For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.

$$\begin{array}{c} 0.5 x+0.3 y=4 \\ 0.25 x-0.9 y=0.46 \end{array}$$

For the following exercises, write an equation describing the relationship of the given variables. y varies directly as the cube of x and when x = 36, y = 24.

Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following series converge. $\sum_{k=1}^{\infty} \frac{1}{\sqrt[4]{27 k^{2}}}$

Suppose an investment account is opened with an initial deposit of $10,500 earning 6.25% interest, compounded continuously. How much will the account be worth after 25 years?

Does the fine structure, as we have calculated it, have any effect on the n = 1 level?

For the following exercises, find all zeros of the polynomial function, noting multiplicities. $f(x)=x^{3}-4 x^{2}+x-4$

For the following exercises, use synthetic division to find the quotient and remainder. $\frac{x^{4}-22}{x+2}$

One of the lines in the Brackett series (series limit = 1458 nm) has a wavelength of 1944 nm. Find the next higher and next lower wavelengths in this series.

For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with y-coordinates given. $f(x)=x^{3}+3 x-4, y=0,1,2$

Althea measures the following volumes of water in millilitres in beakers in a chemistry lab:

$$\begin{array}{llllllll} 210 & 215 & 235 & 208 & 210 & 218 & 218 & 215 & 208 \\ 230 & 210 & 218 & 218 & 205 & 202 & 206 & 224 & 225 \\ 207 & 215 & 210 & 228 & 230 & 238 & 234 & 201 & 210 \end{array}$$

Construct a frequency table for these data. Group the data into intervals of 10.

State the sign (positive or negative) of the sine, cosine and tangent in the quadrant. Quadrant III

On an aptitude test measuring reasoning ability on a scale of 0 to 100, a class of 30 students receiving the following scores.

$$\begin{array}{lllllllll} 38 & 75 & 28 & 34 & 56 & 32 & 61 & 28 & 71 & 27 \\ 62 & 50 & 66 & 40 & 38 & 71 & 60 & 52 & 33 & 59 \\ 74 & 69 & 86 & 57 & 65 & 16 & 60 & 56 & 55 & 38 \end{array}$$

Find the mean of the data,

Evaluate each expression when a=2 and b=-3. $\left(a^{2}\right)\left(b^{2}\right)$

Determine whether the statement is true or false. Use the linear system

$$\left\{\begin{array}{r} 2 x+2 y=3 \\ x-y=1 \end{array}\right.$$

. The linear system has a unique solution.