A cargo plane flew roundtrip from Smithtown to Johnsville. It took one hour less time to get there than it did to get back. The
1 answer:
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Step-by-step explanation:
To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..
<h3>Formula :</h3>(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2
(h)^2 = (p)^2 + (b)^2
<h3>therefore, </h3>(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.
<h3>by formula,</h3>→ h^2 = p^2 + b^2
→ (x)^2 = (√12)^2 + (√30)^2
→ x^2 = 12 + 30
→ x^2 = 42
→ x = √42
→ x = 6.480...
→ x = 6.5 cm. (approx)
<h3>___________________________</h3>(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.
<h3>by formula,</h3>→ h^2 = p^2 + b^2
→ (√300)^2 = (x)^2 + (√200)^2
→ 300 = x^2 + 200
→ x^2 = 300 – 200
→ x^2 = 100
→ x = √100
→ x= 10 cm.
<h3>___________________________</h3>(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.
<h3>by formula,</h3>→ h^2 = p^2 + b^2
→ (√66)^2 = (x)^2 + (√17)^2
→ 66 = x^2 + 17
→ x^2 = 66 – 17
→ x^2 = 49
→ x = √49
→ x = 7 cm.
<h3>___________________________</h3>(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.
<h3>by formula,</h3>→ h^2 = p^2 + b^2
→ (x)^2 = (2√3)^2 + (5√12)^2
→ x^2 = 12 + 50
→ x^2 = 62
→ x = √62
→ x = 7.874...
→ x = 7.9 cm. (approx)
<h3>___________________________</h3><h3>Hope it helps you!!</h3>
Answer:
The critical value that corresponds to a confidence interval of 81.2% is 1.32.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
And the standard deviation of the sample means is given by,
In this case the sample selected is of size, <em>n</em> = 63.
As the sample size <em>n</em> = 63 > 30, the sampling distribution of sample mean will be approximately normal.
So, a <em>z</em>-interval will be used to estimate the population mean.
The confidence level is, 81.2%.
The value of <em>α</em> is:
The critical value is:
*Use a <em>z</em>-table.
Thus, the critical value that corresponds to a confidence interval of 81.2% is 1.32.