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3 years ago

What is the ratio 18 to 27 written as a fraction in lowest terms?

Mathematics

2 answers:

Rina8888 [55]3 years ago

8 0

Answer:

6/9

Step-by-step explanation:

NNADVOKAT [17]3 years ago

8 0

Answer:

The answer is B: 2/3

Step-by-step explanation:

Since both number 18 and number 27 are divisible by 9, 18 divided by 9 is 2, and 27 divided by 9 is 3 which will give you the answer of 2 and 3. So 18/27 in its lowest term is 2/3.

Hope this helps :))

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A( 3tx – 2b) = c(dx - 2)

olganol [36]

Answer:

A3tx-A2b=cdx-2c

Step-by-step explanation:

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2 years ago

Which decimal is equivalent to 8.100

larisa86 [58]

Answer:

81/10

Step-by-step explanation:

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2 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

3 years ago

Simplify the expression by combining like terms. 16+8−3+6−9

lyudmila [28]

Answer=18
First step combine the positive like terms
16+8+6
|
|
\/
30
Second step is to combine negative like terms with 30
30-3-9

When you do this you add 9 and 3 together since they are similar to each other so it equals 12 there for the equation becomes.....
30-12

Final answer 18

4 0

2 years ago

Write a word problem that can be described by the division expression 3÷1/4. Use complete sentences in your answer

AURORKA [14]

The question is simply asking us to create a word problem.
The word problem describing the division expression 3÷1/4 will be:
Given that Annie has 3 oranges and he wants to each orange into quarters, how many quarters will Annie have in total?

4 0

2 years ago

Read 2 more answers