2. After the translation, where Is Alocated? Write your answer in the space below. Text

Mathematics

1 answer:

Nataly_w [17]3 years ago

6 0

9514 1404 393

Answer:

A'(-3, 13)

Step-by-step explanation:

The transformation that moves a point 4 left and 8 up is ...

(x, y) ⇒ (x -4, y +8)

The transformation that reflects a point across the y-axis is ...

(x, y) ⇒ (-x, y)

Applied after the translation, the transformation of ∆ABC becomes ...

(x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)

Then point A gets moved to ...

A(7, 5) ⇒ A'(4 -7, 5 +8) = A'(-3, 13)

___

In the attached graph, the purple triangle is the result of the translation 4 left and up 8. Then the blue one is after reflection across the y-axis.

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A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3.1g and

inysia [295]

Question 1

probability between 2.8 and 3.3

The graph of the normal distribution is shown in the diagram below. We first need to standardise the value of X=2.8 and value X=3.3. Standardising X is just another word for finding z-score

z-score for X = 2.8
$z= \frac{2.8-3.1}{0.41} =-0.73$ (the negative answer shows the position of X = 2.8 on the left of mean which has z-score of 0)

z-score for X = 3.3
$z= \frac{3.3-3.1}{0.41}=0.49$

The probability of the value between z=-0.73 and z=0.49 is given by
P(Z<0.49) - P(Z<-0.73)

P(Z<0.49) = 0.9879
P(Z< -0.73) = 0.2327 (if you only have z-table that read to the left of positive value z, read the value of Z<0.73 then subtract answer from one)

A screenshot of z-table that allows reading of negative value is shown on the second diagram

P(Z<0.49) - P(Z<-0.73) = 0.9879 - 0.2327 = 0.7552 = 75.52%

Question 2
Probability between X=2.11 and X=3.5

z-score for X=2.11
$z= \frac{2.11-3.1}{0.41}=-2.41$

z-score for X=3.5
$z= \frac{3.5-3.1}{0.41} =0.98$

the probability of P(Z<-2.41) < z < P(Z<0.98) is given by
P(Z<0.98) - P(Z<-2.41) = 0.8365 - 0.0080 = 0.8285 = 82.85%

Question 3
Probability less than X=2.96

z-score of X=2.96
$z= \frac{2.96-3.1}{0.41}=-0.34$
P(Z<-0.34) = 0.3669 = 36.69%

Question 4
Probability more than X=3.4
$z= \frac{3.4-3.1}{0.41}=0.73$
P(Z>0.73) = 1 - P(Z<0.73) = 1-0.7673=0.2327 = 23.27%