A car is traveling at a speed of 75 miles per hour and arrives at its final destination in total of 5.25 hours. What is the dist
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9514 1404 393
Answer:
-3 ≤ x ≤ 19/3
Step-by-step explanation:
This inequality can be resolved to a compound inequality:
-7 ≤ (3x -5)/2 ≤ 7
Multiply all parts by 2.
-14 ≤ 3x -5 ≤ 14
Add 5 to all parts.
-9 ≤ 3x ≤ 19
Divide all parts by 3.
-3 ≤ x ≤ 19/3
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<em>Additional comment</em>
If you subtract 7 from both sides of the given inequality, it becomes ...
|(3x -5)/2| -7 ≤ 0
Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.
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For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...
|f(x)| < (some number) . . . . or ≤
If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:
|f(x)| > g(x) ⇒ f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0
Any solutions to these inequalities must respect their domains.
Answer:
The p-value is approximately 0.0508
Step-by-step explanation:
The given parameters are;
The expected mass of banana chips bag filled by the machine, μ = 421 gams
The number of bags in the sample of bags filled by the machine, n = 26 bags
The mean mass of the bags in the sample, = 413 grams
The standard deviation of the mass in the bags, s = 24 grams
The level of significance, α = 0.02
The null hypothesis, H₀; μ = 421 grams
The alternative hypothesis, Hₐ; μ < 421 grams
The test statistic is given as follows;
We get;
The t-value = -1.6996731712
The degrees of freedom df = n - 1 = 26 - 1 = 25
From an online source, we get the critical-t = 2.166587
The p-value is obtained using an online source as p(t ≤ -1.6996731712) = 0.0508
From the p-value table, we get
0.05 < p < 0.1