Why is the weather in New York State consistently cooler in January than it is in July? (1) Earth is closer to the sun in July (2) Cloudy weather is more common in January (3) The Northern Hemisphere is tilted away from the sun in January. (4) Sunlight is reflected away from Earth by ice and snow during January

To give a 19-kg child a ride, two teenagers pull on a 3.7-kg sled with ropes. Both teenagers pull with a force of 55 N at an angle of $35^{\circ}$ relative to the forward direction, which is the direction of motion. In addition, the snow exerts a retarding force on the sled that points opposite to the direction of motion and has a magnitude of 57 N. Find the acceleration of the sled and child.

(a) Determine the radius of convergence of the series $x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\dots+(-1)^{n-1} \frac{x^{n}}{n}+\cdots.$ What does this tell us about the interval of convergence of this series? (b) Investigate convergence at the end points of the interval of convergence of this series.

Esquire Inc. uses the LIFO method to report its inventory. Inventory at January 1, 2021, was $500,000 (20,000 units at$25 each). During 2021, 80,000 units were purchased, all at the same price of $30 per unit. 85,000 units were sold during 2021. Calculate the December 31, 2021, ending inventory and cost of goods sold for 2021 based on a periodic inventory system.

Assuming an income tax rate of 25%, what is LIFO liquidation profit or loss that the company would report in a disclosure note accompanying its financial statements?

You are a real estate broker who wants to compare property values in Glen Cove and Roslyn (which are located approximately $8$ miles apart). In order to do so, you will analyze the data in GC and Roslyn, a file that includes samples of houses from Glen Cove and Roslyn. Making sure to include the dummy variable for location (Glen Cove or Roslyn), develop a regression model to predict fair market value, based on the land area of a property, the age of a house, and location. Be sure to determine whether any interaction terms need to be included in the model.

According to the National Crime Victimization Survey, there were over 400,000 bodily injury-causing violent offences against women perpetrated by an intimate partner. An intervention study designed to increase safety behaviors of abused women compared the effectiveness of six telephone intervention sessions with a control group of abused women who received standard care. Fifteen different safety behaviors were examined. ${ }^{17}$ One of the variables analyzed was the total number of behaviors (out of 15) that each woman performed. Here is a summary of the means of this variable at baseline (just before the first telephone call) and at follow-up three and six months later:

(a) Calculate the marginal means. Are they useful for understanding the results of this study? (b) Plot the means. Do you think there is an interaction? Describe the meaning of an interaction for this study. (Note: This exercise is from a repeated-measures design, and the data are not particularly Normal because they are counts with values from 1 to 15 . Although we cannot use the methods in this chapter for statistical inference in this setting, the example does illustrate ideas about interactions.)

In what units is plate thickness specified?

A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at $25.0^{\circ}$ with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is $55.0 \mathrm{~kg}$, and the coefficient of kinetic friction between the skis and the snow is $0.120$. Find the magnitude of the force that the tow bar exerts on the skier.

In Exercises $1$ through $8$, determine the radius of convergence and the interval of absolute convergence for the given power series.

$$\sum_{k=1}^{\infty} \sqrt{k} x^k$$

Many chemical reactions are the result of the interaction of two molecules that undergo a change to produce a new product. The rate of the reaction typically depends on the concentrations of the two kinds of molecules. If $a$ is the amount of substance $A$ and $b$ is the amount of substance $B$ at time $t=0$, and if $x$ is the amount of product at time $t$, then the rate of formation of $x$ may be given by the differential equation

$$\frac{d x}{d t}=k(a-x)(b-x),$$

or

$$\frac{1}{(a-x)(b-x)} \frac{d x}{d t}=k,$$

where $k$ is a constant for the reaction. Integrate both sides of this equation to obtain a relation between $x$ and $t$ if $a=b$. Assume that $x=0$ when $t=0$.

Tristan, Inc., applies the LIFO cost-flow assumption to value inventory. It began the current year with 2,000 units of inventory carried at LIFO cost of $20 per unit. During the first quarter, it purchased 8,000 units at an average cost of$40 per unit and sold 9,500 units at $60 per unit.

Assume the company does not expect to replace the units of beginning inventory sold; it plans to reduce inventory by year-end to 500 units. What amount of cost of goods sold should be recorded for the quarter ended March 31?
a.$335,000
b. $350,000
c.$380,000
d. $387,500

What type of lattice-primitive cubic, body-centered cubic, or face-centered cubic- does each of the following structure types possess: $ZnS?$

Réécrivez cette phrase en utilisant le participe présent du verbe souligné comme adjectif et le verbe $\^{e}$tre. Suivez le mod$\`{e}$le et faites attention $\`{a}$ l'accord !

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The units of an item available for sale during the year were as follows:

There are 57 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using (a) the first-in, first-out (FIFO) method; (b) the last-in, first-out (LIFO) method; and (c) the weighted average cost method.