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2 years ago

Which of the following statements is true for ∠a and ∠b in the diagram?

Mathematics

2 answers:

Iteru [2.4K]2 years ago

8 0

Answer:

B because they are the same angle

Dafna1 [17]2 years ago

6 0

Answer:

B. m∠a = m∠b

Step-by-step explanation:

This statement is true due to the Alternate Interior Angle Theorem, which states: If ∠a = x, then ∠b = x, meaning that if a equals a certain angle measure, then the alternate interior angle, or the angle opposite a, must also be the same measure.

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Thirty students in the fifth grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Green

Mars2501 [29]

Answer:

No, the events "brown hair" and "brown eyes" are not independent.

Step-by-step explanation:

The table that represents the hair and eye colors of thirty students of the fifth grade are given in table as:

Brown hair Blonde hair Total

Green eyes 9 6 15

Brown eyes 10 5 15

Total 19 11 30

No, the events "brown hair" and "brown eyes" are not independent.

Since, two events A and B are said to be independent if:

P(A∩B)=P(A)×P(B)

where P denotes the probability of an event.

Here we have:

A= students having brown hair.

B= students having brown eyes.

A∩B= students having both brown hair and brown eyes.

Now,

P(A)=19/30 (ratio of addition of first column to the total entries)

P(B)=15/30 ( ratio of addition of second row to the total entries)

Also,

P(A∩B)=10/30

Now as:

P(A∩B) ≠ P(A)×P(B)

Hence, the two events are not independent.

8 0

2 years ago

If y is proportional to x and y = -15 when x = -20, what is the value of x when y = 12?

alexandr402 [8]

Maybe i have that you wanted We can represent the situation like that: Y=-15 and x=-20 Then When y=12 x=? We make x(The unknown) *-15=12*(-20) We have an simple équation to solve Thus x=(12*(-20))/-15 X=16

7 0

3 years ago

Read 2 more answers

A closed box has a square base with side length feet and height feet given that the volume of the box is 34 ft.³ express the sur

Deffense [45]

Answer:

$\dfrac{2s^3+136}{s}$

Step-by-step explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box = $34$ ft^3$

Volume of the box = $s^2h$

Then:

$s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}$

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box $= 2(s^2+sh+sh)$

$S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}$