If the instantaneous rate of change of $f(x)$ at $(2,-4)$ is $5$, write the equation of the line tangent to the graph of $f(x)$ at $x=2$.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Because the words BET and BEE both contain three letters, the number of permutations of the letters in each word is 3!, or 6. ____

Suppose that

$$y = x ^ { 2 } + x$$

. The instantaneous rate of change of y with respect to x at x=2,

$$r _ { \text { inst } }$$

is given by the limit _.

Find the instantaneous of change of the volume of a cube with respect to its edge length $x$ as $x$ changes from

$x=5$.

A coin is tossed 500 times. True or false, and explain. a) The SE for the percentage of heads among the 500 tosses is 2.2 percentage points. b) The SE for the percentage of tails among the 500 tosses is 2.2 percentage points. c) The SE for the difference

$$\begin{array} { c } { \text { percentage of heads - percentage of tails } } \\ { \text { is } \sqrt { 2.2 ^ { 2 } + 2.2 ^ { 2 } } \approx 3.1 \text { percentage points. } } \end{array}$$

Find the percentage.

$6 \%$ of $48$

A projectile is fired vertically upward and has a position given by $s(t)=-16 t^2+128 t+192$, for $0 \leq t \leq 9$. (a). Graph the position function, for $0 \leq t \leq 9$. (b). From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time $t=a$. $(c)$. Confirm your answer to part (b) by making a table of average velocities to approximate the instantaneous velocity at $t=a$. (d). For what values of $t$ on the interval $[0,9]$ is the instantaneous velocity positive (the projectile moves upward)? (e). For what values of $t$ on the interval $[0,9]$ is the instantaneous velocity negative (the projectile moves downward)?

When you add a suffix that begins with a vowel to a word that ends in a consonant, the spelling of the original word does not change. For example, inspect + or = inspector. Add -ance, -ish, or -er to each word below to form three properly spelled words. accept

When you add a suffix that begins with a vowel to a word that ends in a consonant, the spelling of the original word does not change. For example, inspect + or = inspector. Add -ance, -ish, or -er to each word below to form three properly spelled words. travel

How can you be a lifelong learner?

Find the length and sketch the curve. r(t)=[a cos³t,a sin³t], total length.

Find the percentage.

7% of 252,000

The following table provides information on the 10 NASDAQ companies with the largest percentage of their stocks traded on July 6, 2009. Specifically, the table gives the information on the percentage of stocks traded and the change (in dollars per share) in each stock's price.

a. With percentage traded as an independent variable and the change in the stock's price as a dependent variable, compute$S S_{x x}, S S_{y y}$, and$S S_{x y}$.

b. Construct a scatter diagram for these data. Does the scatter diagram exhibit a negative linear relationship between the percentage of stock traded and the change in the stock's price?

c. Find the regression equation$ $\hat{y}$=a+b x$.

d. Give a brief interpretation of the values$a$and$b$calculated in part$ $\mathrm{c}.

e. Compute the correlation coefficient$r$.

f. Predict the change in a stock's price if$8.6 \%$ of the stock's shares are traded on a day. Using part b, how reliable do you think this prediction will be? Explain.

Refer to earlier exercise. The Sylvania CFL 65-watt replacement bulbs that utilise only 16 watts are advertised as having an average lifespan of 8000 hours on their packaging. Assume that the average lifespan of each of these bulbs is 8000 hours, with a 400-hour standard deviation. Determine the likelihood that a random sample of 25 of these bulbs will have a mean life of a. less than 7890 hours b. between 7850 and 7910 hours c. within 130 hours of the population mean d. less than the population mean by 150 hours or more