The figure above shows a 10 V battery connected in a circuit with two resistors, a parallel plate capacitor of capacitance , and three ammeters. The circuit has been connected for a long time. Assume the capacitance of the capacitor is known. The gap between the capacitor’s plates is now filled with an unknown insulating material, and the circuit is again left connected for a long time. Measuring which of the following provides enough information to determine the unknown material’s dielectric constant ? A rectangular circuit contains a 10 volt battery on the left side. Along the top branch is an ammeter labeled A sub 1 followed by a 50 ohm resistor. A junction splits to the right and downward. The downward branch passes through capacitor C and an ammeter labeled A sub 2. The right branch passes through ammeter A sub 3 then turn downward through a 100 ohm resistor before turning left to form the bottom branch. The bottom branch completes the loop back to the battery.

A jug of tea is cooled down by putting it in ice. The mass of the tea is 1.8 kg and is initially at 80°C. How many kg of ice, initially at 0°C, are required to bring the mixture to 10°C? (, specific heat of water is 4186 J/kg·°C.)

An engineer has four wires made of the same material and wants to determine the material’s resistivity. The engineer measures the length and cross-sectional area of each wire. The engineer then applies a potential difference across each wire and measures the resulting current . To estimate the resistivity of the material using only at the slope of a graph of the data which of the following should be graphed as a function of ?

A 69-year-old woman has a 10-kg weight loss over the past years and dies of massive pulmonary thromboembolism.  The autopsy findings of her liver is shown as the figure below.  Which of the following best describes the lesions seen in her liver?

What is the internal energy of  gas molecules at a temperature of 300 K?

A 100-g cube of ice at 0°C is dropped into 1.0 kg of water that was originally at 80°C. What is the final temperature of the water after the ice melts?

Unopposed exogenous estrogen administration in women after menopause will increase the risk of cancer of which organ?

In Quarter 1 of 2025, about 11% of US employees used AI few times a month in their work. If there is no change in the population behavior, CLT states that any sample proportion will be around the population proportion. In a recent study of 1250 participants who were working in some US company, Gallup found that 185 of them used AI few times a month in their work. The sample proportion of US employees use AI few times a month in their work is [a] Type in decimal form. Do not round. Assuming all CLT conditions hold, use this sample to find 95% confidence interval and conclude: I am 95% confident that the proportion of all US employees use AI few times a month in their work is between [b] and [c] Type or Copy/paste as in StatCrunch output. Do not round. (Rewriting interval in %) I am 95% confident that the proportion of all US employees use AI few times a month in their work is between [l] % and [m] %. Round to whole number percent. Based on your confidence interval, can you confidently claim that the proportion of all US employees who use AI few times a month in their work has increased from Quarter 1, 2025 value of 11%? ( yes / no) [d]   Is the sample Gallup collected significant enough to claim that the proportion of US employees who use AI few times a month in their work has increased from Quarter 1, 2025 value of 11%?  Test this hypothesis at 5% significance level, Null hypothesis would be  [e] Enter decimal number. Alternate hypothesis would be  [f]  Enter decimal number. The z-stat is [g]. Type or Copy/paste as in StatCrunch output. Do not round. p- value is [h]. Type or Copy/paste as in StatCrunch output. Do not round. The p-value is (less / more) [i] than the level of significance. Conclusion: We (do / do not) [j] have sufficient evidence to reject null hypothesis. Conclusion: [k] (A/ B / C / D) We can confidently claim that the proportion of all US employees who use AI few times a month in their work is now 14.8%. We can confidently claim that the proportion all US employees who use AI few times a month in their work is now 11%. We can confidently claim that the proportion all US employees who use AI few times a month in their work has increased from 11%. We cannot confidently claim that the proportion all US employees who use AI few times a month in their work has increased from 11%

Unusual event – If the probability of it happening is less than 0.025. That is there is less than 2.5% chance that the event will happen. About 55% of this college’s student population are younger than 25 years. Suppose you surveyed a random sample of 420 students to find how many are younger than 25 years. Let X represent sample proportion of students younger than 25 years. Central limit theorem describes the distribution of sample proportion. The mean of the sampling distribution is [a] and standard deviation is [b]. Round to 2 decimals. Use these numbers for next question. Use Central Limit Theorem to find probability. In your sample of 420 students, what is the probability that the sample proportion of students younger than 25 years, is less than 48%? [c] Do not round. Type or copy/paste as in StatCrunch output. In the college where 55% of students are younger than 25 years, we can claim that observing 48% (or lower) of students  younger than 25 years in the sample is [d] (likely / unlikely / very unlikely).

So this exam covers multiple chapters again, now Chs. 19, 20, 21 and 22. Let’s pause and recall that Historiography as defined our second day of class means: