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3 years ago

3.

Mathematics

2 answers:

lutik1710 [3]3 years ago

6 0

Answer:

First quartile: 17

Second quartile: 24.5

Third quartile: 32

ollegr [7]3 years ago

4 0

Answer:

Lower quartile (xL): 16.75

Median (xm): 24.5

Upper quartile (xU): 33.5

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32. Which of the following is horizontal ellipse

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b. 16x² + 25y² = 1

Step-by-step explanation:

Only one of them has a < b in ax² + by² = c formula, making its graph horizontal

All the rest are vertical, see attached

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3 years ago

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If you know that a < b, and both a and b are positive numbers, then what must be true about the relationship between the oppo

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3 years ago

Read 2 more answers

g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur

sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

$\displaystyle V = \pi r^2h$

Substitute:

$\displaystyle (300) = \pi r^2 h$

Solve for <em>h: </em>

$\displaystyle \frac{300}{\pi r^2} = h$

Recall that the surface area of a cylinder is given by:

$\displaystyle A = 2\pi r^2 + 2\pi rh$

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for <em>h</em>.

$\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r} \end{aligned}$

Find its derivative:

$\displaystyle A' = 4\pi r - \frac{600}{r^2}$

Solve for its zero(s):

$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

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3 years ago

Which expressions are equivalent to the one below? Check all that apply.

Shalnov [3]

Answer:

The answer would be A. 3.3x

Step-by-step explanation:

3.3x can be broken down as 3.3.x

3.3 equals 9 and the 'x' is multiplied to 9.

Hence, it equals to 9x.

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3 years ago