Inequality

Problem 401

For each value of $w$ , determine whether it is a solution to $9 w-1>-28$ . \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{ $w$ } & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline 7 & $\bigcirc$ & $\bigcirc$ \\ \hline 4 & $\bigcirc$ & $\bigcirc$ \\ \hline-4 & $\bigcirc$ & $\bigcirc$ \\ \hline-3 & $\bigcirc$ & $\bigcirc$ \\ \hline \end{tabular}

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Problem 402

Practice
1. Mealworms are a healthy food for wild songbirds. Adam buys a 3.5-oz container of mealworms for $\$ 8.75$ . Marco buys a 3.75-oz container of mealworms for $\$ 9.75$ . Which container is the better deal?

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Problem 403

Solve for $w$ . $w+1<-5$

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Problem 404

Fill in the blanks in the sentence below so that the resulting statement is true.
The ordered pair (5.4) is a/an $\square$ of the inequality $x+y>2$ because when 5 is substituted for $\square$ and 4 is substituted for $\square$ the true statement $\square$ is obtained.

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Problem 405

Solve the rational inequality. Write your answer in interval notation. $\frac{x+27}{x+4}<9$

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Problem 406

Question 25 of 33 (1 point)
Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 426 people aged 65 and over, 120 of them had sleep apnea.
Part 1 of 3 (a) Find a point estimate for the population proportion of those aged 65 and over who have sleep apnea. Round the answer to three decimal places.
The point estimate for the population proportion of those aged 65 and over who have sleep apnea is 0.282 .
Part 2 of 3 (b) Construct a $80 \%$ confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round the answer to three decimal places.
A $80 \%$ confidence interval for the proportion of those aged 65 and over who have sleep apnea is $0.254<p<0.310$ .
Part: $2 / 3$
Part 3 of 3 (c) In another study, medical researchers concluded that more than $16 \%$ of elderly people have sleep apnea. Based on the confidence interval, does it appear that more than $16 \%$ of people aged 65 and over have sleep apnea? Explain. Since all of the values in the confidence interval are (Choose one) $\boldsymbol{\nabla} 0.16$ , the confidence interval (Choose one) $\nabla$ contradict the claim.

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Problem 407

The Baker family will host a holiday dinner party. The dinner party will cost $\$ 25$ per person and they will use a $\$ 75$ off coupon towards the bill. Write and solve an inequality to find the maximum number of people that can attend the holiday dinner party, if they want to spend less than $\$ 425$ .

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Problem 408

A $95 \%$ confidence interval for $\mu$ is computed to be $(1.60,4.15)$ . For each of the following hypotheses, state whether $H_{0}$ will be rejected at 0.05 level. Part: $0 / 4$
Part 1 of 4 $H_{0}: \mu=4$ versus $H_{1}: \mu \neq 4$ Since the $95 \%$ confidence interval (Choose one) $\boldsymbol{\nabla} \mu_{0}$ , then $H_{0}$ (Choose one) $\boldsymbol{\nabla}$ be rejected at the 0.05 level.

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Problem 409

Wed Noy 30 15441 mylab, pearson.com llege Algebra - FL 2024 Quanto Griffin nework: HW Units 1.4 \& 1.6 1.4 .27 HW Seores $22.58 \%, 7$ of 31 peints Part 1 of 2 Points: 0 of 1 Save on list Solve. Then graph. $7 x \geq 28$ Choose the solution. A. $\{x \mid x<4\}$ B. $(x \mid x \leqslant 4)$ C. $\{x \mid x>4\}$ D. $(x \mid x=4)$ Clear all Skill builder Cheek answer

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Problem 410

V 20 14\% 1 mylab.pearson.com Algebra - FL 2024 Quanto Griffin HW Units 1.4 \& 1.6 1.4 .33 HW Score: $27.42 \%, 8.5$ of 31 points Points: 0 of 1 Save - Solve the following inequality. $-9 x \geq-4.5$
Select the correct choice below and fill in the answer box to complete your choice. A. The solution set is $\{x \mid x \leq \square\}$ . $\square$ B. The solution set is $\{x \mid x \geq \square$ . $\square$ C. The solution set is $\{x \mid x<\square$ . $\square$ D. The solution set is $\{x \mid x>\square$ . Clear all Skill builder Check a

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Problem 411

Does $(4,2)$ make the inequality $2 x+3 y>14$ true? yes no

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Problem 412

1.6 .71
Solve $|x|<13$
Select the correct cholce below and fill in the answer boxes to complete your choice. (simplify your answers.) A. The solution set is $\{x \mid x \leq \square$ or $x \geq$ $\square$ \}. B. The solution set is $\{x \mid \leq x \leq \square\}$ . $\square$ C. The solution set is $\{x \mid x<\square$ or $x>\square\}$ . $\square$ $\square$ D. The solution set is $\{x \mid \square<x<\square\}$ .

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Problem 413

ege Algebra - FL 2024 HW Score: 82.26\%, 25.5 of 31 HW Units 1.4 \& 1.6 1.6 .97 Points: 0 of 1
Solve. $\left|\frac{x-5}{8}\right|<4$
Select the correct choice below and fill in the answer boxes to complete your choice. (Simplify your answers.) A. The solution set is $\{x \mid x<\square$ or $x>\square\}$ . $\square$ B. The solution set is $\{x \mid x \leq \square$ or $x \geq \square\}$ . $\square$ C. The solution set is $\{x \mid \square \leq x \leq \square\}$ . $\square$ $\square$ D. The solution set is $\{x \mid \square<x<\square\}$ .

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Problem 414

Weights of Vacuum Cleaners Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a random sample of each type. Find the $90 \%$ confidence interval for the difference of the means. Assume the variables are normally distributed and the variances are unequal. Round the sample mean and sample standard deviation to two decimal places and the final answers to at least one decimal place. \begin{tabular}{llll|llll} \multicolumn{4}{c|}{ Hard body types } & \multicolumn{4}{c}{ Soft body types } \\ \hline 21 & 17 & 17 & 20 & 24 & 13 & 11 & 13 \\ 16 & 17 & 15 & 20 & 12 & 15 & & \\ 23 & 16 & 17 & 17 & & & & \\ 13 & & & & & & \end{tabular}
Send data to Excel
Use $\mu_{1}$ for the mean weight of the hard body type. $\square<\mu_{1}-\mu_{2}<\square$

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Problem 415

c. $4 b^{2}+14 b+16<10$

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Problem 416

The losing team in a baseball game scored 2 runs. Which inequality represents the number of runs, $r$ , that the winning team could have scored? $r \leq 2$ $r=2$ $r<2$ $r>2$

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Problem 417

8) In order for a company to break even on jackets they have ordered, it needs to sell $25 \%$ of the jackets. If they sold 54 jackets out of a stock of 205 , have they broken even?

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Problem 418

A sour cream container holds a volume of 5 fluid ounces. Is the volume of 3 sour cream containers greater than 3 cups?

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Problem 419

$-13 \leq-5 r+2$

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Problem 420

Table (Sine) Practice
12. IXL State Standards
Question
Select the inequality which represents the graph shown below.
Answer $30-y \geq-x^{2}-11 x$ $30-y \geq-x^{2}+11 x$ $30-y \leq-x^{2}-11 x$ $30-y \leq-x^{2}+11 x$

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Problem 421

$4.3-1.5 c \leq 10$

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Problem 422

Table (Tangent) Table (Cosine) Table (Sine) Practice 1) IXL State Standards Thelast.
Question
Select the inequality which represents the graph shown below.
Answer $y+5 \geq-x^{2}+6 x$ $y+5 \leq-x^{2}+6 x$ $y+5 \leq-x^{2}-6 x$ $y+5 \geq-x^{2}-6 x$

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Problem 423

Question
Select the inequality which represents the graph shown below.
Answer $y-3 \geq-x^{2}-2 x$ $y-3 \leq-x^{2}+2 x$ $y-3 \geq-x^{2}+2 x$ $y-3 \leq-x^{2}-2 x$

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Problem 424

Question
Select the inequality which represents the graph shown below.
Answer $y+6 \geq-x^{2}-7 x$ $y+6 \geq-x^{2}+7 x$ $y+6 \leq-x^{2}-7 x$ $y+6 \leq-x^{2}+7 x$

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Problem 425

(b) By writing $|x| \geq a$ in the equivalent for $x \geq a$ or $x \leq-a$ , determine the solution set for $\left|\frac{x-3}{2 x-1}\right| \geq \frac{1}{2}$ [6 marks]

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Problem 426

rates 2NB Clacayoff My IXL Learning Assessment Ernest's birthday party will cost $60 if he invites 4 guests. How many guests can there be, at most, if Ernest can afford to spend a total of$ 315 on his birthday party? Solve using unit rates. bmit guests

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Problem 427

Compare $x - y$ and $(x + y)^{2}$ given $x > 0 > y$ .

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Problem 428

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

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Problem 429

Jordan has ingredients for hot chocolate. What's the max servings he can make with 5 chocolate squares, 2 cups sugar, and 7 cups milk?

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Problem 430

A building's height is $180 \mathrm{~m}$ . What is the maximum absolute error if this is rounded to the nearest meter?

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Problem 431

The container's capacity is $450 \mathrm{~mL}$ . Find the max error, lower limit, and upper limit of its actual capacity.

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Problem 432

The weight of powder is $84.2 \mathrm{~g}$ , rounded to the nearest $0.1 \mathrm{~g}$ . Find the range of actual weight $W$ .

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Problem 433

Qui a le plus d'argent entre Lizzy (500 frs), Jean (50 frs) et Fifi (700 frs) ?

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Problem 434

If $x$ is a positive integer such that $(x-1)(x-3)(x-5)\ldots(x-93)<0$ , how many values can $x$ take?

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Problem 435

Find the maximum value of $x$ if $x \leq 5y - 17$ and $y = 3$ .

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Problem 436

Solve the inequality $4^{x} \leq 32$ .

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Problem 437

Solve the inequality $2 \cdot 3^{-x} - 3^{x} \geq 1$ .

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Problem 438

How many days must a skier ski for a season pass ( $450) to be cheaper than daily passes ($ 77 + \ $25$ per day)?

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Problem 439

The weight of a powder is $84.2 \mathrm{~g}$ , rounded to the nearest $0.1 \mathrm{~g}$ . Determine the possible range for $W$ .

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Problem 440

Find the max absolute error, measured time, and percentage error for $t$ with $25.465 \leq t < 25.475$ .

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Problem 441

Find the actual length $L$ of a copper rod measured as $80 \mathrm{~cm}$ with a relative error of $\frac{1}{160}$ .

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Problem 442

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

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Problem 443

In a factory, packs of rice weighing $5000 \mathrm{~g}$ (nearest $50 \mathrm{~g}$ ) are acceptable. Find:
(a) upper limit for 1 pack. (b) upper limit for 48 packs in $\mathrm{kg}$ . (c) can 48 packs weigh $242 \mathrm{~kg}$ (nearest kg)? Explain.

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Problem 444

Solve the inequality $7^{x}-6>7^{1-x}$ .

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Problem 445

Solve the inequality $(-5 q-2)^{2}-4(-2)(p q)<0$ .

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Problem 446

Determine if a 100-m dash time of 24.7 seconds is satisfactory given $\mu=28.5$ and $\sigma=3.1$ .

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Problem 447

Solve the inequality for $y$ : $4x + 3y < 9$ .

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Problem 448

Solve the inequality: $x + 4y > 0$ .

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Problem 449

Solve the inequality $x^2 - 2x - 3 > 0$ .

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Problem 450

A customer wants a 5-line ad for $\$ 45.00$ max. Suggest the best package based on the rates provided.

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Problem 451

Solve the inequality $x^{2} - 5x - 24 > 0$ .

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Problem 452

Solve the inequality $y^{2}+y-2 \leq 0$ .

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Problem 453

Kann Phil in 3 Stunden seine Freundin erreichen, die 80 km entfernt ist, mit dem Fahrrad?

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Problem 454

Find values of $x$ such that: $6 x^{2}+17 x \geq 14$ .

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Problem 455

An investor owns an ETF tracking the ASX 200 with a $2\%$ dividend yield. Buy at \ $50, sell at \$49. Borrow at$ 7\% $, invest at$ 5.5\%$. Find the half-year forward price range with no arbitrage.

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Problem 456

Giải các bất phương trình sau:
1) $\frac{2x+3}{-4x+5}<0$
2) $\frac{x^{2}+3x+2}{(x-1)(-x^{2}+4x-4)} \geq 0$

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Problem 457

An optic fibre cable is $860 \mathrm{~m}$ (nearest $10 \mathrm{~m}$ ). Each piece is $36 \mathrm{~cm}$ (nearest $\mathrm{cm}$ ). Find max $n$ .

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Problem 458

Find the half-year forward price range for an ETF with a 2% dividend yield, bought at \$50 and sold at \$49, with borrowing at 7% and investing at 5.5%.

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Problem 459

Solve the equation $2(x+1) \neq 4x!$ for values of $x$ .

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Problem 460

Express the interval $[2,8]$ using an inequality format.

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Problem 461

Graph the inequality $10 > x \geq 1$ on a number line.

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Problem 462

Khalid compares prices for sandwiches: Store A: 5 ft for \$42.50, Store B: 6 ft for \$49.50. Which is cheaper per foot?

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Problem 463

Khalid is buying sandwiches: Store A has a 5-foot for \$42.50, Store B has a 6-foot for \$49.50. Which is cheaper per foot?

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Problem 464

Two teams paint fences. Blue Team: 15 m² in 6 hrs; Red Team: 8 m² in 4 hrs. Which team is faster? Compare rates: $2.5 > 2$ .

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Problem 465

When is the product of two positive numbers, $x$ and $y$ , less than either $x$ or $y$ ?

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Problem 466

Find the maximum number of pieces $n$ from an $860 \mathrm{~m}$ cable cut into lengths of $36 \mathrm{~cm}$ each.

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Problem 467

Solve the inequality: $7 - 2x > 23$ .

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Problem 468

Solve the inequality $x^{2}+4 x-21<0$ and shade the solution region.

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Problem 469

Find the values of $c$ that satisfy the inequality: $4x + 7 \geq 3(x + 3)$ .

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Problem 470

Find the values of $x$ that satisfy the inequality: $4x + 7 \geq 3(x + 3)$ .

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Problem 471

Explain the relationship between the underlined digits in these pairs:
1. $3. \underline{4}19$ and $3 \underline{4}7$
2. $15,0\underline{6}4$ and $175,9\underline{3}8$
3. $\underline{6} 85$ and $\underline{6}, 293$
4. $7 \underline{9} 2,156$ and $84 \underline{9}, 302$
Are you comparing absolute values or their positional relationships?

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Problem 472

Identify the two whole numbers between which $\sqrt{54}$ lies and justify your answer.

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Problem 473

Determine the two whole numbers between which $\sqrt{98}$ lies. Justify your answer and position $\sqrt{98}$ on the number line.

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Problem 474

Find the two whole numbers between which $\sqrt{77}$ lies. Justify your answer and place $\sqrt{77}$ on a number line.

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Problem 475

Determine the two consecutive whole numbers that $\sqrt{10}$ falls between. Explain your reasoning.

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Problem 476

Find two consecutive whole numbers that $\sqrt{52}$ is between and justify your answer.

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Problem 477

Find the two consecutive whole numbers between which $\sqrt{93}$ lies.

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Problem 478

Find the two whole numbers between which $\sqrt{87}$ lies. Justify your answer and place $\sqrt{87}$ on a number line.

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Problem 479

Find two consecutive whole numbers that $\sqrt{78}$ is between and justify your answer.

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Problem 480

Find two consecutive whole numbers between which $\sqrt{85}$ lies. Justify your answer and locate it on a number line.

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Problem 481

Find two whole numbers between which $\sqrt{92}$ falls. Justify your answer and place $\sqrt{92}$ on a number line.

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Problem 482

Determine the two whole numbers that $\sqrt{50}$ is between and justify your answer.

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Problem 483

Determine the two whole numbers between which $\sqrt{38}$ falls.

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Problem 484

Determine the two consecutive whole numbers that $\sqrt{86}$ falls between and justify your answer.

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Problem 485

¿Cuánto cuesta el estacionamiento por los primeros 60 minutos si 80 min cuestan 15200 y 95 min cuestan 17000?

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Problem 486

El costo de los primeros 60 minutos en el parqueadero está entre \$12.700 y \$15.850. ¿Cuál es el rango exacto?

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Problem 487

Solve the compound inequality: $5 \leq y-1 < 10$ .

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Problem 488

At what time is the diver farther from sea level: at -30 feet (1:00 p.m.) or -45 feet (2:00 p.m.)?

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Problem 489

Find the solution set for the inequality $x(-1+\ln x)<0$ .

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Problem 490

My IXL Google Slides N. 1 Solutions to inequalities G2U Learning (1) MAP Recomn Assessment Analytics [a]. which of the following are solutions to the inequality below? Select all that apply. $-7 a+10 \geq-25$ $a=4$ $a=5$ $a=-12$ $a=8$ Submit

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Problem 491

G2U Assessment (1) MAP Recomimen. Analytics [a]. Which of the following is a solution to the inequality below? $w-3<-5$ $w=12$ $w=-9$ $w=-11$ $w=-12$

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Problem 492

$n<30$ (12.) $-7>20+c$

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Problem 493

Every winter, Trisha teaches a wreath-making workshop. Last year, the glitter pinecones were so popular that she went through a bag of 50 of them. Trisha is making a supply list for this year's workshop and plans to bring at least as many glitter pinecones as last year.
Let $p$ represent the number of glitter pinecones that Trisha might bring to this year's workshop. Which inequality models the story? $p>50$ $p \geq 50$ $\square$ $\square$ Graph the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

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Problem 494

Pablo is making a keychain that looks like Earth. He is using 13 green beads and plans to use more blue beads than green beads.
Let $b$ represent the number of blue beads that Pablo might use. Which inequality models the story? $b>13$ $b \geq 13$ $b<13$ $b \leq 13$
Graph the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Submit Work it out

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Problem 495

Laura needs to make a long skirt for her role in the school play. She doesn't want to trip over the hem, so Laura plans to make it at most 31.25 inches long.
Let $\ell$ represent the length, in inches, Laura's skirt might be. Which inequality models the story? $\ell>31.25$ $\ell \geq 31.25$ $\ell<31.25$ $\ell \leq 31.25$
Graph the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

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Problem 496

Question Show Examples
Eva has a points card for a movie theater. - She receives 60 rewards points just for signing up. - She earns 7.5 points for each visit to the movie theater. - She needs at least 165 points for a free movie ticket.
Use the drop-down menu below to write an inequality representing $v$ , the number of visits she needs to make in order to get a free movie ticket.
Answer Attempt 1 out of 2 $v$ $\square$ Submit Answer

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Problem 497

Keenan and his younger brother, Jamal, are making matching dragon costumes for Halloween. The tail on Jamal's dragon costume is 26 inches long. Since Keenan is taller, he plans to make his tail longer than Jamal's.
Let $\ell$ represent the length, in inches, that Keenan's tail could be. Which inequality models the story? $\ell>26$ $\ell \geq 26$ $\ell<26$ $\ell \leq 26$
Graph the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Submit
Work it out

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Problem 498

$12(x+8) \neq 11 x-5$

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Problem 499

20. Maria has $\$ 10$ and wants to know if she has enough money to rent a bike and ride her bike to the beach, which is 12 miles away. The bike rental company charges a $\$ 2.00$ flat rate plus $\$ 0.75$ per mile. Which inequality can Maria use to determine she has enough money? A. $2+0.75 x \leq 10$ B. $2+0.75 x \geq 10$ c. $2 x+0.75 \leq 10$ D. $0.75 x+10 \leq 2$

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Problem 500

Quiz Active
1 2 3 4. 5.
6 7.
8 9 10 TIME REMAINING 01:58:37 To help solve the trigonometric inequality $2 \sin ^{2}(x)+\cos (2 x)-2<-1$ , Tracey successfully graphed the equations $y=2 \sin ^{2}(x)+\cos (2 x)-2$ and $y=-1$ with her graphing calculator. Which of the following statements is true about the inequality? There is no solution because even though you cannot see it, the graph of the equation $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is above the graph of the equation $y=-1$ for all values of $x$ . There is no solution because the graph of the equation $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is the same as the graph of the equation $y=-1$ , so $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is never below $y=-1$ . There are an infinite number of solutions because even though you cannot see it, the graph of the equation $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is below the graph of the equation $y=-1$ for all values of $x$ . There are an infinite number of solutions because the graph of the equation $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is the same as the graph of the equation $y=-1$ , so $y=2 \sin ^{2}(x)+\cos (2 x)-2$ is never below $y=-1$ .

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1 2 3 4 5 6 7 8 ...20

Inequality

Problem 401

Problem 402

Practice1. Mealworms are a healthy food for wild songbirds. Adam buys a 3.5-oz container of mealworms for $8.75\$ 8.75$8.75. Marco buys a 3.75-oz container of mealworms for $9.75\$ 9.75$9.75. Which container is the better deal?

Problem 403

Solve for www. w+1<−5w+1<-5w+1<−5

Problem 404

Fill in the blanks in the sentence below so that the resulting statement is true.The ordered pair (5.4) is a/an □\square□ of the inequality x+y>2x+y>2x+y>2 because when 5 is substituted for □\square□ and 4 is substituted for □\square□ the true statement □\square□ is obtained.

Problem 405

Solve the rational inequality. Write your answer in interval notation. x+27x+4<9\frac{x+27}{x+4}<9x+4x+27​<9

Problem 406

Problem 407

Problem 408

Problem 409

Problem 410

Problem 411

Does (4,2)(4,2)(4,2) make the inequality 2x+3y>142 x+3 y>142x+3y>14 true? yes no

Problem 412

Problem 413

Problem 414

Problem 415

c. 4b2+14b+16<104 b^{2}+14 b+16<104b2+14b+16<10

Problem 416

The losing team in a baseball game scored 2 runs. Which inequality represents the number of runs, rrr, that the winning team could have scored? r≤2r \leq 2r≤2 r=2r=2r=2 r<2r<2r<2 r>2r>2r>2

Problem 417

8) In order for a company to break even on jackets they have ordered, it needs to sell 25%25 \%25% of the jackets. If they sold 54 jackets out of a stock of 205 , have they broken even?

Problem 418

A sour cream container holds a volume of 5 fluid ounces. Is the volume of 3 sour cream containers greater than 3 cups?

Problem 419

−13≤−5r+2-13 \leq-5 r+2−13≤−5r+2

Problem 420

Problem 421

4.3−1.5c≤104.3-1.5 c \leq 104.3−1.5c≤10

Problem 422

Problem 423

QuestionSelect the inequality which represents the graph shown below.Answer y−3≥−x2−2xy-3 \geq-x^{2}-2 xy−3≥−x2−2x y−3≤−x2+2xy-3 \leq-x^{2}+2 xy−3≤−x2+2x y−3≥−x2+2xy-3 \geq-x^{2}+2 xy−3≥−x2+2x y−3≤−x2−2xy-3 \leq-x^{2}-2 xy−3≤−x2−2x

Problem 424

QuestionSelect the inequality which represents the graph shown below.Answer y+6≥−x2−7xy+6 \geq-x^{2}-7 xy+6≥−x2−7x y+6≥−x2+7xy+6 \geq-x^{2}+7 xy+6≥−x2+7x y+6≤−x2−7xy+6 \leq-x^{2}-7 xy+6≤−x2−7x y+6≤−x2+7xy+6 \leq-x^{2}+7 xy+6≤−x2+7x

Problem 425

(b) By writing ∣x∣≥a|x| \geq a∣x∣≥a in the equivalent for x≥ax \geq ax≥a or x≤−ax \leq-ax≤−a, determine the solution set for ∣x−32x−1∣≥12\left|\frac{x-3}{2 x-1}\right| \geq \frac{1}{2}∣∣​2x−1x−3​∣∣​≥21​ [6 marks]

Problem 426

Problem 427

Compare x−yx - yx−y and (x+y)2(x + y)^{2}(x+y)2 given x>0>yx > 0 > yx>0>y.

Problem 428

Is a 24.7-second 100-m dash satisfactory if last year's average was μ=28.5\mu=28.5μ=28.5 and σ=3.1\sigma=3.1σ=3.1? Explain.

Problem 429

Jordan has ingredients for hot chocolate. What's the max servings he can make with 5 chocolate squares, 2 cups sugar, and 7 cups milk?

Problem 430

A building's height is 180 m180 \mathrm{~m}180 m. What is the maximum absolute error if this is rounded to the nearest meter?

Problem 431

The container's capacity is 450 mL450 \mathrm{~mL}450 mL. Find the max error, lower limit, and upper limit of its actual capacity.

Problem 432

The weight of powder is 84.2 g84.2 \mathrm{~g}84.2 g, rounded to the nearest 0.1 g0.1 \mathrm{~g}0.1 g. Find the range of actual weight WWW.

Problem 433

Qui a le plus d'argent entre Lizzy (500 frs), Jean (50 frs) et Fifi (700 frs) ?

Problem 434

If xxx is a positive integer such that (x−1)(x−3)(x−5)…(x−93)<0(x-1)(x-3)(x-5)\ldots(x-93)<0(x−1)(x−3)(x−5)…(x−93)<0, how many values can xxx take?

Problem 435

Find the maximum value of xxx if x≤5y−17x \leq 5y - 17x≤5y−17 and y=3y = 3y=3.

Problem 436

Solve the inequality 4x≤324^{x} \leq 324x≤32.

Problem 437

Solve the inequality 2⋅3−x−3x≥12 \cdot 3^{-x} - 3^{x} \geq 12⋅3−x−3x≥1.

Problem 438

How many days must a skier ski for a season pass (450)tobecheaperthandailypasses(450) to be cheaper than daily passes (450)tobecheaperthandailypasses(77 + \252525 per day)?

Problem 439

The weight of a powder is 84.2 g84.2 \mathrm{~g}84.2 g, rounded to the nearest 0.1 g0.1 \mathrm{~g}0.1 g. Determine the possible range for WWW.

Problem 440

Find the max absolute error, measured time, and percentage error for ttt with 25.465≤t<25.47525.465 \leq t < 25.47525.465≤t<25.475.

Problem 441

Find the actual length LLL of a copper rod measured as 80 cm80 \mathrm{~cm}80 cm with a relative error of 1160\frac{1}{160}1601​.

Problem 442

Find the range of the actual area of a rectangle with width 3.0 cm3.0 \mathrm{~cm}3.0 cm and length 8.0 cm8.0 \mathrm{~cm}8.0 cm.

Problem 443

In a factory, packs of rice weighing 5000 g5000 \mathrm{~g}5000 g (nearest 50 g50 \mathrm{~g}50 g) are acceptable. Find:(a) upper limit for 1 pack. (b) upper limit for 48 packs in kg\mathrm{kg}kg. (c) can 48 packs weigh 242 kg242 \mathrm{~kg}242 kg (nearest kg)? Explain.

Problem 444

Solve the inequality 7x−6>71−x7^{x}-6>7^{1-x}7x−6>71−x.

Problem 445

Solve the inequality (−5q−2)2−4(−2)(pq)<0(-5 q-2)^{2}-4(-2)(p q)<0(−5q−2)2−4(−2)(pq)<0.

Problem 446

Practice
1. Mealworms are a healthy food for wild songbirds. Adam buys a 3.5-oz container of mealworms for $\$ 8.75$ . Marco buys a 3.75-oz container of mealworms for $\$ 9.75$ . Which container is the better deal?

Solve for $w$ . $w+1<-5$

Fill in the blanks in the sentence below so that the resulting statement is true.
The ordered pair (5.4) is a/an $\square$ of the inequality $x+y>2$ because when 5 is substituted for $\square$ and 4 is substituted for $\square$ the true statement $\square$ is obtained.

Solve the rational inequality. Write your answer in interval notation. $\frac{x+27}{x+4}<9$

Does $(4,2)$ make the inequality $2 x+3 y>14$ true? yes no

c. $4 b^{2}+14 b+16<10$

The losing team in a baseball game scored 2 runs. Which inequality represents the number of runs, $r$ , that the winning team could have scored? $r \leq 2$ $r=2$ $r<2$ $r>2$

8) In order for a company to break even on jackets they have ordered, it needs to sell $25 \%$ of the jackets. If they sold 54 jackets out of a stock of 205 , have they broken even?

$-13 \leq-5 r+2$

$4.3-1.5 c \leq 10$

Question
Select the inequality which represents the graph shown below.
Answer $y-3 \geq-x^{2}-2 x$ $y-3 \leq-x^{2}+2 x$ $y-3 \geq-x^{2}+2 x$ $y-3 \leq-x^{2}-2 x$

Question
Select the inequality which represents the graph shown below.
Answer $y+6 \geq-x^{2}-7 x$ $y+6 \geq-x^{2}+7 x$ $y+6 \leq-x^{2}-7 x$ $y+6 \leq-x^{2}+7 x$

(b) By writing $|x| \geq a$ in the equivalent for $x \geq a$ or $x \leq-a$ , determine the solution set for $\left|\frac{x-3}{2 x-1}\right| \geq \frac{1}{2}$ [6 marks]

Compare $x - y$ and $(x + y)^{2}$ given $x > 0 > y$ .

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

A building's height is $180 \mathrm{~m}$ . What is the maximum absolute error if this is rounded to the nearest meter?

The container's capacity is $450 \mathrm{~mL}$ . Find the max error, lower limit, and upper limit of its actual capacity.

The weight of powder is $84.2 \mathrm{~g}$ , rounded to the nearest $0.1 \mathrm{~g}$ . Find the range of actual weight $W$ .

If $x$ is a positive integer such that $(x-1)(x-3)(x-5)\ldots(x-93)<0$ , how many values can $x$ take?

Find the maximum value of $x$ if $x \leq 5y - 17$ and $y = 3$ .

Solve the inequality $4^{x} \leq 32$ .

Solve the inequality $2 \cdot 3^{-x} - 3^{x} \geq 1$ .

How many days must a skier ski for a season pass ( $450) to be cheaper than daily passes ($ 77 + \ $25$ per day)?

The weight of a powder is $84.2 \mathrm{~g}$ , rounded to the nearest $0.1 \mathrm{~g}$ . Determine the possible range for $W$ .

Find the max absolute error, measured time, and percentage error for $t$ with $25.465 \leq t < 25.475$ .

Find the actual length $L$ of a copper rod measured as $80 \mathrm{~cm}$ with a relative error of $\frac{1}{160}$ .

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

In a factory, packs of rice weighing $5000 \mathrm{~g}$ (nearest $50 \mathrm{~g}$ ) are acceptable. Find:
(a) upper limit for 1 pack. (b) upper limit for 48 packs in $\mathrm{kg}$ . (c) can 48 packs weigh $242 \mathrm{~kg}$ (nearest kg)? Explain.

Solve the inequality $7^{x}-6>7^{1-x}$ .

Solve the inequality $(-5 q-2)^{2}-4(-2)(p q)<0$ .

Determine if a 100-m dash time of 24.7 seconds is satisfactory given $\mu=28.5$ and $\sigma=3.1$ .

Solve the inequality for $y$ : $4x + 3y < 9$ .

Solve the inequality: $x + 4y > 0$ .

Solve the inequality $x^2 - 2x - 3 > 0$ .

A customer wants a 5-line ad for $\$ 45.00$ max. Suggest the best package based on the rates provided.

Solve the inequality $x^{2} - 5x - 24 > 0$ .

Solve the inequality $y^{2}+y-2 \leq 0$ .

Find values of $x$ such that: $6 x^{2}+17 x \geq 14$ .

An investor owns an ETF tracking the ASX 200 with a $2\%$ dividend yield. Buy at \ $50, sell at \$49. Borrow at$ 7\% $, invest at$ 5.5\%$. Find the half-year forward price range with no arbitrage.

Giải các bất phương trình sau:
1) $\frac{2x+3}{-4x+5}<0$
2) $\frac{x^{2}+3x+2}{(x-1)(-x^{2}+4x-4)} \geq 0$

An optic fibre cable is $860 \mathrm{~m}$ (nearest $10 \mathrm{~m}$ ). Each piece is $36 \mathrm{~cm}$ (nearest $\mathrm{cm}$ ). Find max $n$ .

Solve the equation $2(x+1) \neq 4x!$ for values of $x$ .

Express the interval $[2,8]$ using an inequality format.

Graph the inequality $10 > x \geq 1$ on a number line.

Two teams paint fences. Blue Team: 15 m² in 6 hrs; Red Team: 8 m² in 4 hrs. Which team is faster? Compare rates: $2.5 > 2$ .

When is the product of two positive numbers, $x$ and $y$ , less than either $x$ or $y$ ?

Find the maximum number of pieces $n$ from an $860 \mathrm{~m}$ cable cut into lengths of $36 \mathrm{~cm}$ each.

Solve the inequality: $7 - 2x > 23$ .

Solve the inequality $x^{2}+4 x-21<0$ and shade the solution region.

Find the values of $c$ that satisfy the inequality: $4x + 7 \geq 3(x + 3)$ .

Find the values of $x$ that satisfy the inequality: $4x + 7 \geq 3(x + 3)$ .

Identify the two whole numbers between which $\sqrt{54}$ lies and justify your answer.

Determine the two whole numbers between which $\sqrt{98}$ lies. Justify your answer and position $\sqrt{98}$ on the number line.

Find the two whole numbers between which $\sqrt{77}$ lies. Justify your answer and place $\sqrt{77}$ on a number line.