Use the formula for

$$_nC_r$$

to solve. To win in the New York State lottery , one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?

A fossil bone contains 25% of its original carbon-14. What is the approximate age of the bone?

A social security number contains nine digits, such as 074-66-7795. How many different social security numbers

A student claims that h(x) = 3x and j(x) = -3x are inverse functions. Is the student correct? Justify your answer.

Write the first statement as a conditional. If possible, use the Law of Detachment to make a conclusion. If it is not possible to make a conclusion, tell why. All national parks are Interesting. Mammoth Cave is a national park.

A friend is planning a trip to Alaska. He purchased a coat that is recommended for outdoor temperatures from $-15^{\circ} \mathrm{F}$ to $45^{\circ} \mathrm{F}.$ Let t represent the temperature for which the coat is intended.

Suppose a large candy machine has 45% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion

$$\hat{p}$$

of orange candies. Is the sampling distribution of

$$\hat{p}$$

approximately Normal? Check to see if the Large Counts condition is met.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13,... After the first two numbers, each number is the sum of the two previous numbers. What is the eleventh term of the sequence?

solve for X in the equation, where A=[-4 0 , 1 -5 , -3 2] and B=[1 2 , -2 1 , 4 4]. 3X + 2A = B

Solve each inequality using a graphing utility.

$$\frac { x - 4 } { x - 1 } \leq 0$$

What is the probability of an impossible event?

Draw the seven constitutional isomers having molecular formula

$$\mathrm { C } _ { 4 } \mathrm { H } _ { 10 } \mathrm { O }.$$

Identify the functional group in each isomer.

Write the equation of a rational function

$$f ( x ) = \frac { p ( x ) } { q ( x ) }$$

having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. f has no vertical horizontal, or slant asymptotes, and no x-intercepts.

Evaluate each inverse trigonometric function. Round to the nearest hundredth if necessary.

$$\tan \left( \cos ^ { - 1 } \frac { 1 } { 3 } \right)$$