Most of the sentences below have dangling modifiers. If a sentence has a dangling modifier, rewrite the sentence to correct it. If a sentence is already correct, write $C$ on the line provided.

Example 1. Approaching the house, the smell of fresh-baked bread is inviting. $\underline{\text{ Approaching the house, we found the smell of fresh-baked bread inviting.}}$

4. Finding many trees in one area, an important discovery was made. $\underline{\phantom{\text{The silk dress in the comer is softer than any other dress in the store.}}}$

"A $2.5\text{-m}$-long string that has a mass of $0.10 \text{~kg}$ is fixed at both ends and is under a tension of $30 \text{~N}$. When the $n$th harmonic is excited, there is a node $0.50 \text{~m}$ from one end. $(a)$ What is $n$ ?"

Assume that when a purchase of supplies of $2,650 for cash was recorded, both the debit and the credit were journalized and posted as$2,560. Would the trial balance be out of balance if the $2,650 entry had been journalized correctly but the credit to Cash had been posted as$2,560?

Calculate the ground state energy for an electron confined to a cube with sides equal to twice the Bohr radius $(R=0.0529 \mathrm{~nm})$. Determine the spring constant that would give this same ground state energy for a harmonic oscillator.

Solve each compound inequality

$$- 3 \leq x - 2 < 1$$

Predict the major product when each reagent reacts with ethylene oxide. (a) $\mathrm{NaOCH}_{2} \mathrm{CH}_{3}$ (sodium ethoxide). (b) $\mathrm{NaNH}_{2}$ (sodium amide). (c) NaSPh (sodium thiophenoxide) (d) $\mathrm{PhNH}_{2}$ (aniline). (e) KCN (potassium cyanide) (f) $\mathrm{NaN}_{3}$ (sodium azide)

With respect to right-handed Cartesian coordinates, let a=[2, 1, 0], b=[-3, 2, 0], c=[1, 4, -2], and d=[5, -1, 3]. Showing details, find: (a b c)=(b c a)=(c a b)=-(c b a)=-(a c b)

Use a graphing utility to generate the graph of $f$ in the given viewing windows, and specify the window that you think gives the best view of the graph for $f(x)=x^2+12$.

$$[-2,2] \times[11,15]$$

Which factors govern the magnitude of the lattice energy of an ionic compound?

Find the domain and range of the function. $F(t)=t^{2}+2 t+5$

The pin at $A$ has a diameter of $0.25$ in. If it is subjected to double shear, determine the average shear stress in the pin.

Solve. Identify all double roots.

$$x ^ { 2 } \left( x ^ { 4 } + 16 \right) = 8 x ^ { 4 }$$

If you were to travel to a star 125 light-years from Earth at a speed of $2.50 \times 10^{8} \mathrm{m} / \mathrm{s},$ what would you measure this distance to be?

Why not have the objective of a microscope form a case 2 image with a large magnification? (Hint: Consider the location of that image and the difficulty that would pose for using the eyepiece as a magnifier.)