Find the lowest common multiple of 35 and 55

Find the equations of the following lines

White raven [17]

You need these two basic solutions and facts to find the equation of a line:

If you know the gradient $m$ and one point $(x_0,y_0)$ :

$y-y_0=m(x-x_0)$

If you know the gradient two points $(x_1,y_1),\ (x_2,y_2)$ :

$\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}$

The slope of a line is the coefficient m when you write it in the $y=mx+q$ form
Parallel lines have the same slope
The slopes of perpendicular lines give -1 when multiplied

We can use this list to solve all the exercises:

b)

Use the first equation to get

$y-1=-4(x-2) \iff y=-4x+9$

c)

Use the second equation to get

$\dfrac{x-4}{2-4}=\dfrac{y-2}{-1-2} \iff \dfrac{x-4}{-2}=\dfrac{y-2}{-3}\iff 3(x-4)=2(y-2) \iff 3x-12=2y-4 \iff 2y = 3x-8 \iff y = \frac{3}{2}x-4$

d) same as c)

e) We derive the slope of the line by writing it as

$5y = -x-15 \iff y = -\dfrac{1}{5}x-3$

So, the slope is -1/5. From here, it's the same as b)

f) same as e)

g) Again we find the slope as

$3x+y+2=0\iff y=-3x-2$

so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).

6 0

4 years ago

What is the Expected value of the probability distribution also called?

Fittoniya [83]

Answer:

The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment.

8 0

3 years ago

What is the answer to 8

sergejj [24]

Your paper is not full

8 0

3 years ago

A woman is looking for a biker square office. She finds at office twice the area of her current office. If the perimeter of her

MatroZZZ [7]

Answer:

968

Step-by-step explanation:

Current office length = 22

22 * 22 = 484

484 * 2 = 968

8 0

3 years ago

Read 2 more answers

An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of

ANEK [815]

Answer:

(a) 0.152

(b) 0.789

(c) 0.906

Step-by-step explanation:

Let's denote the events as follows:

F = The word free occurs in an email

S = The email is spam

V = The email is valid.

The information provided to us are:

The probability of the word free occurring in a spam message is, $P(F|S)=0.60$
The probability of the word free occurring in a valid message is, $P(F|V)=0.04$
The probability of spam messages is,

$P(S)=0.20$

First let's compute the probability of valid messages:

$P (V) = 1 - P(S)\\=1-0.20\\=0.80$

(a)

To compute the probability of messages that contains the word free use the rule of total probability.

The rule of total probability is:

$P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The probability that a message contains the word free is:

$P(F)=P(F|S)P(S)+P(F|V)P(V)\\=(0.60*0.20)+(0.04*0.80)\\=0.152\\$

The probability of a message containing the word free is 0.152

(b)

To compute the probability of messages that are spam given that they contain the word free use the Bayes' Theorem.

The Bayes' theorem is used to determine the probability of an event based on the fact that another event has already occurred. That is,

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

The probability that a message is spam provided that it contains free is:

$P(S|F)=\frac{P(F|S)P(S)}{P(F)}\\=\frac{0.60*0.20}{0.152} \\=0.78947\\$

The probability that a message is spam provided that it contains free is approximately 0.789.

(c)

To compute the probability of messages that are valid given that they do not contain the word free use the Bayes' Theorem. That is,

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

The probability that a message is valid provided that it does not contain free is:

$P(V|F^{c})=\frac{P(F^{c}|V)P(V)}{P(F^{c})} \\=\frac{(1-P(F|V))P(V)}{1-P(F)}\\=\frac{(1-0.04)*0.80}{1-0.152} \\=0.90566$

The probability that a message is valid provided that it does not contain free is approximately 0.906.

4 0

4 years ago