You work for a medical supplies company that spends $38,000 annually for researching new product ideas.$5,700 of that money was spent researching a new tool for surgery. What percentage of the overall research dollars does this represent?

Solve each inequality Graph the solution set on a number line.

$$| q | \geq - 1$$

$$\dfrac{4x+3}{4}-\dfrac{2x}{x+1}=x$$

Evaluate the given determinants by expansion by minors.

$$\left|\begin{array}{rrr} 4 & -5 & -1 \\ 6 & 1 & 6 \\ -2 & 4 & -3 \end{array}\right|$$

Express $\mathbf{w}=(-1,2,6,0)$ in the form $\mathbf{w}=\mathbf{w}_{1}+\mathbf{w}_{2}$, where $\mathrm{w}_{1}$ lies in the plane W spanned by the vectors $\mathbf{u}_{1}=\left(\frac{4}{5}, 0,-\frac{3}{5}\right)$ and $\mathbf{u}_{2}=(0,1,0)$, and $\mathbf{w}_{2}$ is orthogonal to W.

Choose the word or phrase that best answers the question. Which of the following is a natural fiber? A) nylon B) polyester C) silk D) acrylic

a. What are the duties and responsibilities of citizenship? b. How might the country be affected if citizens failed to perform their duties and responsibilities? c. What are some ways you can help in your community?

Prove that $\sum_{n=1}^{\infty} x / n^{\alpha}\left(1+n x^{2}\right)$ converges uniformly on every finite interval in R if $\alpha>\frac{1}{2}$. Is the convergence uniform on R?

Some material consisting of a collection of microscopic objects is kept at a high temperature. A photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 eV, 0.5 eV, 0.8 eV, 2.0 eV, 2.5 eV, and 2.8 eV. These are the only photon energies observed. Draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. On the diagram, indicate the transitions corresponding to the emitted photons. Explain briefly.

The Curiosity rover sent to explore the surface of Mars has an electric generator powered by heat from the radioactive decay of $^{238} \mathrm { Pu }$, a plutonium isotope that decays by alpha emission with a half-life of 88 years. At the start of the mission, the generator contained $9.6 \times 10 ^ { 24 }$ nuclei of $^{238} \mathrm { Pu }$. What was the approximate activity of the plutonium source at the start of the emission? A. $2 \times 10 ^ { 21 } \mathrm { Bq }$ B. $2 \times 10 ^ { 19 } \mathrm { Bq }$ C. $2 \times 10 ^ { 17 } \mathrm { Bq }$ D. $2 \times 10 ^ { 15 } \mathrm { Bq }$ E. $2 \times 10 ^ { 13 } \mathrm { Bq }$

When you place an egg in water, it sinks. If you start adding salt to the water, after some time the egg floats. Explain.

One step in the following list contains an error. Identify it and explain what is wrong.

$$\begin{array}{c} x =2 \quad (1)\\ 3 x-2 x =2 \quad (2)\\ 3 x =2 x+2 \quad (3)\\ x^{2}+3 x =x^{2}+2 x+2 \quad (4) \end{array}\\ \begin{array}{c} x^{2}+3 x-10 =x^{2}+2 x-8 \quad (5)\\(x-2)(x+5) =(x-2)(x+4) \quad (6)\\ x+5 =x+4 \quad (7)\\ 1 =0 \quad (8)\end{array}$$

Determine an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a. f(x)=

$$\frac { 2 } { 3 x + 1 }$$

; a=-1

The number of chin-ups each student can do at the beginning of the year is shown below. Carrie, 16 Franco, 17 Destiny, 7 Vince, 23 Write fractions to represent how far the students are toward reaching their goals. Carrie: Franco: Destiny: Vince: