Triangle ABC is reflected across the line y = x. What are the coordinates of the vertex B' of the resulting triangle A'B'C?

Mathematics

1 answer:

Ganezh [65]3 years ago

6 0

Answer:

B' (2, - 5 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

B (- 5, 2 ) → B' (2, - 5 )

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in one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean

VARVARA [1.3K]

Answer:

$a=1050 -0.126*218=1022.53$

So the value of height that separates the bottom 45% of data from the top 55% is 1022.53.

Step-by-step explanation:

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 energy consumption of a population, and for this case we know the distribution for X is given by:

$X \sim N(1050,218)$

Where $\mu=1050$ and $\sigma=218$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.55$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.126. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55

If we use condition (b) from previous we have this:

$P(X$