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3 years ago

Compute the perimeter of the rectangle using the distance formula. (round to the nearest integer)

Mathematics

2 answers:

GenaCL600 [577]3 years ago

5 0

The answer is D 45.
Using the distance formula and the ordered pairs (1,8) & (4,5) for the short side and ((4,5) & (17,18) for the long side.
sqrt [(x2-x2)^2 + (y2-y1)^2]
sqrt [(4-1)^2 + (5-8)^2] = sqrt [ 9 + 9 ] = sqrt (18) (short side)
sqrt [(17-4)^2 + (18-5)^1 = sqrt [169 + 169] = sqrt (338) long side
P = 2L + 2W
P = 2sqrt18 + 2sqrt 338 = 45.25 = 45

Nuetrik [128]3 years ago

4 0

You have to take the sum of the distance between each point. It doesn't matter what order you use just keep it consistent, the shortest distance between any 2 points in the plane is a straight line.

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2 years ago

Which of the following is equivalent to 5√13^3?

sergeinik [125]

LOL...it took me a few seconds to realize what you were attempting to express...which is the fifth root of 13 cubed...

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3 years ago

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Da

alexgriva [62]

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.</em>

<em />

We start calculating the sample mean M and standard deviation s:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\$

$s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\$

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075$

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.25 \cdot 1.075=3.49$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3$

The 99% confidence interval for the mean germination time is (12.3, 19.3).

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3 years ago

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