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3 years ago

A line passes through the point (0, 2) and has a slope of -1/4 What is the equation of the line?

Mathematics

1 answer:

maw [93]3 years ago

3 0

Answer:

The required equation is x + 4y = 8 !!

Step-by-step explanation:

Given :-  the line passes through the point ( 0 , 2 ) and the slope of the line is ( -1/4 )

• Also, to form an equation when a point through which line passes and slope of line is given we use the formula ;

( y - y1 ) = m ( x - x1 )

Where , y and x are variables

and ( x1 , y1 ) are the points through which line passes

also, m = slope of the required line

Here , x1 = 0 , y1 = 2 and m = ( -1/4 )

[ Refer to the attached file for further process ]

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Write an equation in point-slope form of the line that passes through the point 4,-1and has slope of -5

Basile [38]

Answer:

y=-5+19

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -5. So you can right away fill in the equation for a line somewhat to read:

y=-5x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,-1). When x of the line is 4, y of the line must be -1.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,-1).

So, why not plug in for x the number 4 and for y the number -1? This will allow us to solve for b for the particular line that passes through the point you gave!.

(4,-1). y=mx+b or -1=-5 × 4+b, or solving for b: b=-1-(-5)(4). b=19.

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2 years ago

A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute

nlexa [21]

Answer:

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

$P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}$

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

$P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301$

b. What is the probability of finding eight or more defective pens in a carton?

This can be calculated as one minus the probablity of having 7 or less defective pens.

$P(k\geq8)=1-P(k$

$P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\$

$P(k$

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.

$P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002$

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3 years ago

NEED HELP ASAP, WORTH 80PTS

sp2606 [1]

This is because the expression can be simplified to get the same result. -1+2log_4((1/4)x)

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2 years ago

Read 2 more answers