Math

Problem 55301

The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.
Bacteria A \begin{tabular}{|l|c|c|c|c|} \hline Time (days) & 0 & 2 & 4 & 6 \\ \hline Bacteria Count & 60 & 240 & 960 & 3,840 \\ \hline \end{tabular}
Bacteria B \begin{tabular}{|l|c|c|c|c|} \hline Time (days) & 0 & 1 & 3 & 5 \\ \hline Bacteria Count & 90 & 180 & 720 & 2,880 \\ \hline \end{tabular}
How do the functions in the table compare? Since $x$ -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start. Since $y$ -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start. Since the maximum value in the table for bacteria $A$ is greater than the maximum value in the table for bacteria B , bacteria A has a faster growth rate than bacteria B . Since the minimum value in the table for bacteria $A$ is less than the minimum value in the table for bacteria $B$ , bacteria $A$ has a slower growth rate than bacteria B .

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Problem 55302

Rewrite the mixed number $4 \frac{1}{2}$ as an equivalent fraction with a denominator equal to 12. $\begin{array}{c} 4 \frac{1}{2}=\frac{?}{12} \\ 4 \frac{1}{2}=\frac{\square}{12} \end{array}$

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Problem 55303

Expand and combine $-3(3 x-4 a 1)-a(2 y+5 x)$

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Problem 55304

Find the exact value of $\sin \left(\frac{10 \pi}{3}\right)$ . What quadrant is $\theta=\frac{10 \pi}{3}$ in? Reference angle? $\theta_{\mathrm{R}}=$

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Problem 55305

Find $\csc \left(\frac{8 \pi}{3}\right)$ and identify the quadrant of $\theta=\frac{8 \pi}{3}$ .

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Problem 55306

Find $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. Where's the angle's quadrant? What's the reference angle? Choose the equivalent expression.

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Problem 55307

Find the value of $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. What quadrant is $\theta=\frac{8 \pi}{3}$ in? What is the reference angle? $\theta_{\mathrm{R}}=$

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Problem 55308

The cosecant function is positive here. Find the reference angle: $\theta_{\mathrm{R}}=\frac{\pi}{3}$ . Which is $\csc \left(\frac{8 \pi}{3}\right)$ ? Options: A. $\csc \left(\frac{\pi}{3}\right)$ , B. $\csc \left(\frac{\pi}{6}\right)$ , C. $-\csc \left(\frac{\pi}{6}\right)$ , D. $-\csc \left(\frac{\pi}{3}\right)$ . What is $\csc \left(\frac{8 \pi}{3}\right)$ ?

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Problem 55309

The angle $\theta=-\frac{17 \pi}{6}$ is in which quadrant?

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Problem 55310

Count the number of zoos with more than 50 bears from the stem-and-leaf plot given.

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Problem 55311

Count the zoos with more than 18 sloths from the given stem-and-leaf plot.

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Problem 55312

How many zoos have exactly 27 tigers based on the stem-and-leaf plot? Key: $2 \mid 7 = 27$ tigers.

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Problem 55313

Find the value of $\tan \left(-\frac{19 \pi}{6}\right)$ .
(a) Which quadrant is $\theta=-\frac{19 \pi}{6}$ in? (b) Is tangent positive or negative there? (c) What is the reference angle $\theta_{R}=$ ?

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Problem 55314

What is the maximum number of pairs of glasses from the stemand-leaf plot: $4 \mid 1=41$ ?

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Problem 55315

Find the exact value of $\cot \left(-\frac{17 \pi}{6}\right)$ and answer: a. Which quadrant is $\theta$ in? b. Is cotangent positive or negative there?

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Problem 55316

The terminal side of the angle $\theta=-\frac{11 \pi}{4}$ lies in which quadrant?

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Problem 55317

How many stores have less than 60 pairs of boots based on the stem-and-leaf plot provided?

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Problem 55318

Find $\cot \left(-\frac{17 \pi}{6}\right)$ without a calculator. Determine the quadrant, sign, and reference angle.

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Problem 55319

How many stores have fewer than 60 pairs of boots based on the stem-and-leaf plot?

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Problem 55320

Find the exact value of $\sec \left(-\frac{11 \pi}{4}\right)$ without a calculator. What quadrant is it in and is secant positive or negative?

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Problem 55321

Find the value of $\sec \left(-\frac{11 \pi}{4}\right)$ . Determine the quadrant, sign, and reference angle $\theta_{\mathrm{R}}=$ .

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Problem 55322

Find sec $\left(-\frac{11 \pi}{4}\right)$ , determine the reference angle $\theta_{\mathrm{R}}=\frac{\pi}{4}$ , and choose the correct expression.

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Problem 55323

Find $f^{\prime}(x)$ using the Fundamental Theorem of Calculus for $f(x)=\int_{-4}^{x^{3}} \sqrt{t^{2}+9} dt$ .

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Problem 55324

Find $\tan \left(\frac{11 \pi}{6}\right)$ exactly without a calculator. A. $\tan \left(\frac{11 \pi}{6}\right)=$ B. Undefined.

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Problem 55325

Find $\sec \left(-\frac{11 \pi}{4}\right)$ and answer: (d) which is equivalent? (e) Find its exact value.

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Problem 55326

Calculate the percentage difference: $\frac{3.5-3.14159}{3.14159} \times 100$ .

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Problem 55327

Determine the interval(s) where the curve $y=\int_{0}^{x} \frac{t^{2}}{t^{2}-3 t+5} d t$ is concave upward.

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Problem 55328

Karan borrowed \$3,650 for 5 months at 10% interest. What is her monthly payment?

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Problem 55329

Find a function $f$ and a number $a$ such that $2+\int_{a}^{x} \frac{f(t)}{t^{5}} dt=6 x^{-1}$ . What is $f(x)$ ?

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Problem 55330

Find the value of $\tan \left(-\frac{5 \pi}{6}\right)$ without a calculator. A. $\tan \left(-\frac{5 \pi}{6}\right)=$ B. Undefined.

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Problem 55331

Calculate the integral $\int_{3}^{19}(7-|x-11|) d x$ using area formulas.

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Problem 55332

Evaluate the integral from 9 to 15 of $-(4x + 5)$ using area formulas. What is $\int_{9}^{15}(-(4x+5)) dx$ ?

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Problem 55333

Estimate the integrals using Riemann sums: (a) left-endpoint $\int_{0}^{10} f(x) dx \approx$ and (b) right-endpoint $\int_{0}^{10} f(x) dx \approx$ .

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Problem 55334

Find a function $f$ and a number $a$ such that $2 + \int_{a}^{x} \frac{f(t)}{t^{5}} dt = 6 x^{-1}$ .

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Problem 55335

Use the table of the increasing function $f$ to find lower and upper estimates for $\int_{0}^{25} f(x) dx$ . Lower estimate = , Upper estimate = .

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Problem 55336

Find the hypotenuse of a right triangle with sides 24 and 7 using the Pythagorean theorem: $c^2 = 24^2 + 7^2$ .

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Problem 55337

Compute the following integrals using given values:
(a) $\int_{0}^{4} 4 f(x) d x=$ (b) $\int_{0}^{4}(-1 f(x)-3 g(x)) d x=$ (c) $\int_{0}^{4}(3-5 h(x)) d x=$

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Problem 55338

Given the integrals:
1. $\int_{2}^{6} f(x) dx = -10$ , $\int_{6}^{8} f(x) dx = -10$
2. $\int_{2}^{6} g(x) dx = -4$ , $\int_{6}^{8} g(x) dx = 4$
Find:
(a) $\int_{2}^{8}(f(x)+g(x)) dx=$ (number)
(b) $\int_{2}^{8}(f(x)-g(x)) dx=$ (number)
(c) $\int_{2}^{8}(7 f(x)-3 g(x)) dx=$ (number)

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Problem 55339

Compute the integrals given:
(a) $\int_{0}^{4} 4 f(x) d x = 62$
(b) $\int_{0}^{4}(-1 f(x)-3 g(x)) d x=$ ?

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Problem 55340

Find the average value $f_{\text{ave}}$ of $f(x)=32-|4x|$ from $x=-8$ to $x=8$ and points $c$ where $f(c)=f_{\text{ave}}$ .

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Problem 55341

Find the average value $f_{\text {ave }}$ of $f(x)=32-|4 x|$ for $x$ in the range $[-8, 8]$ . What is $f_{\text {ave }}$ ?

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Problem 55342

Evaluate the integral from 3 to 19 of $7 - |x - 11|$ using area formulas. What is $\int_{3}^{19}(7 - |x - 11|) d x$ ?

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Problem 55343

Boy scouts hike 5 miles in 2 hours. How long will it take to hike 10 miles at the same rate?

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Problem 55344

Find the exact value of $\cos (8 \pi)$ . Answer parts a, b, c, and d. a. Where is the terminal side of angle $\theta=8 \pi$ ?

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Problem 55345

Given $\sum_{i=3}^{117} a_{i}=30$ and $\sum_{i=3}^{117} b_{i}=18$ , find: (a) $\sum_{i=3}^{117}(a_{i}+b_{i})$ and (b) $\sum_{i=3}^{117}(19 a_{i}-10 b_{i})$ .

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Problem 55346

Find $\sin \left(-\frac{9 \pi}{2}\right)$ without a calculator.
a. Where is the angle's terminal side? b. Coordinates for $r=1$ ? c. General definition of $\sin \theta$ ? d. Exact value of $\sin \left(-\frac{9 \pi}{2}\right)$ ?

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Problem 55347

Karbis on 7 valget ja 2 musta küünalt. Leia tõenäosus:
a. mõlemad valged b. mõlemad mustad c. erinevat värvi d. üks punane e. ühte värvi.

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Problem 55348

Find the right endpoint Riemann sum for $f(x)=\frac{15}{x}$ on $[2,6]$ using 8 rectangles of width 0.5. What is the sum?

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Problem 55349

Calculate the left endpoint Riemann sum for $f(x)=\frac{15}{x}$ over $[2,6]$ using 8 rectangles of width 0.5.

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Problem 55350

Find $\cos(8\pi)$ by answering: a) where is the angle? b) coordinates on terminal side? c) definition of $\cos \theta$ ?

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Problem 55351

Find $\cos(8\pi)$ without a calculator: a. Where does $\theta=8\pi$ end? b. What are the coordinates for $r=1$ ?

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Problem 55352

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 55353

Calculate the left endpoint Riemann sum for $f(x)=\frac{x^{2}}{12}$ on $[2,6]$ and explain why it's an underestimate.

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Problem 55354

Find $\sec \theta$ given $\tan \theta=\frac{1}{3}$ and $\csc \theta<0$ . Simplify your answer.

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Problem 55355

Find $\sin \theta$ given $\sec \theta=\frac{4}{3}$ and $\tan \theta>0$ . What is $\sin \theta$ ?

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Problem 55356

Find the reference angle for $\theta=-\frac{26 \pi}{7}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

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Problem 55357

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{11}$ . What is $\theta_{R}$ ?

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Problem 55358

Find the reference angle for $\theta = -\frac{26 \pi}{7}$ . What is the least nonnegative coterminal angle $\theta_{C}$ ? In which quadrant is $\theta_{C}$ ?

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Problem 55359

Find the indefinite integral: $\int \frac{1}{(x-1)(x+3)} dx = \sqrt{2} + C$ .

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Problem 55360

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{11}$ . In which quadrant is $\theta_{C}$ ?

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Problem 55361

Evaluate the integral using partial fractions: $\int -\frac{2}{(x-6)^{2}(x+6)} \, dx = C$

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Problem 55362

Evaluate the expression: $-\frac{1}{18} \int \frac{1}{x-6} dx + \frac{1}{108} \int \frac{1}{(x-6)^{2}} dx - \frac{1}{216} \int \frac{1}{x+6} dx$ .

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Problem 55363

Find the expression to calculate the total height of two towers: $\frac{89}{100}$ m and $\frac{7}{10}$ m. Choose 1 answer: (A) $\frac{89}{100}+\frac{7}{100}$ (B) $\frac{89}{10}+\frac{7}{10}$ (C) $\frac{89}{100}+\frac{70}{100}$ (D) $890 \quad 70$

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Problem 55364

Evaluate the integral: $\int \frac{7 x+25}{(7-x)\left(x^{2}+25\right)} d x=$

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Problem 55365

How much longer is Fluffy's tail ( $1 \frac{1}{3}$ m) than Fireball's tail ( $1 \frac{1}{4}$ m)?

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Problem 55366

Find the reference angle for $\theta=-\frac{26 \pi}{7}$ . What is $\theta_{C}$ and the reference angle $\theta_{R}$ ?

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Problem 55367

Calculate the result of $\frac{3}{4} - \frac{2}{3}$ .

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Problem 55368

Laual on 4 kahvlit ja 5 nuga. Jaan võtab 4 eset. Arvuta tõenäosus, et seal on vähemalt 2 kahvlit.

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Problem 55369

Calculate the value of $\frac{2}{3} - \frac{1}{6} = \square$

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Problem 55370

Our pirate ship had $\frac{5}{6}$ of a chest of gold and took $\frac{3}{8}$ more. How many chests do we have now?

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Problem 55371

Find $A$ in the equation: $A=\frac{4(3)^{4}-3(3)^{3}-1(3)^{2}-10(3)-4}{(3^{2}+1)^{2}}$ .

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Problem 55372

Noor had $\frac{5}{7}$ L of coconut milk and used $\frac{1}{2}$ L. How much is left? Identify the correct number line.

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Problem 55373

Find the distance $d$ traveled by a particle with velocity $v(t)=\frac{7 t^{2}}{t^{2}+1}$ after $t=3$ sec.

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Problem 55374

Find coefficients A, B, C, D, and E for the partial fraction expansion of
$\frac{4 x^{4}-3 x^{3}-1 x^{2}-10 x-4}{(x-3)(x^{2}+1)^{2}} = \frac{A}{x-3}+\frac{B x+C}{x^{2}+1}+\frac{D x+E}{(x^{2}+1)^{2}}.$

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Problem 55375

Find the remainder when 87 is divided by 17. What is $87 \div 17$ remainder?

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Problem 55376

Find $\cos \left(-\frac{2 \pi}{3}\right)$ . Which quadrant is the angle $\theta=-\frac{2 \pi}{3}$ in?

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Problem 55377

Calculate the product of 12 and 0.75: $12 \times 0.75$ .

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Problem 55378

Find the coefficients A, B, C, D, and E for the partial fraction expansion of $\frac{4 x^{4}-3 x^{3}-1 x^{2}-10 x-4}{(x-3)(x^{2}+1)^{2}}$ .

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Problem 55379

Find the exact value of $\cos \left(-\frac{2 \pi}{3}\right)$ . In which quadrant is this angle, and is cosine positive or negative there?

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Problem 55380

Find $\csc \left(\frac{5 \pi}{6}\right)$ without a calculator. Reference angle is $\theta_{\mathrm{R}}=\frac{\pi}{6}$ . Which is equivalent: A, B, C, or D?

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Problem 55381

A rumor spreads in a school. Given $y^{\prime}(t)=k y(1-y)$ , find when $90\%$ of 1000 students hear it.

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Problem 55382

Find the value of $\square$ in the equation $300 \div \square=30$ .

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Problem 55383

Solve the logistic equation $\frac{d y}{d x}=5 y\left(1-\frac{y}{10}\right)$ for $y$ and find $y(0)=6$ .

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Problem 55384

Draw an arc from vertex $B$ that intersects both sides of $\angle B$ . Label the intersections as points $A$ and $C$ .

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Problem 55385

Find the remainder when 945 is divided by 35. What is $945 \div 35$ ?

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Problem 55386

Which option shows the correct multiplication of $409 \times 7$ using the standard algorithm? Choose A, B, or C.

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Problem 55387

Find the equation of the line through the points $(0,-4)$ and $(5,-4)$ .

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Problem 55388

Calculate the value of $\frac{1.4}{374}$ .

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Problem 55389

Solve the equation: $2(4x - 7) = 10$ .

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Problem 55390

Construct $\angle F$ so that $m \angle F=2 m \angle B$ . Complete the steps to find point $F$ .

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Problem 55391

Find the value of $\cot \left(\frac{15 \pi}{4}\right)$ .
a) Which quadrant is $\theta=\frac{15 \pi}{4}$ in? b) Is cotangent negative here? c) What is the reference angle? d) Which expression equals $\cot \left(\frac{15 \pi}{4}\right)$ ? A. $-\cot \left(\frac{\pi}{4}\right)$ B. $\cot \left(\frac{\pi}{3}\right)$ C. $\cot \left(\frac{\pi}{4}\right)$ D. $-\cot \left(\frac{\pi}{3}\right)$

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Problem 55392

Evaluate $\left(5.38 \times 10^{5}\right) \div\left(2 \times 10^{-2}\right)$ and express your answer in scientific notation.

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Problem 55393

Find $\sin \left(\frac{3 \pi}{4}\right)$ exactly without a calculator. A. $\sin \left(\frac{3 \pi}{4}\right)=$ B. Undefined.

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Problem 55394

What is the weight of a phone that weighs 0.068125 pounds, rounded to the nearest hundredth in scientific notation?

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Problem 55395

Find the exact value of $\cos \left(\frac{13 \pi}{4}\right)$ without a calculator. A. $\cos \left(\frac{13 \pi}{4}\right)=$ B. Undefined.

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Problem 55396

Factor $y=x^{2}-7 x+12$ into the form $y=(x-h)(x-k)$ .

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Problem 55397

Find $\sin \left(-\frac{13 \pi}{4}\right)$ and determine which expression is equivalent to $\sin \left(-\frac{1}{4}\right)$ .

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Problem 55398

Find $\sin \left(-\frac{13 \pi}{4}\right)$ , reference angle $\theta_{\mathrm{R}}=\frac{\pi}{4}$ , and its equivalent expression (A-D).

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Problem 55399

Find $\tan \left(-\frac{11 \pi}{3}\right)$ exactly without a calculator. Simplify your answer or state if it's undefined.

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Problem 55400

Solve the equation: $-8=-(x+4)$ .

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Math

Problem 55301

Problem 55302

Rewrite the mixed number 4124 \frac{1}{2}421​ as an equivalent fraction with a denominator equal to 12. 412=?12412=□12\begin{array}{c} 4 \frac{1}{2}=\frac{?}{12} \\ 4 \frac{1}{2}=\frac{\square}{12} \end{array}421​=12?​421​=12□​​

Problem 55303

Expand and combine −3(3x−4a1)−a(2y+5x)-3(3 x-4 a 1)-a(2 y+5 x)−3(3x−4a1)−a(2y+5x)

Problem 55304

Find the exact value of sin⁡(10π3)\sin \left(\frac{10 \pi}{3}\right)sin(310π​). What quadrant is θ=10π3\theta=\frac{10 \pi}{3}θ=310π​ in? Reference angle? θR=\theta_{\mathrm{R}}= θR​=

Problem 55305

Find csc⁡(8π3)\csc \left(\frac{8 \pi}{3}\right)csc(38π​) and identify the quadrant of θ=8π3\theta=\frac{8 \pi}{3}θ=38π​.

Problem 55306

Find csc⁡(8π3)\csc \left(\frac{8 \pi}{3}\right)csc(38π​) without a calculator. Where's the angle's quadrant? What's the reference angle? Choose the equivalent expression.

Problem 55307

Find the value of csc⁡(8π3)\csc \left(\frac{8 \pi}{3}\right)csc(38π​) without a calculator. What quadrant is θ=8π3\theta=\frac{8 \pi}{3}θ=38π​ in? What is the reference angle? θR=\theta_{\mathrm{R}}= θR​=

Problem 55308

Problem 55309

The angle θ=−17π6\theta=-\frac{17 \pi}{6}θ=−617π​ is in which quadrant?

Problem 55310

Count the number of zoos with more than 50 bears from the stem-and-leaf plot given.

Problem 55311

Count the zoos with more than 18 sloths from the given stem-and-leaf plot.

Problem 55312

How many zoos have exactly 27 tigers based on the stem-and-leaf plot? Key: 2∣7=272 \mid 7 = 272∣7=27 tigers.

Problem 55313

Find the value of tan⁡(−19π6)\tan \left(-\frac{19 \pi}{6}\right)tan(−619π​). (a) Which quadrant is θ=−19π6\theta=-\frac{19 \pi}{6}θ=−619π​ in? (b) Is tangent positive or negative there? (c) What is the reference angle θR=\theta_{R}=θR​=?

Problem 55314

What is the maximum number of pairs of glasses from the stemand-leaf plot: 4∣1=414 \mid 1=414∣1=41?

Problem 55315

Find the exact value of cot⁡(−17π6)\cot \left(-\frac{17 \pi}{6}\right)cot(−617π​) and answer: a. Which quadrant is θ\thetaθ in? b. Is cotangent positive or negative there?

Problem 55316

The terminal side of the angle θ=−11π4\theta=-\frac{11 \pi}{4}θ=−411π​ lies in which quadrant?

Problem 55317

How many stores have less than 60 pairs of boots based on the stem-and-leaf plot provided?

Problem 55318

Find cot⁡(−17π6)\cot \left(-\frac{17 \pi}{6}\right)cot(−617π​) without a calculator. Determine the quadrant, sign, and reference angle.

Problem 55319

How many stores have fewer than 60 pairs of boots based on the stem-and-leaf plot?

Problem 55320

Find the exact value of sec⁡(−11π4)\sec \left(-\frac{11 \pi}{4}\right)sec(−411π​) without a calculator. What quadrant is it in and is secant positive or negative?

Problem 55321

Find the value of sec⁡(−11π4)\sec \left(-\frac{11 \pi}{4}\right)sec(−411π​). Determine the quadrant, sign, and reference angle θR=\theta_{\mathrm{R}}=θR​=.

Problem 55322

Find sec (−11π4)\left(-\frac{11 \pi}{4}\right)(−411π​), determine the reference angle θR=π4\theta_{\mathrm{R}}=\frac{\pi}{4}θR​=4π​, and choose the correct expression.

Problem 55323

Find f′(x)f^{\prime}(x)f′(x) using the Fundamental Theorem of Calculus for f(x)=∫−4x3t2+9dtf(x)=\int_{-4}^{x^{3}} \sqrt{t^{2}+9} dtf(x)=∫−4x3​t2+9​dt.

Problem 55324

Find tan⁡(11π6)\tan \left(\frac{11 \pi}{6}\right)tan(611π​) exactly without a calculator. A. tan⁡(11π6)=\tan \left(\frac{11 \pi}{6}\right)=tan(611π​)= B. Undefined.

Problem 55325

Find sec⁡(−11π4)\sec \left(-\frac{11 \pi}{4}\right)sec(−411π​) and answer: (d) which is equivalent? (e) Find its exact value.

Problem 55326

Calculate the percentage difference: 3.5−3.141593.14159×100\frac{3.5-3.14159}{3.14159} \times 1003.141593.5−3.14159​×100.

Problem 55327

Determine the interval(s) where the curve y=∫0xt2t2−3t+5dty=\int_{0}^{x} \frac{t^{2}}{t^{2}-3 t+5} d ty=∫0x​t2−3t+5t2​dt is concave upward.

Problem 55328

Karan borrowed \$3,650 for 5 months at 10% interest. What is her monthly payment?

Problem 55329

Find a function fff and a number aaa such that 2+∫axf(t)t5dt=6x−12+\int_{a}^{x} \frac{f(t)}{t^{5}} dt=6 x^{-1}2+∫ax​t5f(t)​dt=6x−1. What is f(x)f(x)f(x)?

Problem 55330

Find the value of tan⁡(−5π6)\tan \left(-\frac{5 \pi}{6}\right)tan(−65π​) without a calculator. A. tan⁡(−5π6)=\tan \left(-\frac{5 \pi}{6}\right)=tan(−65π​)= B. Undefined.

Problem 55331

Calculate the integral ∫319(7−∣x−11∣)dx\int_{3}^{19}(7-|x-11|) d x∫319​(7−∣x−11∣)dx using area formulas.

Problem 55332

Evaluate the integral from 9 to 15 of −(4x+5)-(4x + 5)−(4x+5) using area formulas. What is ∫915(−(4x+5))dx\int_{9}^{15}(-(4x+5)) dx∫915​(−(4x+5))dx?

Problem 55333

Estimate the integrals using Riemann sums: (a) left-endpoint ∫010f(x)dx≈\int_{0}^{10} f(x) dx \approx∫010​f(x)dx≈ and (b) right-endpoint ∫010f(x)dx≈\int_{0}^{10} f(x) dx \approx∫010​f(x)dx≈.

Problem 55334

Find a function fff and a number aaa such that 2+∫axf(t)t5dt=6x−12 + \int_{a}^{x} \frac{f(t)}{t^{5}} dt = 6 x^{-1}2+∫ax​t5f(t)​dt=6x−1.

Problem 55335

Use the table of the increasing function fff to find lower and upper estimates for ∫025f(x)dx\int_{0}^{25} f(x) dx∫025​f(x)dx. Lower estimate = , Upper estimate = .

Problem 55336

Find the hypotenuse of a right triangle with sides 24 and 7 using the Pythagorean theorem: c2=242+72c^2 = 24^2 + 7^2c2=242+72.

Problem 55337

Compute the following integrals using given values:(a) ∫044f(x)dx=\int_{0}^{4} 4 f(x) d x=∫04​4f(x)dx= (b) ∫04(−1f(x)−3g(x))dx=\int_{0}^{4}(-1 f(x)-3 g(x)) d x=∫04​(−1f(x)−3g(x))dx= (c) ∫04(3−5h(x))dx=\int_{0}^{4}(3-5 h(x)) d x=∫04​(3−5h(x))dx=

Problem 55338

Problem 55339

Compute the integrals given: (a) ∫044f(x)dx=62\int_{0}^{4} 4 f(x) d x = 62∫04​4f(x)dx=62 (b) ∫04(−1f(x)−3g(x))dx=\int_{0}^{4}(-1 f(x)-3 g(x)) d x=∫04​(−1f(x)−3g(x))dx= ?

Problem 55340

Find the average value favef_{\text{ave}}fave​ of f(x)=32−∣4x∣f(x)=32-|4x|f(x)=32−∣4x∣ from x=−8x=-8x=−8 to x=8x=8x=8 and points ccc where f(c)=favef(c)=f_{\text{ave}}f(c)=fave​.

Problem 55341

Find the average value fave f_{\text {ave }}fave ​ of f(x)=32−∣4x∣f(x)=32-|4 x|f(x)=32−∣4x∣ for xxx in the range [−8,8][-8, 8][−8,8]. What is fave f_{\text {ave }}fave ​?

Rewrite the mixed number $4 \frac{1}{2}$ as an equivalent fraction with a denominator equal to 12. $\begin{array}{c} 4 \frac{1}{2}=\frac{?}{12} \\ 4 \frac{1}{2}=\frac{\square}{12} \end{array}$

Expand and combine $-3(3 x-4 a 1)-a(2 y+5 x)$

Find the exact value of $\sin \left(\frac{10 \pi}{3}\right)$ . What quadrant is $\theta=\frac{10 \pi}{3}$ in? Reference angle? $\theta_{\mathrm{R}}=$

Find $\csc \left(\frac{8 \pi}{3}\right)$ and identify the quadrant of $\theta=\frac{8 \pi}{3}$ .

Find $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. Where's the angle's quadrant? What's the reference angle? Choose the equivalent expression.

Find the value of $\csc \left(\frac{8 \pi}{3}\right)$ without a calculator. What quadrant is $\theta=\frac{8 \pi}{3}$ in? What is the reference angle? $\theta_{\mathrm{R}}=$

The angle $\theta=-\frac{17 \pi}{6}$ is in which quadrant?

How many zoos have exactly 27 tigers based on the stem-and-leaf plot? Key: $2 \mid 7 = 27$ tigers.

Find the value of $\tan \left(-\frac{19 \pi}{6}\right)$ .
(a) Which quadrant is $\theta=-\frac{19 \pi}{6}$ in? (b) Is tangent positive or negative there? (c) What is the reference angle $\theta_{R}=$ ?

What is the maximum number of pairs of glasses from the stemand-leaf plot: $4 \mid 1=41$ ?

Find the exact value of $\cot \left(-\frac{17 \pi}{6}\right)$ and answer: a. Which quadrant is $\theta$ in? b. Is cotangent positive or negative there?

The terminal side of the angle $\theta=-\frac{11 \pi}{4}$ lies in which quadrant?

Find $\cot \left(-\frac{17 \pi}{6}\right)$ without a calculator. Determine the quadrant, sign, and reference angle.

Find the exact value of $\sec \left(-\frac{11 \pi}{4}\right)$ without a calculator. What quadrant is it in and is secant positive or negative?

Find the value of $\sec \left(-\frac{11 \pi}{4}\right)$ . Determine the quadrant, sign, and reference angle $\theta_{\mathrm{R}}=$ .

Find sec $\left(-\frac{11 \pi}{4}\right)$ , determine the reference angle $\theta_{\mathrm{R}}=\frac{\pi}{4}$ , and choose the correct expression.

Find $f^{\prime}(x)$ using the Fundamental Theorem of Calculus for $f(x)=\int_{-4}^{x^{3}} \sqrt{t^{2}+9} dt$ .

Find $\tan \left(\frac{11 \pi}{6}\right)$ exactly without a calculator. A. $\tan \left(\frac{11 \pi}{6}\right)=$ B. Undefined.

Find $\sec \left(-\frac{11 \pi}{4}\right)$ and answer: (d) which is equivalent? (e) Find its exact value.

Calculate the percentage difference: $\frac{3.5-3.14159}{3.14159} \times 100$ .

Determine the interval(s) where the curve $y=\int_{0}^{x} \frac{t^{2}}{t^{2}-3 t+5} d t$ is concave upward.

Find a function $f$ and a number $a$ such that $2+\int_{a}^{x} \frac{f(t)}{t^{5}} dt=6 x^{-1}$ . What is $f(x)$ ?

Find the value of $\tan \left(-\frac{5 \pi}{6}\right)$ without a calculator. A. $\tan \left(-\frac{5 \pi}{6}\right)=$ B. Undefined.

Calculate the integral $\int_{3}^{19}(7-|x-11|) d x$ using area formulas.

Evaluate the integral from 9 to 15 of $-(4x + 5)$ using area formulas. What is $\int_{9}^{15}(-(4x+5)) dx$ ?

Estimate the integrals using Riemann sums: (a) left-endpoint $\int_{0}^{10} f(x) dx \approx$ and (b) right-endpoint $\int_{0}^{10} f(x) dx \approx$ .

Find a function $f$ and a number $a$ such that $2 + \int_{a}^{x} \frac{f(t)}{t^{5}} dt = 6 x^{-1}$ .

Use the table of the increasing function $f$ to find lower and upper estimates for $\int_{0}^{25} f(x) dx$ . Lower estimate = , Upper estimate = .

Find the hypotenuse of a right triangle with sides 24 and 7 using the Pythagorean theorem: $c^2 = 24^2 + 7^2$ .

Compute the following integrals using given values:
(a) $\int_{0}^{4} 4 f(x) d x=$ (b) $\int_{0}^{4}(-1 f(x)-3 g(x)) d x=$ (c) $\int_{0}^{4}(3-5 h(x)) d x=$

Compute the integrals given:
(a) $\int_{0}^{4} 4 f(x) d x = 62$
(b) $\int_{0}^{4}(-1 f(x)-3 g(x)) d x=$ ?

Find the average value $f_{\text{ave}}$ of $f(x)=32-|4x|$ from $x=-8$ to $x=8$ and points $c$ where $f(c)=f_{\text{ave}}$ .

Find the average value $f_{\text {ave }}$ of $f(x)=32-|4 x|$ for $x$ in the range $[-8, 8]$ . What is $f_{\text {ave }}$ ?

Evaluate the integral from 3 to 19 of $7 - |x - 11|$ using area formulas. What is $\int_{3}^{19}(7 - |x - 11|) d x$ ?

Find the exact value of $\cos (8 \pi)$ . Answer parts a, b, c, and d. a. Where is the terminal side of angle $\theta=8 \pi$ ?

Find $\sin \left(-\frac{9 \pi}{2}\right)$ without a calculator.
a. Where is the angle's terminal side? b. Coordinates for $r=1$ ? c. General definition of $\sin \theta$ ? d. Exact value of $\sin \left(-\frac{9 \pi}{2}\right)$ ?

Karbis on 7 valget ja 2 musta küünalt. Leia tõenäosus:
a. mõlemad valged b. mõlemad mustad c. erinevat värvi d. üks punane e. ühte värvi.

Find the right endpoint Riemann sum for $f(x)=\frac{15}{x}$ on $[2,6]$ using 8 rectangles of width 0.5. What is the sum?

Calculate the left endpoint Riemann sum for $f(x)=\frac{15}{x}$ over $[2,6]$ using 8 rectangles of width 0.5.

Find $\cos(8\pi)$ by answering: a) where is the angle? b) coordinates on terminal side? c) definition of $\cos \theta$ ?

Find $\cos(8\pi)$ without a calculator: a. Where does $\theta=8\pi$ end? b. What are the coordinates for $r=1$ ?

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Calculate the left endpoint Riemann sum for $f(x)=\frac{x^{2}}{12}$ on $[2,6]$ and explain why it's an underestimate.

Find $\sec \theta$ given $\tan \theta=\frac{1}{3}$ and $\csc \theta<0$ . Simplify your answer.

Find $\sin \theta$ given $\sec \theta=\frac{4}{3}$ and $\tan \theta>0$ . What is $\sin \theta$ ?

Find the reference angle for $\theta=-\frac{26 \pi}{7}$ and the least nonnegative coterminal angle. $\theta_{\mathrm{C}}=$

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{11}$ . What is $\theta_{R}$ ?

Find the reference angle for $\theta = -\frac{26 \pi}{7}$ . What is the least nonnegative coterminal angle $\theta_{C}$ ? In which quadrant is $\theta_{C}$ ?

Find the indefinite integral: $\int \frac{1}{(x-1)(x+3)} dx = \sqrt{2} + C$ .

Find the reference angle for $\theta=\frac{29 \pi}{11}$ and the coterminal angle $\theta_{C}=\frac{7 \pi}{11}$ . In which quadrant is $\theta_{C}$ ?

Evaluate the integral using partial fractions: $\int -\frac{2}{(x-6)^{2}(x+6)} \, dx = C$

Evaluate the expression: $-\frac{1}{18} \int \frac{1}{x-6} dx + \frac{1}{108} \int \frac{1}{(x-6)^{2}} dx - \frac{1}{216} \int \frac{1}{x+6} dx$ .

Evaluate the integral: $\int \frac{7 x+25}{(7-x)\left(x^{2}+25\right)} d x=$

How much longer is Fluffy's tail ( $1 \frac{1}{3}$ m) than Fireball's tail ( $1 \frac{1}{4}$ m)?

Find the reference angle for $\theta=-\frac{26 \pi}{7}$ . What is $\theta_{C}$ and the reference angle $\theta_{R}$ ?

Calculate the result of $\frac{3}{4} - \frac{2}{3}$ .

Calculate the value of $\frac{2}{3} - \frac{1}{6} = \square$

Our pirate ship had $\frac{5}{6}$ of a chest of gold and took $\frac{3}{8}$ more. How many chests do we have now?

Find $A$ in the equation: $A=\frac{4(3)^{4}-3(3)^{3}-1(3)^{2}-10(3)-4}{(3^{2}+1)^{2}}$ .

Noor had $\frac{5}{7}$ L of coconut milk and used $\frac{1}{2}$ L. How much is left? Identify the correct number line.

Find the distance $d$ traveled by a particle with velocity $v(t)=\frac{7 t^{2}}{t^{2}+1}$ after $t=3$ sec.