Answer:
Yes, Based on this data, baldness and being over 45 are independent events, because P(bald | over 45) = P(bald).
Step-by-step explanation:
The given data is as following:
Under 45 Over 45 Total
Bald : 24 16 40
Not Bald : 36 24 60
Total : 60 40 100
<u>We should know that:</u>
The events A and B are independent when If P(A∩B) = P(A) * Pr(B)
Using conditional probabilities this property can be written as:
P(A|B) = P(A∩B)/P(B) = P(A) * Pr(B)/ P(B) = P(A)
So, we will check baldness and being over 45 independent events.
From the given data:
1. P(man is bald) = 40/100 = 0.4
3. P(bald | over 45) = 16/40 = 0.4
So, P(man is bald) = P(bald | over 45) = 0.4
<u>So, The events are independent. </u>
The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
<h3>Percentage</h3>
- Amount paid for shoes = $x
- Tax = 5%
Total cost = x + (5% of x)
= x + (0.05 × x)
= x + (0.05x)
Total cost = 1.05x
Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
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Answer:
159 m
Step-by-step explanation:
From the information given:
It was stated that if the ostrich ran towards the east direction in 7.95 s, let say the distance from the starting point is O towards the east side E, let called the distance towards the east side to be OE.
Again, the ostrich then runs in the south direction for 161 m, let the distance be OS.
Also, let the magnitude of the resultant displacement between the east direction to the south direction be ES = 226m.
We are to find, the magnitude of the ostrich's eastward component.
i.e. The distance traveled from the center to the east direction within the time frame of 7.95 s.
Using the Pythagoras rule:
ES² = OE² + OS²
226² = OE² + 161²
226² - 161² = OE²
OE² = 226² - 161²
OE² = 51076 - 25921
OE² = 51076 - 25921
OE² = 25155
OE = 158.60 m
OE ≅ 159 m
Thus, the magnitude of the ostrich's towards the eastward component. = 159 m.