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2 years ago

Use the chain rule to find dz/dt. z = xy9 − x2y, x = t2 + 1, y = t2 − 1

1 answer:

7 0

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial 
x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial 
y}\dfrac{\mathrm dy}{\mathrm dt}$
$\dfrac{\mathrm dz}{\mathrm dt}=(y^9-2xy)(2t)+(9xy^8-x^2)(2t)$
$\dfrac{\mathrm dz}{\mathrm dt}=20t^{19}-144t^{17}+432t^{15}-672t^{13}+504t^{11}-336t^7+282t^5-112t^3+18t$

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What is the average speed of a runner if he ran 2 1/3 of a mile in 20 minutes?

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7 MPH because 2 1/3
in 20 minutes. So you multiply 20 by 3 you get 60. Then you multiply 2 by 3 you get 6. Then you multiply 1/3 x 3 and you get 1. 6=1=7 Hope This Helps

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2 years ago

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Identify whether the series summation of 12 open parentheses 3 over 5 close parentheses to the I minus 1 power from 1 to infinit

Finger [1]

∑ from 1 to infinity of 12(3/5)^(i - 1)
Since the common ratio is less than 1, the series is convegent. [i.e. 3/5 < 1]

Sum to infinity of a geometric series is given by a/(1 - r); where a is the first term, and r is the common ratio.

Sum = 12/(1 - 3/5) = 12/(2/5) = 30.

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2 years ago

The grocery store is having a sale on frozen vegetables. 4 bags are being sold for $11.96. At this rate what is the cost of: 9 b

Alexandra [31]

Answer:

$26.91

Step-by-step explanation:

11.96 divided 4 = 2.99

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2 years ago

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According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per w

Nadusha1986 [10]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 17

For the alternative hypothesis,

µ < 17

This is a left tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 80,

Degrees of freedom, df = n - 1 = 80 - 1 = 79

t = (x - µ)/(s/√n)

Where

x = sample mean = 15.6

µ = population mean = 17

s = samples standard deviation = 4.5

t = (15.6 - 17)/(4.5/√80) = - 2.78

We would determine the p value using the t test calculator. It becomes

p = 0.0034

Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.

The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.

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2 years ago

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected resi

SVETLANKA909090 [29]

Answer:

a) Mean = 1030; Standard deviation = 12.38.

b) The county result is unusually high.

Step-by-step explanation:

Problems of normally distributed samples can be 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

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

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This first question is a binomial propability distribution.

We have a sample of 1210 Amricans, so $n = 1210$ .