Use the surface integral in Stokes' Theorem to calculate the circulation of the field \( F \) around the curve \( C \) in the indicated direction. \( F=y i+x z j+x^{2} k \) \( C: \) The boundary of the triangle cut from the plane \( 5 x+y+z=5 \) by the first octant, counterclockwise when viewed from above. The circulation is (Type an integer or a fraction.)

\( 3 \times 10 ^ { 3 } ; 5 \times 10 ^ { 2 } ; 8 \times 10 ^ { + } \)

When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 120 lb and 191 lb . Weights of women are now normally distributed with a mean of 170 lb and a standard deviation of 37 lb. Complete parts (a) through (c) below. a. If 1 woman is randomly selected, find the probability that her weight is between 120 lb and 191 lb , The probability is approximately 0.6272 . (Round to four decimal places as needed.) b. If 28 different women are randomly selected, find the probability that their mean weight is between 120 lb and 191 lb. The probability is approximately \( \square \). (Round to four decimal places as needed.)

A las \( 6^{\circ} \mathrm{a} . \mathrm{m} \). el termómetro marca \( -8^{\circ} \). De las \( 6 \mathrm{a} . \mathrm{m} \). a las 11 a m . sube a razón de \( 4^{\circ} \) por hora. Expresar la temperatura a las \( 7 \mathrm{a} . \mathrm{m} \), a las \( 8 \mathrm{a} . \mathrm{m} \). y a las 11 a m .

\( x \int _ { 15 } ^ { 85 } \)

Crecimiento bacteriano El crecimiento de una colonia de bacterias sigue una relación cuadrática: \( N(t)=-2 t^{2}+8 t+20 \), donde \( N(t) \) es el número de bacterias en miles y t es el tiempo en horas. 1. ¿Cuál es el número inicial de bacterias? 2. ¿Después de cuántas horas alcanzan su máximo número de bacterias? ¿Cuántas bacterias hay en ese momento? 3. Grafica la función y describe el comportamiento de la población de bacterias.