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4 years ago

Which pair of fractions and mixed numbers have a common denominator of 20?

Mathematics

1 answer:

Tomtit [17]4 years ago

8 0

Answer:

D 3 3/4 and 7/10

Step-by-step explanation:

A) 2 3/8 and 3/4

4 goes into 20 evenly but 8 does not

B) 1 5/6 and 2/5

5 goes into 20 evenly but 6 does not

C) 4 1/3 and 1/4

4 goes into 20 evenly but 3 does not

D) 3 3/4 and 7/10

4 goes into 20 evenly and 10 goes into 20 evenly

YES 3 3/4 = 3 15/20 and 7/10 = 14/20

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Alenkasestr [34]

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3 years ago

Simplify 5 (3 1/5 +2 4/5−0.6)

never [62]

Step-by-step explanation:

l dont understand your question

is it 3 and a fifth or 31/5

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3 years ago

I need help on numbers 11-16

agasfer [191]

Recall your SOH CAH TOA, or $\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}$

now, bear in mind that, the opposite side, to an angle, is the side right "in front of it", that is, if you were to put your eye on that angle, "the wall" you'd see on the other end, is the opposite side

the adjacent side, adjacent = next to, is the side that's touching the angle itself

and the hypotenuse, is always the slanted and longest side of all three

for example on 16, tangent of Z

if you put one eye on Z, you'll see on the other end, the side of 30 units
the adjacent side is the one touching Z, or the 40 units side

$\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(Z)=\cfrac{30}{40}
\\\\\\
\textit{which can be simplified to }\cfrac{3}{4}
$

and you'd do all others, the same way, using those ratios

use $\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}$

8 0

3 years ago

What is the distance between (-6,8) and (-3,9)?

atroni [7]

Answer:

The answer is C.

Step-by-step explanation:

6 0

3 years ago

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>

5 0

3 years ago