The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution y = 0.7979e^-(x-5.4)^2/0.5, 4 ≤ x ≤ 7 where x is the number of hours. Use a graphing utility to graph the function.

A car is skidding to a stop on a level stretch of road. Identify all the action/reaction pairs of forces between the car and the road surface. Then draw a free-body diagram for the car.

Prove that for $\mathrm{n} \geq 2,$ the hypercube Qn has a Hamilton cycle.

Education The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution $y=0.7979 e^{-(x-5.4)^2 / 0.5}$, $4 \leq x \leq 7$, where $x$ is the number of hours.

(a) Use a graphing utility to graph the function.

Determine whether the following reactions conserve or violate strangeness: use $\pi ^ { 0 } = \mathrm { d } \overline { \mathrm { d } }, K ^ { + } = u \overline s, \Lambda ^ { 0 } = u d s , \mathrm { K } ^ { 0 } = \mathrm { ds } ^ { - } , \Sigma ^ { - } = \mathrm { d } \mathrm { ds } )$ $a. \pi ^ { - } + \mathrm { p } ^ { + } \rightarrow \mathrm { K } ^ { 0 } + \Lambda ^ { 0 }$ $b. \mathrm { p } ^ { 0 } + \mathrm { n } \rightarrow \mathrm { K } ^ { + } + \Sigma ^ { - }$ $c. \mathrm { K } ^ { 0 } \rightarrow \pi ^ { - } + \pi ^ { + }$ $d. \pi ^ { - } + \mathrm { p } ^ { + } \rightarrow \pi ^ { - } + \Sigma ^ { + }$

Right, or wrong? Say which for each formula and give a brief reason for each answer.

$$a. \quad \int \tan \theta \sec ^{2} \theta d \theta=\frac{\sec ^{3} \theta}{3}+C$$

$$b. \quad \int \tan \theta \sec ^{2} \theta d \theta=\frac{1}{2} \tan ^{2} \theta+C$$

$$c. \quad \int \tan \theta \sec ^{2} \theta d \theta=\frac{1}{2} \sec ^{2} \theta+C$$

use the acidity model given by pH = -log[H+], where acidity (pH) is a measure of the hydrogen ion concentration [H+] (measured in moles of hydrogen per liter) of a solution. The pH of a solution decreases by one unit. By what factor does the hydrogen ion concentration increase?

use the acidity model given by pH = -log [H^+], where acidity (pH) is a measure of the hydrogen ion concentration [H^+] (measured in moles of hydrogen per liter) of a solution. Find the pH when [H^+] = 2.3 x 10^-5

use the acidity model given by pH = -log[H+], where acidity (pH) is a measure of the hydrogen ion concentration [H+] (measured in moles of hydrogen per liter) of a solution. Find the pH when

$$[H+] = 1.13 x 10^-5.$$

The ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is R = 1/8^14. Estimate the age of the piece of wood.

$$\dfrac{3}{8}+\dfrac{3}{8}$$

A frictionless piston-cylinder device contains saturated liquid water at 40-psia pressure. Now 600 Btu of heat is transferred to water from a source at 1000$^\circ{}$F, and part of the liquid vaporizes at constant pressure. Determine the total entropy generated during this process, in Btu/R.

Find four solutions of the equation. Show each solution in a table of ordered pairs. y = 2x - 3

Match the statement about an event with one of the probabilities that follow. 0, 0.01, 0.3, 0.6, 0.99, 1 This event is very unlikely, but it will occur once in a while in a long sequence of trials.