After a 20% price reduction, a cordless phone sold for $48. What was the phone's price before the reduction?

Photoelectron spectroscopy studies have determined the orbital energies for fluorine atoms to be 1s - 689 eV, 2s - 34e V, 2p - 12 eV. Estimate the value of Z eff for F in each of these orbitals.

At a pressure of 0.1 atm, determine (a) the melting temperature for ice and (b) the boiling temperature for water.

Prove that

$$\operatorname { span } \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\} = \operatorname { span } \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } \right\}$$

if and only if

$$\mathbf v_3$$

can be written as a linear combination of

$$\mathbf { v } _ { 1 } \text { and } \mathbf { v } _ { 2 }.$$

How are the measures of the angles related when parallel lines are cut by a transversal?

What happens when someone experiences sensory deprivation for long periods? Why?

The function fails to be differentiable at x = 0. Tell whether the problem is a corner, a cusp, a vertical tangent, or a discontinuity. y = 3x - 2│x│ - 1

Solve the proportion. 3/7 = d/42

Find the slope of the line passing through the given points. (1, -3), (5, 0)

Solve.

On a test, a student got $72$ items correct, which was $80 \%$ of the total number of items. How many items were on the test?

Use built-in functions of some form of technology to determine rank(A) and, if possible,

$$A ^ { - 1 }.$$

$$A = \left[ \begin{array} { r r r r } { 7 } & { 13 } & { 15 } & { 21 } \\ { 9 } & { - 2 } & { 14 } & { 23 } \\ { 17 } & { - 27 } & { 22 } & { 31 } \\ { 19 } & { - 42 } & { 21 } & { 33 } \end{array} \right].$$

(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume

$$\lambda = 550 \mathrm { nm }$$

. (b) Find the distance between these barely resolved stars if each of them is 18 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens "errors."

Solve the application problem.

The list price of a bike at Olympic Sports is $149.99. Find the dealer’s cost if given a 20/20 trade discount and a 3/20, n/30 cash discount. Assume that the dealer earns the maximum cash discount.

Use deductive reasoning to prove that the solution of the equation x – 5 = -2 is x = 3. Be sure to justify each step in your proof.