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dem82 [27]
2 years ago
6

find three consecutive integers for which 3 times the sum of the first and third integers is -342? show step by step

Mathematics
1 answer:
Artyom0805 [142]2 years ago
3 0

Answer:

-58, -57, -56

Step-by-step explanation:

if the first integer is x,

the second integer must be x + 1 (because it's consecutive)

and the third must be x + 2

Therefore:

3 times the sum of the first and third integers is -342:

3 * (x + (x+2) ) = -342

Combine like terms in parentheses

3 * (2x + 2) = -342

Distribute the 3 to the 2x and the 2:

6x + 6 = -342

Subtract 6 on both sides

6x = -348

Divide by 6 on both sides

x = -58

x + 1 = -57

x + 2 = -56

-58, -57, -56

Check:

3 * (-58 + -56) = 3 * -114 = -342

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Answer:

The answer to your question is: letter B

Step-by-step explanation:

Data

diameter = 6 ft

area = ?

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radius = diameter / 2

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At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the schoo
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Answers:

The z scores are approximately:

  • Care of Magical Creatures:  z = 0.333
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  • Transfiguration:  z = -0.263
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From those scores, we can say:

  • Best grade = Defense Against the Dark Arts
  • Worst grade = Potions

=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

  • x = given grade for each class
  • mu = mean
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Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

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z = (2.50 - 2.90)/(0.75)

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This grade is below average as well.

----------------------------

To summarize, we have these z scores

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

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