Answer:
90% confidence interval -> {0.4529, 0.5871}
Step-by-step explanation:
<u>Check conditions for a 1-proportion z-interval:</u>
np>10 -> 150(0.52)>10 -> 78>10 √
n(1-p)>10 -> 150(1-0.52)>10 -> 72>10 √
Random sample √
n>30 √
For a 90% confidence interval, the critical value is z=1.645
The formula for a confidence interval is:
CI = p ± z√[p(1-p)/n]
<u>Given:</u>
p = 78/150 = 0.52
n = 150
z = 1.645
Therefore, the 90% confidence interval is:
CI = 0.52 ± 1.645√[0.52(1-0.52)/150] = {0.4529, 0.5871}
Context: We are 90% confident that the true proportion of all voters who
plan to vote for the incumbent candidate is contained within the interval
Answer:
16-Current age = A
A x 52 weeks in a year x 100 dollars per week + $200 in her account when 16
Ax52x100+200=Money saved up
16-Sara Age = B
B x 52 weeks in a year x 50dollars per week + $800 in her account = money saved up when 16
Bx52x50+800=Money Saved
Step-by-step explanation:
GIVEN :
a = 1/√10 ( 3i + k) and
b = 1/7 ( 2i + 3j - 6k)
TO FIND :
( 2a- b) . [ ( a x b ) x ( a + 2b)]
SOLUTION :
◆Going with the equation given,
( 2a - b) . [ ( a x b ) x ( a + 2b)]
= (2a - b) [( a×b×a) + 2(a×b)×b]
◆BAC - CAB RULE,
A×B×C = B( A.B ) - C(A.B )
= (2a- b ) [ (b (a.a ) - a (a.b ) + 2b ( a.b) -2b (a.b]
Solving further
= (2a - b )(b - 2a)
= -4a.a -b.b
=-5.
Answer:
( 2 - b) . [ ( a x b ) x ( a + 2b)] = -5
Hoped I helped
Answer:
<h2>A)
x = 6, m∠LMN = 138°</h2><h2>
</h2>
Step-by-step explanation:
∠LMO = ∠NMO
15x - 21 = x + 63
15x - x = 63 + 21
14x = 84
x = 84/14
x = 6
∠LMN = ∠LMO + ∠NMO
∠LMN = 15x - 21 + x + 63
∠LMN = 15(6) - 21 + 6 + 63
∠LMN = 138°
1.
Area of shaded region,
=(Area of bigger circle) - (Area of smaller circle)
=πR^2 - πr^2
=π ( R^2 - r^2 )
=3.14 ( 8^2 - 4^2)
=3.14 × ( 64 - 16 )
=3.14 × 48
=150.72 cm^2
2.
Area of shaded region,
=(Area of big semi-circle) - ( Area of small semi-circle)
=(πR^2)/2 - (πr^2)/2
=π/2 ( R^2 - r^2 )
=3.14/2 ( 6^2 - 3^2 )
=1.57 × ( 36 - 9 )
=1.57 × 27
=42.39 cm^2
HOPE THIS WILL HELP YOU
