Question276406: Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B). 7/24 is the answer but I would really love to know why. This question is worded in a very confusing manner. Found 2 solutions by stanbon, edjones:
Incases 1-3, the data are judged inconsistent with a population mean difference of 0. The P values are less than 0.05 and the 95% confidence intervals do not contain 0. The sample mean difference is much larger than can be explained by random variability about a population mean difference of 0.
Solutionfor P(3, -2, -1), Q(1, 5, 4), R(2, 0, -6), S(-4, 1, 5) find proj PS. QR
Produced 1925-1929. Number built. 202 built as PW-8, P-1, P-2, P-3, P-5, AT-4 and AT-5. Variants. F6C Hawk. P-6 Hawk. The P-1 Hawk ( Curtiss Model 34) was a 1920s open- cockpit biplane fighter aircraft of the United States Army Air Corps. An earlier variant of the same aircraft had been designated PW-8 prior to 1925.
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ïŧŋQ2 - p/3 = 1/6p/2 - q/6 = 5 Get the answers you need, now! ayomieyipoajayi2006 ayomieyipoajayi2006 11/15/2020 Mathematics High School Q/2 - p/3 = 1/6 p/2 - q/6 = 5 2
. Basic Math Examples Solve for p p-3 1/6=-2 1/2 Step 1Step to an improper mixed number is an addition of its whole and fractional write as a fraction with a common denominator, multiply by .Step the numerators over the common 2Step to an improper mixed number is an addition of its whole and fractional write as a fraction with a common denominator, multiply by .Step the numerators over the common 3Move all terms not containing to the right side of the to both sides of the write as a fraction with a common denominator, multiply by .Step each expression with a common denominator of , by multiplying each by an appropriate factor of .Step the numerators over the common the common factor of and .Step the common the common 4The result can be shown in multiple FormDecimal Form
Find a common denominator. I can see that 3p-6 is actually 3p-2 There's also a 2 in 1/2. So a common denominator is 6p-2 Take this common denominator and multiply everything by that 6p-3p-2=6 Distribute the 3 6p-3p+6=6 Combine the ps 3p+6=6 Subtract 6 on both sides 3p=0 Divide 3 on both sides to solve for p p=0 Plug p=0 back into the equation to make sure it works 0/0-2-1/2=3/30-6 -1/2=3/-6 Simplifying 3/-6 would get -1/2 so the answer works!
Pre-Algebra Examples Popular Problems Pre-Algebra Solve for P 2P-3>P+6 Step 1Move all terms containing to the left side of the for more steps...Step from both sides of the from .Step 2Move all terms not containing to the right side of the for more steps...Step to both sides of the and .Step 3The result can be shown in multiple FormInterval Notation
In fact the result holds a bit more generally, namely Lemma $\rm\ \ 24\ \ M^2 - N^2 \;$ if $\rm \; M,N \perp 6, \;$ coprime to $6.\;$ Proof $\rm\ \ \ \ \ N\perp 2 \;\Rightarrow\,\bmod 8\!\,\ N = \pm 1, \pm 3 \,\Rightarrow\, N^2\equiv 1$ $\rm\qquad\qquad N\perp 3 \;\Rightarrow\,\bmod 3\!\,\ N = \pm 1,\ $ hence $\rm\ N^2\equiv 1$ Thus $\rm\ \ 3, 8\ \ N^2 - 1 \;\Rightarrow\; 24\ \ N^2 - 1 \ $ by $\ {\rm lcm}3,8 = 24,$ by $\,\gcd3,8=1,\,$ or by CCRT. Remark $ $ It's easy to show that $\,24\,$ is the largest natural $\rm\,n\,$ such that $\rm\,n\mid a^2-1\,$ for all $\rm\,a\perp n.$ The Lemma is a special case $\rm\ n = 24\ $ of this much more general result Theorem $\ $ For naturals $\rm\ a,e,n $ with $\rm\ e,n>1 $ $\rm\quad n\ \ a^e-1$ for all $\rm a\perp n \ \iff\ \phi'p^k\\e\ $ for all $\rm\ p^k\\n,\ \ p\$ prime with $\rm \;\;\; \phi'p^k = \phip^k\ $ for odd primes $\rm p\,\ $ where $\phi$ is Euler's totient function and $\rm\ \quad \phi'2^k = 2^{k-2}\ $ if $\rm k>2\,\ $ else $\rm\,2^{k-1}$ The latter exception is due to $\rm \mathbb Z/2^k$ having multiplicative group $\,\rm C2 \times C2^{k-2}\,$ for $\,\rm k>2$. Notice that the least such exponent $\rm e$ is given by $\rm \;\lambdan\; = \;{\rm lcm}\;\{\phi'\;{p_i}^{k_i}\}\;$ where $\rm \; n = \prod {p_i}^{k_i}\;$. $\rm\lambdan$ is called the universal exponent of the group $\rm \mathbb Z/n^*,\;$ the Carmichael function. So the case at hand is simply $\rm\ \lambda24 = lcm\phi'2^3,\phi'3 = lcm2,2 = 2\.$ See here for proofs and further discussion.
Dado um polinÃīmio px, temos que seu valor numÃĐrico ÃĐ tal que x = a ÃĐ um valor que se obtÃĐm substituindo x por a, onde a pertence ao conjunto dos nÚmeros reais. Dessa forma, concluÃmos que o valor numÃĐrico de pa corresponde a px onde x = a. Por exemplo, dado o polinÃīmio px = 4xÂē â 9x temos que seu valor numÃĐrico para x = 2 ÃĐ calculado da seguinte maneira px = 4xÂē â 9x p2 = 4 * 2Âē â 9 * 2 p2 = 4 * 4 â 18 p2 = 16 â 18 p2 = â2 Se, ao calcularmos o valor numÃĐrico de um polinÃīmio determinarmos pa = 0, temos que esse nÚmero dado por a corresponde à raiz do polinÃīmio px. Observe o polinÃīmio px = xÂē â 6x + 8 quando aplicamos p2 = 0. p2 = 2Âē â 6 * 2 + 8 p2 = 4 â 12 + 8 p2 = 12 â 12 p2 = 0 Dessa forma, percebemos que o nÚmero 2 ÃĐ raiz do polinÃīmio px = xÂē â 6x + 8, pois temos que p2 = 0. Exemplo 1 Dado o polinÃīmio px = 4xÂģ â 9xÂē + 8x â 10, determine o valor numÃĐrico de p3. p3 = 4 * 3Âģ â 9 * 3Âē + 8 * 3 â 10 p3 = 4 * 27 â 9 * 9 + 24 â 10 p3 = 108 â 81 + 24 â 10 p3 = 41 O valor de px = 4xÂģ â 9xÂē + 8x â 10 para p3 ÃĐ 41. Exemplo 2 Determine o valor numÃĐrico de px = 5x4 â 2xÂģ + 3xÂē + 10x â 6, para x = 2. p2 = 5 * 24 â 2 * 23 + 3 * 22 + 10 * 2 â 6 p2 = 5 * 16 â 2 * 8 + 3 * 4 + 20 â 6 p2 = 80 â 16 + 12 + 20 â 6 p2 = 90 De acordo com o polinÃīmio fornecido temos que p2 = pare agora... Tem mais depois da publicidade ;
Algebra Examples Popular Problems Algebra Solve for p 3p-3-5p>-3p-6 Step 1Simplify .Tap for more steps...Step each for more steps...Step the distributive by .Step from .Step 2Move all terms containing to the left side of the for more steps...Step to both sides of the and .Step 3Move all terms not containing to the right side of the for more steps...Step to both sides of the and .Step 4The result can be shown in multiple FormInterval Notation
p 2 p 3 1 p 6