The diagram shows a quadrilateral ABCD with each of its sides extended. ab=ad show that abcd is a kite give a reason for each st
age of your working.
1 answer:
Answer:
The rest of the question is the attached figure.
Construct the line segment AC
As shown at the graph:
∠BAD = 110° and ∠C = 20°
∴∠BCD = 20° (Vertically opposite angles).
∠CDA = 180°-65° = 115°
∠B = 360 - (∠A+∠D+∠C) = 360 - (110 + 115 + 20) = 115°
Now in ΔACB and ΔACD
AC = AC (common)
AB = AD (given)
∠CBA =∠CDA (proved)
ΔACB ≅ ΔACD
∵ CPCTC ⇒ ∴ CB = CD
So, AD = AB and CB = CD (adjacent sides are equal)
∠D =∠B (A pair of opposite angles equal)
<u>∴ ABCD is a kite .</u>
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Answer:
a)
And we can find this probability using the normal standard table and we got:
b)
And we can find this probability using the complement rule and the normal standard table and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Part a
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table and we got:
Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and the normal standard table and we got: