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marta [7]
2 years ago
9

A carpenter is building a rectangular room with a fixed perimeter of 180ft. What are the dimensions of the largest room that can

be built? What is it’s area?
Mathematics
1 answer:
kodGreya [7K]2 years ago
5 0

Answer:

90ft x 90ft. 8100ft^2

Step-by-step explanation:

Perimeter(P) = 180 = length + width

Length(L) = 180 - width

Width(W) = 180 - length

Area = length*width = length*(180-length) = 180*length - length^2

Because the sum of length and width must always be 180, when one increases, the other decreases.

The largest area will happen when the derivative of the area is equal to 0. The derivative can be found with the power rule.

Derivative of Area (slope of Area) = 180 - 2*length

180 - 2*length = 0

180 = 2*length

length = 180/2 = 90ft

When the length is 90ft and width is 90ft, the area is 8100ft^2.

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Complete the missing value in the solution to the equation.<br> y=2x+5<br> x=2
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9

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Write <br>(6b)^2 without exponents
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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.
aleksandr82 [10.1K]

Answer:

The probability is 0.508 = 50.8%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.0525 g.

This means that \mu = 0.8544, \sigma = 0.0525

If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8535 g.

This is 1 subtracted by the pvalue of Z when X = 0.8535. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0.8535 - 0.8544}{0.0525}

Z = -0.02

Z = -0.02 has a pvalue of 0.492

1 - 0.492 = 0.508

The probability is 0.508 = 50.8%.

8 0
3 years ago
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