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2 years ago

Equation of plane ( Cartesian form ) ~

Mathematics

1 answer:

eimsori [14]2 years ago

6 0

The equation for the cartesian form of representation of a plane is given by ax + by + cz = d.

<h3>What is the cartesian form?</h3>

The cartesian form is a mathematical model which is used for the graphical representation of either a point, line, or plane in a two-dimensional (2D) or three-dimensional (3D) plane.

Mathematically, the cartesian form of representation of a plane is given by this equation:

ax + by + cz = d.

<u>Where:</u>

a, b, c are the direction on each axis.

d is the distance from the origin.

Read more on cartesian form here: brainly.com/question/13147873

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An oil drilling company ventures into various locations, and its success or failure is independent from one location to another.

densk [106]

Answer:

a) 18.77% probability that the driller drills at 10 locations and has 1 success

b) 75.60% probability that the driller drills at 10 locations and has at least 2 success

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a success, or it is not. The probability of a drill being a success is independent of other drills. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

10 locations

This means that $n = 10$

Suppose the probability of a success at any specific location is 0.25.

This means that $p = 0.25$

(a) What is the probability that the driller drills at 10 locations and has 1 success?

This is P(X = 1).

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

$P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877$

18.77% probability that the driller drills at 10 locations and has 1 success

(b) What is the probability that the driller drills at 10 locations and has at least 2 success?

Either there are less than 2 success, or there are at least 2. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$

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

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{10,0}.(0.25)^{0}.(0.75)^{10} = 0.0563$

$P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0563 + 0.1877 = 0.2440$

$P(X < 2) = P(X = 0) + P(X = 1) = 1 - 0.244 = 0.756$

75.60% probability that the driller drills at 10 locations and has at least 2 success

8 0

3 years ago

3. A solid sphere of radius 3 cm is melted and then recast into small spherical balls, each of

Viefleur [7K]

Answer:

3.6

Step-by-step explanation:

6 0

3 years ago

a maxicool consists of a cone full of ice cream with a hemisphere of ice cream on top. the radius of a hemisphere is 3cm. The he

Gemiola [76]

According to the information, it can be inferred that the volume of the ice cream is close to 207.33 cm³

<h3>How to calculate the volume of the maxicool?</h3>

To calculate the volume of the maxicool, we must calculate the volume of the sphere of ice cream, and the volume of the cone that is filled with ice cream.

<h3>Volumen of the sphere</h3>

V = $\frac{4}{3}$ × π × R³

V = $\frac{4}{3}$ × π × 3³

V = 113.09 cm³

<h3>Cone volume</h3>

V = $\frac{1}{3}$ × π × R² × <em>h</em>

V = $\frac{1}{3}$ × π × 3² × 10

V= 94.24 cm³

Finally we must add both values to know the total volume of the maxicool.

113.09 + 94.24 = 207.33 cm³

Learn more about volume in: brainly.com/question/13338592

5 0

3 years ago

In an article about the cost of health care, USA Today reported that a visit to a hospital emergency room has a mean cost of $14

Misha Larkins [42]

Answer: 0.8461

Step-by-step explanation:

Given : $\mu=144\ \ ; \sigma=392$

Let x be the random variable that represents the cost for the hospital emergency room visit.

We assume that cost for the hospital emergency room visit is normally distributed .

z-score for x=1000 ,

$z=\dfrac{1000-1400}{392}\approx-1.02\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]$

Using z-value table , we have

P-value =P(x>1000)=P(z>-1.02)=1-P(z≤ -1.02)=1-0.1538642

=0.8461358≈0.8461 [Rounded nearest 4 decimal places]

Hence, the probability that the cost will be more than $1000 = 0.8461

3 0

3 years ago

A paper company produces 3,580 notebooks in 4 days. How many notebooks can it produce in 12 days?

RoseWind [281]

10,740

Step-by-step explanation:

multiply by 3, because 4 x 3 equals 12, so that infers 3580 x 3, which equals 10,740

7 0

3 years ago

Read 2 more answers

Equation of plane ( Cartesian form ) ~ ​

Equation of plane ( Cartesian form ) ~