All categories

3 years ago

Help I’m not sure with this one!! Urgent help

Mathematics

1 answer:

Nastasia [14]3 years ago

8 0

This system has exactly one solution, because the two equation are linearly independent (i.e. one is not a multiple of the other).

We can explicitly find the solutions: from the first equation we deduce

$x = \dfrac{c-by}{a}$

Plug this value for x in the second equation:

$\dfrac{a}{3}\cdot \dfrac{c-by}{a}+\dfrac{by}{2}=\dfrac{c}{6} \iff \dfrac{c-by}{3}+\dfrac{by}{2}=\dfrac{c}{6} \iff \dfrac{2(c-by)+3by}{6}=\dfrac{c}{6}$

Multiply both sides by 6 to get

$2(c-by)+3by=c \iff 2c-2by+3by=c \iff by=-c \iff y=-\dfrac{c}{b}$

Plug this value for y in the expression for x:

$x = \dfrac{c-by}{a} = \dfrac{c-b\cdot\frac{-c}{b}}{a}=\dfrac{2c}{a}$

Since both a,b are not zero, both solutions are well defined.

You might be interested in

The time T required to repair a machine is an exponentially distributed random variable with mean 10 hours.

Firdavs [7]

It can be expected about 36.79% of chance that repair time exceeds

The probability that a repair time exceeds 15 hours is 0.3679

What is the exponential distribution?

It explains about the time between events or the distance between two random events is termed the exponential distribution. Here, the occurrence of the events is continuous and also independent. Moreover, the average rate is constant.

The cumulative distribution function of T is obtained below:

From the information given, let the random variable T be the required time to repair a machine follows exponential distribution with parameter λ
with mean. 1/2 hours

That is, E(x) = 1/2 hours.
The parameter of the random variable T is,
E(x) = 1/λ
λ = 1/E(x)
= 1/(1/2)
= 2

The probability density function of T is,
$f(t) = \left \{ {{2e^{-2t} \ \ \ t > 0} \ \atop {0} \ \ \ elsewhere} \ \right.$
The cumulative density function of T is,
FT(t) = P(T <= t)

$= 1 - e^{- \lambda t}$

$= 1 - e^{- 2t}$
The CDF of T is,
P(T <= t) $= 1 - e^{- 2t}$ 0 <= T <= ∞
= 0 otherwise
to obtain the probability that a repair time exceeds

1/2 hours.
(a) The probability that a repair time exceeds 1/2 hours.
From the given information, the CDF of T is,
P(T <= t) $= 1 - e^{- 2t}$ 0 <= T <= ∞
= 0 otherwise

The required probability is,
P(T <= 1/2) = 1 - P(T <= 1/2)
= 1 - [ $= 1 - e^{- 2(1/2)}$ ]
$= e^{-1}$
= 0.3679

om total probability. It can be expected about 36.79% of chance that repair time exceeds

P(X => x) = 1 - P(X < x)
to obtain the probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.

(b), The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained below:
From the given information, the CDF of T is,
P(T <= t) $= 1 - e^{- 2t}$ 0 <= T <= ∞
= 0 otherwise
The required probability is,
P = P(T => 12.5∩T>12) / P(T>12)
$= e^{- 25 + 24}$

$= e^{- 1}$
= 0.3679
The probability that a repair takes at least 12.5 hours given that its duration exceeds 12 hours is obtained by dividing the
P = P(T => 12.5∩T>12) / P(T>12)
with
P(T>12).

It can be expected about 36.79% of chance that a repair takes at least 12.5 hours given that its duration exceeds 12 hours.

Hence, It can be expected about 36.79% of chance that repair time exceeds,

The probability that a repair time exceeds 15 hours is 0.3679

To learn more about the product of the fraction visit,
brainly.com/question/22692312
#SPJ4

7 0

1 year ago

Which of the following sequences is arithmetic?

neonofarm [45]

Answer:
0, 3, 6, 9, 12 .....

Explanation:
An arithmetic sequence is defined as a sequence of numbers that increases or decreases by a constant value. 
The values are increasing when the same number is added or subtracted onto the number.
The rest of the choices do not have a constant number being added or subtracted they are either:
multiplied: option (D),
divided: option (C),
a list of perfect squares: option (B).

The answer (A) had the constant of 3 added to each term increasing forever.

6 0

3 years ago

Read 2 more answers

The standard form of the number 5, 976,000,000,000,000,000,000,000 is

nirvana33 [79]

Answer:

$5.976\times10^{24}$

Step-by-step explanation:

Standard form, also called scientific notation, is a more compact way of writing very big or very small numbers. All numbers in scientific notation have the form

$m\times10^b$

where m is a number between 1 and 10, and b is an integer that represents how we've shifted the decimal point from the original number. For example, the number 23,000 in standard form would be written as 2.3 × 10⁴, since we have to shift the decimal point 4 places to the right to get back our original number.

We can turn 5,976,000,000,000,000,000,000,000 into a number between 1 and 10 by shifting the decimal 24 places to the left, giving us 5.976. We'll save that 24 as the exponent for our 10, giving us the final form

$5.976\times10^{24}$

5 0

3 years ago

2. When you take a taxi, the driver charges an initial fee

Nostrana [21]

Answer:

The

mile cab ride includes a basic charge as well as the cost for the distance covered.

For a

mile trip, the cost is

4.80

which means that :

The cost of

miles is

4.80

−

3.00

1.80

Therefore the cost for

mile is

1.80

0.60

The basic fee for hiring the cab is

3.00

−

1.80

1.20

So the total cost,

for a trip of

miles will be:

0.6

1.2

Check:

0.6

(

)

1.2

0.6

(

)

1.2

4.8

Step-by-step explanation:

8 0

3 years ago

What is x on these triangles?

Elena-2011 [213]

Answer:

both of them have already been solved.

7 0

3 years ago