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(i) When x is an integer: To solve the inequality 3x + 8 > 2 when x is an integer, we need to isolate x. Subtracting 8 from both sides: 3x > 2 - 8 3x > -6 Now, dividing both sides by 3 (remember, when dividing or multiplying by a negative number, flip the inequality sign): x > -2

So, when x is an integer, x can be any integer greater than -2.

(ii) When x is a real number: Again, we start with 3x + 8 > 2. Subtracting 8 from both sides: 3x > 2 - 8 3x > -6 Now, dividing both sides by 3: x > -2

So, when x is a real number, x can be any real number greater than -2.

In summary, whether x is an integer or a real number, the solution to the inequality 3x + 8 > 2 is x > -2. And remember, if you need further clarification or more assistance, don't hesitate to reach out to a qualified tutor on UrbanPro!

As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your question.

To determine the number of items that must be sold to realize some profit, we first need to understand the concept of profit in terms of these cost and revenue functions.

Profit (P) is calculated by subtracting the total cost (C(x)) from the total revenue (R(x)). Mathematically, it can be expressed as:

P(x)=R(x)−C(x)P(x)=R(x)−C(x)

Given that C(x)=20x+4000C(x)=20x+4000 and R(x)=60x+2000R(x)=60x+2000, we can substitute these into the profit function:

P(x)=(60x+2000)−(20x+4000)P(x)=(60x+2000)−(20x+4000) P(x)=60x+2000−20x−4000P(x)=60x+2000−20x−4000 P(x)=40x−2000P(x)=40x−2000

Now, for the company to realize some profit, P(x)P(x) must be greater than zero. So, we set up the inequality:

40x−2000>040x−2000>0

To solve for xx:

40x>200040x>2000 x>200040x>402000 x>50x>50

So, the company must sell more than 50 items to realize some profit.

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Let's break down the problem step by step:

Ravi scored 70 and 75 marks in the first two unit tests. Now, he wants to ensure his average score is at least 60 marks across all three tests.

To find out the minimum mark Ravi needs to achieve in the third test, we'll use the concept of averages.

Ravi's total marks in the first two tests = 70 + 75 = 145.

To maintain an average of at least 60 across all three tests, the total marks for all three tests should be at least 3×60=180.3×60=180.

Therefore, in the third test, Ravi needs to score at least 180−145=35180−145=35 marks.

So, Ravi should aim to score a minimum of 35 marks in the third test to achieve an average of at least 60 marks across all three tests.

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As a seasoned tutor on UrbanPro, I'd be glad to help with this question.

To convert Celsius to Fahrenheit, we'll use the formula F = (9/5)C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

Given that the solution needs to be kept between 40°C and 45°C, let's find the corresponding range in Fahrenheit:

For 40°C: F = (9/5) * 40 + 32 F = 72 + 32 F = 104°F

For 45°C: F = (9/5) * 45 + 32 F = 81 + 32 F = 113°F

So, the range of temperature in degrees Fahrenheit is from 104°F to 113°F.

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