Is (-3, 2) a solution of -4r - 10y< - 9?
1 answer:
Answer:
<em>The point (-3,2) is not a solution of the inequality</em>
Step-by-step explanation:
<u>Inequality</u>
Inequalities relate the left and the right side of an expression with an operator other than the equal sign.
The inequality given in the question is
There are many combinations of r and y that make inequality be true. For example, for r=1 and y=1
This relation is true since -14 is less than -9.
Also, there are many combinations that make the given inequality be false.
For example, for r=2 and y=-1
This inequality is false.
Let's test the point (-3,2)
Which is false, thus the point (-3,2) is not a solution of the inequality
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Answer:
No,
12.8 = 12.800
Obviously, 12.800 <u>< </u>12.815.
Answer:
95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].
Yes, this data suggest that the tensile strength was changed after the adjustment.
Step-by-step explanation:
We are given that the tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm 2 and a standard deviation of 2.15.
A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean strength of 50 items = 74.28
= population standard deviation = 2.15
n = sample of items = 50
= population mean tensile strength after machine was adjusted
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
So, 95% confidence interval for the population mean, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of
significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u><em>95% confidence interval for</em></u> = [
,
]
= [ ,
]
= [73.68 kg/mm2 , 74.88 kg/mm2]
Therefore, 95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].
<em>Yes, this data suggest that the tensile strength was changed after the adjustment as earlier the mean tensile strength was 72 kg/mm2 and now the mean strength lies between 73.68 kg/mm2 and 74.88 kg/mm2 after adjustment.</em>