Which of the following describes the end behavior of the

The vertices of ABC are A(2, -3), B(-3,-5), and C(4,1). For each translation,

Snezhnost [94]

Answer:

all of ABOVW

Step-by-step explanation:

6 0

2 years ago

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$

Where $\mu=55$ and $\sigma=0.5$

We are interested on this probability

$P(X>55.4)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

And we can find this probability using the complement rule:

$P(Z>0.8)=1-P(Z\leq 0.8)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z>0.8)=1-0.788=0.212$

8 0

3 years ago

Is a function always a relation

ziro4ka [17]

Answer:

No, to be a function a relation must fulfill two requirements: existence and unicity.

Step-by-step explanation:

Existence is a condition that establish that every element of te domain set must be related with some element in the range. Example: if the domain of the function is formed by the elements (1,2,3), and the range is formed by the elements (10,11), the condition is not respected if the element "3" for example, is not linked with 10 or 11 (the two elements of the range set).
Unicity is a condition that establish that each element of the domain of a relation must be related with <u>only one</u> element of the range. Following the previous example, if the element "1" of the domain can be linked to both the elements of the range (10,11), the relation is not a function.

3 0

2 years ago

24x=3y solve for x and y

olga2289 [7]

$\ 24x=3y \\ \\ \ x=3 \ ; \ y=24$

4 0

3 years ago

How do I write 10^4 as a product of the same factor

mars1129 [50]

10x10x10x10, you have to multiply 10 by 10 four times, since it's 10 to the power of 4.

8 0

3 years ago