Answer:
Hello,
Answer 6
Step-by-step explanation:

The smallest number to be susbtracted is 6
Answer: The 95% confidence interval is approximately (55.57, 58.43)
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Explanation:
At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.
The sample size is n = 17
The sample mean is xbar = 57
The population standard deviation is sigma = 3
The lower bound of the confidence interval is
L = xbar - z*sigma/sqrt(n)
L = 57 - 1.960*3/sqrt(17)
L = 55.5738905247863
L = 55.57
The upper bound is
U = xbar + z*sigma/sqrt(n)
U = 57 + 1.960*3/sqrt(17)
U = 58.4261094752137
U = 58.43
Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.
Let's solve your equation step-by-step.<span><span><span>0.2<span>(<span>x+50</span>)</span></span>−6</span>=<span>0.4<span>(<span><span>3x</span>+20</span>)</span></span></span>Step 1: Simplify both sides of the equation.<span><span><span>0.2<span>(<span>x+50</span>)</span></span>−6</span>=<span>0.4<span>(<span><span>3x</span>+20</span>)</span></span></span><span><span><span><span><span><span>(0.2)</span><span>(x)</span></span>+<span><span>(0.2)</span><span>(50)</span></span></span>+</span>−6</span>=<span><span><span>(0.4)</span><span>(<span>3x</span>)</span></span>+<span><span>(0.4)</span><span>(20)</span></span></span></span>(Distribute)<span><span><span><span><span>0.2x</span>+10</span>+</span>−6</span>=<span><span>1.2x</span>+8</span></span><span><span><span>(<span>0.2x</span>)</span>+<span>(<span>10+<span>−6</span></span>)</span></span>=<span><span>1.2x</span>+8</span></span>(Combine Like Terms)<span><span><span>0.2x</span>+4</span>=<span><span>1.2x</span>+8</span></span><span><span><span>0.2x</span>+4</span>=<span><span>1.2x</span>+8</span></span>Step 2: Subtract 1.2x from both sides.<span><span><span><span>0.2x</span>+4</span>−<span>1.2x</span></span>=<span><span><span>1.2x</span>+8</span>−<span>1.2x</span></span></span><span><span><span>−<span>1x</span></span>+4</span>=8</span>Step 3: Subtract 4 from both sides.<span><span><span><span>−<span>1x</span></span>+4</span>−4</span>=<span>8−4</span></span><span><span>−<span>1x</span></span>=4</span>Step 4: Divide both sides by -1.<span><span><span>−<span>1x</span></span><span>−1</span></span>=<span>4<span>−1</span></span></span><span>x=<span>−4</span></span>Answer:<span>x=<span>−<span>4</span></span></span>
The answer for your question is 6