An engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 110 engines and the mean pressure was 4.6 lbs/square inch. assume the standard deviation is known to be 0.8. if the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

NO.

Step-by-step explanation:

As per given , we have to test the hypothesis.

∵ is two-tailed , so our test is a two-tailed test.

Also, the standard deviation is known to be 0.8 , so we use z-test.

Test statistic:

, where = Sample mean

= population mean

= Population standard deviation

n= Sample size

Put  

n=  110 , we get

P-value for two tailed test = 2P(Z>|z|)

= 2P(Z>|1.31|) = 2(1-P(Z<1.31))   [∵ P(Z>z)=1-P(Z<z)]

=2(1- 0.9049)  [By z-table]

=0.1902

Decision : ∵ P-value (0.1902) > Significance level (0.02).

It means we do not reject the null hypothesis.

[When P-values < Significance level then we reject the null hypothesis.]

Conclusion : We do not have sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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