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3 years ago

Point P'(-3, 2) is the image of point P(3, 8) under a translation. What is the image of (0, -6) under the

Mathematics

1 answer:

Goshia [24]3 years ago

5 0

Answer:

The image of the point (0, -6) under the same translation is (-6, -12)

Step-by-step explanation:

Let us revise the rules of translation

If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)

If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)

If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)

If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

∵ The coordinate of point P are (3, 8)

∵ The coordinates of its image P' are (-3, 2)

→ The x-coordinate is changed from 3 to -3, that means the point

translated to the left by h units

∵ h = -3 - 3

∴ h = -6

→ The y-coordinate is changed from 8 to 2, that means the point

translated down by k units

∵ k = 2 - 8

∴ k = -6

→ By using the rule above

∴ The rule of translation is (x, y) → (x - 6, y - 6)

∵ The coordinates of the point are (0, -6)

∴ The coordinates of its image are (0 - 6, -6 - 6)

∴ The coordinates of its image are (-6, -12)

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Step-by-step explanation:

Given -

Mean $(\nu )$ = 4

Standard deviation $(\sigma )$ = 1.5

Let X be the diameter of tree

proportion of the trees will have diameters between 2 and 6 inches =

$P(2< X< 6)$ = $P(\frac{2 - 4 }{1.5}< \frac{X - \nu }{\sigma}< \frac{6 - 4 }{1.5})$

= $P(\frac{-2 }{1.5}< Z< \frac{2 }{1.5})$ Put [ $Z = \frac{X - \nu }{\sigma}$ ]

= $P(-1.33< Z< 1.33)$

= $(Z< 1.33) - (Z< -1.33)$

= .9082 - .0918

= 0.8164

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. At a clothing store, 12 people purchased blue sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 purchased

DedPeter [7]

Answer:

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

P(A)= the probability that they purchased a green sweater
P(B)= the probability that they purchased a gray sweater
Mutually exclusive events

You know:

8 purchased green sweaters
4 purchased gray sweaters
number of possible cases= 12 + 8 + 4+ 7= 21

So:

$P(A)=\frac{8}{31}$

$P(B)=\frac{4}{31}$

P(A⋂B) = 0

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= $\frac{8}{31}+ \frac{4}{31}$

P(A∪B)= $\frac{12}{31}$

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

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3 years ago