Write the corollary as a conditional statement and its converse. Then explain why each statement is true. Rhombus Corollary.

Use order of operations to simplify.

$$5 \times 4 - [ 3 \times ( 2 - 1 ) ]$$

Central Park is a rectangular shaped park in the middle of New York City. The area of the park is 3.41 km2. How many acres is the park to the nearest acre? (Note: 1 km2 = 247 acres) Use a unit multiplier and show your work.

In order to gauge the effectiveness of the OHaganBooks.com site, you recently commissioned a survey of online shoppers. According to the results, 2% of online shoppers visited OHaganBooks.com during a one-week period, while 5% of them visited at least one of OHaganBooks.com’s two main competitors: JungleBooks.com and FarmerBooks.com. Use this information to answer. Assuming that visiting OHaganBooks.com was independent of visiting a competitor, what percentage of online shoppers visited either OHaganBooks.com or a competitor?

When a 3.0-kg block is pushed against a massless spring of force constant 4.5 × 10³ N/m, the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?

Say whether the given distribution can be a relative frequency distribution. If your answer is no, indicate why not.

$$\begin{matrix} \text{Outcome} & \text{HH} & \text{HT} & \text{TH} & \text{TT}\\ \text{Rel. Frequency} & \text{.5} & \text{.4} & \text{.5} & \text{-.4}\\ \end{matrix}$$

Find the value of k that would make the left side of each equation a perfect square trinomial. $36 x^{2}-k x+1=0$

Picture Compare how the nervous, respiratory, and circulatory systems interrelate to provide life support to body cells. How would homeostasis be affected if one of these systems could not function?

Let L be the line 2x + ky = 3k. Prove that (a) if k is not equal to -6 , then L does not have slope $\dfrac{1}{3}$. (b) for every real number k, line Lis not parallel to the x-axis. (c) there is a unique real number k such that L passes through (1, 4). (d) the x-intercept of L is less thank if and only if k is negative.

Solve the equation.

$$5 x ^ { 2 } + 33 = 3$$

a) Graph the function

$$f\left(x\right)=-2\left(x+1\right)^2+3$$

. b)

$$f\left(-3\right)$$

. c) What does

$$f\left(-3\right)$$

represent on the graph of

$$f$$

? d) Use the equation to determine i)

$$f\left(1\right)-f\left(0\right)$$

, ii)

$$3f\left(2\right)-5$$

, and iii)

$$f\left(2-x\right)$$

.

Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.

$$\begin{array}{l}{f(x)=x} \\ {g(x)=x-4} \\ {h(x)=3 x}\end{array}$$

Sketch the graph, noting the transition points and asymptotic behavior.

$$y = \sqrt { 2 - x ^ { 3 } }$$

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) Σ_(n=1)^∞ k(k+1)(k+2)...(k+n-1)x^n / n!, k ≥ 1