y = x^2 + 2x...eqn 1
y = 3x + 20...eqn 2
subst for y in eqn 1...
=> x^2 +2x = 3x +20
=> x^2 - x - 20 =0
=> (x-5) (x+4) =0
=> x = 5 or -4
for x =5, y = 35 (sub for x in eqn 1 or 2)
for x = -4, y = 8 (sub for x in eqn 1 or 2)
Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is 
and the standard deviation is 
In this problem, we have that:
.
So
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer:
D. About 800 years
Step-by-step explanation:
Use the half-life equation:
A = A₀ (½)ⁿ
where A is the final amount,
A₀ is the initial amount,
and n is the number of half-lives.
0.90A₀ = A₀ (½)ⁿ
0.90 = (½)ⁿ
To solve for n, take log of both sides:
log 0.9 = n log 0.5
n = (log 0.9) / (log 0.5)
n = 0.152
It takes 0.152 half-lives. The half-life of carbon-14 is 5730 years.
0.152 × 5730 years = 871 years
The closest answer is D.
Answer:
0.162
Step-by-step explanation:
(12+13)/154
25/154
0.162
