Math Statement

Problem 21301

If a snack has 6 grams of fat, find the grams of protein using $4p + 6f = 60$ .

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Problem 21302

Solve for $\alpha$ in the equation $\cos \alpha=\sin \left(\alpha+30^{\circ}\right)$ , with acute angles only.

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Problem 21303

Solve for acute angle $\beta$ in the equation: $\sec(3\beta + 37^{\circ}) = \csc(\beta + 9^{\circ})$ .

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Problem 21304

Find the real solutions for the equation $x^{4}+12 x^{3}+10 x^{2}-9 x+22=0$ . What is the solution set?

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Problem 21305

Find the missing value of $a$ if $M$ is the midpoint of $\overline{F G}$ with $F G=14 a+1$ and $F M=4.5$ .

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Problem 21306

Find the real solutions of the equation $5 x^{3}-3 x^{2}-35 x+21=0$ . Choose A or B for the solution set.

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Problem 21307

Find an acute angle solution for the equation: $\sec(2\beta + 28^\circ) = \csc(3\beta + 7^\circ)$

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Problem 21308

Which graph shows the inverse of the function $f(x) = x + 4$ ?

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Problem 21309

Simplify the expression: $9(2 x)$ .

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Problem 21310

Simplify the expression: $\frac{22 x y}{3 x}$ .

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Problem 21311

List the negative multiples of 6 in the set $\{x \mid x \text{ is a negative multiple of 6}\}$ .

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Problem 21312

Identify the property illustrated by each statement: 1. $75+6=6+75$ 2. $\frac{7}{9} \cdot 1=\frac{7}{9}$ .

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Problem 21313

List the elements of the set of positive integer powers of 3: $\{3^n | n \in \mathbb{Z}^+\}$ .

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Problem 21314

Find the domain of the function $R(x)=\frac{13 x}{x+17}$ . Is it A: $x \neq -17$ or B: all real numbers?

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Problem 21315

Simplify the expression: $\frac{56 a b}{b}$ .

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Problem 21316

Write the set of even numbers from 2 to 8 in set-builder notation.

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Problem 21317

Find the domain of the function $H(x)=\frac{-3 x^{2}}{(x-1)(x+1)}$ . What values of $x$ are excluded?

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Problem 21318

Identify the property illustrated by each statement: 1. $75+6=6+75$ , 2. $\frac{7}{9} \cdot 1=\frac{7}{9}$ , 4. $389 \cdot 0=0$ , 5. $27 \cdot \pi=\pi \cdot 27$ .

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Problem 21319

Find the domain of the function $H(x)=\frac{-4 x^{2}}{(x-5)(x+6)}$ . Is it A: $x \neq \square$ or B: all real numbers?

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Problem 21320

Find the domain of the function $F(x)=\frac{9 x(x-1)}{2 x^{2}-9 x-5}$ . Is it A. $x \neq \square$ or B. all real numbers?

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Problem 21321

Find the sum of $\frac{4}{9}$ and $\frac{5}{9}$ .

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Problem 21322

What is $\frac{1}{2} + 1$ ?

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Problem 21323

Is $1.01 + 0.99$ equal to 2?

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Problem 21324

Find the derivative of $(x+1) \sin x$ .

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Problem 21325

Find the missing value in the equation: $\frac{2}{3}=\frac{8}{-}$ .

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Problem 21326

Solve the inequality $4|x+6|+2<26$ .

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Problem 21327

Solve the equations: a) $4x - 12 = 7x + 15$ ; b) $18 - (16 - x) = 1$ .

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Problem 21328

Calculate: $\frac{1}{3} \times \frac{3}{4}=$

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Problem 21329

Calculate the variance and standard deviation for the words spoken by toddlers: 27, 45, 38, 42, 4, 10.

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Problem 21330

Convert the mixed number $2 \frac{1}{3}$ into an improper fraction.

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Problem 21331

Define $x$ as a number. The expression for "ten more than a number" is $x + 10$ .

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Problem 21332

Alsha's expression $2\left(\frac{1}{2}\right)(4 \cdot 3)+6(3+4+5)$ shows how to calculate the net's area. Explain why.

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Problem 21333

Calculate $81 - 19$ .

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Problem 21334

Calculate the product of the expression: $\frac{14 \frac{2}{3}}{3} \times \frac{18}{18}$ .

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Problem 21335

Evaluate the expression: $-3 e + 1 + 400 + 20 + 6$ .

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Problem 21336

Find the product of $2 \frac{5}{8} \times \frac{4}{7}$ in simplest form.

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Problem 21337

Find the product in simplest form: $2 \frac{5}{8} \times \frac{4}{7}$ .

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Problem 21338

Multiply the mixed numbers: $4 \frac{2}{11} \times 1 \frac{10}{23}$ .

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Problem 21339

Solve for $r$ in the equation: $10=-\frac{2}{3} r$ .

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Problem 21340

Calculate: $4,509 - 1 \frac{0 \times 4160}{16} + 0 + 9$

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Problem 21341

Calculate $42 \times 3 = ?$ Choose from: 1200, 600, 4.0, 2.0.

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Problem 21342

Convert the mixed number -4 6/7 to an improper fraction.

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Problem 21343

Convert the fraction $-\frac{9}{4}$ into a mixed number.

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Problem 21344

Simplify the expression $x+x+x+x+y+y+3+3$ into an equivalent form using the numbers 1, 2, 3, 4, 5, 6, 7, 9.

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Problem 21345

Calculate $8 \times \frac{2}{3}$ .

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Problem 21346

Classify the polynomial $-9q - 3$ as cubic, quadratic, linear, or none of these.

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Problem 21347

Calculate $\frac{3}{4} \times 2 \frac{2}{3}$ . What is the result?

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Problem 21348

Classify the polynomial $4 j^{9}+4 j$ as monomial, binomial, trinomial, or none of these.

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Problem 21349

Classify the polynomial $-2 p^{3}$ as monomial, binomial, trinomial, or none of these.

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Problem 21350

Classify the polynomial $9 f^{3}-9 f$ : cubic, quadratic, linear, or none of these?

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Problem 21351

Classify the polynomial $-2k$ as monomial, trinomial, binomial, or none of these.

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Problem 21352

Solve for $v$ in the equation $u = v w + z$ .

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Problem 21353

Classify the polynomial $3g^{2} - g$ . Options: monomial, trinomial, binomial, none of these.

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Problem 21354

Classify the polynomial $-3s$ . Is it linear, quadratic, cubic, or none of these?

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Problem 21355

Solve for $x$ in the equation $[\log (x !)] = x$ .

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Problem 21356

Find $x$ such that $\lfloor \log(x!) \rfloor = x$ using Stirling's approximation for $x!$ .

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Problem 21357

Show that for any nonzero integer $n$ , the expression $\frac{n+1}{n}$ is always greater than 1.

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Problem 21358

Convert the fraction $\frac{38}{3}$ into a mixed number.

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Problem 21359

Divide $1 \frac{1}{6}$ by $2 \frac{5}{8}$ .

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Problem 21360

Calculate $2 \frac{1}{2} + \frac{9}{10}$ .

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Problem 21361

Calculate $-\frac{1}{5}+\frac{7}{10}$ .

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Problem 21362

Convert the mixed number $-6 \frac{3}{4}$ to an improper fraction.

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Problem 21363

Convert the angle $279^{\circ} 33^{\prime}$ to decimal degrees, rounding to 2 decimal places.

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Problem 21364

Solve for $x$ where $\lfloor \log_{10}(x!) \rfloor = x$ using Stirling's approximation for $x!$ .

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Problem 21365

Convert 34.9° to degrees and minutes. $34.9^{\circ} =$

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Problem 21366

Simplify the expression: $\frac{\sqrt{250 x^{3}}}{\sqrt{2 x^{-5}}}$ .

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Problem 21367

Multiply and simplify: $\frac{2}{9} \cdot \frac{2}{9}$ .

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Problem 21368

Multiply and simplify: $7 \frac{1}{3} \times 1 \frac{5}{8}$ .

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Problem 21369

Add the angles: $(44^{\circ} 36^{\prime}) + (43^{\circ} 39^{\prime}) =$

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Problem 21370

Calculate $2+\left(\frac{1}{4}+2\right) \times \frac{1}{9}$ . What is the answer?

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Problem 21371

Find the sum of 741,852 and 125,896. Estimate to verify if the answer is reasonable.

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Problem 21372

Calculate $\sin(67^{\circ} 25^{\prime})$ and round to 4 decimal places.

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Problem 21373

Evaluate the angles for these inverse functions: $\sin^{-1}\left(\frac{1}{3}\right)$ , $\tan^{-1}\left(\frac{27}{7}\right)$ , $\cos^{-1}(0.2)$ .

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Problem 21374

Expresa "todas las películas son infantiles" usando predicados y cuantificadores. Opciones: a. $\exists x(q(x))$ , b. $\exists x(\neg q(x))$ , c. $\forall x(\neg q(x))$ , d. $\forall x(q(x))$ .

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Problem 21375

Simplify the expression: $\frac{\sqrt{250 x^{3}}}{\sqrt{2 x^{-5}}}$ .

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Problem 21376

Calculate $\frac{4}{11} \div \frac{5}{2}$ .

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Problem 21377

La negación de "María no estudia precálculo todos los días o extravía el trabajo independiente" es: $María estudia precálculo todos los días y no extravía el trabajo independiente$ .

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Problem 21378

Factor the expression $25 x^{2}-4$ .

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Problem 21379

Factor the expression $k^{2}-64$ completely over the integers.

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Problem 21380

Simplify the expression: $\frac{\sqrt{84 x^{7}}}{\sqrt{3 x^{-5}}}$ .

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Problem 21381

Find the batting average greater than $2 \times 0.1 + 6 \times 0.01 + 9 \times 0.001$ . Options: A 0.27, B 0.2, C 0.264, D 0.25.

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Problem 21382

Expresa "Ninguna película es de suspenso ni de drama" usando predicados y cuantificadores.

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Problem 21383

Solve the equation: $x - 8\pi = \pi$ .

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Problem 21384

Factor or find the roots of $x^{4}-14 x^{2}+45=0$ .

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Problem 21385

Simplify the expression: $\frac{2 b+6}{3 b+9}=$

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Problem 21386

Solve the equations: $y=-3x-5$ and $y=\frac{4}{3}x-5$ . Find their intersection point.

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Problem 21387

Factor the expression $x^{2}(x^{2}-9)^{2}$ .

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Problem 21388

Solve the equation $\frac{6 h-2}{8}=\frac{7}{2}$ .

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Problem 21389

Solve for $x$ in the equation $2x - y = y$ .

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Problem 21390

Solve for $a$ in the equation $a x - 5 = b$ .

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Problem 21391

Find the sum of the first 200 terms of the sequence $-4, 0, 4, -4, 0, 4, \ldots$ .

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Problem 21392

Solve the inequality $\frac{2}{3}a - \frac{3}{4} < \frac{3}{4}a$ for the variable $a$ .

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Problem 21393

Solve for $x$ in the equation: $9x + 4 = 9(3) + 4$ .

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Problem 21394

Solve for $a$ in the equation $\frac{10 a c - x}{11} = -3$ .

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Problem 21395

Check if $(1,1.5)$ and $(12,4)$ satisfy $y=\frac{1}{4} x+\frac{5}{4}$ . Also, find the $x$ -intercept.

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Problem 21396

Solve for $a$ in the equation $\frac{10 a c - x}{11} = -3$ .

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Problem 21397

Find the net change and average rate of change of $f(x)=x^{3}-5x^{2}$ from $x=0$ to $x=10$ .

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Problem 21398

Given the function $f(z)=2-5 z^{2}$ , find (a) the net change from $z=-2$ to $z=0$ and (b) the average rate of change.

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Problem 21399

Find the net change and average rate of change of $h(t)=2 t^{2}-t_{i}$ for $t=5$ and $t=6$ .

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Problem 21400

Find $s(t(2))$ where $s(x)=-4x-3$ and $t(x)=5x+1$ .

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Math Statement

Problem 21301

If a snack has 6 grams of fat, find the grams of protein using 4p+6f=604p + 6f = 604p+6f=60.

Problem 21302

Solve for α\alphaα in the equation cos⁡α=sin⁡(α+30∘)\cos \alpha=\sin \left(\alpha+30^{\circ}\right)cosα=sin(α+30∘), with acute angles only.

Problem 21303

Solve for acute angle β\betaβ in the equation: sec⁡(3β+37∘)=csc⁡(β+9∘)\sec(3\beta + 37^{\circ}) = \csc(\beta + 9^{\circ})sec(3β+37∘)=csc(β+9∘).

Problem 21304

Find the real solutions for the equation x4+12x3+10x2−9x+22=0x^{4}+12 x^{3}+10 x^{2}-9 x+22=0x4+12x3+10x2−9x+22=0. What is the solution set?

Problem 21305

Find the missing value of aaa if MMM is the midpoint of FG‾\overline{F G}FG with FG=14a+1F G=14 a+1FG=14a+1 and FM=4.5F M=4.5FM=4.5.

Problem 21306

Find the real solutions of the equation 5x3−3x2−35x+21=05 x^{3}-3 x^{2}-35 x+21=05x3−3x2−35x+21=0. Choose A or B for the solution set.

Problem 21307

Find an acute angle solution for the equation: sec⁡(2β+28∘)=csc⁡(3β+7∘)\sec(2\beta + 28^\circ) = \csc(3\beta + 7^\circ)sec(2β+28∘)=csc(3β+7∘)

Problem 21308

Which graph shows the inverse of the function f(x)=x+4f(x) = x + 4f(x)=x+4?

Problem 21309

Simplify the expression: 9(2x)9(2 x)9(2x).

Problem 21310

Simplify the expression: 22xy3x\frac{22 x y}{3 x}3x22xy​.

Problem 21311

List the negative multiples of 6 in the set {x∣x is a negative multiple of 6}\{x \mid x \text{ is a negative multiple of 6}\}{x∣x is a negative multiple of 6}.

Problem 21312

Identify the property illustrated by each statement: 1. 75+6=6+7575+6=6+7575+6=6+75 2. 79⋅1=79\frac{7}{9} \cdot 1=\frac{7}{9}97​⋅1=97​.

Problem 21313

List the elements of the set of positive integer powers of 3: {3n∣n∈Z+}\{3^n | n \in \mathbb{Z}^+\}{3n∣n∈Z+}.

Problem 21314

Find the domain of the function R(x)=13xx+17R(x)=\frac{13 x}{x+17}R(x)=x+1713x​. Is it A: x≠−17x \neq -17x=−17 or B: all real numbers?

Problem 21315

Simplify the expression: 56abb\frac{56 a b}{b}b56ab​.

Problem 21316

Write the set of even numbers from 2 to 8 in set-builder notation.

Problem 21317

Find the domain of the function H(x)=−3x2(x−1)(x+1)H(x)=\frac{-3 x^{2}}{(x-1)(x+1)}H(x)=(x−1)(x+1)−3x2​. What values of xxx are excluded?

Problem 21318

Identify the property illustrated by each statement: 1. 75+6=6+7575+6=6+7575+6=6+75, 2. 79⋅1=79\frac{7}{9} \cdot 1=\frac{7}{9}97​⋅1=97​, 4. 389⋅0=0389 \cdot 0=0389⋅0=0, 5. 27⋅π=π⋅2727 \cdot \pi=\pi \cdot 2727⋅π=π⋅27.

Problem 21319

Find the domain of the function H(x)=−4x2(x−5)(x+6)H(x)=\frac{-4 x^{2}}{(x-5)(x+6)}H(x)=(x−5)(x+6)−4x2​. Is it A: x≠□x \neq \squarex=□ or B: all real numbers?

Problem 21320

Find the domain of the function F(x)=9x(x−1)2x2−9x−5F(x)=\frac{9 x(x-1)}{2 x^{2}-9 x-5}F(x)=2x2−9x−59x(x−1)​. Is it A. x≠□x \neq \squarex=□ or B. all real numbers?

Problem 21321

Find the sum of 49\frac{4}{9}94​ and 59\frac{5}{9}95​.

Problem 21322

What is 12+1\frac{1}{2} + 121​+1?

Problem 21323

Is 1.01+0.991.01 + 0.991.01+0.99 equal to 2?

Problem 21324

Find the derivative of (x+1)sin⁡x(x+1) \sin x(x+1)sinx.

Problem 21325

Find the missing value in the equation: 23=8−\frac{2}{3}=\frac{8}{-}32​=−8​.

Problem 21326

Solve the inequality 4∣x+6∣+2<264|x+6|+2<264∣x+6∣+2<26.

Problem 21327

Solve the equations: a) 4x−12=7x+154x - 12 = 7x + 154x−12=7x+15; b) 18−(16−x)=118 - (16 - x) = 118−(16−x)=1.

Problem 21328

Calculate: 13×34=\frac{1}{3} \times \frac{3}{4}=31​×43​=

Problem 21329

Calculate the variance and standard deviation for the words spoken by toddlers: 27, 45, 38, 42, 4, 10.

Problem 21330

Convert the mixed number 2132 \frac{1}{3}231​ into an improper fraction.

Problem 21331

Define xxx as a number. The expression for "ten more than a number" is x+10x + 10x+10.

Problem 21332

Alsha's expression 2(12)(4⋅3)+6(3+4+5)2\left(\frac{1}{2}\right)(4 \cdot 3)+6(3+4+5)2(21​)(4⋅3)+6(3+4+5) shows how to calculate the net's area. Explain why.

Problem 21333

Calculate 81−1981 - 1981−19.

Problem 21334

Calculate the product of the expression: 14233×1818\frac{14 \frac{2}{3}}{3} \times \frac{18}{18}31432​​×1818​.

Problem 21335

Evaluate the expression: −3e+1+400+20+6-3 e + 1 + 400 + 20 + 6−3e+1+400+20+6.

Problem 21336

Find the product of 258×472 \frac{5}{8} \times \frac{4}{7}285​×74​ in simplest form.

Problem 21337

Find the product in simplest form: 258×472 \frac{5}{8} \times \frac{4}{7}285​×74​.

Problem 21338

Multiply the mixed numbers: 4211×110234 \frac{2}{11} \times 1 \frac{10}{23}4112​×12310​.

Problem 21339

Solve for rrr in the equation: 10=−23r10=-\frac{2}{3} r10=−32​r.

Problem 21340

If a snack has 6 grams of fat, find the grams of protein using $4p + 6f = 60$ .

Solve for $\alpha$ in the equation $\cos \alpha=\sin \left(\alpha+30^{\circ}\right)$ , with acute angles only.

Solve for acute angle $\beta$ in the equation: $\sec(3\beta + 37^{\circ}) = \csc(\beta + 9^{\circ})$ .

Find the real solutions for the equation $x^{4}+12 x^{3}+10 x^{2}-9 x+22=0$ . What is the solution set?

Find the missing value of $a$ if $M$ is the midpoint of $\overline{F G}$ with $F G=14 a+1$ and $F M=4.5$ .

Find the real solutions of the equation $5 x^{3}-3 x^{2}-35 x+21=0$ . Choose A or B for the solution set.

Find an acute angle solution for the equation: $\sec(2\beta + 28^\circ) = \csc(3\beta + 7^\circ)$

Which graph shows the inverse of the function $f(x) = x + 4$ ?

Simplify the expression: $9(2 x)$ .

Simplify the expression: $\frac{22 x y}{3 x}$ .

List the negative multiples of 6 in the set $\{x \mid x \text{ is a negative multiple of 6}\}$ .

Identify the property illustrated by each statement: 1. $75+6=6+75$ 2. $\frac{7}{9} \cdot 1=\frac{7}{9}$ .

List the elements of the set of positive integer powers of 3: $\{3^n | n \in \mathbb{Z}^+\}$ .

Find the domain of the function $R(x)=\frac{13 x}{x+17}$ . Is it A: $x \neq -17$ or B: all real numbers?

Simplify the expression: $\frac{56 a b}{b}$ .

Find the domain of the function $H(x)=\frac{-3 x^{2}}{(x-1)(x+1)}$ . What values of $x$ are excluded?

Identify the property illustrated by each statement: 1. $75+6=6+75$ , 2. $\frac{7}{9} \cdot 1=\frac{7}{9}$ , 4. $389 \cdot 0=0$ , 5. $27 \cdot \pi=\pi \cdot 27$ .

Find the domain of the function $H(x)=\frac{-4 x^{2}}{(x-5)(x+6)}$ . Is it A: $x \neq \square$ or B: all real numbers?

Find the domain of the function $F(x)=\frac{9 x(x-1)}{2 x^{2}-9 x-5}$ . Is it A. $x \neq \square$ or B. all real numbers?

Find the sum of $\frac{4}{9}$ and $\frac{5}{9}$ .

What is $\frac{1}{2} + 1$ ?

Is $1.01 + 0.99$ equal to 2?

Find the derivative of $(x+1) \sin x$ .

Find the missing value in the equation: $\frac{2}{3}=\frac{8}{-}$ .

Solve the inequality $4|x+6|+2<26$ .

Solve the equations: a) $4x - 12 = 7x + 15$ ; b) $18 - (16 - x) = 1$ .

Calculate: $\frac{1}{3} \times \frac{3}{4}=$

Convert the mixed number $2 \frac{1}{3}$ into an improper fraction.

Define $x$ as a number. The expression for "ten more than a number" is $x + 10$ .

Alsha's expression $2\left(\frac{1}{2}\right)(4 \cdot 3)+6(3+4+5)$ shows how to calculate the net's area. Explain why.

Calculate $81 - 19$ .

Calculate the product of the expression: $\frac{14 \frac{2}{3}}{3} \times \frac{18}{18}$ .

Evaluate the expression: $-3 e + 1 + 400 + 20 + 6$ .

Find the product of $2 \frac{5}{8} \times \frac{4}{7}$ in simplest form.

Find the product in simplest form: $2 \frac{5}{8} \times \frac{4}{7}$ .

Multiply the mixed numbers: $4 \frac{2}{11} \times 1 \frac{10}{23}$ .

Solve for $r$ in the equation: $10=-\frac{2}{3} r$ .

Calculate: $4,509 - 1 \frac{0 \times 4160}{16} + 0 + 9$

Calculate $42 \times 3 = ?$ Choose from: 1200, 600, 4.0, 2.0.

Convert the fraction $-\frac{9}{4}$ into a mixed number.

Simplify the expression $x+x+x+x+y+y+3+3$ into an equivalent form using the numbers 1, 2, 3, 4, 5, 6, 7, 9.

Calculate $8 \times \frac{2}{3}$ .

Classify the polynomial $-9q - 3$ as cubic, quadratic, linear, or none of these.

Calculate $\frac{3}{4} \times 2 \frac{2}{3}$ . What is the result?

Classify the polynomial $4 j^{9}+4 j$ as monomial, binomial, trinomial, or none of these.

Classify the polynomial $-2 p^{3}$ as monomial, binomial, trinomial, or none of these.

Classify the polynomial $9 f^{3}-9 f$ : cubic, quadratic, linear, or none of these?

Classify the polynomial $-2k$ as monomial, trinomial, binomial, or none of these.

Solve for $v$ in the equation $u = v w + z$ .

Classify the polynomial $3g^{2} - g$ . Options: monomial, trinomial, binomial, none of these.

Classify the polynomial $-3s$ . Is it linear, quadratic, cubic, or none of these?

Solve for $x$ in the equation $[\log (x !)] = x$ .

Find $x$ such that $\lfloor \log(x!) \rfloor = x$ using Stirling's approximation for $x!$ .

Show that for any nonzero integer $n$ , the expression $\frac{n+1}{n}$ is always greater than 1.

Convert the fraction $\frac{38}{3}$ into a mixed number.

Divide $1 \frac{1}{6}$ by $2 \frac{5}{8}$ .

Calculate $2 \frac{1}{2} + \frac{9}{10}$ .

Calculate $-\frac{1}{5}+\frac{7}{10}$ .

Convert the mixed number $-6 \frac{3}{4}$ to an improper fraction.

Convert the angle $279^{\circ} 33^{\prime}$ to decimal degrees, rounding to 2 decimal places.

Solve for $x$ where $\lfloor \log_{10}(x!) \rfloor = x$ using Stirling's approximation for $x!$ .

Convert 34.9° to degrees and minutes. $34.9^{\circ} =$

Simplify the expression: $\frac{\sqrt{250 x^{3}}}{\sqrt{2 x^{-5}}}$ .

Multiply and simplify: $\frac{2}{9} \cdot \frac{2}{9}$ .

Multiply and simplify: $7 \frac{1}{3} \times 1 \frac{5}{8}$ .

Add the angles: $(44^{\circ} 36^{\prime}) + (43^{\circ} 39^{\prime}) =$

Calculate $2+\left(\frac{1}{4}+2\right) \times \frac{1}{9}$ . What is the answer?

Calculate $\sin(67^{\circ} 25^{\prime})$ and round to 4 decimal places.

Evaluate the angles for these inverse functions: $\sin^{-1}\left(\frac{1}{3}\right)$ , $\tan^{-1}\left(\frac{27}{7}\right)$ , $\cos^{-1}(0.2)$ .

Expresa "todas las películas son infantiles" usando predicados y cuantificadores. Opciones: a. $\exists x(q(x))$ , b. $\exists x(\neg q(x))$ , c. $\forall x(\neg q(x))$ , d. $\forall x(q(x))$ .