A person stands a distance R from a door's hinges and pushes with a force F directed perpendicular to its surface. By what factor does the applied torque change if the person's position and force change to 2R and F.

A student stretches a spring, attaches a 1.00-kg mass to it, and releases the mass from rest on a frictionless surface. The resulting oscillation has a period of 0.500 s and an amplitude of 25.0 cm. Determine the spring constant.

Kaitlin knows that if she needs to add antifreeze to her car’s radiator the mixture used must contain 50% antifreeze and 50% water. How many gallons of a mixture containing 80% antifreeze must be added to a 3-gallon mixture containing 40% antifreeze to obtain the mixture Kaitlin needs?

$\alpha-\beta,$ Inc., a high-tech company in San Diego, whose stock trades on the NYSE exchange, uses a MARR of 25% per year. If the chief financial officer (CFO) said the company expects to make a real rate of return of 20% per year on its investments over the next 3-year period, what is the company expecting the annual inflation rate to be over that time period?

Assume you have a total of $200,000 to invest in two corporate stocks identified as Z1 and Z2. The overall rate of return you require on the$200,000 is 26% per year. (a) If $40,000 is invested in Z2 with an estimated$i_{Z 2}^{}$of 14$i_{Z 1}^{}$ exceed to realize at least 26% per year? (b) If the best return expected from the Z1 stock is 27%, determine the threshold level of investment in Z2 to maintain an overall ROR of 26% per year. Solve by hand or using Goal Seek, as instructed.

What "confidence" is associated with each of the following random intervals? Assume that the $Y_{i}$'s are normally distributed.

$$(a) \quad \left[\bar{Y}-2.0930\left(\frac{S}{\sqrt{20}}\right), \bar{Y}+2.0930\left(\frac{S}{\sqrt{20}}\right)\right]$$

$$(b) \quad \left[\bar{Y}-1.345\left(\frac{S}{\sqrt{15}}\right), \bar{Y}+1.345\left(\frac{S}{\sqrt{15}}\right)\right]$$

$$(c) \quad \left[\bar{Y}-1.7056\left(\frac{S}{\sqrt{27}}\right), \bar{Y}+2.7787\left(\frac{S}{\sqrt{27}}\right)\right]$$

$$(d) \quad \left[-\infty, \bar{Y}+1.7247\left(\frac{S}{\sqrt{21}}\right)\right]$$

Factor each trinomial, if possible. $9 x^{2}+4 x-2$

A camera takes a properly exposed photo at f /5.6 and 1/125 s. What shutter speed should be used if the lens is changed to f/4.0?

Find all partition numbers of the function. $f(x)=\frac{2 x+7}{5 x-1}$

Apply the graphing strategy and summarize the pertinent information. Round any approximate values to two decimal places. $f(x)=0.25 x^{4}-5 x^{3}+31 x^{2}-70 x$

Find a function y=f(x) that satisfies both conditions: $\frac{d y}{d x}=3 x^{-1}-x^{-2} \quad f(1)=5$

At what pressure will the mean free path in room-temperature $\left(20^{\circ} \mathrm{C}\right)$ nitrogen be 1.0 m?

The following statements are related to household circuits and electrical safety. Determine whether each statement is true (T) or false (F). Three-wire electrical cords help prevent dangerous electrical shocks by grounding the case of a device.

An f/2.80 CCD camera has a 105-mm focal length lens and can focus on objects from infinity to as near as 30.0 cm from the lens. maximum distances from the CCD sensor over which the lens must be able to travel during focusing. Note: ''f/2.80" means "an f-number of 2.80."