When making a connection at an airport, Jasmine arrives on a plane that is due to arrive at 2:15 P.M. However, the amount by which her plane arrives late has a normal distribution with a mean $\mu = 32$ minutes and a standard deviation $\sigma = 11$ minutes. Jasmine wants to transfer to a plane that is due to depart at 3:25 P.M., although the actual departure time is late by an amount that is normally distributed with a mean $\mu = 10$ minutes and a standard deviation $\sigma = 3$ minutes. If Jasmine needs 30 minutes at the airport to get from the arrival gate to the departure gate, what is the probability that she will be able to make her connection?

Within your lifetime, tourists may be able to travel to the moon. If you were taking a trip to the moon, what would you pack? Remember that the moon is dry, has almost no liquid water, and has no atmosphere. List two items that you could not use on the moon. Why would they not work?

Determine whether the following statements are true and give an explanation or counterexample. The graphs of r=2 and

$$\theta = \pi / 4$$

intersect exactly once.

Determine whether the congruence is true or false.

$$25 \equiv 85 \text { mod } 12$$

Compute the integral of the scalar function or vector field over

$$\mathbf { r } ( t ) = ( \cos t , \sin t , t )$$

for

$$0 \leq t \leq \pi.$$

$$f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$$

Use the substitution method to find all solutions of the system of equations.

$$\left\{\begin{aligned} x ^ { 2 } + y ^ { 2 } & = 25 \\ y & = 2 x \end{aligned} \right.$$

Use the function ln x. If you are unable to find intersection points analytically, use a calculator. Find the area of the region enclosed by x = 1 and y = 5 above y = ln x.

Solve each system by elimination.

$$\begin{cases} x + 2y = -1 \\ x - y = 8 \end{cases}$$

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year. If rounding is required, round to the nearest tenth of a percent. 5% compounded monthly; 5.25% compounded quarterly

The owner of a clothing store understands that the demand for shirts decreases with the price. In fact, she has developed a model that predicts that at a price of $x per shirt, she can sell D(x)=$ $40 e ^ { - x / 50 }$ $shirts in a day. It follows that the revenue (total money taken in) in a day is R(x)=xD(x)($x/shirt

$$\cdot$$

D(x)shirts). What price should the owner charge to maximize revenue?

Determine whether

$$\subseteq , { C }$$

both, or neither can be placed in each blank to form a true statement.

$$A = \{ x | x \in \mathbf { N } \quad \text { and } \quad 3 < x < 10 \}$$

B = the set of natural numbers between 3 and 10 A __B

The magnitude of the electrostatic force between point charges

$$q _ { 1 } = 26.0 \mu \mathrm { C } \text { and } q _ { 2 } = 47.0 \mu \mathrm { C }$$

is initially 5.70 N. The separation is then changed such that the force magnitude is then 0.570 N. (a) What is the ratio of the new separation to the initial separation? (b) What is the new separation?

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If all houses meet the hurricane code, then none of them are destroyed by a category 4 hurricane. Some houses were destroyed by Andrew , a category 4 hurricane . Therefore , ...

$$\begin{array} { l } { \text { Find } a , b , c \text { in } Q \text { such that } } \\ { ( 1 + \sqrt [ 3 ] { 4 } ) / ( 2 - \sqrt [ 3 ] { 2 } ) = a + b \sqrt [ 3 ] { 2 } + c \sqrt [ 3 ] { 4 } } \\ { \text { Note that such } a , b , c \text { exist, since } } \\ { ( 1 + \sqrt [ 3 ] { 4 } ) ( 2 - \sqrt [ 3 ] { 2 } ) \in Q ( \sqrt [ 3 ] { 2 } ) = \{ a + b \sqrt [ 3 ] { 2 } + c \sqrt [ 3 ] { 4 } | a , b , c \in Q \} } \end{array}$$