Answer:
The second function represents an even function;
Step-by-step explanation:
A function f(x) is said to be even if f(x) = f(-x). All we need to do is replace x with -x in each equation, simplify it and assess whether the equation remains unchanged. If the equation is identical to the original one then it is said to be even. Another good example of an even function is the cosine function. Moreover, even functions have y-axis symmetry
Answer:
A 98% confidence interval for the mean assembly time is [21.34, 26.49] .
Step-by-step explanation:
We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample average time = 23.92 minutes
s = sample standard deviation = 6.72 minutes
n = sample of times = 40
= population mean assembly time
<em> Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>
<u>So, a 98% confidence interval for the population mean, </u><u> is;
</u>
P(-2.426 < < 2.426) = 0.98 {As the critical value of z at 1% level
of significance are -2.426 & 2.426}
P(-2.426 < < 2.426) = 0.98
P( <
<
) = 0.98
P( <
<
) = 0.98
<u>98% confidence interval for</u> = [
,
]
= [ ,
]
= [21.34, 26.49]
Therefore, a 98% confidence interval for the mean assembly time is [21.34, 26.49] .
Answer:
30 gallons of 20% acid solution should be mixed.
Step-by-step explanation:
Let x gallons of a 20% acid solution was mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solution.
Therefore, final volume of the solution will be (x + 30) gallons.
Now concept to solve this question is
20%.(x) + 40%.(30) = 30%.(x + 30)
0.20(x) + 0.40(30) = 0.30(x + 30)
0.20x + 12 = 0.30x + 9
0.30x - 0.20x = 12 - 9
.10x = 3
x =
x = 30 gallons
Therefore, 30 gallons of the 20% acid solution should be mixed.