Do spells such as Hex or enhance ability affect attack rolls made using the affected ability score?  These spells reference advantage/disadvantage on ability checks, but I am unsure whether an attack roll constitutes an ability check.  I did reference these spells specifically in case there is a difference between a specific ruling and the general rule.
The Barbarian's Rage ability gives advantage on Strength checks and saving throws.  Does this mean that the Barbarian gets advantage to attack rolls as well? Is an attack a check, or since saving throws are mentioned, that means it does not apply to attacks?
The junction has a stop sign on each of the four entrances.   The junction has a stop sign on each of the 4 entrances.   The first is preferred, for some reason, by many English texts. Why? I haven't seen this phenomenon in other languages. Words for "a bit sad" and "a bit happy"? Does opacity:0 have exactly the same effect as visibility:hidden help with some Hilbert style proofs in a propositional logic axiom system. I'm very new to classical propositional logic, and my lecturer is using a system with the following axioms:  A1. X→(Y→X)  A2. (X→(Y→Z))→((X→Y)→(X→Z))  A3. (¬Y→¬X)→(X→Y)  Use uniform substitution and Modes Ponens (MP) as rule of inference. Deduction Theorem also allowed.  I'd like to deduce the following:  (a) X, Y ⊢ ¬(X→(¬Y)) (conjunction, but expressed in terms of NOT and IMPLIES)  (b) X→((X→Y)→Y)  (c) (X→Y)→(((¬Y)→X)→Y)  (d) (((¬Y)→X)→Y)→(X→Y)  Remark: The last two are to show that the axiom (A3) can be replaced with a different axiom:  B3. (¬Y→¬X)→(((¬Y)→X)→Y).  Solution: Bram28 proves (b) and (c) below. I demonstrate (a) and (d).  (d) is alright; first, I claim that X, ((¬Y→X)→Y) ⊢ Y.  Axiom (A1) gives ⊢X→(¬Y→X) so that ((¬Y→X)→Y)⊢X→Y by Hypothetical Syllogism (HS), which Bram28 shows to be valid.  Now that we have ((¬Y→X)→Y)⊢X→Y just apply the deduction theorem to get what we want: ⊢((¬Y→X)→Y)→(X→Y).  (a) is slightly trickier. Axiom (A1) gives ⊢ Y→(X→Y) so that X, Y ⊢ (X→Y).  Next, by part (b), we have as a theorem that ⊢X→((X→¬Y)→¬Y).  Therefore X, Y ⊢(X→¬Y)→¬Y.  But ⊢(¬¬(X→¬Y))→(X→¬Y) by DN Elim, which Bram28 shows to be valid.  By HS, X, Y ⊢(¬¬(X→¬Y))→¬Y.  By Axiom (A3) and MP, X, Y ⊢(Y→¬(X→¬Y)).  Also, rather trivially X, Y ⊢Y.  Finally by MP we conclude X, Y ⊢¬(X→¬Y) as required. How to minimize residual sum of squares of an exponential fit? I have the following data and would like to fit a negative exponential growth model to it:  Days &lt;- c( 1,5,12,16,22,27,36,43) Emissions &lt;- c( 936.76, 1458.68, 1787.23, 1840.04, 1928.97, 1963.63, 1965.37, 1985.71) plot(Days, Emissions) fit &lt;- nls(Emissions ~ a* (1-exp(-b*Days)), start = list(a = 2000, b = 0.55)) curve((y = 1882 * (1 - exp(-0.5108*x))), from = 0, to =45, add = T, col = "green", lwd = 4)   The code is working and a fitting line is plotted. However, the fit is visually not ideal, and the residual sum of squares seems to be quite huge (147073).   How can we improve our fit? Does the data allow a better fit at all?  We could not find a solution to this challenge on the net. Any direct help or linkage to other websites/posts is greatly appreciated. What is the difference between "I've been to China" and "I've gone to China"? Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. Paying off student loan or using that money for a downpayment on a house I'm attempting to make an elevation profile from a DEM in ArcMap using the Interpolate Line tool.  I've done this before, and it has worked great--basically I just draw a line with Interpolate Line, then click Profile Graph to get the elevation profile.  However, for some reason, it's not working now: when I draw out my line, nothing shows up on the map.  I don't get a line, and I can't figure out what I'm doing wrong.  I've searched online for an answer, but to no avail.    Any tips? In the 3d-view workspace, we can use a random color to give our separated object a distinct look.  What if I don't like the result and I want to randomize the color again?   Swapping the setting doesn't change the random seed in color.    (Blender 2.80.64.) Bounty not awarded automatically — bug? Why sum of two little "o" notation is equal little "o" notation from sum? Why sum of two little "o" notation is equal little "o" notation from sum?  $o( f(n) ) + o( g(n) ) = o( f(n) + g(n) ) ?$  For example:   $f(n) = n^3$  $g(n) = 1/n$   so    $o(f(n)) = n^2$  $o(g(n)) = 1/n^2$   and    $o( f(n) ) + o( g(n) ) = n^2 + 1/n^2$ $o( f(n) + g(n) ) = n^2$   Of course, I could write it like   $o( f(n) ) + o( g(n) ) = n^2 + o( g(n) )$ $o( f(n) + g(n) ) = n^2 + o( g(n) )$   My question is why? I don't understand it, because in first we always get two parameters. I have created this with cycles:  But the edge between the glowing and non glowing materials is very sharp. The material was manually applied to faces in edit mode. Is there any way I can smooth the edge between them in cycles? Prove: $$ (a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}, \qquad \forall n \in \mathbb{N} $$ I have have tried using the triangle inequlity $ |a + b| \le |a| + |b| $,  without any success. Given a list ["foo", "bar", "baz"] and an item in the list "bar", how do I get its index (1) in Python? Let $a,b,c$ be positive real numbers satisfying $$(1+a+b+c)\left(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=16,$$ then $a+b+c=3$.  I thought about the application of the AM-GM-HM inequality, but in vain. I also thought about splitting 16 into factors and comparing but went nowhere. Any ideas. Thanks beforehand. How to sanity check a date in Java I find it curious that the most obvious way to create Date objects in Java has been deprecated and appears to have been "substituted" with a not so obvious to use lenient calendar.  How do you check that a date, given as a combination of day, month, and year, is a valid date?  For instance, 2008-02-31 (as in yyyy-mm-dd) would be an invalid date. Cardinality of a totally ordered union Let $(X_{\alpha})_{\alpha \in A}, (Y_{\alpha})_{\alpha \in A}$ be families of sets such that for $\{X_{\alpha} \mid \alpha \in A \}$ and $\{Y_{\alpha} \mid \alpha \in A \}$ are totally ordered by inclusion. We have $(X_{\alpha},Y_{\alpha}) \neq (X_{\beta},Y_{\beta})$ for $\alpha \neq \beta$. Suppose that $|X_{\alpha}| \leq |Y_{\alpha}|$ for any $\alpha \in A$. It is true that $|\bigcup_{\alpha} X_{\alpha}| \leq |\bigcup_{\alpha} Y_{\alpha}|$? Using "of" or apostrophe, which is more common? How do I run a Perl script from within a Perl script? I've got a Perl script that needs to execute another Perl script. This second script can be executed directly on the command line, but I need to execute it from within my first program. I'll need to pass it a few parameters that would normally be passed in when it's run standalone (the first script runs periodically, and executes the second script under a certain set of system conditions).  Preliminary Google searches suggest using backticks or a system() call. Are there any other ways to run it? (I'm guessing yes, since it's Perl we're talking about :P ) Which method is preferred if I need to capture output from the invoked program (and, if possible, pipe that output as it executes to stdout as though the second program were invoked directly)?  (Edit: oh, now SO suggests some related questions.  is close, but not exactly the same as what I'm asking. The second program will likely take an hour or more to run (lots of I/O), so I'm not sure a one-off invocation is the right fit for this.) I recently got a lenovo Y40 laptop and after i installed ubuntu 14.04 (also in the live usb) Wireless doesn't work. It says that it is disabled by hardware switch, however the hardware switch doesnt work (its intention is to put on airplane mode but does nothing when pressed in ubuntu) wireless works in windows and the BIOS has it enabled. I tried resetting the BIOS but it still doesn't work. Here are some command outputs  lspci:  03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 10) 04:00.0 Network controller: Intel Corporation Wireless 3160 (rev 93)   rfkill list all:   0: ideapad_wlan: Wireless LAN     Soft blocked: no     Hard blocked: yes 1: ideapad_bluetooth: Bluetooth     Soft blocked: no     Hard blocked: yes 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no 3: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no   lswh:     *-network         description: Ethernet interface         product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:03:00.0         logical name: eth0         version: 10         serial: f8:a9:63:31:2e:b6         size: 1Gbit/s         capacity: 1Gbit/s         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation         configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168g-3_0.0.1 04/23/13 ip=192.168.1.4 latency=0 link=yes multicast=yes port=MII speed=1Gbit/s         resources: irq:64 ioport:4000(size=256) memory:c0604000-c0604fff memory:c0600000-c0603fff *-pci:3      description: PCI bridge      product: Lynx Point-LP PCI Express Root Port 4      vendor: Intel Corporation      physical id: 1c.3      bus info: pci@0000:00:1c.3      version: e4      width: 32 bits      clock: 33MHz      capabilities: pci normal_decode bus_master cap_list      configuration: driver=pcieport      resources: irq:59 memory:c0500000-c05fffff    *-network DISABLED         description: Wireless interface         product: Wireless 3160         vendor: Intel Corporation         physical id: 0         bus info: pci@0000:04:00.0         logical name: wlan0         version: 93         serial: a0:88:69:90:0a:38         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical wireless         configuration: broadcast=yes driver=iwlwifi driverversion=3.13.0-32-generic firmware=22.24.8.0 latency=0 link=no multicast=yes wireless=IEEE 802.11abgn         resources: irq:66 memory:c0500000-c0501fff