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Snowcat [4.5K]
2 years ago
10

In a ten pin bowling the highest possible score in a single game is 300. At one point in the season, John had an average score o

f 177. In his next game he obtained a score of 199 which caused his average to increase to 178. After one more game John would like his average to be 183. is it possible for him to accomplish this. If so what score does he need to make his next game if not explain why not.
Mathematics
1 answer:
Sindrei [870]2 years ago
8 0

Answer:

John need to get 293 in his next game to bring his average up to 183.

Step-by-step explanation:

John starts with N games played and averaging 177 points per game.

In game N+1, John scored 199 points.

\frac{177N + 199}{N+1}=178\\177N+199=178N+178\\N=21\\

So, John has now played (N+1) = 22 games.

We need to know what score John needs in game 23 to bring his average to 183.

\frac{177*21 + 199+Y}{23}=183\\3916+Y=4209\\Y=293\\

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Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel
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This question is incomplete because it lacks the appropriate attachment containing the argument of Paul and Manuel

Kindly find attached the appropriate attachment necessary to solve this question.

The attachment was sourced online

Answer:

a) Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X

Step-by-step explanation:

From the above question, we are given two shapes: Cone W and Square Pyramid

Cone W: Radius = 8cm, Height = 5cm

Volume of a Cone = 1/3 πr²h

Where π = 3.14

Volume of Cone X = 1/3 × 3.14 × 8² × 5

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For Square pyramid X

Volume = 1/3 × Base Area × Height

Base Area of Cone W = Base Area of square pyramid X = πr²

Where π = 3.14

Base area = 3.14 × 8² = 200.96cm²

Height of Square pyramid X = Height of Cone W = 5cm

Volume of Square pyramid = 1/3 ×200.96cm² × 5cm

= 334.93cm³

Therefore, from my above calculation and compared with the arguments of Paul and Manuel, Option a) "Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X" is the correct option.

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Manuel on the other hand used the formula: Base Area × Height to find the volume of cone W. This formula is wrong.

Option a, is the correct answer.

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