Lesson 6.4 areal world problem:percent

Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie?

Daniel [21]

Rotation in mathematics involves movement of a figure along a given point and a given angle. It is described by giving a the center of rotation and the angle of rotation, the angle indicates the direction of rotation whether clockwise or anticlockwise, such that if the angle is positive then the rotation is to the anticlockwise direction and if the angle is negative then the direction of rotation is clockwise. In our case the center of rotation is origin (0,0) and the angle of rotation is +180 degrees thus the direction of rotation is anticlockwise. Therefore if an object DEFG is rotated to an image D'E'F'G' , assuming point G was in the first quadrant then its image G' will fall on the third quadrant of the Cartesian plane.

7 0

3 years ago

Find the distance between points (2,2) and (-2,5) to the nearest tenth.

Zolol [24]

Answer:

5

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(-2 - 2)² + (5 - 2)²

√(-4)² + (3)²

√16 + 9

√25

= 5

5 0

3 years ago

Explain how 585 is divded by 3

Alik [6]

Answer:

Because 3 can go into 15 five times wich means 585 divided by 15 is 39 and that proves that 3 can go into a number that has a five in it

3 0

3 years ago

A window washing company is hired to wash the windows in a condominium. The building is 50 m by 30 m by 300 m. Windows cover abo

BARSIC [14]

Answer:

12,000. I made the assumption that the windows cover exactly 1/4 of the building.

Step-by-step explanation:

Length = 50

Width = 30

Height = 300

(Becuase it is always length, width and height)

To find surface area you do length x height x 2. (Becuase there are two walls with the length)

And another is width x height x 2 (Becuase there are two walls with the width.

(50 x 300) x 2 = 30000

(30 x 300) x 2 = 18000

Then add those two together getting 48,000. You have to dived that by 4 to get quarters. Which is 12,000. So 1/4 of the building is 12,000.

8 0

3 years ago

Read 2 more answers

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you

Brut [27]

Answer:

a) $P(A \cup M)= P(A) + P(M) -P(A \cap M)$

And if we solve for P(M) we got:

$P(M) = P(A\cup B) +P(A \cap B) -P(A)$

And replacing we got:

$P(M) = 0.3 +0.11-0.18= 0.23$

b) In order to A and M be mutually exclusive we need to satisfy:

$P(A \cap M ) =0$

And for this case since $P(A \cap M) = 0.11 \neq 0$ the events A and M are NOT mutually exclusive

c) In order to satisfy independence we need to have the following relation:

$P(A \cap B) = P(A) *P(B)$

And for this case we have that:

$0.11 \neq 0.23*0.18$

So then A and M are NOT independent

d) $P(A|M)$

And we can use the Bayes theorem and we got:

$P(A|M) = \frac{P(A \cap M)}{P(M)}$

And replacing we got:

$P(A|M)= \frac{0.11}{0.23}= 0.478$

e) $P(M|A)$

And we can use the Bayes theorem and we got:

$P(M|A) = \frac{P(M \cap A)}{P(A)}$

And replacing we got:

$P(M|A)= \frac{0.11}{0.18}= 0.611$

Step-by-step explanation:

For this case we define the following events:

A denote the event of receiving an Athletic Scholarship.

M denote the event of receiving a Merit scholarship.

For this case we have the following probabilities given:

$P(A) =0.18, P(A \cap M) =0.11, P(A \cup M) =0.3$

Part a

For this case we can use the total rule of probability and we have this:

$P(A \cup M)= P(A) + P(M) -P(A \cap M)$

And if we solve for P(M) we got:

$P(M) = P(A\cup B) +P(A \cap B) -P(A)$

And replacing we got:

$P(M) = 0.3 +0.11-0.18= 0.23$

Part b

In order to A and M be mutually exclusive we need to satisfy:

$P(A \cap M ) =0$

And for this case since $P(A \cap M) = 0.11 \neq 0$ the events A and M are NOT mutually exclusive

Part c

In order to satisfy independence we need to have the following relation:

$P(A \cap B) = P(A) *P(B)$

And for this case we have that:

$0.11 \neq 0.23*0.18$

So then A and M are NOT independent

Part d

For this case we want this probability:

$P(A|M)$

And we can use the Bayes theorem and we got:

$P(A|M) = \frac{P(A \cap M)}{P(M)}$

And replacing we got:

$P(A|M)= \frac{0.11}{0.23}= 0.478$

Part e

For this case we want this probability:

$P(M|A)$

And we can use the Bayes theorem and we got:

$P(M|A) = \frac{P(M \cap A)}{P(A)}$

And replacing we got:

$P(M|A)= \frac{0.11}{0.18}= 0.611$

4 0

3 years ago