Write the recursive formula for the arithmetic sequence {an}={2.6,4,5.4,6.8,8.2,...}
1 answer:
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Answer:
The amount invested at 8% rate is $1,200
The amount invested at 10% rate is $2,000
The amount invested at 12% rate is $3,500
Step-by-step explanation:
step 1
Let
x-----> the amount invested at 8% rate
y-----> the amount invested at 10% rate
z-----> the amount invested at 12% rate
----> equation A
----> equation B
substitute equation A in equation B
-----> equation C
we know that
The simple interest formula is equal to
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
substitute in the formula above
substitute equation A
-----> equation D
step 2
Solve the system of equations
x+y=3,200 -----> equation C
-----> equation D
Solve the system by graphing
The solution is the point (1,200,2,000)
see the attached figure
Find the value of z
therefore
The amount invested at 8% rate is $1,200
The amount invested at 10% rate is $2,000
The amount invested at 12% rate is $3,500
Answer:
We are given that Among 180 homes in Hyde Park, 25 were found to have unsafe radon levels. Among 230 homes in La Grange, 50 were found to have unsafe radon levels.
Claim : the two towns have different rates of unsafe radon levels.
Let and
be the rates of unsafe radon levels of Hyde Park and LaGrange respectively .
Among 180 homes in Hyde Park, 25 were found to have unsafe radon levels
So,
Among 230 homes in La Grange, 50 were found to have unsafe radon levels.
So,
We will use Comparing Two Proportions
Formula of test statistic :
Substitute the values
test statistic :
test statistic : −2.053
Refer the z table for p value
p value = 0.0202
α= 0.05
Since p value < α
So, we reject the null hypothesis that the two towns have same rates of unsafe radon levels.
So, Claim is true.