Each spring, sandhill cranes migrate through the Platte River valley in central Nebraska. An estimated maximum of a half-million of these birds reach the region by April 1 each year. If there are only 100,000 sandhill cranes 15 days later and the sandhill cranes leave the Platte River valley at a rate proportional to the number of sandhill cranes still in the valley at the time, (a) How many sandhill cranes remain in the valley 30 days after April 1? (b) How many sandhill cranes remain in the valley 35 days after April 1? (c) How many days after April 1 will there be less than 1000 sandhill cranes in the valley?

New York City has 10 trash districts and is trying to determine which of the districts should be a site for dumping trash. It costs $1,000 to haul one ton of trash one mile. The location of each district, the number of tons of trash produced per year by the district, the annual fixed cost (in millions of dollars) of running a dumping site, and the variable cost (per ton) of processing a ton of trash at a site are shown in Table 112. For example, district 3 is located at coordinates (10,8). District 3 produces 555 tons of trash a year, and it costs$1 million per year in fixed costs to operate a dump site in district 3. Each ton of trash processed at site 3 incurs $51 in variable costs. Each dump site can handle at most 1,500 tons of trash. Each district must send all its trash to a single site. Determine how to locate the dump sites in order to minimize total cost per year. TABLE 112:

$$\begin{matrix} \text{District} & \text{Coordinates} & \text{ } & \text{Cost (\$ Millions)}\\ \text{ } & \text{x} & \text{y} & \text{Tons} & \text{Fixed} & \text{Variable}\\ \text{1} & \text{4} & \text{3} & \text{49} & \text{2} & \text{310}\\ \text{2} & \text{2} & \text{5} & \text{874} & \text{1} & \text{40}\\ \text{3} & \text{10} & \text{8} & \text{555} & \text{1} & \text{51}\\ \text{4} & \text{2} & \text{8} & \text{352} & \text{1} & \text{341}\\ \text{5} & \text{5} & \text{3} & \text{381} & \text{3} & \text{131}\\\text{6} & \text{4} & \text{5} & \text{428} & \text{2} & \text{182}\\ \text{7} & \text{10} & \text{5} & \text{985} & \text{1} & \text{20}\\ \text{8} & \text{5} & \text{1} & \text{105} & \text{2} & \text{40}\\ \text{9} & \text{5} & \text{8} & \text{258} & \text{4} & \text{177}\\\text{10} & \text{1} & \text{7} & \text{210} & \text{2} & \text{75}\\ \end{matrix}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

$$( 3 + 7 i ) ( 3 - 7 i )$$

is an imaginary number.

Solve the equation by using the Quadratic Formula. Round to the nearest tenth if necessary.

$$4 x ^ { 2 } + 15 x = 25$$

How are living mammals classified into groups? (A) method of development (B) structure of kidneys (C) method of respiration (D) method of regulating body temperature (E) type of circulatory system

If 15 boxes of cereal costs $67.50, what is the unit price?

A pile of empty aluminum cans has a volume of

$$1.0 \mathrm { m } ^ { 3 }$$

The density of aluminum is

$$2700 \mathrm { kg } / \mathrm { m } ^ { 3 }$$

Explain why the mass of the pile is not

$$\rho _ { \mathrm { A } 1 } V = \left( 2700 \mathrm { kg } / \mathrm { m } ^ { 3 } \right) \left( 1.0 \mathrm { m } ^ { 3 } \right) = 2700 \mathrm { kg }$$

Between low tide and high tide, the width of a beach changes by −17 feet per hour. Write and evaluate an expression to show how much the width of the beach changes in 3 hours.

use a graphing utility to graph the quadratic function. Identify the vertex, axis of symmetry, and x-intercept(s). Then check your results algebraically by writing the quadratic function in standard form. f(x) = - (x^2 + 2x - 3)

The supply and demand equations for sugar have been estimated to be given by the equations

$$S=0.7p+0.4\ \ \ \ \ D=-0.5p+1.6$$

where p is the price in dollars per pound and S and D are in millions of pounds.

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(a) Find the market price.

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(b) What quantity of supply is demanded at this market price?

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(c) Graph both the supply and demand equations.

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(d) Interpret the point of intersection of the two lines.

Let S be the hemisphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = a ^ { 2 }$, for $z \geq 0$, and let T be the paraboloid $z=a-\left( x ^ { 2 } + y ^ { 2 } \right) / a$, for $z \geq 0$, where $a>0$. Assume the surfaces have outward normal vectors.

Verify that S and T have the same base $\left( x ^ { 2 } + y ^ { 2 } \leq a ^ { 2 } \right)$ and the same high point (0, 0, a).

Club members equally share the cost of $1500 to charter a fishing boat. Shortly before the boat is to leave, four people decide not to go due to rough seas. As a result, the cost per person is increased by$100. How many people originally intended to go on the fishing trip?

Draw a model and find the percent that is represented by the ratio. If it is not possible to find the exact percent using the model, estimate. 6 out of 24

El sacapuntas esta ______________________________________.