Explain how Redi's experiment disproved the hypothesis that flies formed in food by spontaneous generation.

Describe Pasteur's experiment, and explain how it disproved spontaneous generation.

You just read that life arose from nonlife billions of years ago. Could life arise from nonlife today? Explain.

Evaluate the expression if a = 12 and b = 8. a + 5b

Find the indicated scalar or vector without using (5), (13), or (15). $\|4 \mathbf{j}-5(\mathbf{i} \times \mathbf{j})\|$

Did Spallanzani's experiment disprove the hypothesis that microorganisms could arise spontaneously from a "vital force" contained in the air? Discuss why Spallanzani's procedure did or did not disprove such a possibility.

What would have happened if Pasteur had tipped one of his flasks so that the broth in the flask had come into contact With the curve of the neck?

The height, in feet, of a t-shirt launched from a t-shirt cannon high in the stands at a football stadium is given by

$$h(x) = -16x^2 + 64x + 80,$$

where x is the time in seconds after the t-shirt is launched. How long will it take before the t-shirt reaches the ground?

Explain how to determine the domain of a square root function.

draw the plane given by the equation

$$x + y + z = 0$$

Simplify the expression.

$$\frac{\frac{4}{5}}{6\frac{2}{3}}$$

A certain flow field is described by the stream function $\phi = 2x^{2}y - \left(\frac{2}{3}\right)y^{3}$ where $\phi$ has the units of m$^{2}$/s when x and y are in meters. Determine the pressure at the point x = 2 m, y = 2 m if the pressure at x = 1 m, y = 1 m is 200 kPa. Elevation changes can be neglected and the fluid is water.

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A census is a count of part of a population.

(a) The BVM Corp., a construction company, purchased a used hybrid electric pickup truck for $30,000 and used MACRS depreciation in the income tax return. During the time the company had the truck, they estimated that it saved$9500 a year. At the end of 4 years, BVM sold the truck for $9000. The combined federal and state income tax rate for BVM is 40%. Compute the after-tax rate of return for the truck. (b) Hybrid electric vehicles (HEVs), such as the truck purchased by BVM Corp., are recognized for their fuel efficiency and earth-friendliness. However, no major technology is without negative environmental impacts. Summarize the key environmental issues, such as greenhouse emissions in use, life-cycle impacts of battery sources (such as lithium-ion and nickel metal hydride), vehicle production impacts, and other life-cycle impacts.