-3(x - 3) > 5 - 5x
use the distributive property
-3x + 9 > 5 - 5x
subtract 5 from both sides
-3x + 4 > -5x
add -3x to both sides
4 > -2x
divide both sides by -2 to isolate x
x > -2
The correct answer is D. x > -2.
Answer:
A. neither a relation nor a function
Step-by-step explanation:
A relation between two sets is a collection of ordered pairs containing one object from each set.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Quadratic equations are not functions. Quadratic equations are not a function because they touch two points that is on the same y-axis. Furthermore, if they are two points that have the same x axis, then it is not a function either. It doesn't have a relation either because there are two outputs that are the same by the x axis for 3x^2 - 9x + 20. Those are x = 1 and x = 2. For proof, you can plug both of them in.
3(1)^2 - 9(1) + 20 = 14
3(2)^2 - 9(2)+ 20 = 14
Both answers have 14 as the y-axis/output. This proves that this quadratic equation is not a relation either. Therefore, this equation is neither a relation nor a function.
Answer:
a) ![[-0.134,0.034]](https://tex.z-dn.net/?f=%5B-0.134%2C0.034%5D)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where
.
The mean difference
.
The confidence interval is

![= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]](https://tex.z-dn.net/?f=%3D%20-0.05%5Cpm%201.995%20%5Ctimes%200.042%20%3D%20-0.05%20%5Cpm%200.084%20%3D%20%5B-0.134%2C0.034%5D)
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.
Answer:
1.625
Step-by-step explanation:
Add 13 to both sides
8n = 26 - 8n
Add 8n to both sides
16n = 26
Divide both sides by 16
Your answer is 1.625
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