Researchers have determined that teenagers' memories are negatively affected by getting less than 10 hours of sleep. Being good scientists, the math students at North Middle School were skeptical, so they did their own study. They asked 300 students to memorize 10 objects. The next day, each student was asked how much sleep he or she got and then was asked to list the ten items. The results are below.

$$\begin{matrix} \text{ } & \text{Remembered all 10 items?} & \text{ } & \text{ }\\ \text{ } & \text{Yes} & \text{No} & \text{TOTAL}\\ \text{Less than 7 hours sleep} & \text{6} & \text{149} & \text{155}\\ \text{7-9 hours sleep} & \text{11} & \text{109} & \text{120}\\ \text{At least 10 hours sleep} & \text{5} & \text{20} & \text{25}\\ \text{TOTAL} & \text{22} & \text{278} & \text{300}\\ \end{matrix}$$

Make a relative frequency table to determine if there is an association between hours of sleep and memory.

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

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

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

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

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

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.

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."

A person standing 1.00 m from a portable speaker hears its sound at an intensity of $7.50 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2}$. Find the corresponding decibel level.

Assume that the random variable Z is described by a standard normal curve $f_{Z}(z)$. For what values of z are the following statements true? (a) $P(Z \leq z)=0.33$ (b) $P(Z \geq z)=0.2236$ (c) $P(-1.00 \leq Z \leq z)=0.5004$ (d) $P(-z<Z<z)=0.80$ (e) $P(z \leq Z \leq 2.03)=0.15$

Find each indefinite integral. Check by differentiating. $\int 8 x d x$