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3241004551 [841]
3 years ago
6

4.5x – 2y = 15 3x - y =10 (answer as a combined pair)

Mathematics
1 answer:
prisoha [69]3 years ago
7 0

Answer:

x = 10/3 , y = 0

Step-by-step explanation:

Solve the following system:

{4.5 x - 2 y = 15

3 x - y = 10

In the first equation, look to solve for x:

{4.5 x - 2 y = 15

3 x - y = 10

4.5 x - 2 y = (9 x)/2 - 2 y:

(9 x)/2 - 2 y = 15

Add 2 y to both sides:

{(9 x)/2 = 2 y + 15

3 x - y = 10

Multiply both sides by 2/9:

{x = (4 y)/9 + 10/3

3 x - y = 10

Substitute x = (4 y)/9 + 10/3 into the second equation:

{x = (4 y)/9 + 10/3

3 ((4 y)/9 + 10/3) - y = 10

3 ((4 y)/9 + 10/3) - y = ((4 y)/3 + 10) - y = y/3 + 10:

{x = (4 y)/9 + 10/3

y/3 + 10 = 10

In the second equation, look to solve for y:

{x = (4 y)/9 + 10/3

y/3 + 10 = 10

Subtract 10 from both sides:

{x = (4 y)/9 + 10/3

y/3 = 0

Multiply both sides by 3:

{x = (4 y)/9 + 10/3

y = 0

Substitute y = 0 into the first equation:

Answer:  {x = 10/3 , y = 0

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3 years ago
A colony of bacteria triples in link every 10 minutes. It's length is now 1 mm. How long will be in 40 minutes
Nuetrik [128]
If the bacteria is tripling every 10 minutes, that means the "rate of increase" on that period is 200%, so if say the current amount is "c", 200% of "c" is just 2c, so c + 2c is 3c, a tripled amount.

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A=I(1 + r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
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6 0
3 years ago
The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the oth
Gala2k [10]

Answer:

(a) There are 70 different ways set up 4 computers out of 8.

(b) The probability that exactly three of the selected computers are desktops is 0.305.

(c) The probability that at least three of the selected computers are desktops is 0.401.

Step-by-step explanation:

Of the 9 new computers 4 are laptops and 5 are desktop.

Let X = a laptop is selected and Y = a desktop is selected.

The probability of selecting a laptop is = P(Laptop) = p_{X} = \frac{4}{9}

The probability of selecting a desktop is = P(Desktop) = p_{Y} = \frac{5}{9}

Then both X and Y follows Binomial distribution.

X\sim Bin(9, \frac{4}{9})\\ Y\sim Bin(9, \frac{5}{9})

The probability function of a binomial distribution is:

P(U=k)={n\choose k}\times(p)^{k}\times (1-p)^{n-k}

(a)

Combination is used to determine the number of ways to select <em>k</em> objects from <em>n</em> distinct objects without replacement.

It is denotes as: {n\choose k}=\frac{n!}{k!(n-k)!}

In this case 4 computers are to selected of 8 to be set up. Since there cannot be replacement, i.e. we cannot set up one computer twice or thrice, use combinations to determine the number of ways to set up 4 computers of 8.

The number of ways to set up 4 computers of 8 is:

{8\choose 4}=\frac{8!}{4!(8-4)!}\\=\frac{8!}{4!\times 4!} \\=70

Thus, there are 70 different ways set up 4 computers out of 8.

(b)

It is provided that 4 computers are randomly selected.

Compute the probability that exactly 3 of the 4 computers selected are desktops as follows:

P(Y=3)={4\choose 3}\times(\frac{5}{9})^{3}\times (1-\frac{5}{9})^{4-3}\\=4\times\frac{125}{729}\times\frac{4}{9}\\  =0.304832\\\approx0.305

Thus, the probability that exactly three of the selected computers are desktops is 0.305.

(c)

Compute the probability that of the 4 computers selected at least 3 are desktops as follows:

P(Y\geq 3)=1-P(Y

Thus, the probability that at least three of the selected computers are desktops is 0.401.

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3 years ago
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Ilia_Sergeevich [38]

Answer:

No conclusion

Step-by-step explanation:

The two patterns have no relationship

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This is for the one with the green background :) I corrected a few of the errors that collided with the answers for the 3 qns you didn’t know. Hope this helps!!!

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