Natural Numbers

Problem 1301

Prove that for a sector with radius $r$ cm and perimeter 50 cm, $\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)$ .

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Problem 1302

Théo paie $71,40 €$ pour $70 \mathrm{~L}$ . Quel est le prix d'un litre de carburant pour Théo ?

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Problem 1303

Find the height $h$ of triangle $ABC$ with area $27 \mathrm{~cm}^2$ and base $AB=6 \mathrm{~cm}$ .

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Problem 1304

Calcule la quantité de chocolat nécessaire pour 20 personnes si 180 g sont prévus pour 6 personnes.

See Solution

Problem 1305

See Solution

Problem 1306

Deux amis comparent leurs frais de parking : 2,50€ pour 50 min et 3,50€ pour 1 h 10 min. Le prix est-il proportionnel au temps ?

See Solution

Problem 1307

Pour 20 personnes, combien de cL de lait pour 1 œuf/personne et 3 œufs pour $35 \mathrm{cL}$ de lait ? Suffit-il avec 3 L de lait ?

See Solution

Problem 1308

Alex and Chris share sweets in a $7:3$ ratio. Alex has 20 more sweets than Chris. Find how many sweets Chris gets.

See Solution

Problem 1309

Un commerçant applique une réduction de $45\%$ . Quelle formule pour la réduction en B2 et le prix après en B3 ? Prix soldé : $33€$ . Prix initial ?

See Solution

Problem 1310

Deux amis comparent le coût du parking: 2,50 € pour 50 min et 3,50 € pour 1 h 10 min. Le prix est-il proportionnel au temps?

See Solution

Problem 1311

Pour 20 personnes, calculez le lait nécessaire en respectant 3 œufs pour $35 \mathrm{cL}$ de lait. 3 L de lait suffisent-ils ?

See Solution

Problem 1312

Théo a acheté un T-shirt à $39 €$ avec une remise de $20 \%$ . Quel est le prix soldé ?

See Solution

Problem 1313

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de $x$ m. Montre que la clôture fait $50 + 8x$ m et l'aire des allées de gazon est $50x + 4x^2$ . Calcule pour $x=2$ m.

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Problem 1314

Find the area of a rectangle with one side $12 \mathrm{~cm}$ and diagonal $13 \mathrm{~cm}$ .

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Problem 1315

Calculate $(3 \times 10^{199}) + (2 \times 10^{201})$ and express the result in standard form.

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Problem 1316

Calculate the result of $5 - 2$ .

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Problem 1317

Find $h(3)$ for the function $h(x)=9 \cdot\left(\frac{1}{2}\right)^{x}$ .

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Problem 1318

Find the derivative of the function $100+(t-3)^{4}(t-5)^{2}$ with respect to $t$ .

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Problem 1319

Find the largest perimeter of an isosceles triangle with sides $8.2 \mathrm{~cm}$ and $9.4 \mathrm{~cm}$ measured to the nearest mm.

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Problem 1320

Find the derivative of $y$ with respect to $x$ for the expression $x+\ln |x-3|+\frac{2}{x-3}$ .

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Problem 1321

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ ; AB = 30 cm. Find length of BD.

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Problem 1322

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ . Given AB=30 cm, find BD. a. 26 cm b. 56 cm

See Solution

Problem 1323

Solve the equation $4(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=0$ .

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Problem 1324

Développe $(x+1)^{2}-(x-1)^{2}$ et utilise-le pour calculer $203^{2}-201^{2}$ .

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Problem 1325

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

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Problem 1326

Soit $n$ un entier. Trouve l'entier précédent et suivant de $n$ . Prouve que la somme de 3 entiers consécutifs est un multiple de 3.

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Problem 1327

Which statement is TRUE? A: $\sum_{i=1}^{n} 2 x_{i}=2 \sum_{i=1}^{n} x_{i}$ or B: $\sum_{i=1}^{n}(x_{i})^{2}=(\sum_{i=1}^{n} x_{i})^{2}$ ? Choose: a. A only, b. Neither, c. Both, d. B only.

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Problem 1328

Solve the equation: $1+\frac{1}{x-3}-\frac{2}{(x-3)^{2}}=0$ .

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Problem 1329

Convert the ratio $3:8$ into a percentage. Choose one: a. $22,5 \%$ b. $19 \%$ c. $27 \%$ d. $37,5 \%$

See Solution

Problem 1330

Définis $R$ en fonction de $x$ pour le programme donné. Prouve que $R$ est le carré de $x$ . Factorise $64-25 x^{2}-(8-5 x)^{2}$ et $49 x^{2}+28 x+4-25$ .

See Solution

Problem 1331

Le mât mesure 3,6 m. Vérifie si les triangles VEN et VNT sont rectangles avec les longueurs 4,2 m et 3,9 m. Justifie.

See Solution

Problem 1332

Find the formula for the marginal average profit of the profit function $P(x)=100 \ln (2 x+1)-5 x-10$ . Options are provided.

See Solution

Problem 1333

Find the point elasticity of demand for cellphones at the price $p=4600$ , given the demand function $q=85000-4p$ .

See Solution

Problem 1334

Anthony turned $90^{\circ}$ right, then $90^{\circ}$ , and $135^{\circ}$ more. Did he complete a circle? How much more to finish?

See Solution

Problem 1335

Find eigenvalues for the generalized eigenvalue problem involving matrices $K$ , $M$ , and transformations to standard form.

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Problem 1336

Find the excess supply of jeans when the price is set at \ $R 650, given demand$ p_{d}=500-2 q_{d} $and supply$ p_{s}=-30+8 q_{s}$.

See Solution

Problem 1337

Find the equilibrium price $p$ and quantity $q$ where $q_{d}=330-2 p_{d}$ and $q_{s}=-170+3 p_{s}$ .

See Solution

Problem 1338

Calcule o lucro de uma empresa que produz e vende 150 copos, com custo fixo de R 1250 e custo de R 12 por copo, vendido a R 55.

See Solution

Problem 1339

Find the intersection point(s) of the demand $q=710-5.5p$ and supply $p=3.5q+57.5$ functions.

See Solution

Problem 1340

Find the equilibrium number of workers and hourly wage given the demand $l_{d}=45-5.1 w_{d}$ and supply $l_{s}=-15+4.9 w_{s}$ .

See Solution

Problem 1341

Find the profit function in terms of $p$ given $q=6000-30p$ , fixed costs of \R 72000, and variable costs of \R 60 per unit.

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Problem 1342

Find the number that is the "opposite" of 7 among \{46, 48, 49, 44\}.

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Problem 1343

Find the firm's profit when $q=20$ given $TR=150q-3q^2$ and $TC=-24q^2+143q-200$ .

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Problem 1344

How many years are in a decade? Options: 10, 5, 20, 15.

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Problem 1345

Identify which option is not a subset of real numbers: Natural numbers, Whole numbers, Rational numbers, or none of the above.

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Problem 1346

Calculate $15 \times 10$ .

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Problem 1347

Calculate the product of 15 and 70. What is $15 \times 70$ ?

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Problem 1348

What is the sum of $42.6 + 0.45 + 30.22$ ? Provide your answer.

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Problem 1349

Identify the even number from this list: 113-144, $330-366$ , 471-510, $890-899$ .

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Problem 1350

Identify the odd number from this list: 782, 984, 102, 633.

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Problem 1351

The next odd number after 37 is: 39.

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Problem 1352

What is the value of 7 in the product of 2.7 and $10^{2}$ ? A. 0.007 B. 0.07 C. 7 D. 70

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Problem 1353

Round 2.078 to the hundredths place. Options: M. 2.10, P. 2.08, R. 2.07, S. 2.00.

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Problem 1354

Choose three numbers less than 12.13 from the options: A. 12.146 B. 12.025 C. 12.5 D. 12.103 E. 12.072.

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Problem 1355

Given a table of student activities, find the probability a senior is in sports:
$P(\text{sports} \mid \text{senior}) = \frac{P(\text{sports and senior})}{P(\text{senior})} = [?]\%$
Round to the nearest whole percent.

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Problem 1356

Given a class table, find the probability a student is a sophomore if they are female:
$P(\text{sophomore} \mid \text{female}) = \frac{P(\text{sophomore and female})}{P(\text{female})} = [?] \%$
Round to the nearest whole percent.

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Problem 1357

Find the derivatives of these functions: 1. $f(x)=6 x^{3}-9 x+4$ , 2. $y=2 t^{4}- t^{2}+13 t$ , 3. $g(z)=4 z^{7}-3 z^{-7}+9 z$ .

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Problem 1358

Un point $\mathrm{P}$ de masse $\mathrm{m}$ se déplace en coordonnées polaires. Trouvez les équations du mouvement et les expressions pour $\mathrm{r}(t)$ et $\omega$ quand $\omega$ est constant.

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Problem 1359

Calculate: $64 \div(15-5+12 \div 2)+9 \times 2-1$ . What is the result?

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Problem 1360

Find the probability a student is in sports or work using the table. Round $\mathrm{P}(\text{sports or work})$ to the nearest percent.

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Problem 1361

Find the probability a sophomore is in drama: $\mathrm{P}(\text{drama} \mid \text{sophomore}) = \frac{\mathrm{P}(\text{drama and sophomore})}{\mathrm{P}(\text{sophomore})} = [?]\%$ . Round to the nearest whole percent.

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Problem 1362

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male:
$\mathrm{P}(\text { junior } \mid \text { male })=[?] \%$ Round to the nearest whole percent.

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Problem 1363

Multiply and simplify $(2 x-5)(3 x-3)$ .

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Problem 1364

A diver is at $5.2 \mathrm{~m}$ depth in water ( $1000 \mathrm{kgm}^{-3}$ density). Find the pressure on the diver ( $\mathrm{g}=10 \mathrm{~m/s}^{2}$ ).

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Problem 1365

Calculate the force on a submarine door at $500 \mathrm{~m}$ depth with area $0.4^{2}$ and water density $1.03$ .

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Problem 1366

A faulty barometer shows $72.6 \mathrm{cmHg}$ when actual pressure is $75.0 \mathrm{cmHg}$ . Find pressure at $72.0 \mathrm{cmHg}$ .

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Problem 1367

A man exerts a pressure of $2.8 \times 10^{3} \mathrm{Nm}^{-2}$ over $4 \times 10^{-2} \mathrm{~m}^{2}$ . Find his weight.

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Problem 1368

Find the height of liquid in a barometer for pressure $204000 \mathrm{Nm}^{-2}$ and density $5200 \mathrm{kgm}^3$ .

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Problem 1369

A model of an 800m tower is built at a scale of $1: 4000$ . What is the model's height? Options: 5cm, 20cm, 200cm, 320cm.

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Problem 1370

Find the pressure at the middle of a tank filled with $1.0 \times 10^{3} \mathrm{~kg}$ of liquid, height $4 \mathrm{~m}$ . Options: A. $1.0 \times 10^{4} \mathrm{Nm}^{-2}$ B. $2.0 \times 10^{3} \mathrm{Nm}^{-2}$ C. $1.5 \times 10^{3} \mathrm{Nm}^{-2}$ D. $1.0 \times 10^{3} \mathrm{Nm}^{-2}$ .

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Problem 1371

A tower is 800 m tall. If a model is built at a scale of $1: 4000$ , what is the model's height?

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Problem 1372

In a sale, pencil boxes are \$20 and chocolates are \$50. If 100 items sold raise \$3950, how many pencil boxes were sold?

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Problem 1373

A model of an 800 m tower is built at a scale of $1:4000$ . What is the model's height? Options: 5 cm, 20 cm, 200 cm, 320 cm.

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Problem 1374

Mary and Susan have 100 postcards. After Mary gives $\frac{4}{5}$ of hers to Susan, Susan has 85. Find Mary's original postcards.

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Problem 1375

La distance de freinage $d$ d'un véhicule est-elle proportionnelle à $v$ ou à $v^2$ avec $d(v)=0,005 v^{2}$ ?

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Problem 1376

In a charity sale, a pencil box costs \$20 and a pack of chocolate costs \$50. If 100 items are sold for \$3950, how many pencil boxes were sold?

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Problem 1377

Une piscine de dimensions $30 \mathrm{dm} \times 54 \mathrm{dm}$ doit être recouverte de carreaux carrés.
(a) Décompose $30$ en facteurs premiers. (b) Décompose $54$ en facteurs premiers. (c) Quel est le plus grand diviseur commun de $30$ et $54$ ?
Quelle est la taille maximale des carreaux en dm et combien en faut-il pour couvrir le fond ?

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Problem 1378

Réduis la fraction $\frac{280}{224}$ en utilisant les facteurs premiers de 280 et 224.

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Problem 1379

Multiply the mixed numbers: $3 \frac{2}{5} \times 354 \frac{2}{5}$ .

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Problem 1380

Calculate $354 \frac{2}{5} - \left(114 \frac{2}{10} + 150 \frac{2}{15}\right)$ .

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Problem 1381

Calcule la division de 2000 par 8 et complète : $2000=8 \times$ . Combien d'arbres sont le long du canal ?

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Problem 1382

Calculate the sum of $\frac{2}{5}$ and $\frac{12}{7}$ .

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Problem 1383

Sur une route sèche, la distance de freinage $d(v)=0,005 v^{2}$ . Est-elle proportionnelle à $v$ ou à $v^{2}$ ?

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Problem 1384

Find the largest common factor of $3 x^{3} y + 2 x^{2} y^{2}$ . Options: a) $6 x^{3} y^{2}$ , b) $6 x^{5} y^{3}$ , c) $x^{2} y$ , d) $x^{3} y^{2}$ , e) $2 x^{2} y$ .

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Problem 1385

Identify the decreasing exponential function with a $y$ -intercept of 20 from these options: (1) $y=20\left(\frac{4}{3}\right)^{x}$ (2) $y=20\left(\frac{1}{2}\right)^{x}$ (3) $y=-2 x+20$ (4) $y=\left(\frac{1}{3}\right)^{x}+20$

See Solution

Problem 1386

If $|x-3|>5$ , which inequalities are true? a) $-2<x<8$ b) $-8<x<2$ c) $x<-8 \cup x>2$ d) $x<-2 \cup x>8$ e) $x<-8 \cup x>-2$

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Problem 1387

Find $f(0)$ for the function $f(x)=10(2)^{x}$ and describe its point on the graph of $y=f(x)$ .

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Problem 1388

Calculate the sum: $\frac{2}{5}+\frac{21}{7}$ .

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Problem 1389

Solve $2 x^{2}-8 \leq 0$ and choose the correct interval for $x$ .

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Problem 1390

Which function best fits the data: $y=10 x+2$ , $y=8 x+2$ , $y=5(2)^{x}$ , or $y=2(5)^{x}$ ? Data: $(0,2), (1,10), (2,50), (3,250), (4,1250)$ .

See Solution

Problem 1391

Combine the following mixed numbers and fractions to lowest terms:
1. $\frac{2}{5}+\frac{12}{7}$
2. $\frac{9}{10}+\frac{11}{12}$
3. $25 \frac{3}{5}+39 \frac{3}{5}$
4. $\frac{15}{20}+\frac{6}{15}$
5. $3 \frac{5}{9}+6 \frac{10}{14}$
6. $4 \frac{1}{12}+\frac{1}{6}$
7. $6 \frac{2}{3}+19 \frac{1}{9}+2 \frac{4}{6}$
8. $15 \frac{3}{4}+\frac{5}{6}+11 \frac{6}{12}$

See Solution

Problem 1392

Find $(x+y)^{-1 / 2}$ if $x=11$ and $y=25$ . Choices: a) 6 b) -6 c) $\frac{\sqrt{11}}{55}$ d) $\frac{1}{6}$ e) $-\frac{1}{6}$

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Problem 1393

Calculate the expression: $5^{5} \times e^{4} \times 4 \times 5^{5} \times 5 e^{3}$ .

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Problem 1394

Solve $\frac{1}{2 x+18}-\frac{x}{x^{2}-81}=$ for options a) to e).

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Problem 1395

Simplify the expression: $2^{5} \times 2^{8} \times a^{3}$ .

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Problem 1396

A paper is 0.01 cm thick. Each fold doubles its thickness. Find thickness after 4, 5 folds, and derive a formula $T = 0.01 \cdot 2^f$ .
(d) Thickness at $f=10$ ? (e) Thickness after 20 folds in meters? (f) Does it reach the Moon (384,000 km) after 40 folds? Show calculations.

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Problem 1397

Simplify the expression: $x^{2} y^{3} \div x y^{2}$ .

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Problem 1398

Factor $16 x^{4}-1$ . Choose the correct option from: a) $(2 x-1)^{2}(2 x+1)^{2}$ , b) $(4 x-1)^{2}(4 x+1)^{2}$ , c) $(2 x-1)(2 x+1)(4 x^{2}+1)$ , d) $(2 x-1)(2 x+1)(2 x^{2}-1)$ , e) $(2 x-1)(2 x+1)(2 x^{2}+1)$ .

See Solution

Problem 1399

Solve for $\frac{xy}{\frac{1}{x^2} - \frac{y}{x}}$ . Choose the correct option: a) $\frac{y}{x}$ , b) $\frac{x}{y}$ , c) $\frac{1-xy}{x}$ , d) $xy$ , e) $xy-1$ .

See Solution

Problem 1400

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

See Solution

1 ...11 12 13 14 15 16 17 ...28

Natural Numbers

Problem 1301

Prove that for a sector with radius rrr cm and perimeter 50 cm, θ=360π(25r−1)\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)θ=π360​(r25​−1).

Problem 1302

Théo paie 71,40€71,40 €71,40€ pour 70 L70 \mathrm{~L}70 L. Quel est le prix d'un litre de carburant pour Théo ?

Problem 1303

Find the height hhh of triangle ABCABCABC with area 27 cm227 \mathrm{~cm}^227 cm2 and base AB=6 cmAB=6 \mathrm{~cm}AB=6 cm.

Problem 1304

Calcule la quantité de chocolat nécessaire pour 20 personnes si 180 g sont prévus pour 6 personnes.

Problem 1305

Problem 1306

Deux amis comparent leurs frais de parking : 2,50€ pour 50 min et 3,50€ pour 1 h 10 min. Le prix est-il proportionnel au temps ?

Problem 1307

Pour 20 personnes, combien de cL de lait pour 1 œuf/personne et 3 œufs pour 35cL35 \mathrm{cL}35cL de lait ? Suffit-il avec 3 L de lait ?

Problem 1308

Alex and Chris share sweets in a 7:37:37:3 ratio. Alex has 20 more sweets than Chris. Find how many sweets Chris gets.

Problem 1309

Un commerçant applique une réduction de 45%45\%45%. Quelle formule pour la réduction en B2 et le prix après en B3 ? Prix soldé : 33€33€33€. Prix initial ?

Problem 1310

Deux amis comparent le coût du parking: 2,50 € pour 50 min et 3,50 € pour 1 h 10 min. Le prix est-il proportionnel au temps?

Problem 1311

Pour 20 personnes, calculez le lait nécessaire en respectant 3 œufs pour 35cL35 \mathrm{cL}35cL de lait. 3 L de lait suffisent-ils ?

Problem 1312

Théo a acheté un T-shirt à 39€39 €39€ avec une remise de 20%20 \%20%. Quel est le prix soldé ?

Problem 1313

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de xxx m. Montre que la clôture fait 50+8x50 + 8x50+8x m et l'aire des allées de gazon est 50x+4x250x + 4x^250x+4x2. Calcule pour x=2x=2x=2 m.

Problem 1314

Find the area of a rectangle with one side 12 cm12 \mathrm{~cm}12 cm and diagonal 13 cm13 \mathrm{~cm}13 cm.

Problem 1315

Calculate (3×10199)+(2×10201)(3 \times 10^{199}) + (2 \times 10^{201})(3×10199)+(2×10201) and express the result in standard form.

Problem 1316

Calculate the result of 5−25 - 25−2.

Problem 1317

Find h(3)h(3)h(3) for the function h(x)=9⋅(12)xh(x)=9 \cdot\left(\frac{1}{2}\right)^{x}h(x)=9⋅(21​)x.

Problem 1318

Find the derivative of the function 100+(t−3)4(t−5)2100+(t-3)^{4}(t-5)^{2}100+(t−3)4(t−5)2 with respect to ttt.

Problem 1319

Find the largest perimeter of an isosceles triangle with sides 8.2 cm8.2 \mathrm{~cm}8.2 cm and 9.4 cm9.4 \mathrm{~cm}9.4 cm measured to the nearest mm.

Problem 1320

Find the derivative of yyy with respect to xxx for the expression x+ln⁡∣x−3∣+2x−3x+\ln |x-3|+\frac{2}{x-3}x+ln∣x−3∣+x−32​.

Problem 1321

Points A, B, C, and D divide segment AD in the ratio 212:113:562 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}221​:131​:65​; AB = 30 cm. Find length of BD.

Problem 1322

Points A, B, C, and D divide segment AD in the ratio 212:113:562 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}221​:131​:65​. Given AB=30 cm, find BD. a. 26 cm b. 56 cm

Problem 1323

Solve the equation 4(t−3)3(t−5)2+2(t−3)4(t−5)=04(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=04(t−3)3(t−5)2+2(t−3)4(t−5)=0.

Problem 1324

Développe (x+1)2−(x−1)2(x+1)^{2}-(x-1)^{2}(x+1)2−(x−1)2 et utilise-le pour calculer 2032−2012203^{2}-201^{2}2032−2012.

Problem 1325

Express the polynomial 52x3+3x4+72x5+4x6\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}25​x3+3x4+27​x5+4x6 in sigma notation. Which option is correct?

Problem 1326

Soit nnn un entier. Trouve l'entier précédent et suivant de nnn. Prouve que la somme de 3 entiers consécutifs est un multiple de 3.

Problem 1327

Problem 1328

Solve the equation: 1+1x−3−2(x−3)2=01+\frac{1}{x-3}-\frac{2}{(x-3)^{2}}=01+x−31​−(x−3)22​=0.

Problem 1329

Convert the ratio 3:83:83:8 into a percentage. Choose one: a. 22,5%22,5 \%22,5% b. 19%19 \%19% c. 27%27 \%27% d. 37,5%37,5 \%37,5%

Problem 1330

Définis RRR en fonction de xxx pour le programme donné. Prouve que RRR est le carré de xxx. Factorise 64−25x2−(8−5x)264-25 x^{2}-(8-5 x)^{2}64−25x2−(8−5x)2 et 49x2+28x+4−2549 x^{2}+28 x+4-2549x2+28x+4−25.

Problem 1331

Le mât mesure 3,6 m. Vérifie si les triangles VEN et VNT sont rectangles avec les longueurs 4,2 m et 3,9 m. Justifie.

Problem 1332

Find the formula for the marginal average profit of the profit function P(x)=100ln⁡(2x+1)−5x−10 P(x)=100 \ln (2 x+1)-5 x-10 P(x)=100ln(2x+1)−5x−10. Options are provided.

Problem 1333

Find the point elasticity of demand for cellphones at the price p=4600p=4600p=4600, given the demand function q=85000−4pq=85000-4pq=85000−4p.

Problem 1334

Anthony turned 90∘90^{\circ}90∘ right, then 90∘90^{\circ}90∘, and 135∘135^{\circ}135∘ more. Did he complete a circle? How much more to finish?

Problem 1335

Find eigenvalues for the generalized eigenvalue problem involving matrices KKK, MMM, and transformations to standard form.

Problem 1336

Find the excess supply of jeans when the price is set at \R650,givendemandR 650, given demand R650,givendemandp_{d}=500-2 q_{d}andsupply and supply andsupplyp_{s}=-30+8 q_{s}$.

Problem 1337

Find the equilibrium price ppp and quantity qqq where qd=330−2pdq_{d}=330-2 p_{d}qd​=330−2pd​ and qs=−170+3psq_{s}=-170+3 p_{s}qs​=−170+3ps​.

Problem 1338

Calcule o lucro de uma empresa que produz e vende 150 copos, com custo fixo de R 1250 e custo de R 12 por copo, vendido a R 55.

Problem 1339

Find the intersection point(s) of the demand q=710−5.5pq=710-5.5pq=710−5.5p and supply p=3.5q+57.5p=3.5q+57.5p=3.5q+57.5 functions.

Problem 1340

Find the equilibrium number of workers and hourly wage given the demand ld=45−5.1wdl_{d}=45-5.1 w_{d}ld​=45−5.1wd​ and supply ls=−15+4.9wsl_{s}=-15+4.9 w_{s}ls​=−15+4.9ws​.

Problem 1341

Prove that for a sector with radius $r$ cm and perimeter 50 cm, $\theta = \frac{360}{\pi} \left(\frac{25}{r} - 1\right)$ .

Théo paie $71,40 €$ pour $70 \mathrm{~L}$ . Quel est le prix d'un litre de carburant pour Théo ?

Find the height $h$ of triangle $ABC$ with area $27 \mathrm{~cm}^2$ and base $AB=6 \mathrm{~cm}$ .

Pour 20 personnes, combien de cL de lait pour 1 œuf/personne et 3 œufs pour $35 \mathrm{cL}$ de lait ? Suffit-il avec 3 L de lait ?

Alex and Chris share sweets in a $7:3$ ratio. Alex has 20 more sweets than Chris. Find how many sweets Chris gets.

Un commerçant applique une réduction de $45\%$ . Quelle formule pour la réduction en B2 et le prix après en B3 ? Prix soldé : $33€$ . Prix initial ?

Pour 20 personnes, calculez le lait nécessaire en respectant 3 œufs pour $35 \mathrm{cL}$ de lait. 3 L de lait suffisent-ils ?

Théo a acheté un T-shirt à $39 €$ avec une remise de $20 \%$ . Quel est le prix soldé ?

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de $x$ m. Montre que la clôture fait $50 + 8x$ m et l'aire des allées de gazon est $50x + 4x^2$ . Calcule pour $x=2$ m.

Find the area of a rectangle with one side $12 \mathrm{~cm}$ and diagonal $13 \mathrm{~cm}$ .

Calculate $(3 \times 10^{199}) + (2 \times 10^{201})$ and express the result in standard form.

Calculate the result of $5 - 2$ .

Find $h(3)$ for the function $h(x)=9 \cdot\left(\frac{1}{2}\right)^{x}$ .

Find the derivative of the function $100+(t-3)^{4}(t-5)^{2}$ with respect to $t$ .

Find the largest perimeter of an isosceles triangle with sides $8.2 \mathrm{~cm}$ and $9.4 \mathrm{~cm}$ measured to the nearest mm.

Find the derivative of $y$ with respect to $x$ for the expression $x+\ln |x-3|+\frac{2}{x-3}$ .

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ ; AB = 30 cm. Find length of BD.

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ . Given AB=30 cm, find BD. a. 26 cm b. 56 cm

Solve the equation $4(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=0$ .

Développe $(x+1)^{2}-(x-1)^{2}$ et utilise-le pour calculer $203^{2}-201^{2}$ .

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

Soit $n$ un entier. Trouve l'entier précédent et suivant de $n$ . Prouve que la somme de 3 entiers consécutifs est un multiple de 3.

Solve the equation: $1+\frac{1}{x-3}-\frac{2}{(x-3)^{2}}=0$ .

Convert the ratio $3:8$ into a percentage. Choose one: a. $22,5 \%$ b. $19 \%$ c. $27 \%$ d. $37,5 \%$

Définis $R$ en fonction de $x$ pour le programme donné. Prouve que $R$ est le carré de $x$ . Factorise $64-25 x^{2}-(8-5 x)^{2}$ et $49 x^{2}+28 x+4-25$ .

Find the formula for the marginal average profit of the profit function $P(x)=100 \ln (2 x+1)-5 x-10$ . Options are provided.

Find the point elasticity of demand for cellphones at the price $p=4600$ , given the demand function $q=85000-4p$ .

Anthony turned $90^{\circ}$ right, then $90^{\circ}$ , and $135^{\circ}$ more. Did he complete a circle? How much more to finish?

Find eigenvalues for the generalized eigenvalue problem involving matrices $K$ , $M$ , and transformations to standard form.

Find the excess supply of jeans when the price is set at \ $R 650, given demand$ p_{d}=500-2 q_{d} $and supply$ p_{s}=-30+8 q_{s}$.

Find the equilibrium price $p$ and quantity $q$ where $q_{d}=330-2 p_{d}$ and $q_{s}=-170+3 p_{s}$ .

Find the intersection point(s) of the demand $q=710-5.5p$ and supply $p=3.5q+57.5$ functions.

Find the equilibrium number of workers and hourly wage given the demand $l_{d}=45-5.1 w_{d}$ and supply $l_{s}=-15+4.9 w_{s}$ .

Find the profit function in terms of $p$ given $q=6000-30p$ , fixed costs of \R 72000, and variable costs of \R 60 per unit.

Find the firm's profit when $q=20$ given $TR=150q-3q^2$ and $TC=-24q^2+143q-200$ .

Calculate $15 \times 10$ .

Calculate the product of 15 and 70. What is $15 \times 70$ ?

What is the sum of $42.6 + 0.45 + 30.22$ ? Provide your answer.

Identify the even number from this list: 113-144, $330-366$ , 471-510, $890-899$ .

What is the value of 7 in the product of 2.7 and $10^{2}$ ? A. 0.007 B. 0.07 C. 7 D. 70

Find the derivatives of these functions: 1. $f(x)=6 x^{3}-9 x+4$ , 2. $y=2 t^{4}- t^{2}+13 t$ , 3. $g(z)=4 z^{7}-3 z^{-7}+9 z$ .

Un point $\mathrm{P}$ de masse $\mathrm{m}$ se déplace en coordonnées polaires. Trouvez les équations du mouvement et les expressions pour $\mathrm{r}(t)$ et $\omega$ quand $\omega$ est constant.

Calculate: $64 \div(15-5+12 \div 2)+9 \times 2-1$ . What is the result?

Find the probability a student is in sports or work using the table. Round $\mathrm{P}(\text{sports or work})$ to the nearest percent.

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male:
$\mathrm{P}(\text { junior } \mid \text { male })=[?] \%$ Round to the nearest whole percent.

Multiply and simplify $(2 x-5)(3 x-3)$ .

A diver is at $5.2 \mathrm{~m}$ depth in water ( $1000 \mathrm{kgm}^{-3}$ density). Find the pressure on the diver ( $\mathrm{g}=10 \mathrm{~m/s}^{2}$ ).

Calculate the force on a submarine door at $500 \mathrm{~m}$ depth with area $0.4^{2}$ and water density $1.03$ .

A faulty barometer shows $72.6 \mathrm{cmHg}$ when actual pressure is $75.0 \mathrm{cmHg}$ . Find pressure at $72.0 \mathrm{cmHg}$ .

A man exerts a pressure of $2.8 \times 10^{3} \mathrm{Nm}^{-2}$ over $4 \times 10^{-2} \mathrm{~m}^{2}$ . Find his weight.

Find the height of liquid in a barometer for pressure $204000 \mathrm{Nm}^{-2}$ and density $5200 \mathrm{kgm}^3$ .

A model of an 800m tower is built at a scale of $1: 4000$ . What is the model's height? Options: 5cm, 20cm, 200cm, 320cm.

A tower is 800 m tall. If a model is built at a scale of $1: 4000$ , what is the model's height?

A model of an 800 m tower is built at a scale of $1:4000$ . What is the model's height? Options: 5 cm, 20 cm, 200 cm, 320 cm.

Mary and Susan have 100 postcards. After Mary gives $\frac{4}{5}$ of hers to Susan, Susan has 85. Find Mary's original postcards.