All categories

3 years ago

20 points!!!

Mathematics

1 answer:

OverLord2011 [107]3 years ago

8 0

Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - $y_{1}$ = m ( x - $x_{1}$ ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - $y_{1}$ = m ( x - $x_{1}$ )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

You might be interested in

Here is a formula for the amount of water needed to cook rice. w = 1.5r + 0.5 w is the number of cups of water needed r is the n

Degger [83]

Answer:

Step-by-step explanation:

19 cups of rice

8 0

3 years ago

A rectangle is 3 times as long as it is wide. If the length is increased by 6 and the width is increased by 8, its area is incre

Butoxors [25]

Answer:

Length = 6, Breadth = 2

Step-by-step explanation:

Given:

A rectangle is 3 times as long as it is wide.

If the length is increased by 6 and the width is increased by 8, its area is increased by 108.

Question asked:

Find the original dimensions.

Solution:

Let width of rectangle = $x$

As given that a rectangle is 3 times as long as it is wide.

Length of rectangle = $3x$

$Area\ of\ rectangle=length\times breadth$

$=x\times3x=3x^{2}$

Now, as given that length is increased by 6 and the width is increased by 8,

New length = $3x+6$

New breadth = $x+8$

New area = $(3x+6)(x+8)$

$=3x(x+8)+6(x+8)\\\\=3x^{2} +24x+6x+48\\=3x^{2} +30x+48$

As new area increased by 108, we can say:-

New area - old area = 108

$3x^{2} +30x+48-(3x^{2} )=108\\3x^{2} +30x+48-3x^{2} =108\\\\30x+48=108\\$

Subtracting both sides by 48

$30x+48-48=108-48\\30x=60$

Dividing both sides by 30

$x=2$

Width of rectangle = $x$ = 2

Length of rectangle = $3x$ = $3\times2=6$

Therefore, original length of rectangle was 6 and original width of rectangle was 2.

3 0

4 years ago

Twenty-five percent of the customers entering a grocery store between 5 P.M. and 7 P.M. use an express checkout. Consider five r

diamong [38]

Answer:

a) $P(X=1)=(5C1)(0.25)^1 (1-0.25)^{5-1}=0.39551$

b) $P(X \leq 1) = P(X=0) +P(X=1)=0.23730+0.39551 =0.63281$

c) $P(X \geq 2) = 1-P(X$

And for this case we can use the result from part b

$P(X \geq 2) = 1-P(X$

d) $P(X \neq 1)$ since the random variable just takes values between 0 and 5 we can use the complement rule like this:

$P(X \neq 1) = 1-P(X=1)= 1-0.39551=0.60449$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$