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9966 [12]
3 years ago
5

Find the value of t in the diagram

Mathematics
2 answers:
12345 [234]3 years ago
5 0

In a trapezoid, with bases b and B and height h, the area is given by


A = \frac{(B+b)h}{2}


In your case:


B = BC = 3t

b = AD = t

h = AB = t


so, the formula becomes


A = \frac{(3t+t)t}{2} = \frac{4t^2}{2} = 2t^2


Since the area is 50 \text{cm}^2, we have


2t^2 = 50 \iff t^2 = 25 \iff t = 5

igomit [66]3 years ago
4 0

Answer


5 cm



Explanation

The figure shown is a trapezium.

The area of a trapezium is given by;


Area = 1/2 h( a+b)

Where h ⇒perpendicular distance between the two parallel sides 

a and b ⇒length of the parallel sides.

h = t

a =t

b = 3t


1/2 t(t+3t) = 50

1/2 ×t × 4t = 50

1/2 ×4t²=50

2t² = 50

dividing both sides by 2

t² = 25

t = √25

= 5 cm

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Records indicate that for parts coming out a hydraulic repair shop at an airplane rework facility, 30\% will have a shaft defect
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Answer:

P(A|B) = P(A∩B)/P(B) = 100%

Which means that there is 100% probability that the item has at least one type of defect given that the item has only a shaft defect.

Step-by-step explanation:

Conditional probability P(A|B) can be expressed as;

P(A|B) = P(A∩B)/P(B) .....1

Given;

30% will have a shaft defect,

15% will have a bushing defect,

and 65% will be defect-free

Total probability = 100% = P(shaft or/and bushing defect) + P(defect free)

P(shaft or/and bushing defect) = 100% - P(defect free)

= 100% - 65% = 35%

And

P(shaft or/and bushing defect) = P(shaft def only) + P(bushing def only) + P(shaft and bushing defect)

P(shaft or/and bushing defect) = P(shaft defect) + P(bushing defect) - P(shaft and bushing defect)

Substituting the values we have;

35% = 30% + 15% - P(shaft and bushing defect)

P(shaft and bushing defect) = 45% - 35% = 10%

Let A="The item has at least one type of defect"; and B="The item has only a shaft defect".

P(A) = P(shaft or/and bushing defect) = 35%

P(B) = P(shaft only defect) = 30% - 10% = 20%

P(A∩B) = 20%

Substituting into equation 1

P(A|B) = P(A∩B)/P(B) = 20%/20%

P(A|B) = 1/1 = 100%

Which means that there is 100% probability that the item has at least one type of defect given that the item has only a shaft defect.

5 0
3 years ago
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