In the article "Bigger Teeth for Longer Life? Longevity and Molar Height in Two Roe Deer Populations", researchers developed a model to predict the tooth height (in mm),y, of roe deer based on their age, $x_1$, gender, $x_2$(0=female, 1=male), and location, $x_3$ (Trois Fontaines deer, which have a shorter life expectancy, and Chaize, which have a longer life expectancy, $x_3$=0 for Trois Fontaines, $x_3$=1 for (Chize). The model is $\hat{y}=7.790-0.382 x_{1}-0.587 x_{2}-0.925 x_{3}+0.091 x_{2} x_{3}$.

What is the expected tooth length of a female roe deet who is 12 years old and lives in Trois Fontaines?

In the European Union, it has become important to be able to determine an individual's age when legal documentation of the birth date of an individual is unavailable. In the article "Age Estimation in Children by Measurement of Open Apices in Teeth, researchers developed a model to predict the age, y, of an individual based on the gender of the individual, $x_1$(0=female, 1=male), the height of the second premolar, $x_2$, the number of teeth with root development, $x_3$, and the sum of the normalized heights of seven teeth on the left side of the mouth, $x_4$. The normalized height of the seven teeth was found by dividing the distance between teeth by the height of the tooth. Their model is $\hat{y}=9.063+0.386 x_{1}+1.268 x_{2}+0.676 x_{3}-0.913 x_{4}-0.175 x_{3} x_{4}$

Based on the model, what is the expected age of a female with $x_2$=28 mm, $x_3=8$, and $x_4$=18 mm?

Adult female black bears have masses from about 50 kilograms to 125 kilograms. Adult male black bears have masses from about 60 kilograms to 250 kilograms. Researchers measured the masses of five adult female black bears in their natural habitat. You can see their results in the table.

Adult Female

Black Bear Masses

Which mass is anomalous data?

The wind chill factor depends on wind speed and air temperature. The following data represent the wind speed (in mph) and wind chill factor at an air temperature of $15^{\circ}$ Fahrenheit.

$$\begin{matrix} \text{Wind Speed, x (mph)} & \text{Wind Chill Factor, y} & \text{Wind Speed, x (mph)} & \text{Wind Chill Factor, y}\\ \text{5} & \text{12} & \text{25} & \text{-22}\\ \text{10} & \text{-3} & \text{30} & \text{-25}\\ \text{15} & \text{-11} & \text{35} & \text{-27}\\ \text{20} & \text{-17}\\ \end{matrix}$$

Draw a scatter diagram of the data treating wind speed as the explanatory variable.

If the independent variable in a line of best fit y = -0.008x + 14 is credit score, and the dependent variable is the interest rate on a used car loan, then the slope is interpreted as “if credit score increases by 1 point, the interest rate will ___________ (increase/decrease) by percent, on average.

Simple random samples of high-interest (8.9%) mortgages and low-interest (6.3%) mortgages were obtained. For the 40 high-interest mortgages, the borrowers had a mean FICO credit score of 594.8 and a standard deviation of 12.2. For the 40 low-interest mortgages, the borrowers had a mean FICO credit score of 785.2 and a standard deviation of $16.3$ (based on data from USA Today). Construct a 98% confidence interval estimate of the difference between the mean FICO credit score of borrowers with high-interest rates and the mean FICO credit score of borrowers with low-interest rates. What does the result suggest about the FICO credit rating score of a borrower and the interest rate that is paid?

Determine whether the sequence is arithmetic, geometric, or neither. Find the next three terms.

$$14,21,28,35, \dots$$

Prove or disprove: If R and S are two equivalence relations on a set A, then $R \cup S$ is also an equivalence relation on A.

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 2 months. Ten months after a repair, it breaks down again. Is this surprising? (Assume that the times between failures are normally distributed.)

Use a graphing utility to approximate any solutions of the equation. [Remember to write the equation in the form f(x) = 0.] $-|x-2|=-6$

Solve each absolute value equation. Check your answers. $|6-5 x|=18$

Use the method of proof by contradiction to prove the following statements. (In each case, you should also think about how a direct or contrapositive proof would work. You will find in most cases that proof by contradiction is easier.) If $a, b \in \mathbb{Z}$, then $a^{2}-4 b-2 \neq 0$.

You are designing a system to cool an insulated silver plate of dimensions $2.00 \mathrm{cm} \times 2.00 \mathrm{cm} \times 0.50 \mathrm{cm}$. One end of a thermally insulated copper wire (diameter D=2.50 rrun and length L=15.0 cm) is dipped into a vat of liquid nitrogen (T=77.2 K), and the other end is attached to the bottom of the silver plate. (a) If the silver plate starts at room temperature $\left(72.0^{\circ} \mathrm{F}\right)$, what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir? (b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.

Tu compañero (a) siempre exagera. Tú no le crees y se lo dices. Usa estas expresiones: no es cierto que... / no es verdad que... / no estar seguro (a) de que... / es dudoso que / es improbable que...
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