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3 years ago

6

Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes. He estimates that the whole CD is about 30 minutes long.

Which statement about Maurice's estimate is true?

1 answer:

nlexa [21]3 years ago

6 0

Answer:

The estimate is less than the actual length of the CD.

Step-by-step explanation:

Consider the provided information.

Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes.

That means the minimum length of the CD should be: 12×3=36 minutes.

The maximum length of the CD should be: 12×4=48 minutes

He estimates that the whole CD is about 30 minutes long.

30 minutes is less than 36 minutes.

That means, the estimate is less than the actual length of the CD.

Hence, the correct statement is: The estimate is less than the actual length of the CD.

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Answer:
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Step-by-step explanation:
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3 years ago

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Answer:

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Step-by-step explanation:

The answer is because:

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3 years ago

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Step-by-step explanation:

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This can be carried out easily in stat-crunch;

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3 years ago

Three forces act on an object. Two of the forces are at an angle of 95◦ to each other and have magnitudes 35 N and 7 N. The thir

Cerrena [4.2K]

We want to find $\vec F_4$ such that the object needs is in equilibrium:

$\vec F_1+\vec F_2+\vec F_3+\vec F_4=\vec0$

We're told that $F_1=35\,\mathrm N$ , $F_2=7\,\mathrm N$ , and $F_3=9\,\mathrm N$ . We also know the angle between $\vec F_1$ and $\vec F_2$ is 95º, which means

$\vec F_1\cdot\vec F_2=F_1F_2\cos95^\circ=245\cos95^\circ$

$\vec F_3$ is perpendicular to both $\vec F_1$ and $\vec F_2$ , so $\vec F_1\cdot\vec F_3=\vec F_2\cdot\vec F_3=0$ .

If we take the dot product of $\vec F_1$ with the sum of all four vectors, we get

$\vec F_1\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\vec F_1\cdot\vec F_1+\vec F_1\cdot\vec F_2+\vec F_1\cdot\vec F_3+\vec F_1\cdot\vec F_4=0$

${F_1}^2+\vec F_1\cdot\vec F_2+0+\vec F_1\cdot\vec F_4=0$

$\implies\vec F_1\cdot\vec F_4=-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)$

We can do the same thing with $\vec F_2$ and $\vec F_3$ :

$\vec F_2\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies\vec F_2\cdot\vec F_4=-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)$

$\vec F_3\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies\vec F_3\cdot\vec F_4=-{F_3}^2$

Finally, if we do this with $\vec F_4$ , we get

$\vec F_4\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies{F_4}^2=-\left(\vec F_1\cdot\vec F_4+\vec F_2\cdot\vec F_4+\vec F_3\cdot\vec F_4\right)$

$\implies{F_4}^2=-\left(-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)-{F_3}^2\right)$

$\implies F_4=\sqrt{{F_1}^2+{F_2}^2+{F_3}^2+2(\vec F_1\cdot\vec F_2)}$

$\implies\boxed{F_4\approx36.2\,\mathrm N}$

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3 years ago