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leva [86]
2 years ago
15

I have 30 ones,82thousands,4 hundred thousands,60 tens,and 100 hundreds , what number am I?​

Mathematics
1 answer:
Anvisha [2.4K]2 years ago
8 0
You add all the numbers so it become 400,082,190

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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
2 years ago
Given the sequence rn defined recursively below, find r3. r1rn=2=−rn−1+n−2
kifflom [539]

Answer:

r_3=3

Step-by-step explanation:

Given:

r_1=2\\r_n=-r_{n-1}+n-2

We want to find the value of r_3 .

\\r_2=-r_{2-1}+2-2\\r_2=-r_1\\r_2=-2\\\\r_3=-r_{3-1}+3-2\\r_3=-r_{2}+1\\r_3=-(-2)+1\\r_3=2+1\\r_3=3

7 0
3 years ago
Marcus is selling lemonade and peanuts. Each cup of lemonade cost $0.75, and each bag of peanuts costs $0.35. On Saturday, Marcu
andreev551 [17]
Marcus sold 8 cups of lemonade and 3 bags of peanuts. 0.75 times 8 equals $6.00. 0.35 times 3 equals $1.05. $6.00+ $1.05= $7.05. Your welcome dude

7 0
2 years ago
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still w
prohojiy [21]

Step-by-step explanation:

Given that,

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,

We know that,

Speed = distance/time

The rate while moving downstream=\dfrac{60}{3}=20\ mph

The rate while moving upstream =\dfrac{60}{5}=12\ mph

The rate of the boat in still water is the average of these:

v_s=\dfrac{20+12}{2}=16\ mph

The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph

Hence, this is the required solution.

7 0
2 years ago
What is the parallel slope intercept form pls answerr​
lys-0071 [83]

Answer:

the paralell slope is -4. The slope intercept equation is -4x-4

Step-by-step explanation:

hope this helps!

7 0
2 years ago
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