Answer:
Step-by-step explanation:
Please refer to the attached figure for the labeling and construction in the given figure:
Given that minor angle of arc AB is 
.
Or in other words, we can say that angle subtended on the center O by the arc is .
Now, PA and PB are the tangents so, if we join the center of circle O with A and B, the angles formed are right angles.
i.e.
Now, we know that sum of internal angles of a quadrilateral is equal to 
.
Here, we have the quadrilateral AOPB.
Hence, the correct answer is:
The ordered pair that makes both inequalities true is (4,0).
we have
y<3x-1 ----> inequality A
y > –x + 4----> inequality B
we know that
If an ordered pair is a solution to the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
Verify each ordered pair
case 1) (4,0)
Inequality A
0<3(4)-1 ----> is true
Inequality B
0> –4 + 4 ----> is true
<h3>What is inequality?</h3>
A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
So, The ordered pair makes both inequalities true
case 2) (1,2)
Inequality A
2< 3(1) – 1
2<3-1
2<2----> is not true
So the ordered pair does not make both inequalities true
case 3) (0,4)
Inequality A
0 < 3(4) – 1
0<12-1
0<11 ----> is not true
So, the ordered pair does not make both inequalities true
case 4) (2,1)
Inequality A
1< 3(2) – 1
1<6-1
1<5----> is true
Inequality B
----> is not true
So the ordered pair does not make both inequalities true.
To learn more about the inequalities visit:
brainly.com/question/24372553
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The sum of the polygon is 27
Answer:
Mean = 20
Variance = 16
Step-by-step explanation:
Solution:-
- Let X be the number of customers paying with a debit card. X has the binomial distribution with n = 100 trials and success probability p = 0.2
- In general, if X has the binomial distribution with (n) trials and a success probability of (p) then:
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.
- The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
- Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.
X ~ Binomial( n = 100 , p = 0.2 )
- The mean of the binomial distribution is n * p = 20
- The variance of the binomial distribution is n * p * (1 - p) = 16
<span>You need to do this to make it correct = (65/100)*80
= 52</span>
