Solve the percent problem. 1.8 is 72% of what number?

For each of these Gaussian integers, find its factorization into Gaussian primes and a unit where each Gaussian prime has a positive real part and a nonnegative imaginary part. a) 7+6i, b) 3-13i, c) 28, d) 400i.

Consider a hyperbola, where the difference of the distance between the two foci is the constant 2a, and choose one focus at O and the other at $(-2 \varepsilon a, 0)$. (In this case, we must have $\varepsilon>1$). Show that we obtain the exact same equation in polar coordinates $r=\frac{\Lambda}{1+\varepsilon \cos \theta}$ as we obtained for an ellipse.

Complete each sentence by writing the correct present-tense form of the verb indicated. Many a teacher and student _____ through these halls every day. (pass)

Underline the verb in parentheses that best completes each sentence. Either bike (is, are) a good buy.

Calculate the product: (x - 7)(x + 8)

Find the sequence obtained by applying successively the modular multiplications with multipliers and moduli (7,92), (11,95), and (6,101), respectively, on the super-increasing sequence (3, 4, 8, 17, 33, 67).

Determine whether the equation is an identity or a conditional equation. 2(x-1)=2x-2

Calculations of this sort may be used to evaluate limits that we might otherwise try to find through laborious use of I'Hópital's Rule. Find the following: $\lim _{x \rightarrow 0} \frac{(\sin x)(\arctan x)-x^{2}}{1-\cos \left(x^{2}\right)}$.

Find the real solution(s) of the equation involving fractions. Check your solution(s). $\frac{4}{x+1}-\frac{3}{x+2}=1$

Let A be a $3 \times 3$ matrix with real entries. Prove that, if A is not similar over R to a triangular matrix, then A is similar over C to a diagonal matrix.

Draw one line under each transitive verb and two lines under each intransitive verb. Draw three lines under each direct object and circle each indirect object. These richly decorated tombs give archaeologists valuable information.

Use the Pollard rho method with $x_{0}=2$ and $f(x)=x^{2}+1$ to find the prime factorization of each of the following integers. a) 133, b) 1189, c) 1927, d) 8131, e) 36,287, f) 48,227.

What is Daines’s purpose in writing this essay? How does his job as state health commissioner influence your reaction to his argument?