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arlik [135]
3 years ago
6

How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?

Mathematics
1 answer:
Svet_ta [14]3 years ago
5 0

There are \dbinom{10}2 ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are \dbinom83 ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's \dbinom55=1 way of doing that.

So we have

\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520

The last expression has a more compact form in terms of the so-called multinomial coefficient,

\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520

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<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2
MrMuchimi

Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1)  + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

<em>angle 1 + 2*angle 1 + 6 = 180</em>

<em>3*angle 1 = 174</em>

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

<em>angle 2 + 58 = 180</em>

angle 2  = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

7 0
4 years ago
Please Hurry) What is the length of side AC of the triangle? □ units. ​
NARA [144]

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

\boxed{\mathrm{AC = 25 \:\: units ~}}

\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}

As we can see in the given figure, Angles A and B are equal. therefore their opposite sides will be equal to one another, that is ~

  • AB = BC

now, let's plug the values of AB and BC in terms of x and equate them to find the value of x ~

  • 5x + 5 = 7x - 1

  • 7x - 5x  = 5 + 1

  • 2x = 6

  • x = 6 \div 2

  • x = 3 \:  \: units

now , let's find the measure of side AC ~

  • AC = 6x + 7

that is ~

  • 6(3) + 7

  • 18 + 7

  • 25 \:  \: units

8 0
3 years ago
Please help :( : Solve the equation 3x + 5y = 15 for y
Gala2k [10]

Answer:

y = -3/5 x +3

Step-by-step explanation:

3x + 5y = 15

Subtract 3x from each side

-3x+3x + 5y = -3x+15

5y = -3x+15

Divide each side by 5

5y/5 = -3x/5 +15/5

y = -3/5 x +3

6 0
3 years ago
16a^2-4b^2 in factored form
Serga [27]

Answer:

16a^2 - 4b^2 = (4a + 2b)(4a - 2b)

6 0
3 years ago
A light bulb consumes 5400 watt-hours in 3 days and 18 hours. How many watt-hours does it consume per day?
dezoksy [38]

<u>We are given:</u>

Time period: 3 days and 18 hours

Energy consumed in given time period: 5400 watt-hours

<u>Converting time to hours:</u>

We know that one day is 24 hours

So, 3 days = 72 hours

Time period = 3 days + 18 hours

Time period = 72 hours + 18 hours      

Time period = 90 hours

Converting to days

Time period = 3.75 days

<u>Watt-hour consumption in a day:</u>

Consumption = 5400 watt-hours / 3.75 days

Consumption = 1440 watt-hours/day

8 0
3 years ago
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