10,886 Matching Annotations
  1. Aug 2021
  2. Jul 2021
    1. Step 1: Write the unbalanced ionic equation.

      Fe2+(aq)+Cr2O2−7(aq)→Fe3+(aq)+Cr3+(aq)(22.10.1) Notice that the equation is far from balanced, as there are no oxygen atoms on the right side. This will be resolved by the balancing method.

      Step 2: Write separate half-reactions for the oxidation and the reduction processes. Determine the oxidation numbers first, if necessary.

      Oxidation:Fe2+(aq)→Fe3+(aq)Reduction:Cr2+6O2−7(aq)→Cr3+(aq)(22.10.2)(22.10.3) Step 3: Balance the atoms in the half-reactions other than hydrogen and oxygen. In the oxidation half-reaction above, the iron atoms are already balanced. The reduction half-reaction needs to be balanced with the chromium atoms.

      Cr2O2−7(aq)→2Cr3+(aq)(22.10.4) Step 4: Balance oxygen atoms by adding water molecules to the appropriate side of the equation. For the reduction half-reaction above, seven H2O molecules will be added to the product side.

      Cr2O2−7(aq)→2Cr3+(aq)+7H2O(l)(22.10.5) Now the hydrogen atoms need to be balanced. In an acidic medium, add hydrogen ions to balance. In this example, fourteen H+ ions will be added to the reactant side.

      14H+(aq)+Cr2O2−7(aq)→2Cr3+(aq)+7H2O(l)(22.10.6) Step 5: Balance the charges by adding electrons to each half-reaction. For the oxidation half-reaction, the electrons will need to be added to the product side. For the reduction half-reaction, the electrons will be added to the reactant side. By adding one electron to the product side of the oxidation half-reaction, there is a 2+ total charge on both sides.

      Fe2+(aq)→Fe3+(aq)+e−(22.10.7) There is a total charge of 12+ on the reactant side of the reduction half-reaction (14−2) . The product side has a total charge of 6+ due to the two chromium ions (2×3) . To balance the charge, six electrons need to be added to the reactant side.

      6e−+14H+(aq)+Cr2O2−7(aq)→2Cr3+(aq)+7H2O(l)(22.10.8) Now equalize the electrons by multiplying everything in one or both equations by a coefficient. In this example, the oxidation half-reaction will be multiplied by six.

      6Fe2+(aq)→6Fe3+(aq)+6e−(22.10.9) Step 6: Add the two half-reactions together. The electrons must cancel. Balance any remaining substances by inspection. If necessary, cancel out H2O or H+ that appear on both sides.

      6Fe2+(aq)6e−+14H+(aq)+Cr2O2−7(aq)14H+(aq)+6Fe2+(aq)+Cr2O2−7(aq)→6Fe3+(aq)+6e−→2Cr3+(aq)+7H2O(l)→6Fe3+(aq)+2Cr3+(aq)+7H2O(l)(22.10.10)(22.10.11)(22.10.12) Step 7: Check the balancing. In the above equation, there are 14H , 6Fe , 2Cr , and 7O on both sides. The net charge is 24+ on both sides. The equation is balanced.

    1. annotation you can easily find it by going to your homepage in hypothes.is and then filtering by tags.  So you may want to make tags like "exam 1", or "nomenclature".  If you then filter with your hypothes.is user name and exam 1, you see those items you tagged (see video 11\PageIndex{1} at 3:00 min.  If you just do exam 1, you filter for everything the class tagged exam 1.  You can then click the contextual link by the annotation, and hypothes.is will open that page, navigate to the highlighted text and display the annotation. (Note: In LibreText the highlights are hidden by default, and you need to click the "eye" with the slash over it (figure 22\PageIndex{2}.  

      third annotation

    2. n annotation you simply highlight the text you want to annotate, choose "Annotate" and write in the overlay.   Note, the first time you open up a page it will post to "Public" and you need to change that to your class group.  Once you have started posting to the class group that will be the default option, but initially the default is publ

      Weird, it said you can not annotate, but it worked. I am double checking.

    3. . Annotations can be used in two fundamentally different ways.  First, through the proper use of tags you can use it as a tool to assist you in organizing your notes and preparing for exams, quizzes and laboratory experiments. Second, if annotations are posted to your class group you can use it as a tool to communicate with your instructo

      Testing to see if an annotation in transcluded text works. I do not expect it to work

    1. Thene

      Then we

    2. category / type change  event fact system stage / phase task / obligation / duty tendency / trend / pattern

      It's sort of arbitrary, but I'd cut these items off the list to shorten it a bit. I think students would get the least mileage out of these words, and deleting them focuses students where they need to be with the other words.

    1. used in two fundamentally different ways.  First, through the proper use of tags you can use it to organize your no

      checkthis out

    1. Metacognition is "thinking about thinking"

      This is a public annotation trying to get students to think about the use of tags as they study from the perspective of metacognition

    1. Enter each data set into an appropriate quantitative software analysis environment and generate Stern-Volmer plots for each (i.e. plot the data according to Equation 1010\ref{10} and include a best-fit line

      kl

    1. Lincoln
    2. Abraham Lincoln

      Post Emancipation Lincoln wanted to kick former slaves out of America. https://psmag.com/news/remember-that-time-abraham-lincoln-tried-to-get-the-slaves-to-leave-america-55802

    3. immediatist

      a policy or practice of gaining a desired end by immediate action specifically : a policy advocating the immediate abolition of slavery.

    4. stockholders

      I did not know about this people. Very interesting

    5. manumitted

      release from slavery; set free.

    6. Harriet Tubman

      I found a video of Harriet Tubman's decedents. https://www.youtube.com/watch?v=8fLf20vJNiU&ab_channel=WUSA9

    7. Fugitive Slave Law of 1850

      June 28, 1864, that both of the Fugitive Slave Acts were repealed by an act of Congress

    8. The master is frequently compelled to sell this class of his slaves, out of deference to the feelings of his white wife; and, cruel as the deed may strike any one to be, for a man to sell his own children to human flesh-mongers, … for, unless he does this, he must not only whip them himself, but must stand by and see one white son tie up his brother, of but few shades darker … and ply the gory lash to his naked back.”

      This is horrifying. I do not like this at all.

    9. prominent

      important; famous.

    1. miscellany

      a group or collection of different items; a mixture.

    2. hawthorns

      New word Hawthorn: Crataegus, commonly called hawthorn, quickthorn, thornapple, May-tree, whitethorn, or hawberry, is a genus of several hundred species of shrubs and trees in the family Rosaceae, native to temperate regions of the Northern Hemisphere in Europe, Asia, North Africa, and North America.

    1. For example, there is a difference between “No thanks, I’m not hungry” and “I’ve told you, I’m not hungry.”

      Reminds of the Robot devil's quote “Your lyrics lack subtlety! You can't just have your characters announce how they feel! That makes me feel angry!"

    2. 1st person

      I saw my sister at the park with her baby and a much older man. I always forget how much older her husband is.

    3. Dear White People Volume 1 or Arrested Development Season 4, both Netflix TV series

      Also Pulp fiction

    4. Consider, for example, the ways in which the desert itself might be considered a character in "Bajadas" by Francisco Cantú.

      I never considered giving personally to objects or terrains.

    5. Nonlinear Narrative

      I think this is like a Tarurtino movie. This would be an intresting way of writing. It would allow for different perspectives of the main players in the events.

    6. In Medias Res

      Oh I bet you wanna know how I got here

    7. the sharks with laser beams attached to their heads

      Austin Powers!

    8. zero in on the events that drive a story and prune out extraneous information.

      This is an interesting concept that I will have to focus on.

    9. While it's fine to have an outline or first draft that recounts the events of the story, the final draft should include dialogue, immersive description, plot twists, and metaphors to capture your reader's attention as you write.

      I have not at length about my life or it being and this process makes sense since your telling a story. I would write what happened first then go back and add the flavor

    10. tactile (touch), or gustatory (taste)

      fancy words I didn't know

    11. My breath escaped in ragged bursts, my quadriceps burning as I crested the summit. The lake stretched before me, aquamarine, glistening in the hot August afternoon sun. Ponderosa pines lined its shores, dropping their spicy-scented needles into the clear water. Despite the heat, the Montana mountain air tasted crisp.

      This was a better lake to visit

    1. Frederick Douglass' creative nonfiction account of the horrors of slavery and his escape from it was so powerfully written that it is largely credited, along with Douglass' speeches, as helping end slavery and empower African-American citizens (Ceasar).

      I read an excerpt from his memoir and it was introduced by a white man that was stating that this black man was actually smart enough and how impressed he was by Douglas.

  3. human.libretexts.org human.libretexts.org
    1. the set of sun

      Homonym of “son.” This line foreshadows the conflict revolving around succession aka the “set of son.”

      [note by Elizabeth Ferry]

    1. other marginalized groups. 

      Another annotation note might help right after this sentence that shows how the author shifts to a discussion of terms for other marginalized groups.

    2. ends

      I would not say "ends" here, because there is another paragraph to the essay that takes another turn.

    3. W.E.B Dubois

      Something is needed here. I would suggest making Dubois possessive.

    1. lysogeny

      Imma stay into into you aloof all by self until my "mind" changes. Then I'll one day detach from you and BOOM I'll kill you then. Ain't I an angel?

      Funny how everyone understands who is narrating this story 😶🔫

    1. default value

      預設值,為0

    2. The for loop traverses the string. Each time through the loop, if the character c is not in the dictionary, we create a new item with key c and the initial value 1 (since we have seen this letter once). If c is already in the dictionary we increment d[c]

      看到幾次就藉由迴圈加幾次 藉由字典來儲存字元

    1. For example, consider the following without these commands:

      second test

    2. rendering of complicated mathematics, there's also a great app called MathPix that you can get on your smart phone and computer that will allow you to scan or select an equation, and it will give you the LaTeX for it.  Since your account synchs between the phone app and the computer, you can access the resulting LaTeX on your computer to copy and paste into LibreTexts.  You can also select an image of an equat

      test will remove

  4. Jun 2021
    1. Es imposible medir el cambio de entalpía partiendo de un cristal sólido y convirtiéndolo en sus iones gaseosos dispersos. Es aún más difícil imaginar cómo podría hacer lo contrario: comience con iones gaseosos dispersos y mida el cambio de entalpía cuando estos se conviertan en un cristal sólido. En cambio, las entalpías de celosía siempre deben calcularse, y hay dos formas completamente diferentes de hacerlo. Puede utilizar un ciclo de la ley de Hess (en este caso llamado ciclo de Born-Haber) que implica cambios de entalpía que se pueden medir. Las entalpías de celosía calculadas de esta manera se describen como valores experimentales. O puede hacer cálculos al estilo de la física para determinar cuánta energía se liberaría, por ejemplo, cuando los iones considerados como cargas puntuales se unen para formar una red. Estos se describen como valores teóricos. De hecho, en este caso, lo que realmente está calculando se describe correctamente como energías reticulares.

      entañpia celosia

    1. /*<![CDATA[*/ var front = "auto"; if(front=="auto"){ front = "Cellular Respiration Graphic Organizer"; if(front.includes(":")){ front = front.split(":")[0]; if(front.includes(".")){ front = front.split("."); front = front.map((int)=>int.includes("0")?parseInt(int,10):int).join("."); } front+="."; } else { front = ""; } } front = front.replace(/_/g," "); MathJaxConfig = { TeX: { equationNumbers: { autoNumber: "all", formatNumber: function (n) { if(false){ return front + (Number(n)+false); } else{return front + n; } } }, macros: { PageIndex: ["{"+front+" #1}",1], test: ["{"+front+" #1}",1] }, Macros: { PageIndex: ["{"+front+" #1}",1], test: ["{"+front+" #1}",1] }, SVG: { linebreaks: { automatic: true } } } }; MathJax.Hub.Config(MathJaxConfig); MathJax.Hub.Register.StartupHook("End", ()=>{if(activateBeeLine)activateBeeLine()}); /*]]>*/ /*<![CDATA[*/window.addEventListener('DOMContentLoaded', function () { $('iframe').on('load', function () { $(this).iFrameResize({ warningTimeout: 0, scrolling: 'omit' }); }) })/*]]>*/  Get Page Citation Get Page Attribution Back to top Cell Structures: A Graphic Organizer Cheek Cell Lab Was this article helpful?YesNo/*<![CDATA[*/{"Page.FeedbackRating.label.last-rated":"-- You last rated this article on {0}","Page.FeedbackRating.message.contact.no":"No","Page.FeedbackRating.message.contact.yes":"Yes","Page.FeedbackRating.message.submit.error":"An error occurred while attempting to send your feedback. Please try again at a later time.","Page.FeedbackRating.message.submit.success":"Your feedback has been successfully submitted. You can submit more feedback at any time."}/*]]>*/ Recommended articles Cell Signaling: How Is Glucose Taken Up by Cells?How Do Viruses Infect Cells?Reinforcement: Cell DivisionWhat Causes Mitochondrial Disease – CERMitochondria, Aging, and Metabolism - CER {"Skin.Columbia.label.no-recommended-articles":"There are no recommended articles."} Classifications This page has no classifications. Tags This page has no tags. © Copyright 2021 Biology LibreTexts Powered by MindTouch ® The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Legal. Have questions or comments? For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. /*<![CDATA[*/ MathJax.Ajax.config.path["mhchem"] = "https://cdnjs.cloudflare.com/ajax/libs/mathjax-mhchem/3.3.2"; MathJax.Hub.Config({ jax: ["input/TeX","input/MathML","output/SVG"], extensions: ["tex2jax.js","mml2jax.js","MathMenu.js","MathZoom.js"], TeX: { extensions: ["autobold.js","mhchem.js","color.js","cancel.js", "AMSmath.js","AMSsymbols.js","noErrors.js","noUndefined.js"] }, "HTML-CSS": { linebreaks: { automatic: true , width: "90%"}, scale: 85, mtextFontInherit: false}, menuSettings: { zscale: "150%", zoom: "Double-Click" }, SVG: { linebreaks: { automatic: true } }}); /*]]>*/

      glucose

    1. Perhaps mention as well that textbooks - well, any source, but textbooks specifically can be written from the dominant cultural view and have certainly been inaccurate - the need for critical examination no matter how "expert" the source - I think a note about how textbooks have erased or hidden the history of some people, generally people of color, poor, etc.

    2. probably

      You may know - better so that it doesn't assume that they do know

    1. data gathered from an experiment on color perception, an interview, or Farm Service Administration photographs from the 1930s.

      Also can we have examples that are representative of people of color - maybe instead of Kurt Vonnegut (though I love him! ) - the letters of Toni Morrison (?) - just a made up example, but look to get more primary sources that reflect diversity - or say the redlining map drawn in Jim Crow, etc.

    2. Also, these are skills needed for a member of a democracy and for all levels of work - the phrase professional leadership role seems elitist a bit? Emphasize for democracy and for all critically thinking students (?)

    1. Exercise 5.1.15.1.1\PageIndex{1}

      This instant feedback is cool! Can you build more of these into other practice exercises? The opportunity to actively engage and then get feedback is great!

    2. I wonder if you can emphasize the equity aspect even more that reading and analyzing deeply empowers us to share our own informed perspective. We are able to take part in the conversation. We develop our own authority and our ideas join the academic conversation

    1. 3.02×10−33photonsmin

      The correct answer is 3.02*10^27 photons/minute

    2. E=1.99×1037J

      The correct answer is E = 1.99*10^-23 J

    3. 1.658×1040

      The correct answer is 1.66*10^22 photons/minute

    4. E=1.99×1037J

      This is incorrect. The correct answer is 1.99*10^-23J.

    5. E=3.618×10−37J

      The correct answer is 3.614*10^-19 J and not 3.618*10^-37

    6. (6.634×10−34J⋅s

      The value of h is 6.62610^-34 J/s and not 6.63410^-34

    7. 550×109m

      The wavelength is 550 nm = 550*10^-9 and not 550*10^9

    8. E=4.3×10−19J

      The correct answer is 4.3 * 10^-47 and not 4.3*10^-19

    1. calculating the Ka value for acids

      calculating the Keq values for solutes

      calculating the dissociation and equilibrium values for solutions

      you need a certain doss

      from table 2.8.1 of representative acid constants and from knowledge of functional groups you can guestimate the relative acidity of compounds

    1. [A]0/2.

      $$[A]o/2$$

    2. ln[A]0[A]=kt

      What is A? Not defined and does not need [ ] around it.

      Concentration should be re-framed from use with nuclear decay!

    3. The half-life of a first-order reaction is independent of the concentration of the reactants

      both half-life and number of nuclides, N are independent variables

      use of concentration is not typical with nuclear reactions!

    4. Radiocarbon Dating. A plot of the specific activity of 14C versus age for a number of archaeological samples shows an inverse linear relationship between 14C content (a log scale) and age (a linear scale).

      Reference?

    5. The half-lives of radioactive isotopes can be used to date objects.

      This is incorrect. The N/No ratio is used to determine the age of materials. The half-life influence the range of ages that can be determined.

    1. Figure 1.2.11.2.1\PageIndex{1}:  Raspbian download options as of 01/22/2019

      figure 1.2.1 is outdated because the raspberrypi website has been updated

    2. Raspbian Buster with desktop and recommended software

      The name of the software has been changed from Raspbian Buster to Raspberry Pi OS

    1. Each element below should be addressed or each question should be answered.

      This formatting style is very convenient. Following these "elements" step by step is a helpful way to put together an abstract and structure the format of the paper.

    2. Plan to spend much time on this Abstract and the Introduction; the other sections will come more quickly the more time you spend on the Abstract and the Introduction.

      I have never written an IMRAD style paper before, so learning about the Abstract was interesting. This sentence stood out to me, because, previously, I did not realize that the Abstract could be so beneficial in writing the other sections of an IMRAD paper. I've learned that the Abstract acts as a summary or overview of a paper, but I had no idea the Abstract could help the writer in this way. I will keep this in mind as I write IMRAD papers in the future.

    1. Python 3.7 version

      Python version is outdated. Instead of 3.7 version Anaconda now supports the 3.8 version. Because of this figure 1.1.2 is outdated.

    2. latest version (3.2.6 as of 1/21/2020)

      Thonny latest version is outdated. The latest version is currently 3.3.10. Because of this figure 1.1.15 is also outdated.

    1. The reaction can be followed visually because the product (NO2NO2\ce{NO_2}) is colored, whereas the reactant (N2O4N2O4\ce{N_2O_4}) is colorless

      My teacher showed us this in AP chem last year!

  5. chem.libretexts.org chem.libretexts.org
    1. Lycopene from the neo-Latin lycopersicum, the tomato species, is a bright red carotene and carotenoid pigment and phytochemical found in tomatoes and other red fruits and vegetables, such as red carrots, watermelons, gac, and papayas, although not in strawberries, or cherries. Foods that are not red may also contain lycopene, such as asparagus and parsley.

      Lycopene

    1. iℏ∂∂tΨ(x,t)=−ℏ2m∇2Ψ(x,t)+V(x)Ψ(x,t)(1.5.1)

      Equation 1.5.1

      effectively describes matter as a wave that fluctuates with both displacement and time.

    2. iℏ∂∂tΨ(x,t)=−ℏ2m∇2Ψ(x,t)+V(x)Ψ(x,t)(1.5.1)(1.5.1)iℏ∂∂tΨ(x,t)=−ℏ2m∇2Ψ(x,t)+V(x)Ψ(x,t) i\hbar\dfrac{\partial}{\partial t}\Psi(x,t)=\dfrac{-\hbar}{2m}\nabla^2\Psi(x,t) +V(x)\Psi(x,t) \label{1.1} Equation 1.5.11.5.1\ref{1.1} effectively describes matter as a wave that fluctuates with both displacement and time.

      iℏ∂∂tΨ(x,t)=−ℏ2m∇2Ψ(x,t)+V(x)Ψ(x,t)(1.5.1) Equation 1.5.1 effectively describes matter as a wave that fluctuates with both displacement and time.

    1. he above video shows, placing zinc metal into the copper(II) solution results in a spontaneous redox reaction (ΔG<0ΔG<0\Delta G <0), and if we placed the copper metal into the zinc solution no reaction would occur (ΔG>0ΔG>0\Delta G >0). In an electrochemical cell, we allow electrons to be transferred, which will spontaneously occur in the direction of ΔG<0ΔG<0\Delta G <0, and a cell operating in this fashion is called a galvanic or voltaic cell, which can be used to provide energy to do work, like the common "battery" we use in flashlights and electrical devices. Just as

      test

    1. No one is perfect and you might come across some parts in Fritzing that just don’t fit the breadboard. For example, depending on the library version, your Adafruit T-Cobbler Plus could be the wrong size

      this needs to be clearer. I think....

    1. A radial node is a sphere (rather than an angular node which is a flat plane) that occurs when the radial wavefunction for an atomic orbital is equal to zero or changes sign

      an area having zero electrons is known as a radial node /.

  6. May 2021
    1. -ate suffix, while the one with the fewer number of oxygen atoms gets the -ite suffix. The four oxoanions of chlorine are as follows:

      Chemistry.

    1. \[\begin{array}{rll} \mathfrak{A} \models \phi \left[ s \right] & \text{if and only if} \: \mathfrak{A} \models \neg \alpha \left[ s \right] & \\ & \text{if and only if} \: \mathfrak{A} \not\models \alpha \left[ s \right] & \\ & \text{if and only if} \: \mathfrak{B} \not\models \alpha \left[ s \right] & \text{inductive hypothesis \\ & \text{if and only if} \: \mathfrak{B} \models \neg \alpha \left[ s \right] & \\ & \text{if and only if} \: \mathfrak{B} \models \phi \left[ s \right]. \end{array}\]

      Seems to be broken for me

    1. will start by solving the single reactant rate law. Then show how to reduce multi-reactant problems to single reactant problems. We will also introduce two different techniques for solving these. First the Ratio (Two State) Technique, which works well for "precise data", and then the graphing technique, which needs to be used when the data is unpreci

      help

    2. to reduce the number of independent variables to one. This is done by making successive measurements where all reactant concentrations are held constant except for one, with that data showing the rate law as expressed for that reactant, and it can then be solved as a single reactant problem This lesson will start by solving the single reactant rate law. Then show how to reduce multi-reactant problems to single reactant problems. We will also introduce two different techniques for solving these. First the Ratio (Two State) Technique, which works well for "precise data", and then the graphing technique, which needs to be used when the data is unprecise data.

      test

    1. he solution is

      where does this function come from?

    2. Writing this as a differential equation in x, we obtain

      x is motion, and the derivative of velocity is acceleration, so since v = change in distance over time, deriving the derivative gives you the 2nd derivative, acceleration.

      TIME IS CHANGE, thus it is deltax

    3. damping caused by the fluid.

      drag caused by the fluid

    1. Load the sample by jabbing the open end of a capillary tube into a pile of the sample. With closed end down, drop the tube down a long hollow tube so that it hits the benchtop and packs the sample into the closed end of the tube. Load the sample to a height of 222-3mm3mm3 \: \text{mm}. Place the sample into a slot in the MelTemp. Turn the dial to begin heating. Heat at a medium rate to 20oC20oC20^\text{o} \text{C} below the expected melting point. Then heat very slowly (1oC1oC1^\text{o} \text{C} every 30 seconds). Record the temperature where the first droplet of liquid is seen (there is movement in the tube). Record the second temperature when the entire sample liquefies (the entire sample changes from opaque to transparent). Record a melting range, e.g. 120120120-122oC122oC122^\text{o} \text{C}. If another melting point trial is to be performed, cool the metal block to at least 20oC20oC20^\text{o} \text{C} below the next melting point, by wiping it with a wet paper towel or cooling with a jet of air.

      Summary of the determination of melting points

    1. Carbon is the most important element to life. Without this element, life as we know it would not exist. As you will see, carbon is the central element in compounds necessary for life.

      carbon is involved also in cellular processes!

    1. Thus, the crystal has a net negative charge and is referred to as N-type material. The energy level of the donor electrons is just below the bottom of the conduction band. In other words, the difference between the donor level and the bottom of the conduction band is much, much smaller than the band gap itself.

      N-type semiconducotr

    1. The hand is a straight (consecutive ranks, as in 5, 6, 7, 8, 9, but not all from the same suit).

      The back of the book gives the answer as 10(4^5-1), which is incorrect. There are 10 4^5 "straights" where the suit doesn't matter, the sequence can even all be the same suit among the 10 4^5 such hands. So you want to subtract out the "straights" of the same suit, there are 40 such hands. There are 10 possible sequences 1)A2345 2)23456,3)34567,...10)10JQKA. Each sequence can be one of the 4 suits so thats 4 10=40 total. A straight of all the same suit is a straight flush, which is part h of the question. So the final answer to the number of straights but not from the same suit is 104^5-40.

    1. m+nm∼n⇔m+nm\sim n \,\Leftrightarrow\, m+n is even

      The answer in the back of the book states that there are 3 equivalence classes(ECs): [0], [1], & [2]. But I think it is incorrect and there are only 2, one for evens and one for odds because if you add any 2 even numbers you get an even sum, same if you add 2 odd numbers. Only way you get an odd sum is if you add one even and one odd #. So all the even numbers would belong to the even EC and all the odd numbers would belong to the odd EC.

    2. |m−3|=|n−3

      The answer in the back of the book states that the equivalence classes(ECs) are of the form {3−k, 3+k} but I dont think that is correct. I believe the correct answer is that the ECs are [a] where a \(\in\) Z, so an equivalence class for each integer in Z.

    1. [−1,1]⋂x∈(1,2)(1−2x,x2)=[−1,1]\bigcap_{x\in(1,2)} (1-2x,x^2) = [-1,1], ⋃x∈(1,2)(1−2x,x2)=(−3.4)

      Correction: Part a) (-1,1) Part b) (-3,4)

    2. En=E0={0}

      Correction: Since 0 is not a natural number and 1 is the smallest natural number, the correct answer to part a,the intersection question is {-1,0,1}.

    3. {(−2,−3),(−2,0),(−2,3),(−2,−3),(−2,0),(−2,3)}{(−2,−3),(−2,0),(−2,3),(−2,−3),(−2,0),(−2,3)}\{(-2,-3), (-2,0), (-2,3), (-2,-3), (-2,0), (-2,3)\}

      Correction, should be: {(−2,−3),(−2,0),(−2,3),(2,−3),(2,0),(2,3)}

    4. true

      2 is not a member of the interval (2,3) because (2,3)={x | 2<x<3}. It does not include 2. So the answer should be false.

    5. PQRS is a parallelogram

      Should read: "PQRS is not a parallelogram."

    6. For all integers nnn, if nnn is prime and nnn is even, then n≤2n≤2n\leq2.

      There's a typo, it should read: For all integers n, if n is prime and n>2, then n is not even.

    7. true

      I think there's an error in this solution. The left hand side of the equation in question 2.5.9, is equivalent to the truth value True. Thus, it is not equivalent to Not(P).

    1. You can remember this with the anagram CORN.

      The proceeding sentence here in no way, shape, or form lends itself to spelling the word corn while being in anyway remotely useful as a anagram.

    1. rigid container

      Because if we don't have the rigid contained ,the volume of the container will increase on increasing the temperature.

    1. Una

      I like how the article is split into Spanish and English. It makes it much easier for me to understand. I can see now where the adjective will fit after the adjective clause. I also now understand how the adjective clauses are introduced with lo que when the antecedent is not mentioned.

    2. El subjuntivo se usa en cláusulas adjetivas cuando la existencia del antecedente es desconocida, irreal o incierta para quien habla:

      This idea that the subjunctive can be used to help express a statement even if you don't know if it is true is interesting. It's something that we use heavily within your daily life, but we rarely realize that we are doing it.

    1. he left part of Figure 12.7 b shows two isobaric transitions for converting ice to steam. The top transition at 1 atm is above the triple point and so liquid water is stable, while the lower transition is below the triple point and the ice sublimes to steam without ever forming a liquid phase. It is important to understand the relationship of these graphs and the differences. The phase diagram represents the phase that would exist for a system at equilibrium as a function of the pressure and temperature. The ri

      test

    1. convolution of number sequences, multiplication of polynomials, and the multiplication of integers (except for the carry operation) are all the same operations

      不进行进位的integer multiplication,实际上就是有限域上的multiplication,因此用于FFT的技术,也能用于NTT 多项式运算的特点正是,只能合并同类项,而不能从低次项向高次项"进位"

  7. Apr 2021
    1. requency is the accumulation of the previous relative frequencies

      Best responses from the following table

    2. how frequently e

      Whoa. This entire text is what I'm studying for my STATs class. Apparently, this is worth the struggle.

    1. [Cl−] = (1.0 + x)

      Why??

    2. Thus the solubility of AgCl in pure water at 25°C is 1.33 × 10−5 M.

      We can practice this same type of problem in Aleks. As long as there is 1:1 mol ratio, pure water solubility of a compound will be xx=Ksp.

    3. Kf

      [products]/[reactants]

    1. Neither solid calcium oxalate monohydrate nor water appears in the solubility product expression because their concentrations are essentially constant.

      Are reactants ever in a Ksp expression? If it's measuring the solubility product, do we assume the reactant(s) are always solid?

    1. Then Henderson-Hasselbalch equation is used to calculate the pH of a solution given the pKa and the concentration of acid and conjugate base. (15 pts) The equation is:

      this assignment teaches the use of random number generators