bonds there are, the more you will see peaks at higher wavelengths, because it takes less energy to excite the electrons in those double bonds.
For example: C=C-C=C-C=C-C=C-C=C-C=C will give a signal at a higher wavelength than C=C-C=C=C=C=C=C-C=C. This is because in the second compound, there are fewer CONJUGATED double bonds (even though there are more double bonds total).
Why does this phenomena happen? A double bond is between two pi-orbitals. Basically they look like 8's. One lobe comes up from the carbon atom, and one lobe goes down. The electrons float around in there. If you have a double bond, the pi-orbitals on adjacent carbons share their electrons. Now, if you look at an extended conjugated system, you can see that there is an 8 on every single carbon in line! This means that basically the "electron cloud" is dispersed over the entire molecule. Much more stable, and much less energetic (remember, high energy means not stable).
Hope this helps!
By the way,
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/UV-Vis/spectrum.htm
might be a good reference for you.
How does the rotating function work?
This question is similar to "How does linear motion function? With the exception of the planetary system, first it must be driven by power. When driven and no load applied to it, then its just an object in motion. In other words a motion without load or work whether it be rotation or linear motion does not serve a function.
You would multiply the probabilities. The probability the first marksmen hits the target x the probability the second marksmen hits the target x the probability the third marksmen hits the target x the probability the fourth marksmen hits the target. So you take .80 x .80 x .80 x .80 = .4096 or about 41%. So if they all fire at the target with each having an 80% probability of hitting, there will be about a 41% chance they will all hit. If you actually think about this question, though, you would be wise to hesitate about the answer. What causes marksmen to miss? In general it would be many things, often acting in combination: trembling of the hands, distractions, shifts of the wind, variations in the ammunition being fired, and so on. If all four marksmen are shooting simultaneously, or nearly so, then some of these causes will be acting in the same way on all four. These would include the wind and the environmental distractions, for instance. It's therefore conceivable that when one marksman misses, so will all the others, and (usually) when one marksman hits the target, the others will be able to as well. In this situation the probability that four marksmen will all hit the target will be close to 80%, not 41%. The question itself couches some ambiguities. For instance, at a tournament of 100 marksmen, the probability that some four will all hit their target is likely close to 100%. (Problems like this in interpreting the intended meaning of probability questions go all the way back to the very first book on probability by Christian Huygens in 1657. There was argument among very good mathematicians for a long time about the answer to one of his problems because it had three distinct interpretations.)
How do you answer 'When something goes wrong at work how do you fix it'?
When something goes wrong at work, I address the issue promptly by identifying the root cause, discussing solutions with my team or supervisor, and implementing an effective solution while keeping open communication channels to prevent similar issues in the future.
What happens if you never have an IUD removed?
Purportedly, an IUD that remains in the uterus beyond its recommended term can become embedded in the uterine wall. If this happens, there is an increased risk of bleeding, scarring, and pelvic infection.
The probability of this risk is undocumented, however. Moreover, an embedded IUD may not, in itself, represent a health risk independent of the trauma of removal.
What is the probability of death?
P(death) =1 It is an absolute certainty.
However, we do NOT know when it will occur.
What is the likelihood that a particular event will occur?
The likelihood of a particular event occurring can vary depending on various factors such as the probability distribution, historical data, and potential influencing factors. It is typically expressed as a probability ranging from 0 (impossible) to 1 (certain). Analyzing these factors can help estimate the likelihood of the event.
What will affect the sample size calculation for a clinical trial?
A cost-benefit analysis. In particular,
the cost of the experiment,
the consequences of getting the wrong result,
the rarity (or otherwise) of the condition that you want to study,
the variability of that condition in the population.
What two interests does probable cause balance?
Probable cause balances the rights of the individual and that of a police officer it makes it so the individual is safe from being wrongly accused and so the officer has enough of a reason to question them. It makes sure both have a chance.
How probability sampling is used?
Probability sampling is used to select a sample from a population in such a way that every individual or element in the population has a known and non-zero chance of being selected. This method ensures that the sample is representative of the population, allowing for generalizations and statistical inferences to be made with greater validity and accuracy. Probability sampling techniques include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.
What is conclusion for additional mathematics project work 2009?
The conclusion for an Additional Mathematics Project Work in 2009 would summarize the key findings and results obtained from the project. It would also mention any limitations encountered during the project and propose further areas of research or improvement for future studies. Additionally, the conclusion might reflect on the overall significance of the project in the context of Additional Mathematics.
How do you make normal distribution curve in Excel?
In An Introduction to Excel's Normal Distribution Functions I presented several figures like the one below. This article explains how to create these figures in Excel.
Even if you have no particular reason to chart a normal curve, you might find the techniques interesting. This is because you might need to use similar techniques when you create other charts.
One general technique that I used in this workbook was to set up two worksheets, a Control worksheet and a Data worksheet.
Let's address each of these separately.
First, however, you might wonder how Excel could produce the colors used for this figure. This link explains how to get the free workbook that uses these colors and the free workbook that I explain how to create below.
Set Up the Control WorksheetIn general, you create a normal curve just as you create any other chart in Excel: You set up the data and then chart it.To set up the data, open a new workbook with at least two worksheets. Name one of these Control and the other Data.
In the Control worksheet, first set up the area shown here.
After you enter the labels in column A, assign them as range names in column B. To do so, select the range A2:B8 and choose Insert, Name, Create. Ensure that only Left Column is checked, then choose OK. Do the same for the range A11:B14.
The numbers in the Settings section are values; enter them as shown. Here's a short explanation of each:
Mean. The average value of your data.
StdDev. The Standard Deviation of your data.
NumRows. The number of rows of data to be plotted.
Zmin. The smallest standard deviation to be plotted.
Zmax. The largest standard deviation to be plotted.
PctClear. The percentage of the unshaded area from the left side of the curve, from .0001% to 99.999%.
PctShade. The percentage of the shaded area from the left side of the curve, from .0001% to 99.999%.
The numbers in the Calculations section are returned by formulas:
ShadeLeft =NORMSINV(PctClear)*StdDev+Mean
NORMSINV is the inverse of NORMSDIST function. Given the probability that a variable is within a certain distance of the mean, it finds the z value...the number of standard deviations. To calculate the extent of the shade at its left side, we multiply the NORMSINV result by the amount of the standard deviation, then add the mean.
ShadeRight =NORMSINV(PctShade)*StdDev+Mean
We use the same logic with the PctShade area as for the PctClear area. By doing so, we define the right side of the shaded area.
CurveMin =Zmin*StdDev+Mean
This formula defines the left side of the curve.
CurveMax =Zmax*StdDev+Mean
This formula defines the right side of the curve.
Set Up the Data SheetThis figure shows the top of the Data sheet. Let's take each of these columns in turn:The Sequence value in column A is a counter, from 1 to the number of rows of data. The counter is for convenience only; it's not used in the formulas. In this example, I used 100 rows.
Enter 1 in cell A2, then select the column from cell A2 through the bottom of your spreadsheet. To do so, hold down Ctrl and Shift; and press the Down arrow key. To enter the values, choose Edit, Insert, Series; enter 100 as the stop value in the Series dialog; then choose OK.
Column B returns the Z values from the lowest value to the highest value:
B2: =Zmin
B3: =(Zmax-Zmin)/(NumRows-1)+B2
Column C calculates the chart's X value for each Z value:
C2: =B2*StdDev+Mean
Column D calculates the chart's Y value:
D2: =NORMDIST(C2,Mean,StdDev,FALSE)
Column E calculates the Y values for the area to be shaded:
E2: =IF(C2>ShadeRight,NA(),IF(C2 Copy cell B3 and the formulas in the range C2:E2 down their columns to the last sequence number, in row 101. To complete this step, assign the labels in row 1 of the Data sheet to the data beneath those labels. To do so, first select the range A1:E101. Choose Insert, Name, Create. In the Create Names dialog, make sure only Top Row is checked; then choose OK. To set up the chart of the normal curve, select the range C2:D101. Choose Insert, Chart, or click the Chart Wizard icon. Under Chart Type, choose XY (Scatter). Under Chart Sub-Type, choose "Scatter with data points connected by smooth Lines without markers." Then choose Finish. If you click on the curve, your formula should look something like this: =SERIES(,Data!$C$2:$C$101,Data!$D$2:$D$101,1) You'll find this formula easier work with if you convert its cell references to range names. To do so, edit the formula to: =SERIES(,NormalCurve.xls!X,NormalCurve.xls!Y,1) Here, NormalCurve.xls is the name of my workbook. Your SERIES formula could have a different name. At this point, your chart should look something like the one shown here. To set up the data series for the shaded area beneath the curve, it's easiest to copy the first data series and then modify it. To copy the data series, first select the curve in the chart. Then select the SERIES formula in the formula bar. Copy this formula by pressing Ctrl+C. Then press Esc to de-select the formula. To paste the data series, first click anywhere on the edge of the chart object. After you do so, the SERIES formula will disappear and the words "Chart Area" will appear at the far left side of your formula bar. To paste the formula, click in the formula bar area and then press Ctrl+V. After you paste the SERIES formula, your chart will look something like this. At this point, the chart displays two identical data series, Series 1 and Series 2. Because we want the curve to be shown on top of the shaded area, we'll modify Series 1 to display the shading, and we'll leave Series 2 undisturbed. To select Series 1, first click on the curve. Then look in your formula bar to see which series you've selected. If you see Series 2, press your Down Arrow key once to select Series 1. With Series 1 displayed in your formula bar, change the formula so that it looks like one of these two versions: =SERIES(,Data!$C$2:$C$101,Data!$E$2:$E$101,1) =SERIES(,NormalCurve.xls!X,NormalCurve.xls!Area,1) You'll use the second version if you have assigned range names as I suggested above. At this point, your chart will look the same as it did before. It's now time to change that condition. With Series 1 selected, choose Format, Selected Data Series. In the Y Error Bars tab, choose to display the Minus version of the error bar, and set the Error Amount to a Percentage value of 100%. Then press OK. Here's your initial result. It doesn't look very good, but at least we're heading in the right direction. We next need to change the format the error bars in two ways. We need to make them thicker, which will eliminate the banding in the shaded area, and we typically will change the color of the shaded area. To format the error bars, first click on the error-bar area in your chart. Choose Format, Selected Error Bars. In the Patterns tab, modify the Line settings. Set its color to any color you prefer. And set the line's weight to its thickest setting. Then choose OK. After you make these changes, your chart should look something like this. Now all you need to do is to clean up the chart slightly. To eliminate the legend at the right, select the Legend object within the Chart Area, and then press Delete. To remove the shading in the Plot Area, first select the Plot Area. Choose Format, Selected Plot Area and set the Area shading to None. Then choose OK. Your chart now will look like this. If you want to format the chart so that it looks more like the figure at the beginning of this article, you need to take several additional steps. First, you assign a color patter to the Chart Area, and remove its border. To do so, select the Chart Area. Choose Format, Selected Chart Area, in the Patterns tab choose a color for the Area and choose None for both the Border. If you want to remove the gridlines, select the chart. Choose Chart, Chart Options. In the Gridlines tab, deselect all axes. Then choose OK. If you want to remove the border, select the Plot Area. Choose Border, Selected Plot Area. Set the Border pattern to None, then choose OK. Finally, to assign a number format to the Y axis, first select the axis. Then choose Format, Selected Axis. In the Number tab choose the Custom category and type in this number format: #,###.00. Then choose OK. Your chart should look something like the one shown here. Now, you merely need to adjust its size as needed. As I mentioned at the beginning of this article, use this link to download a free copy of the workbook described here.
"Pro" is a prefix that typically means "in favor of" or "contributing to." It is often used to indicate support, approval, or intensity.
The disappearance of Neandertals was probably caused by?
a combination of factors, including competition with modern humans, interbreeding, and environmental changes such as climate fluctuations. These factors likely contributed to the decline and eventual extinction of the Neandertals.
