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3 years ago

9

John knows that his first 4 tests grades were 84, 79, 82, and 88. Find John's grade on the test if his average was 83.8.

1 answer:

iren2701 [21]3 years ago

7 0

Answer:

86

Step-by-step explanation:

The average is the sum of all the grades divided by the number of tests.

83.8 = (84 + 79 + 82 + 88 + x) / 5

419 = 333 + x

x = 86

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To find volume of a rectangular prism, you simply need to multiply length times width times height. We know from the text that our block of ice is 3 meters long, 1.5 meters wide, and 2 meters high. So all we need to do is multiply:

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4.5 * 2 = 9

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<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

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<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

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We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

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Therefore, on checking, we observe that,

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On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

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<u>At, </u>

<u>n = 2</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

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<u>At, </u>

<u>n = 3</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

<u>At, </u>

<u>n = 4</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

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