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3 years ago

An architect is constructing a model building by using a ratio os 1:300. If the height of the scale model is 3 1/2 inches what i

s the height in yards

Mathematics

1 answer:

atroni [7]3 years ago

7 0

$\bf \cfrac{model}{actual}\qquad 1:300\qquad \cfrac{1}{300}\qquad \qquad \cfrac{3\frac{1}{2}}{a}=\cfrac{1}{300}\implies \cfrac{\frac{3\cdot 2+1}{2}}{a}=\cfrac{1}{300}
\\\\\\
\cfrac{\quad \frac{7}{2}\quad }{a}=\cfrac{1}{300}\implies \cfrac{\quad \frac{7}{2}\cdot 300\quad }{1}=a\implies 1050=a$

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Step-by-step explanation:

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3 years ago

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The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.

Now we have everything in order to replace into formula (1):

$30.9-1.97\frac{7.5}{\sqrt{174}}=29.780$

$30.9+1.97\frac{7.5}{\sqrt{174}}=32.020$

So on this case the 95% confidence interval would be given by (29.780;32.020)

The value 29.6 is not contained on the interval calculated.

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3 years ago

a square measuring 9 inches by 9 inches is cut from a corner of a square measuring 15 inches by 15 inches. what is the area of t

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Your final answer should be:
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3 years ago