Answer:
-5 =x
Step-by-step explanation:
3^(x-1) = 9^(x+2)
Replace 9 with 3^2
3^(x-1) = 3^2^(x+2)
We know that a power to a power means the powers are multiplied
a^b^c = a^(b*c)
3^(x-1) = 3^(2x+2)
When the bases are the same, the powers have to be the same
x-1 = 2x+4
Subtract x from each side
x-x-1 =2x-x+4
-1 =x+4
Subtract 4 from each side
-1-4 =x+4-4
-1-4 = x
-5 =x
Answer:
90% CI expects to capture u 90% of time
(a) This means 0.9 * 1000 = 900 intervals will capture u
(b) Here we treat CI as binomial random variable, having probability 0.9 for success
n = 1000
p = 0.9
For this case, applying normal approximation to binomial, we get:
mean = n*p= 900
variance = n*p*(1-p) = 90
std dev = 9.4868
We want to Find : P(890 <= X <= 910) = P( 889.5 < X < 910.5) (integer continuity correction)
We convert to standard normal form, Z ~ N(0,1) by z1 = (x1 - u )/s
so z1 = (889.5 - 900 )/9.4868 = -1.11
so z2 = (910.5 - 900 )/9.4868 = 1.11
P( 889.5 < X < 910.5) = P(z1 < Z < z2) = P( Z < 1.11) - P(Z < -1.11)
= 0.8665 - 0.1335
= 0.733
Answer:

Step-by-step explanation:
Multiply (x + 1) by (2x + 2).
x × 2x is 
x × 2 is 2x
1 × 2x is 2x
1 × 2 is 2
+ 2x + 2x + 2 = 