A $\textrm{57-kg}$ packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of $37^{\circ}$ above the horizontal. If the tension in the rope is $142 \mathrm{~N}$, how much work is done on the crate to move it $6.1 \mathrm{~m}$ ?

$\textbf{ Describe}$ the role fungi play in the environment.

Suppose we have two numbers that both have the same remainder when divided by 57. If we subtract the two numbers, are there any numbers that we know will definitely divide evenly into this difference? What is the largest number that we are certain will divide into the difference? Use this observation to state a general principle about two numbers that have the same remainder when divided by another number.

How does the environment impact a species’s survival?

Use the fourth-order Runge-Kutta subroutine with $h = 0.1$ to approximate the solution to

$$y' = \cos (5y) - x, \qquad y( 0) = 0 ,$$

at the points $x = 0, 0.1 , 0.2, \ldots , 3.0.$ Use your answers to make a rough sketch of the solution on $[ 0, 3 ] .$

The sum of two numbers is 5 and their difference is 9. Let x be the greater number and y be the lesser number. Write a system of linear equations to represent this information, and use graphing to find the two numbers.

Determine whether each sum, difference, product, or quotient represents a rational number or an irrational number. Explain how you know without simplifying. Is the difference of two rational numbers always a rational number? Explain.

Determine whether each trinomial is a difference of two squares. If so, factor. If not, explain.

$$r ^ { 4 } - t ^ { 2 }$$

$f$ defines a mapping from $\mathbb{R}$ (or subset of $\mathbb{R}$) to $\mathbb{R}$. Determine if this mapping is onto or one-to-one. Also describe $f(P)$ in this case, for $P$ the set of positive real numbers.

$$f(x) = x^2 + x$$

Factor the difference between two squares. Asstune that any variable exponents represent whole numbers.

$$x^{2 n}-25$$

Assume that $\mathrm{p} 1=0.3, \mathrm{n} 1=80, \mathrm{p} 2=0.6, \mathrm{n} 2=120$. (a) Find the mean and the standard deviation of the sampling distribution of $\mathrm{p} 1-\mathrm{p} 2$. (b) The sample sizes here are four times as large as those in the previous exercise while the population proportions are the same. Compare the results for this exercise with those that you found in the previous exercise. What is the effect of multiplying the sample sizes by 4 ?

Why is EDTA added to commercial mayonnaise and salad dressings? Explain what is happening.

The sum of two numbers is twice their difference. The larger number is $6$ more than twice the smaller. Find the numbers.

For the given equation: $y=$x^2(x-1)^2(x+1)^3$: (i) Make a conjecture about the behavior of the graph in the vicinity of its x-intercepts. (ii) Make a rough sketch of the graph based on your conjecture and the limits of the polynomial as x$\rightarrow+\infty$and as x$\rightarrow-\infty$.