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3 years ago

Find the number of permutations that can be formed from all letters in the word connecticut

1 answer:

4 0

Connecticut as a permutation, 1 example would be c1,o,n1,n2,e,c2,t1,I,c3,u,t2. 10 items can form 10! permutations. Considering c1=c2=c3, n1=n2, t1=t2, let’s look at the c all equal condition: 3cs existing one in front of or behind another may form c1, c2, c3; c1, c3, c2; c2,c1,c3… totally 6 different ôkkkiojobvarieties

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John walks in the bearing of 75° and stops when he is 12 km North of his starting point.

AlladinOne [14]

75 something 12 km north is where he at

7 0

3 years ago

A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

scoray [572]

Answer:

a) $P(t) = 660 e^{\frac{ln(6)}{6} t}$

b) $P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

Step-by-step explanation:

For this case we have the following info:

$P(0) = 660$ represent the initial amount of bacteria

$P(6) = 3960$ represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

$\frac{dP}{dt}= kP$

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

$\frac{dP}{P} = k dt$

And if we integrate both sides we got:

$ln |P|= kt + C$

Now if we apply exponential we got:

$P = e^{kt +c}= e^{kt} e^C$

$P(t)= P_o e^{kt}$

For this case using the initial condition:

$660 = P_o e^{0k}, P_o = 660$

We have the following model:

$P(t) = 660 e^{kt}$

Using the second condition $P(6) = 3960$ we have this:

$3960 = 660e^{6k}$

We can divide both sides by 660 and we got:

$6= e^{6k}$

Now we can apply natural log on both sides and we got:

$ln (6)= 6k$

$k = \frac{ln(6)}{6}=0.2986265782$

So then the model would be given by:

$P(t) = 660 e^{\frac{ln(6)}{6} t}$

Part b

For this case we just need to replace t=3 into the model and we got:

$P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

4 0

3 years ago

Heidi has an average score of 78 for her first six chemistry tests. If Heidi"s scores for the first four tests were 82,78,87, an

elixir [45]

Answer:

(A)74

Explanation:

Let her average score on the last two tests = x.

The six scores will now be: 82,78,87,73, x and x.

Since the average score for her first six chemistry tests = 78

$\frac{82+78+87+73+x+x}{6}=78$

We then solve for x.

$\begin{gathered} 320+2x=78\times6 \\ 320+2x=468 \\ 2x=468-320 \\ 2x=148 \\ x=\frac{148}{2} \\ x=74 \end{gathered}$

Her average score for the last two tests is 74.

3 0

1 year ago

There are only 6 blue pens, 5 green pens and 8 red pens in a box.

Ronch [10]

Answer:

0.316

Step-by-step explanation:

Probability = (number of outcomes)/(total number of outcomes)

In this case,

the total number of outcomes is 6+5+8 = 19, and

the number of outcomes for getting a blue pen = 6

Hence,

P(blue) = 6/19 = 0.31578947368 ≈ 0.316

<em>Hope this helps and be sure to have a wonderful time ahead at Brainly! :D</em>

8 0

3 years ago

Would anyone like to help me

Sergeu [11.5K]

1st system: 2x = 14 <=> x = 7

2nd system: 2x = 4 <=> x = 2

5 0

3 years ago

Read 2 more answers