Iron corrodes to produce rust, $Fe_2O_3,$ but other corrosion products that can form are $Fe(O)(OH),$ iron oxyhydroxide, and magnetite, $Fe_3O_4.$ The oxidation number for Fe in magnetite was controversial for a long time. If we assume that oxygen's oxidation number is - 2, and Fe has a unique oxidation number, what is the oxidation number for Fe in magnetite?

use a graphing utility to graph the curve represented by the parametric equations. Prolate cycloid:

$$x=2θ-4 sin θ, y = 2 - 4 cos θ$$

Find the product. Write your answer using exponents.

$$2^{11} • 2^3$$

Copper corrodes to cuprous oxide, $Cu_2O,$ or cupric oxide, CuO, depending on environmental conditions. What is the oxidation state of copper in cupric oxide?

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject

$$H _ { 0 }$$

for the level of significance

$$\alpha$$

. Right-tailed test z = 2.46

$$\alpha = 0.01$$

Sketch a sinusoidal function that passes through (0, -4) and has a period of 20, an amplitude of 3, and an equation of the axis y = -1.

Suppose in galvanization, copper was plated on iron instead of zinc. Would copper continue to protect the iron from corrosion, as zinc does, if the copper coating became broken or cracked? Explain.

Graph each function, either by translating the graph of

$$y = \sqrt { x }$$

or by making a table of values.

$$y = \sqrt { x + 7 }$$

Li-ion batteries used in a utomobiles typically use a $LiMn_2O_4$ cathode in place of the $LiCoO_2$ cathode found in Which material has a higher percentage of lithium? Does this help to explain why batteries made with $LiMn_2O_4$ cathodes deliver less power on discharging?

Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is

$$N(μ_X, σ^2_X)$$

and Y is

$$N(μ_Y, σ^2_Y)$$

. Given that n = 25, x̅ = 33.80,

$$s^2_x = 4.88$$

, m = 29, y̅ = 31.66, and

$$s^2_y = 5.81$$

, test the null hypothesis

$$H_0: μ_X = μ_Y$$

against

$$H_1: μ_X > μ_Y$$

with α = 0.01.

Solve the proportion.

$$\frac { 1 } { 2 } = \frac { x } { 4 }$$

In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.0 cm) enters an aneurysm with a radius of 3.0 cm, how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta? The average flow rate through the aorta is 120

$$\mathrm { cm } ^ { 3 } / \mathrm { s }$$

. Assume the blood is nonviscous and the patient is lying down so there is no change in height.

Li-ion batteries used in a utomo biles typ ically use a $LiMn_2O_4$ cathode in place of the $LiCoO_2$ cathode found in most Li-ion batteries. Calculate the mass percent lithium in each electrode material.

Where appropriate, round your answer to the nearest tenth of percent. Unlike the population of Russia, the population of the United States has been increasing since 1990. In 1990, the population of the United States was about 249 million people. In 2014, the population of the United States was about 317 million people. Determine the percent increase in the U.S. population during this time period.