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3 years ago

The mean cost for a pint of frozen yogurt is $1.50, with a standard deviation of $0.10.

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

The correct answer is:

0.01$ (c)

Step-by-step explanation:

Standard deviation is a measure of how spread out numbers are from the mean value. The formula for standard deviation is given by:

$s = \sqrt{\frac{\sum(x - \bar x)}{n} } \\where:\\x = sample\ \\\bar x\ = mean\\n\ = number\ of\ samples\$

Variance is a measure of the squared differences from the mean.

Variance is simply the square of the standard deviation. It is mathematically shown as:

$s^2 = \frac{\sum(x - \bar x)}{n} }$

Now in our example,

Stabnard deviation = $0.10

Variance = (standard deviation)²

Variance = (0.10)²

Variance = $0.01

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3 years ago

Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

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The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
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and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
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3 years ago

Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can tra

alex41 [277]

Youssef lives 15 blocks away from his work

Solution:

Given that Youssef can either way from his home to his workplace or ride his bicycle

Let "x" be number of blocks away from work Youssef works

Case 1: walking

He walks at a pace of 1 block per min

Therefore,

1 block = 1 minute

Thus to cross "x" blocks he takes "x" minutes

Case 2: Bicycle

He can travel 1 block in 20 sec on his bicycle

We know that,

To convert seconds to minute, divide the time value by 60

$\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes$

Thus he takes 1/3 minutes for 1 block

So to cross "x" blocks he will take $\frac{x}{3}$ minutes

Given that it takes youssef 10 min longer to walk to work than to ride his bike

This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

$\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15$

Thus he lives 15 blocks away from his work

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3 years ago

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Andreas93 [3]

9514 1404 393

Answer:

Step-by-step explanation:

The product of the given numbers is 38.4888. Rounding this to two significant digits gets you 38.

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