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2 years ago

What is the equation of the line that passes through the points (5,3) and (9,-13)?

Mathematics

1 answer:

vekshin12 years ago

6 0

The equation of the line that passes through the given points is y= -4x+23.

<h3>Linear Function</h3>

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

From the stardard form equation:

For point (5,3) : 3=5a+b ( equation 1)
For point (9,-13) : -13=9a+b (equation 2)

Solving the system for equations 1 and 2.

3=5a+b

-13=9a+b * (-1)

3=5a+b

13=-9a-b * (-1)

16= -4a

4= -a

a= -4

If a= -4 from equation 1, you have

3= 5 * (-4)+b

3= -20+b

b=23

Therefore, the line equation is y= -4x+23.

Read more about the system linear equations here:

brainly.com/question/12691830

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Lannister checks out 6 set of books from the library each set has the same number of books she reads 7 of the books and she has

fgiga [73]

Answer:

Step-by-step explanation:

Lannister checks out 6 sets of book

Each set had the same number of books

She reads 7 books and has 11 more to go

Therefore the number of books in each set can be calculated as follows

= 11+7

= 18

18/6

= 3

Hence there are 3 books in each set

6 0

3 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.

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

5 0

3 years ago

What is the area of the square?<br> 2 m<br> square meters

Mariulka [41]

Answer:

Step-by-step explanation:

the ratio to find a square’s area is <em>side length</em> times <em>side length</em>, i.e.

sl * sl = a

2m * 2m = 4m

hope this helps!

5 0

2 years ago

Read 2 more answers

The ratio of boys to girls in WIN is 2:3. If there are 8 boys how many girls are there

IRISSAK [1]

If there is 8 boys then there is 12 girls because 2x4=8 boys so 3x4=12 girls.

4 0

3 years ago

F(x)= 9-x^2, x ≥ 0. f^-1(x)=??

julia-pushkina [17]

$y=9-x^{2},\ x\ge0$

Reverse $x$ and $y$ :
$x=9-y^{2},\ y\ge0$
Solve for $y$ :
$x=9-y^{2}$
$\rightarrow y^{2}=9-x$
$\rightarrow y=\sqrt{9-x}$ since $y\ge0$

7 0

3 years ago