Well, since the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%, that means there is a 90% confidence interval. 9 / 10 = .90 = 90% 90% = 1.645 1.645 * .9 = 1.4805 Margin of Error - 1.4805and The margin of error is the distance from x-bar, the center of the confidence interval ,to the end of the interval. This distance is 6% of 80% which is given by: 80×6100=4.8 Therefore the margin of error is 4.8% and the confidence interval is: ({80 - 4.8}%, {80 + 4.8}%)
(55 km/h) * (1 mi)/(1.609344 km) ≈ 34.2 mi/h
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You can do units conversions pretty easily by multiplying by a conversion factor whose value is 1. That is, since
.. 1 mi = 1.609344 km
dividing by the left side we have
.. (1 mi)/(1.609344 km) = 1
This factor has the convenience that it will cancel km and give mi when multiplied by some number off km. That is what we did above. (The "per hour" just went along for the ride. It did not get involved in the units conversion.)
Answer:
1) x = 40° & y = 50°
2) x = 100° & y = 80°
Step-by-step explanation:
1)
ABCD is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are touching on the circle). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠ADC + ∠ABC = 180°
⇒ 130° + y = 180°
⇒ y = 180 - 130 = 50°
In ΔABC ,
∠ACB = 90° (∵ AB is the diameter of the circle and a diameter subtends an angle of 90° on any point on circle.)
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠CAB = 180°
⇒ y + 90° + x = 180°
⇒ x + 50° + 90° = 180°
⇒ x + 140° = 180°
⇒ x = 180 - 140 = 40°
2)
ΔABC is an isosceles triangle (∵AB = AC). As it is an isosceles triangle , it's base angles will be equal. So , ∠ABC = ∠ACB = 50°
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠BAC = 180°
⇒ 50° + 50° + y = 180°
⇒ y + 100° = 180°
⇒ y = 180 - 100 = 80°
ABEC is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are on the circle.). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠BAC + ∠BEC = 180°
⇒ y + x = 180°
⇒ x + 80° = 180°
⇒ x = 180 - 80 = 100°
It tells us that:
(-2,4)
(-1,3)
(1,6)
(3,5)
(4,8)
Look at (3,5) ... it tells us that x = 3 and y = 5
So y = 5
