Answer:
Step-by-step explanation:
Given: quadrilateral ABCD inscribed in a circle
To Prove:
1. ∠A and ∠C are supplementary.
2. ∠B and ∠D are supplementary.
Construction : Join AC and BD.
Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,
∠1=∠2-----(1)
∠3=∠4-----(2)
∠5=∠6-------(3)
∠7=∠8------(4)
Also, sum of angles of quadrilateral is 360°.
⇒∠A+∠B+∠C+∠D=360°
→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4
→→→2∠1+2∠4+2∠6+2∠8=360°
→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,
→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)
As, ∠A+∠B+∠C+∠D=360°
∠A+∠C+180°=360°
∠A+∠C=360°-180°------Using A
∠A+∠C=180°
Hence proved.
credit: someone else
<span>a.
</span>Do you
have sufficient funds to estimate the population mean for the attribute of
interest with a 95% confidence interval 4 units width? Assume that sd= 12
n= {[(Zalpha/2)^2]*[sd]^2}/
se^2
n=
(1.96)^2*(12)^2/ (2)^2
n=
138.297 rounded up to 139
<span>There
is not enough funds for this one
since you’ll need 139 pieces and it costs 10 a piece, you’ll need 1390.</span>
b.
90% confidence interval
n= {[(Zalpha/2)^2]*[sd]^2}/
se^2
n=
(1.645)^2*(12)^2/ (2)^2
n=98
There is enough
funds since 98 pieces for 10 a piece is equal to 980.
Answer:
x = 60°
Step-by-step explanation:
The circle is 360°, thus
2y + y = 360
3y = 360 ( divide both sides by 3 )
y = 120°
The tangent- secant angle ABT is one half the measure of the intercepted arc AB, thus
x = 0.5 × 120° = 60°
