Show that there are no simple groups of order

$$p^rm$$

, where p is a prime, r is a positive integer, and m < p.

If p is prime, prove that there are no simple groups of order 2p.

Isomorphism f maps cyclic group G to group H. Show that H must be cyclic.

When spending large amounts to purchase advertising time, companies want to know what audience they'll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking forward more to the football game or to watching the commercials. Among the men, 16% were planning to watch and were looking for ward primarily to the commercials. Among women, 30% were looking forward primarily to the commercials. a) Was this a stratified sample or a blocked experiment? Explain. b) Was the design of the study appropriate for the advertisers' questions?

A 75.00-ml portion of a solution that is 0.0460 M in HClO4 is treated with 150.00 ml of 0.0230 M KOH(aq). Is the pH of the resulting mixture greater than, less than, or equal to 7.0? Expla in.

If $G$ is a cyclic group and $N$ is a subgroup of $G ,$ show that $G / N$ is a cyclic group.

Impure nickel, refined by smelting sulfide ores in a blast furnace, can be converted into metal from 99.90% to 99.99% purity by the Mond process. The primary reaction involved in the Mond process is $\mathrm { Ni } ( s ) + 4 \mathrm { CO } ( g ) \rightleftharpoons \mathrm { Ni } ( \mathrm { CO } ) _ { 4 } ( g ).$ Calculate the temperature at which $\Delta G ^ { \circ } = 0 ( K = 1 )$ for the preceding reaction, assuming that $\Delta H ^ { \circ }$ and $\Delta S ^ { \circ }$ do not depend on temperature.

Tarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0° with the vertical. Assume that an x axis extends horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 760 N. Just then, what are (a) the force on him from the vine in unit-vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? What are the (e) magnitude and (f) angle of Tarzan’s acceleration just then?

translate the following equations from the given coordinate system (i.e., Cartesian, cylindrical, or spherical) into equations in each of the other two systems. In addition, identify the surfaces so described by providing appropriate sketches.

$$\rho \sin \varphi \sin \theta = 2$$

If G is an abelian group that contains a pair of cyclic subgroups of order 2, show that G must contain a subgroup of order 4. Does this subgroup have to be cyclic?

Instrucciones. Sitúate en el punto negro y camina por la calle Padre Billini. Entra en el parque y siéntate debajo de un árbol. Luego, cruza la calle por el paso de cebra, entra en el edificio de la esquina y toma un café. Después, continúa por la calle Padre Billini hasta la esquina de la calle Arzobispo Meriño. Cruza la calle y entra en el edificio para admirar su fantástica arquitectura. Sube por la calle Arzobispo Meriño y saca dinero en el edificio de la esquina. Continúa por la misma calle, gira a la derecha hasta llegar a la calle Isabel la Católica y gira otra vez a la derecha. Finalmente, continúa una cuadra por la calle Isabel la Católica y entra en el edificio de la esquina. Este es tu destino.

Contesta las preguntas. 1.¿Cuál es tu destino?. 2.¿Qué hay enfrente de tu destino?. 3.¿Qué edificios históricos están en tu ruta?________.

Evaluate the given expression. Take

$$A=\left[\begin{array}{rrr}{1} & {-1} & {0} \\ {0} & {2} & {-1}\end{array}\right]$$

,

$$B=\left[\begin{array}{rrr}{3} & {0} & {-1} \\ {5} & {-1} & {1}\end{array}\right]$$

, and

$$C=\left[\begin{array}{lll}{x} & {1} & {w} \\ {z} & {r} & {4}\end{array}\right]$$

. $2 A^{T}-C^{T}$

Luis helped raise money for his school by jogging in the school jog-a-thon. The total amount of money he raised can be represented by the expression 1.75m, where m is the number of miles he jogged. If Luis raised a total of $21, how many miles did he jog? A. 12 B. 19.25 C. 22.75 D. 36.75

Dry air whose molar analysis is 78.1 percent $\mathrm{N}_{2},$ 20.9 percent $\mathrm{O}_{2},$ and 1 percent Ar flows over a water body until it is saturated. If the pressure and temperature of air remain constant at 1 atm and $25^{\circ} \mathrm{C}$ during the process, determine (a) the molar analysis of the saturated air and (b) the density of air before and after the process. What do you conclude from your results?