The 60-Hz line voltage for a 60-kW, 0.76-pf lagging industrial load is 240$\angle 0^{\circ}$ V rms. Find the value of capacitance that when placed in parallel with the load will raise the power factor to 0.9 lagging.

Evaluate the expression for a = -4, b = 3, and c = 2. 9a^0c^4

The table shows Emma's midyear exam results. The exam results for each subject are normally distributed with the mean $\mu$ and standard deviation $\sigma$ shown in the table.

$$\begin{matrix} \text{Subject} & \text{Emma's score} & {\mu} & {\sigma}\\ \text{English} & \text{48} & \text{40} & \text{4.4}\\ \text{Mandarin} & \text{81} & \text{60} & \text{9}\\ \text{Geography} & \text{84} & \text{55} & \text{18}\\ \text{Biology} & \text{68} & \text{50} & \text{20}\\ \text{Maths} & \text{84} & \text{50} & \text{15}\\ \end{matrix}$$

Arrange Emma's subjects from 'best' to 'worst' in terms of the z-scores.

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

Which statement about retrospective and prospective toxicity studies is correct? (a) Retrospective studies are not conducted on humans. (b) Prospective studies are only conducted on wild animals. (c) Retrospective studies monitor health effects from future chemical exposures. (d) Prospective studies monitor health effects from future chemical exposures. (e) Prospective studies monitor health effects from past chemical exposures.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a true conditional statement, but when I reverse and negate the antecedent and the consequent, my new conditional statement is no longer true.

A stained glass window has an area of 900 square inches. a. One window design is made of rectangular stained glass pieces that are 5 inches by 3 inches. How many stained glass pieces are used in the window? b. Another window design is made of square stained glass pieces that are 6 inches by 6 inches. How many stained glass pieces are used in the window?

(a.) What is meant by tangent line approximation? (b.) Define the terms propagated error, relative error, and percentage error.

Determine whether the given random variable X is discrete or continuous. X measures the living area of a randomly selected house in your neighborhood.

Simplify.

$$\sqrt [ 3 ] { 32 }$$

Southside Landscapes proposes to plant the flower beds for the historic Earle House gardens. The company uses four patterns. Pattern I uses 40 tulips, 25 daffodils, and 6 boxwood. Pattern II uses 25 tulips, 50 daffodils, and 4 boxwood. Pattern III uses 30 tulips, 40 daffodils, and 8 boxwood. Pattern IV uses 45 tulips, 45 daffodils, and 2 boxwood. The profit for each pattern is $48 for Pattern I,$45 for Pattern II, $55 for Pattern III, and$65 for Pattern IV. Southside Landscape has 1250 tulips, 1600 daffodils, and 195 boxwood available. How many of each pattern should be used to maximize profit?

Write the word sentence as an inequality. $y+5 \gt 8 ; y=1$

To be rescued from the roof of a burning building, a 70-kg man must be able to jump straight up and catch hold of a rope ladder hanging from a helicopter. He has to raise his center of mass 2.00 m above the roof to do so. (a) If he crouches down such that his center of mass is 0.50 m above the roof and his feet leave the roof when his center of mass is 1.05 m above the roof, what minimum force must he exert on the roof to reach the ladder? (b) A typical candy bar contains about 850 kJ of food energy. How many candy bars does this jump require?

Calculate. $\int{\dfrac{dx}{1-\sqrt{x}}}$