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dybincka [34]
3 years ago
11

The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3 cm/s. When the length is 2

0 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
Mathematics
1 answer:
Aloiza [94]3 years ago
8 0

Answer:

Step-by-step explanation:

let length=l

width=w

Area A=lw

\frac{dA}{dt}=l \frac{dw}{dt}+w \frac{di}{dt}\\\frac{dl}{dt}=8 cm/s\\\frac{dw}{dt}= 3 cm/s\\\frac{dA}{dt}=20 \times 3+10 \times 8=60+80=140 cm ^{2} /s

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cawnser is 60

Step-by-step explanation:

because 5 times 12 is 60 hours

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Drag numbers to the table so it shows a proportional relationship between x and y.
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6) If the perimeter of the equilateral triangle ABC is x inches. The mid points of the sides are joined to form the smaller tria
Nataliya [291]

Answer:

96 in

Step-by-step explanation:

If the midpoints of the sides are joined to form the smaller triangle, then the perimeter of the smaller triangle is half the perimeter of the greater triangle, because the sides of the smaller triangle are midlines of the greater triangle. By the triangle's midline theorem, each triangle's midline is half the side to which this midline is parallel.

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3 years ago
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly samp
aleksklad [387]

Answer:

95.44% probability the resulting sample proportion is within .04 of the true proportion.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sampling distribution of the sample proportion in sample of size n, the mean is \mu = p and the standard deviation is s = \sqrt{\frac{p(1-p)}{n}}

In this question:

p = 0.2, n = 400

So

\mu = 0.2, s = \sqrt{\frac{0.2*0.8}{400}} = 0.02

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.

X = 0.24

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

By the Central Limit Theorem

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

Z = \frac{0.24 - 0.2}{0.02}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 0.16

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

Z = \frac{0.16 - 0.2}{0.02}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

95.44% probability the resulting sample proportion is within .04 of the true proportion.

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3 years ago
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