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2 years ago

If y=2x+9 and y=6-x what is the solution?

Mathematics

1 answer:

motikmotik2 years ago

4 0

We have:

$\begin{cases}y=2x+9 \\y=-x+6 \\\end{cases}$

First multiply the second equation by 2 to get:

$\begin{cases}y=2x+9 \\2y=-2x+12 \\\end{cases}$

Then add the equations to eliminate the x-terms to get:

$3y=21\Longrightarrow y=7$

And finally use calculated y and plug it in one of the original equations to find x:

$7=6-x\Longrightarrow x=-1$

The solution is a point $P(-1,7)$ where lines $y=2x+9$ and $y=6-x$ intersect.

Hope this helps.

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Suppose X has an exponential distribution with mean equal to 23. Determine the following:

e-lub [12.9K]

Answer:

a) P(X > 10) = 0.6473

b) P(X > 20) = 0.4190

c) P(X < 30) = 0.7288

d) x = 68.87

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Mean equal to 23.

This means that $m = 23, \mu = \frac{1}{23} = 0.0435$

(a) P(X >10)

$P(X > 10) = e^{-0.0435*10} = 0.6473$

P(X > 10) = 0.6473

(b) P(X >20)

$P(X > 20) = e^{-0.0435*20} = 0.4190$

P(X > 20) = 0.4190

(c) P(X <30)

$P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288$

P(X < 30) = 0.7288

(d) Find the value of x such that P(X > x) = 0.05

$P(X > x) = e^{-\mu x}$

$0.05 = e^{-0.0435x}$

$\ln{e^{-0.0435x}} = \ln{0.05}$

$-0.0435x = \ln{0.05}$

$x = -\frac{\ln{0.05}}{0.0435}$

$x = 68.87$

5 0

3 years ago

The price of a stock increased 12 cent Monday morning. On Monday afternoon, the price of the stock decreased 56 cent. On Tuesday

jeyben [28]

Ok, were starting at when the stock increased first which is 12 cents on monday. to find your answer your going to need to add all of the increased cents first; then subtract.

12 + 14 = 26

So we have 26 cents, now we subtract the 56.

26 - 56 = -30

now we have -30. now we find out how far away on the number line it is from 12. your answer would be 42.

now for your answer, (i did all of that for other people who had the same question but different answer)

your answer would be 112 cents (which is option B)

6 0

3 years ago

How to solve 4-35+3.5-1

irga5000 [103]

Well make 3.5 into a whole number then add it together

4 0

2 years ago

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Write the equation for the circle with center (4, -2) and passes through the point (5, 3).

fgiga [73]

The answer should be (x-4)^2+(y+2)^2=radical 26

5 0

2 years ago

What is a Ratio mean?

dybincka [34]

Answer:

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6∶8 and the ratio of oranges to the total amount of fruit is 8∶14.

Step-by-step explanation:

the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

5 0

3 years ago