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timama [110]
3 years ago
5

Muna is making a scale drawing of a gecko. The gecko is 1··2inch wide and 5 inches long. A. She decides to make her drawing of t

he gecko 1 inch wide. How long will the drawing be? Show your work.
Mathematics
1 answer:
almond37 [142]3 years ago
4 0

Answer:

L = 0.83\ in

Step-by-step explanation:

Given

Width = 1.2 in when Length = 1 in

Required

Determine the length when width = 1 in

First, we need to determine the ratio:

Ratio = \frac{Width}{Length}

Ratio = \frac{1.2}{1}

Ratio = 1.2 --- (1)

Let the required Length be represented with L

So:

Ratio = \frac{Width}{Length}

Ratio = \frac{1}{L} --- (2)

Equate (1) and (2)

\frac{1}{L} = 1.2

Multiply through by L

L * \frac{1}{L} = 1.2 * L

1 = 1.2 * L

Divide through by 1.2

L = \frac{1}{1.2}

L = 0.83\ in <em>(Approximated)</em>

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A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const
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Answer:

0.609 \leq \sigma \leq 0.772  

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation  

s=0.68 represent the sample standard deviation  

\bar x =98.90 represent the sample mean  

n=98 the sample size  

Confidence=90% or 0.90  

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 mean or variance 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.  

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .  

2) Calculating the confidence interval  

The confidence interval for the population variance is given by the following formula:  

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}  

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:  

df=n-1=98-1=97  

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,97)" "=CHISQ.INV(0.95,97)". so for this case the critical values are:  

\chi^2_{\alpha/2}=120.990  

\chi^2_{1- \alpha/2}=75.282  

And replacing into the formula for the interval we got:  

\frac{(97)(0.68)^2}{120.990} \leq \sigma \leq \frac{(97)(0.68)^2}{75.282}  

0.371 \leq \sigma^2 \leq 0.596  

Now we just take square root on both sides of the interval and we got:  

0.609 \leq \sigma \leq 0.772  

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

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