Answer:
Step-by-step explanation:
4*3^x+1=27+(3^2)^x
(3^2)^x=(3^x)^2
3^x=t
4t+1=27+t^2
t^2-4t+27-1=0
t^2-4t+26=0
delta=4^2-4*1*26=16-84=-68<0
the equation has not real solutions
The solution to the system of inequalities given is: 
<h3>What is the solutions to a system of inequalities?</h3>
The solution is the set of values that respect all conditions of the system.
The first condition is:



The second condition is:




The intersection of the conditions, which is the solution to the inequality, is:

More can be learned about a system of inequalities at brainly.com/question/3656398
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Answer:
The sum of 5x and 2xis at least 14 as an inequality is: 5x +2x < 14
The product of x and y is less than 4 as an inequality is: x * y < 4
Step-by-step explanation:
The answer is 3 3x3x3=9
Hope this helped:)
Answer:
We conclude that the plant should shut down.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 60
Sample mean,
= 61.498
Sample size, n = 100
Alpha, α = 0.05
Population standard deviation, σ = 6
a) First, we design the null and the alternate hypothesis such that the power plant will be shut down when the null hypothesis is rejected.
We use One-tailed(right) z test to perform this hypothesis.
b) Formula:
Putting all the values, we have
Now,
Since,
We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.
Calculating the p-value from the z-table:
P-value = 0.0063
Since,
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.