Inequality

Problem 1

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats $d$ and Republicans $r$ for a bill to pass:
A) $d+r>15$
B) $d+r<15$
C) $d+r \geq 15$
D) $d+r \leq 15$

See Solution

Problem 2

In the 2017 Wyoming state senate of 30 members, what inequality shows $d + r > 15$ for a bill to pass? A) $d+r>15$ B) $d+r<15$ C) $d+r \geq 15$ D) $d+r \leq 15$

See Solution

Problem 3

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

See Solution

Problem 4

In triangle $D E F$ , find the longest side given $m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ}$ .

See Solution

Problem 5

Find values of $k$ so that $2 x^{2}+k^{2}+2-2(k+2) x > 0$ for all $x$ .

See Solution

Problem 6

Prove $x^{2}-x+2 \geq \frac{7}{4}$ for all values of $x$ .

See Solution

Problem 7

Find $x$ such that $1+x^{2} \geq-\frac{7 x-x^{2}}{3}$ and determine the minimum of $y=1+x^{2}+\frac{7 x-x^{2}}{3}$ .

See Solution

Problem 8

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

See Solution

Problem 9

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) $x<-8 \cup x>-2$

See Solution

Problem 10

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

See Solution

Problem 11

Is the Garamycin dose of $35 \mathrm{mg}$ every $6 \mathrm{h}$ safe for a $42 \mathrm{lb}$ child? Justify your answer.

See Solution

Problem 12

Is a daily dose of $175 \mathrm{mcg}$ of Levothyroxin safe for an 8-year-old weighing $29.5 \mathrm{~kg}$ ? Explain.

See Solution

Problem 13

Is a $600 \mathrm{mg}$ dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the $150-350 \mathrm{mg}$ daily range?

See Solution

Problem 14

Find the safe dose range for a 35-pound child taking Amoxicillin, with a daily dose of $150 \mathrm{mg}-350 \mathrm{mg}$ .

See Solution

Problem 15

A child weighs 29 pounds. Is a dose of $0.125 \mathrm{mg}$ every 12 hours safe, given the range $11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

See Solution

Problem 16

In triangle $ABC$ , with $BC=3\sqrt{2}$ and $\angle ABC=45^{\circ}$ , find the minimum of $CM + MN$ as $M$ and $N$ move on $BD$ and $BC$ .

See Solution

Problem 17

Identify valid triangle side lengths from these options: A. $16,8,10$ B. $4,12,6$ C. $6,9,17$

See Solution

Problem 18

What is the maximum and minimum amount of money that rounds to \$105.40 when rounded to the nearest dime?

See Solution

Problem 19

Roll a fair die twice. Find the probability that the sum is > 5 (Event A) and divisible by 2 or 4 (Event B). Round to two decimals.

See Solution

Problem 20

In a shop, a ruler costs \$5 and a pen costs \$6. If Peter has \$200, how many rulers and pens can he buy at most?

See Solution

Problem 21

Express the inequality $8 \leq 1-2 z < 13$ in terms of $z$ .

See Solution

Problem 22

Si $a \in \mathbb{X}, b \in \mathbb{R}$ y $c \in \mathbb{R}$ , evalúa las proposiciones sobre $a$ , $b$ y $c$ .

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Problem 23

9) Sif estinationale. - Verifica si son verdaderas las siguientes afirmaciones para $a, b, c \in \mathbb{R}$ : a) $(a \leq b) \Rightarrow(a c \leq b c)$ b) $(a \leq b \wedge c>0) \Rightarrow(a c \geq b c)$ c) $(a b=0) \Rightarrow(a=0 \wedge b=0)$ d) $(a b=c) \Rightarrow(a=c \vee b=c)$ e) $(a \geq b \wedge c<0) \Rightarrow(a c \leq b c)$

See Solution

Problem 24

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

See Solution

Problem 25

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

See Solution

Problem 26

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?

See Solution

Problem 27

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

See Solution

Problem 28

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

See Solution

Problem 29

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

See Solution

Problem 30

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

See Solution

Problem 31

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

See Solution

Problem 32

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

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Problem 33

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

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Problem 34

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

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Problem 35

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

See Solution

Problem 36

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

See Solution

Problem 37

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

See Solution

Problem 38

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

See Solution

Problem 39

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

See Solution

Problem 40

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.

See Solution

Problem 41

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

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Problem 42

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

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Problem 43

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

See Solution

Problem 44

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

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Problem 45

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

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Problem 46

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

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Problem 47

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 48

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

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Problem 49

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

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Problem 50

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

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Problem 51

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

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Problem 52

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.

See Solution

Problem 53

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

See Solution

Problem 54

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 55

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%.

See Solution

Problem 56

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

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Problem 57

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

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Problem 58

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

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Problem 59

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 60

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 61

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

See Solution

Problem 62

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

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Problem 63

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 64

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

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Problem 65

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

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Problem 66

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

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Problem 67

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

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Problem 68

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 69

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

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Problem 70

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 71

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 72

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

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Problem 73

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

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Problem 74

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

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Problem 75

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 76

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

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Problem 77

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 78

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 79

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

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Problem 80

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

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Problem 81

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

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Problem 82

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

See Solution

Problem 83

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 84

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

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Problem 85

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 86

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

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Problem 87

Is the statement true or false: $19.7 < |19.7|$ ? Answer: True O False

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Problem 88

Solve the inequality $x^{2}+4 x>77$ . What are the solution intervals?

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Problem 89

What price change in FOJC triggers a margin call if you bought 2 contracts at 286 cents with a \$3,750 maintenance margin?

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Problem 90

Convert the capacities of three milk containers to millilitres and identify the smallest one. Hint: $1000 \mathrm{ml}=1 \mathrm{L}$ .

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Problem 91

Three milk containers have capacities: 1.516 L, $1 \frac{3}{20}$ L, and 1 L + $45 \mathrm{mt}$ . Convert to mL and find the smallest.

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Problem 92

삼각형의 변이 $x-1, x, x+1$ 일 때, $x$ 의 가능한 값 중 아닌 것은? (1) 2 (2) 3 (3) 4 (4) 5 (5) 6

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Problem 93

Determine the inequality for the range of the linear function $p$ given points $(2,-3)$ and $(-4,4)$ .

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Problem 94

Solve the linear inequality: $3 + 2x \leq 7$

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Problem 95

Solve the inequality: $-7x > 56$ . Find the value of $x$ .

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Problem 96

Solve the inequality $|x-3| \leq 5$ .

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Problem 97

Soient $A$ et $B$ deux parties non-vides de $\mathbb{R}$ avec $a \leq b$ pour tout $a \in A$ et $b \in B$ . Montrez que $A$ est majoré, $B$ est minoré et $\sup (A) \leq \inf (B)$ .

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Problem 98

Solve the inequality $|x^{3}-1| \leq x^{2}+x+1$ and find $x \in [0, 2]$ .

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Problem 99

Check if the scale from triangle with sides 1cm, 2cm, 2.5cm to triangle with sides 3cm, 6cm is $1:3$ .

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Problem 100

Find a fraction between $2/3$ and $4/5$ . Options: A. $3/4$ B. $1/2$ C. $5/6$ D. $1/5$

See Solution

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Inequality

Problem 1

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats d d d and Republicans r r r for a bill to pass: A) d+r>15 d+r>15 d+r>15 B) d+r<15 d+r<15 d+r<15 C) d+r≥15 d+r \geq 15 d+r≥15 D) d+r≤15 d+r \leq 15 d+r≤15

Problem 2

In the 2017 Wyoming state senate of 30 members, what inequality shows d+r>15 d + r > 15 d+r>15 for a bill to pass? A) d+r>15 d+r>15 d+r>15 B) d+r<15 d+r<15 d+r<15 C) d+r≥15 d+r \geq 15 d+r≥15 D) d+r≤15 d+r \leq 15 d+r≤15

Problem 3

Find k k k such that x2+k(x+2)+3(x+1)>0 x^{2}+k(x+2)+3(x+1)>0 x2+k(x+2)+3(x+1)>0 for all x x x. What is the range of k k k?

Problem 4

In triangle DEF D E F DEF, find the longest side given m∠D=59∘,m∠E=76∘,m∠F=45∘ m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ} m∠D=59∘,m∠E=76∘,m∠F=45∘.

Problem 5

Find values of k k k so that 2x2+k2+2−2(k+2)x>0 2 x^{2}+k^{2}+2-2(k+2) x > 0 2x2+k2+2−2(k+2)x>0 for all x x x.

Problem 6

Prove x2−x+2≥74 x^{2}-x+2 \geq \frac{7}{4} x2−x+2≥47​ for all values of x x x.

Problem 7

Find x x x such that 1+x2≥−7x−x23 1+x^{2} \geq-\frac{7 x-x^{2}}{3} 1+x2≥−37x−x2​ and determine the minimum of y=1+x2+7x−x23 y=1+x^{2}+\frac{7 x-x^{2}}{3} y=1+x2+37x−x2​.

Problem 8

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 9

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

Problem 10

Solve 2x2−8≤02 x^{2}-8 \leq 02x2−8≤0 and choose the correct interval for xxx.

Problem 11

Is the Garamycin dose of 35mg35 \mathrm{mg}35mg every 6h6 \mathrm{h}6h safe for a 42lb42 \mathrm{lb}42lb child? Justify your answer.

Problem 12

Is a daily dose of 175mcg175 \mathrm{mcg}175mcg of Levothyroxin safe for an 8-year-old weighing 29.5 kg29.5 \mathrm{~kg}29.5 kg? Explain.

Problem 13

Is a 600mg600 \mathrm{mg}600mg dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the 150−350mg150-350 \mathrm{mg}150−350mg daily range?

Problem 14

Find the safe dose range for a 35-pound child taking Amoxicillin, with a daily dose of 150mg−350mg150 \mathrm{mg}-350 \mathrm{mg}150mg−350mg.

Problem 15

A child weighs 29 pounds. Is a dose of 0.125mg0.125 \mathrm{mg}0.125mg every 12 hours safe, given the range 11.3−18.8mg/kg/day11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}11.3−18.8mg/kg/day?

Problem 16

In triangle ABCABCABC, with BC=32BC=3\sqrt{2}BC=32​ and ∠ABC=45∘\angle ABC=45^{\circ}∠ABC=45∘, find the minimum of CM+MNCM + MNCM+MN as MMM and NNN move on BDBDBD and BCBCBC.

Problem 17

Identify valid triangle side lengths from these options: A. 16,8,1016,8,1016,8,10 B. 4,12,64,12,64,12,6 C. 6,9,176,9,176,9,17

Problem 18

What is the maximum and minimum amount of money that rounds to \$105.40 when rounded to the nearest dime?

Problem 19

Roll a fair die twice. Find the probability that the sum is > 5 (Event A) and divisible by 2 or 4 (Event B). Round to two decimals.

Problem 20

In a shop, a ruler costs \$5 and a pen costs \$6. If Peter has \$200, how many rulers and pens can he buy at most?

Problem 21

Express the inequality 8≤1−2z<138 \leq 1-2 z < 138≤1−2z<13 in terms of zzz.

Problem 22

Si a∈X,b∈Ra \in \mathbb{X}, b \in \mathbb{R}a∈X,b∈R y c∈Rc \in \mathbb{R}c∈R, evalúa las proposiciones sobre aaa, bbb y ccc.

Problem 23

Problem 24

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

Problem 25

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 26

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 27

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 28

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 29

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 30

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

Problem 31

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 32

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

Problem 33

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

Problem 34

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

Problem 35

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 36

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 37

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 38

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 39

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 40

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.

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats $d$ and Republicans $r$ for a bill to pass:
A) $d+r>15$
B) $d+r<15$
C) $d+r \geq 15$
D) $d+r \leq 15$

In the 2017 Wyoming state senate of 30 members, what inequality shows $d + r > 15$ for a bill to pass? A) $d+r>15$ B) $d+r<15$ C) $d+r \geq 15$ D) $d+r \leq 15$

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

In triangle $D E F$ , find the longest side given $m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ}$ .

Find values of $k$ so that $2 x^{2}+k^{2}+2-2(k+2) x > 0$ for all $x$ .

Prove $x^{2}-x+2 \geq \frac{7}{4}$ for all values of $x$ .

Find $x$ such that $1+x^{2} \geq-\frac{7 x-x^{2}}{3}$ and determine the minimum of $y=1+x^{2}+\frac{7 x-x^{2}}{3}$ .

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

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) $x<-8 \cup x>-2$

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

Is the Garamycin dose of $35 \mathrm{mg}$ every $6 \mathrm{h}$ safe for a $42 \mathrm{lb}$ child? Justify your answer.

Is a daily dose of $175 \mathrm{mcg}$ of Levothyroxin safe for an 8-year-old weighing $29.5 \mathrm{~kg}$ ? Explain.

Is a $600 \mathrm{mg}$ dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the $150-350 \mathrm{mg}$ daily range?

Find the safe dose range for a 35-pound child taking Amoxicillin, with a daily dose of $150 \mathrm{mg}-350 \mathrm{mg}$ .

A child weighs 29 pounds. Is a dose of $0.125 \mathrm{mg}$ every 12 hours safe, given the range $11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

In triangle $ABC$ , with $BC=3\sqrt{2}$ and $\angle ABC=45^{\circ}$ , find the minimum of $CM + MN$ as $M$ and $N$ move on $BD$ and $BC$ .

Identify valid triangle side lengths from these options: A. $16,8,10$ B. $4,12,6$ C. $6,9,17$

Express the inequality $8 \leq 1-2 z < 13$ in terms of $z$ .

Si $a \in \mathbb{X}, b \in \mathbb{R}$ y $c \in \mathbb{R}$ , evalúa las proposiciones sobre $a$ , $b$ y $c$ .

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.

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

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

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