Write in the blank the expression shown in parentheses that correctly completes the sentence.
More than _____ people attended the rally. (500, five hundred)

Explain why the statement "A week has eight days if and only if October has forty days" is true.

Choose the best Vocabulary word from the following list to complete each analogy below: indisposed, emancipation, insinuate, impudence, and impunity.

JOYOUS : HAPPY ::ILL:

Frieda's construction shop charges 200 dollars per room painted and 150 dollars per room carpeted but gives half off the carpeting for each room that is painted and carpeted. Write an expression showing the cost to have x rooms painted, half of which are also carpeted, while z rooms are just carpeted.

Use a half-angle formula to find the exact value of each expression.

$$\tan \frac { 7 \pi } { 8 }$$

A helium ion $(Q=+2 e)$ whose mass is $6.6 \times 10^{-27} \mathrm{~kg}$ is accelerated by a voltage of $3700 \mathrm{~V}$. What is its speed?

Describe detalladamente la imagen. Incluye la información de las preguntas a continuación en tu descripción. ¿Crees que los demás ven la misma imagen cuando miran al gato? Explica por qué piensas así.

Multiply. Assume that all expressions are defined.

$$\frac { x } { x - 4 } \cdot \frac { - x + 2 } { x ^ { 2 } + x - 6 }$$

Indicate whether each of the following statements is true or false. If the statement is false, restate it to make it true. (a) The formate ion $\left(\mathrm{CHO}_2^{-}\right)$concentration in $0.10 \mathrm{M}$ $\mathrm{HCHO}_2$ is the same as in $0.10 \mathrm{M} \mathrm{NaCHO}$. (b) A buffer can be destroyed by adding too much strong acid. (c) A buffer can be made up by any combination of weak acid and weak base. (d) Because $\mathrm{K}_{\mathrm{a}}$ for $\mathrm{HCO}_3^{-}$is $4.7 \times 10^{-11}, \mathrm{~K}_{\mathrm{b}}$ for $\mathrm{HCO}_3^{-}$ is $2.1 \times 10^{-4}$.

Suppose a spacecraft of mass $17,000 \mathrm{~kg}$ was accelerated to $0.22 c$. How much kinetic energy would it have?

Define the operation # on the sets $A$ and $B$ by $A \# B=A^{\prime} \cup B^{\prime}$.

Show algebraically that

$$A \# A=A^{\prime}$$

For each strong acid solution, determine $\left[\mathrm{H}_3 \mathrm{O}^{+}\right],\left[\mathrm{OH}^{-}\right]$, and $\mathrm{pH}$. a. $0.15 \mathrm{M} \mathrm{HCl}$ b. $0.025 \mathrm{M} \mathrm{HNO}_3$ c. a solution that is $0.072 \mathrm{M}$ in $\mathrm{HBr}$ and $0.015 \mathrm{M}$ in $\mathrm{HNO}_3$ d. a solution that is $0.855 \% \mathrm{HNO}_3$ by mass (Assume a density of $1.01 \mathrm{~g} / \mathrm{mL}$ for the solution.)

Use graphs to find the set.

$$[2, \infty) \cup(4, \infty)$$

A strong base is defined as a molecule that can readily remove protons from water.

True or False?