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3 years ago

Through: (-5, -5), slope=2/5

Mathematics

1 answer:

kakasveta [241]3 years ago

4 0

For this case we have that by definition, the equation of a line in the slope-intersection form is:

$y = mx + b$

Where:

m: It is the slope

b: It is the cut point with the y axis

The slope is: $m = \frac {2} {5}$

Thus, the equation is of the form:

$y = \frac {2} {5} x + b$

We substitute the given point and find "b":

$-5 = \frac {2} {5} (- 5) + b\\-5 = -2 + b\\-5 + 2 = b\\b = -3$

Finally, the equation is:

$y = \frac {2} {5} x-3$

Answer:

$y = \frac {2} {5} x-3$

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A questionnaire asks shareholders of a company to state whether they consider the

Oduvanchick [21]

Using the binomial distribution, it is found that the probabilities are given as follows:

a) 0.5514 = 55.14%.

b) 0.3631 = 36.31%.

c) 0.4082 = 40.82%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

Item a:

In this problem, we have p = 0.82, n = 3, and the probability is P(X = 3), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.82)^{3}.(0.18)^{0} = 0.5514$

Item b:

In this problem, we have p = 0.82, n = 3, and the probability is P(X = 2), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.82)^{2}.(0.18)^{1} = 0.3631$

Item c:

We have to find P(X = 2) for the three probabilities, p = 0.82, p = 0.12, p = 0.05 and add them, hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.82)^{2}.(0.18)^{1} = 0.3631$

$P(X = 2) = C_{3,2}.(0.12)^{2}.(0.88)^{1} = 0.0380$

$P(X = 2) = C_{3,2}.(0.05)^{2}.(0.95)^{1} = 0.0071$

Then:

p = 0.3631 + 0.0380 + 0.0071 = 0.4082.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

7 0

2 years ago

What is the median of 5,2,9,21,12,3

horsena [70]

Answer: 7

Step-by-step explanation:

First order the numbers by least to greatest

2, 3, 5, 9, 12, 21

Then find the number inbetween

In this case it's a tie between 5 and 9.

Find the average of those two numbers

The average is 5+9/2 = 7

Median is 7

6 0

3 years ago

Elimination 7x+2y = 24 (6,-9)

erastovalidia [21]

Answer:

7x + 2y = 24 8x + 2y = 30. Subtract -x = -6 x = 6. Substitute x = 6 into 7x + 2y = 24 7(6)+ 2y = 24 42 + 2y = 24 2y = 24 - 42 2y = -18 y = -9 {6,-9} ...

Step-by-step explanation:

4 0

3 years ago

A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re

bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force $F$ and the distance $d$ that the object moves:

$W=Fd$

If $F$ is measured in newtons and $d$ <em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

$W=\int\limits^b_a {f(x)} \, dx$

Hooke’s Law states that the force required to maintain a spring stretched $x$ units beyond its natural length is proportional to

$f(x)=kx$

where $k$ is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

$4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1$

Thus $F=x$

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

$W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18$

18 J is the work required to stretch a spring from 7 m to 13 m.

5 0

3 years ago

A sample of an unknown liquid has a volume of 24.0 mL and a mass of 6 g. What is its density?

Furkat [3]

Answer:

Hey there!

Density = Mass/Volume

Mass= 6g

Volume=24 mL, which is 24 cm^3

Density= 6g/24 cm^3

Density=0.25 g/cm^3

Let me know if this helps :)

5 0

3 years ago

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