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3 years ago

Reduce 27/42 to the lowest term

Mathematics

2 answers:

Pani-rosa [81]3 years ago

8 0

9/14 would be the lowest possible answer if you want it in decimal form it is 0.64285714

wel3 years ago

5 0

So you need to find a number that goes into both of these numbers:
3 goes into both, so divide both by 3
27/3 = 9
42/3 = 14
so your answer is 9/14

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Austin is watching a football game. His team loses 9 yards and then gains 5 yards. He doesn’t watch the next play, but afterward

katrin [286]

The team gained 3 yards on the play audition missed

7 0

3 years ago

Please help very urgent

Alik [6]

Answer:

32, 16, 8, 4, 2, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

Read 2 more answers

to fill a coffee mug at a local shop costs $2.50. the shop sells coffee beans foe $12 per pound. each pound makes enough coffee

myrzilka [38]

Answer:

There are a few possible answers so read explanation, but the one I will put up here is:

20.83

Step-by-step explanation:

First you have to find how much 100 cups of coffee costs in store.

To do this you will multiply 2.50 by 100 and get 250. So now we know 100 cups of coffee in store costs $250 whereas 100 cups at home is $12.

To find how many times greater the price in store is compared to the at home brew, you have to divide 250 by 12 and get 20.8333333....

We don't stop there though, because it asks us to approximate. I am not sure what it would like us to round to, but here are some possible approximations:

20.83
20.8
21

Any of those re reasonable approximations, you choose whichever you think the question wants, or whatever your teacher asks for.

Hope this helps

3 0

3 years ago

Your bag of rice says to mix 1 cup of rice with 2 cups of water. dela requ prov a. What is the ratio of rice to water? refer to

EastWind [94]

Answer:

(a) 1:2

(b) 6 cups

Step-by-step explanation:

(a) Given,

amount of rice mixture contains= 1 cup

amount of water mixture contains= 2 cups

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=\ \dfrac{1}{2}$

So, the ratio of rice to water is 1:2.

(b) Amount of rice in mixture = 3 cups

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=>\ \dfrac{1}{2}\ =\ \dfrac{3}{\textrm{amount of water in mixture}}$

=> amount of water in mixture = 3 x 2

= 6 cups

(c) $\textrm{amount of rice in mixture}\ =\dfrac{1}{3}$

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=>\ \dfrac{1}{2}\ =\ \dfrac{\dfrac{1}{3}}{\textrm{amount of water in mixture}}$

$=>\textrm{amount of water in mixture}\ =\ \dfrac{2}{3}$

So, the amount of water in the mixture will be $\dfrac{2}{3}$ cup.

7 0

3 years ago

Tough one!

frosja888 [35]

Imx->0 (asin2x + b log(cosx))/x4 = 1/2 [0/0 form] ,applying L'Hospital rule ,we get

= > limx->0 (2a*sinx*cosx - (b /cosx)*sinx)/ 4x3 = 1/2 => limx->0 (a*sin2x - b*tanx)/ 4x3 = 1/2 [0/0 form],

applying L'Hospital rule again ,we get,

= > limx->0 (2a*cos2x - b*sec2x) / 12x2 = 1/2

For above limit to exist,Numerator must be zero so that we get [0/0 form] & we can further proceed.

Hence 2a - b =0 => 2a = b ------(A)

limx->0 (b*cos2x - b*sec2x) / 12x2 = 1/2 [0/0 form], applying L'Hospital rule again ,we get,

= > limx->0 b*(-2sin2x - 2secx*secx.tanx) / 24x = 1/2 => limx->0 2b*[-sin2x - (1+tan2x)tanx] / 24x = 1/2

[0/0 form], applying L'Hospital rule again ,we get,

limx->0 2b*[-2cos2x - (sec2x+3tan2x*sec2x)] / 24 = 1/2 = > 2b[-2 -1] / 24 = 1/2 => -6b/24 = 1/2 => b = -2

from (A), we have , 2a = b => 2a = -2 => a = -1

Hence a =-1 & b = -2

7 0

3 years ago