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3 years ago

Daniel hiked 4 5/8 miles on Saturday and 4 1/2 miles on Sunday. How many miles did he hike in all?

Mathematics

1 answer:

Ivenika [448]3 years ago

7 0

Answer:

He hiked 9 1/8 miles

Step-by-step explanation:

First make the fractions like terms

Multiply 4 1/2 by 4/4 to get 4 4/8

Then add the fractions to get 9/8

9/8 is an improper fraction, make it 1 1/8

then add all the whole numbers 4+4+1=9

add the fraction 1/8 to 9= 9 1/8

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How many grams are 2.7x10-^4 grams

andrew-mc [135]

Answer:

0,00027 grams!

Step-by-step explanation:

This is a scientific notation problem.

When a number is followed by a $10^{-1}$ , it means that said number has one zero at the beginning.

In this case, the number is followed by $10^{-4}$ , so that means that 2.7 has four zeros at the beginning. So, 2.7x $10^{-4}$ grams is equal to 0,00027 grams! (always the comma goes after the first zero).

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4 years ago

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3 years ago

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

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

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

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

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

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

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

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

At,

n = 1

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

which is true.

At,

n = 2

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

Which is also true.

At,

n = 3

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

Which is true.

At,

n = 4

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

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

Therefore, the recursive equation for the pattern followed is given by,

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

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