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Paul [167]
3 years ago
6

Abc2 at a = 4, b = 1/4, c = 5

Mathematics
1 answer:
Aloiza [94]3 years ago
8 0

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> attached</em><em> </em><em>picture</em>

<em>Hope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>be</em><em> </em><em>helpful</em><em> </em><em>to</em><em> </em><em>you</em><em>.</em><em>.</em><em>.</em>

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stiks02 [169]
Cringe to fingernails on a chalkboard
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Read 2 more answers
7) PG &amp; 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
2 years ago
?In the table below, y is a linear function of x.X-214710y09182736What is the y intercept of the function
Aleonysh [2.5K]

y intercept : (0,6)

Explanation:

Use the formula:

. y = mx + b

Find m (the slope), using 2 random points of the graph: (-2,0) and (1,9)

. m = (y-y1) / (x-x1)

m = (0-9) / (-2-1)

m = -9 / -3

m = 3

Replace m in the equation:

. y = 3x + b

Find b by replacing y and x by a random point of the graph: (1,9)

. 9 = 3*1 + b

b = 9 - 3

b = 6

Replace b in the equation:

. y = 3x +6

To find the y-intercept replace x by 0 in the equation:

. y = 3*0 +6

y = 0+6

y = 6

=> y-intercept : (0,6)

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Midge added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week. The table below shows the
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Answer:

f(n) = 16(0.5)ⁿ⁻¹

Step-by-step explanation:

Find f(1) for each option.

a) f(1) = 16(0.5)¹⁻¹ = 16

b) f(1) = 32(0.5)¹⁻¹ = 32

c) f(1) = 16(0.5)¹ = 8

d) f(1) = 32(0.5)¹⁺¹ = 8

Only the first option matches the table.

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