A TV newscaster reports the results of a poll of voters, and then says, “The margin of error is plus or minus 4%.” Explain carefully what that means.

Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease.

What concerns do you have about this sample?

Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of

$$y _ { n + 1 } = y _ { n } + h f \left( x _ { n } , y _ { n } \right)$$

by hand, first using $h = 0.1$ and then using $h = 0.05$.

$$y ^ { \prime } = x + y ^ { 2 } , \quad y ( 0 ) = 0 ; \quad y ( 0.2 )$$

Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease. What concerns do you have about this sample?

Write the decimal as a fraction in simplest form. -2.2

Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease. If the scientists want to cut the margin of error in half, how many deer must they inspect?

Evaluate the following integrals:

$$\int_2^6(3x^2-2x-1)\delta(x-3)dx$$

$$\int_0^5\cos x\delta(s-\pi)dx$$

$$\int_0^3x^3\delta(x+1)dx$$

$$\int_{-\infty}^{\infty}\ln(x+3)\delta(x+2)dx$$

Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease.

If the scientists want to cut the margin of error in half how many deer must they inspect?

In these initial value problem, use the improved Euler method with step sizes $h = 0.1, 0.02, 0.004$, and $0.0008$ to approximate to five decimal places the values of the solution at ten equally spaced points of the given interval. Print the results in tabular form with appropriate headings to make it easy to gauge the effect of varying the step size $h$. Throughout, primes denote derivatives with respect to $x$.

$$y ^ { \prime } = \sin x + \cos y , y ( 0 ) = 0 ; 0 \leqq x \leqq 1$$

What is

$$\cos \theta$$

if

$$\sin \theta = - \frac { 24 } { 25 }$$

and

$$\theta$$

is in Quadrant IV?

A tractor fuel tank has the shape and dimensions shown in the figure. In fabricating the tank, it is necessary to know the angle between two adjacent sides. Find this angle.

Solve the equation algebraically and graphically. Check for extraneous solutions.

$$x+\dfrac{10}{x}=7$$

Find the point(s) on the cone $z ^ { 2 } - x ^ { 2 } - y ^ { 2 } = 0$ that are closest to the point (1, 3, 1). Give an argument showing you have found an absolute minimum of the distance function.

An ideal vapor-compression refrigeration cycle with ammonia as the working fluid has an evaporator temperature of $-20^\circ C$ and a condenser pressure of 12 bar. Saturated vapor enters the compressor and saturated liquid exits the condenser. The mass flow rate of the refrigerant is 3 kg/min. Determine a. the coefficient of performance. b. the refrigerating capacity, in tons. To determine the effect of changing the evaporator temperature on the cycle performance, plot the coefficient of performance and the refrigerating capacity, in tons, for saturated vapor entering the compressor at temperatures ranging from -40 to $-10^\circ C.$