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Alja [10]
2 years ago
9

The following statement is false. Rewrite the statement to make it true.

Mathematics
1 answer:
Ksju [112]2 years ago
6 0

we are given

\sum _{n=0}^55n\:

we can see that

n starts from 0 and goes to 5

so, there are 6 terms

that's why this statement is false

so, true statement can be written as

The are six terms in the series equation.........Answer

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nata0808 [166]
14^2 is the same as saying 14x14
=196
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Find the number of ways of arranging the numbers
Doss [256]

First of all, note that all integers are either 0,1, or 2 modulo 3 (if you're not familiar with this terminology, it means that every integer is either a multiple of 3, or it is 1 or 2 away from a multiple of 3).

So, we can think of our numbers as

\begin{array}{c|c}x&x\mod 3\\0&0\\1&1\\2&2\\3&0\\4&1\\5&2\\6&0\\7&1\\8&2\\9&0\end{array}

In order to make sure that the sum of any three adjacent numbers is divisible by 3, we have to make sure that any group of 3 three adjacent numbers contains a 0, a 1 and a 2. This is possible only if we arrange our 9 numbers in 3 groups of 3 numbers containing 0,1 and 2 exactly once, repeating always the same pattern.

For example, we could arrange our numbers following the pattern

0,1,2,0,1,2,0,1,2

or

2,0,1,2,0,1,2,0,1

We have 3!=6 possible patterns. Suppose for example that we choose the pattern

0,1,2,0,1,2,0,1,2

One possible way of following this pattern would be the arrangement

3,1,2,6,4,5,9,7,8

In fact, we substituted every '0' with a multiple of 3 (3, 6 or 9), every '1' with a number 1 away from a multiple of 3 (1, 4 or 7) and every '2' with a number 2 away from a multiple of 3 (2, 5 or 8).

This means that, once we fix a patter, we have 3 choices for the first 3 slots, 2 choices for the next 3 slots, and the final slot will be fixed. So, we have

3\cdot 3\cdot 3\cdot 2 \cdot 2 \cdot 2 = 216

possible ways of following a fixed pattern. Since the number of patterns was 6, we have

216\cdot 6 = 1296

possible arrangements.

7 0
3 years ago
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Ok. First you have to find the unit rate. Since you can buy 9 packages of grapes for $24, then you can get 1 grape package for $2.6667. If you have $8, you can buy 3 packages of grapes.
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Please help me on this question
AleksandrR [38]

Answer:

The area can be expressed as: \pi r^2+lw.

We have l=10, because 18-2(4)

We have w=8, as given.

Thus, the rectangle area is 80.

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7 0
3 years ago
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One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 183.0 milligrams of vitamin C.
uysha [10]

Answer:

Apple juice there are 95.9 mg

Orange juice there are 87.1 mg

Step-by-step explanation:

We can get a system of equations from the statement.

Let x be the amount of vitamin C in apple juice

Let y be the amount of vitamin C in orange juice

Now, with the statement we have to:

x + y = 183 (1)

2 * x + 3 * y = 453.1 (2)

We have an equation system, of 2 equations with 2 unknowns, that is, it has a solution.

If we multiply the first equation by 2 and subtract the second equation, we are left with:

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Solving

y = 453.1 - 366

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Now to calculate x:

x + y = 183

x + 87.1 = 183

x = 183 - 87.1

x = 95.9

To check:

https://es.symbolab.com/solver/step-by-step/x%20%2B%20y%20%3D%20183%3B%202%5Ccdot%20x%20%2B%203%5Ccdot%20y%20%3D%20453.1

Therefore in apple juice there are 95.9 milligrams of vitamin C and in orange juice there are 87.1 milligrams.

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3 years ago
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