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>
Answer: 1.118
Step-by-step explanation:
Factor x Factor = Product
0.26(Factor) x 4.3(Factor) = 1.118(Product)
To check your work, divide the product by one of the factors and the result you should get is the other factor.
1.118(Product) ÷ 4.3(Factor) = 0.26(Factor)
-or-
1.118(Product) ÷ 0.26(Factor) = 4.3(Factor)
To show work:
.26
<u> x4.3</u>
.078
<u>+1.040</u>
1.118
Answer:
The factorized expression is (-5) × (t - 2.747) ×(t - 1.747)
Step-by-step explanation:
The given expression is -5·t² + 5·t + 24
To factorize the expression by completing the square method, we equate the expression to zero to get;
-5·t² + 5·t + 24 = 0
WE divide by -5 to get;
t² - t - 24/5 = 0
t² - t = 24/5
t² - t + 1/4 = 24/5 + 1/4
(t - 1/2)² = 5.05
t - 1/2 = ±√5.05
t = 1/2 + √5.05, 1/2 - √5.05
The factorized expression becomes;
(t - 1/2 + √5.05) and (t - 1/2 - √5.05)
Which gives;
(t - 2.747) ×(t - 1.747)
The factorized expression is (-5) × (t - 2.747) ×(t - 1.747).
Alright, there's no whole number in this number. The numbers the the right of this numbers 7 and 5, which is, obviously, 75. This will be the numerator.
The last number in this decimal is 5, which is in the hundredth place, so the denominator will be 100.
We get 75/100.
Now simplify. 5 can go into both numbers.
75/5 = 15
100/5 = 20
We end up with 15/20.
Still, 15/20 can be simplified. Divide by 5.
15/5 = 3
20/5 = 4
Our remaining fraction is
.