A loan officer compares the interest rates for $48$-month fixed-rate auto loans and $48$-month variable-rate auto loans. Two independent, random samples of auto loan rates are selected. A sample of eight $48$-month fixed-rate auto loans had the following loan rates:

$$\begin{array}{llll} 4.29 \% & 3.75 \% & 3.50 \% & 3.99 \% \\ 3.75 \% & 3.99 \% & 5.40 \% & 4.00 \% \end{array}$$

while a sample of five $48$-month variable-rate auto loans had loan rates as follows:

$$\begin{array}{llll} 3.59 \% & 2.75 \% & 2.99 \% & 3.00 \% \\ \end{array}$$

Calculate a $95$ percent confidence interval for the difference between the mean rates for fixed- and variable-rate $48$-month auto loans. Can we be $95$ percent confident that the difference between these means exceeds $.4$ percent? Explain.

Repeat the above problem by replacing air by oil with a specific gravity of $0.69$.

Dalling et al. (2001) compared net photosynthetic rates of two pioneer trees—Alseis blackiana and Miconia argenta—as a function of gap size in Barro Colorado Island. They found that net photosynthetic rates (measured on a per-unit basis) increased with gap size for both trees and that the photosynthetic rate for Miconia argenta was higher than that for Alseis blackiana. In the same coordinate system, graph the net photosynthetic rates as functions of gap size for both tree species.

Interest rates fluctuate with the economy. In the 1980s, the highest CD interest rate was over 16%. By 2017, the highest CD interest rates were approximately 2%. If $1,000 is invested at 16% interest, compounded continuously, for 5 years, what is the ending balance? Round to the nearest cent.

Explain why decay rates can be used with confidence in radiometric dating.

Kay, Kat, and Kim are partners. In a liquidation, Kay’s share of partnership losses exceeds her capital account balance. Additionally, she is unable to meet the deficit from her personal assets, and her partners shared the excess losses. Does this relieve Kay of liability?

Estimate using the techniques given.

c. Front-end with adjustment: $753+639$

The daily exchange rates for the five-year period 2008 to 2013 between the euro (EUR) and the British pound (GBP) can be modeled by a Normal distribution with mean $1.19$ euros (to pounds) and standard deviation $0.043$ euros, what would the cutoff rates be that would separate the

b) lowest $50 \%$ ?

The relation between resistance $R$ and temperature $T$ for a thermistor closely follows

$$R=R_0 \exp \left[\beta\left(\frac{1}{T}-\frac{1}{T_0}\right)\right]$$

where $R_0$ is the resistance, in ohms $(\Omega)$, measured at tem. perature $T_0(\mathrm{~K})$ and $\beta$ is a material constant with units of $\mathrm{K}$, For a particular thermistor $R_0=2.2 \Omega$ at $T_0=310 \mathrm{~K}$. From a calibration test, it is found that $R=0.31 \Omega$ at $T=422 \mathrm{~K}$. Determine the value of $\beta$ for the thermistor and make a plot of resistance versus temperature.

Answer the following question in complete sentences, paying special attention to the verb with irregular yo forms

Modelo ¿Siempre dices la verdad? -Sí, yo siempre digo la verdad.

¿Te pareces a alguien de tu familia?

Sí, yo ______ a mi ______.

Collin is asked to repeat what his dad just told him. He says he "forgot" but in reality Collin wasn't paying attention to his dad at all. This is an example of the explanation of forgetting. a. interference c. encoding failure b. memory trace d. repression

The direction angles $\alpha, \beta$, and $\gamma$ of a vector $\mathbf{v}=a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$ are defined as follows: $\alpha$ is the angle between $\mathbf{v}$ and the positive $x$-axis $(0 \leq \alpha \leq \pi)$. $\beta$ is the angle between $\mathbf{v}$ and the positive $y$-axis $(0 \leq \beta \leq \pi)$. $\gamma$ is the angle between $\mathbf{v}$ and the positive $z$-axis $(0 \leq \gamma \leq \pi)$.

(b). Unit vectors are built from direction cosines Show that if $\mathbf{v}=a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$ is a unit vector, then $a, b$, and $c$ are the direction cosines of $\mathbf{v}$.

Find a polar equation of the conic with its focus at the pole. Parabola; vertex: $(2, \pi / 2)$

Water at 100$^{\circ} \mathrm{C}$, quality 50% in a rigid box is heated to 110$^{\circ} \mathrm{C}$. How do the properties (P, v, x, u, and s) change (increase, stay about the same, or decrease)?