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3 years ago

What is 18+(-8) + 11 simplified?

1 answer:

8 0

18 + (-8) + 11

Adding a negative number is the same as subtracting a positive number. So "18-8" is the same thing as "18+ -8".

18 - 8 + 11

10 + 11

21

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Over the past week, 40% of the phone calls to Alicia's cell phone were from her son. Let's say you know that her son called her

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She received 12 calls from her son and 30 calls in total.

40% of 30 is 12.

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2 years ago

Solve the system y = 2x + 9 and 3y = 6x + 18 by using graph paper or graphing technology. What is the solution to the system?

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3 years ago

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

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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

Imagine that you have a very large barrel that contains tens of thousands of M&M's. According to the official M&M websit

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Answer:

(A)20%, 20%, 20%, 20%, 20%

Step-by-step explanation:

We are told that 20% of the M&M's produced by the Mars Corporation are Orange in color. If 5 students take a random sample of 50 M&M's, the most plausible percentage of orange candies that will be obtained is:

20%, 20%, 20%, 20%, 20%

This is as a result of the fact that in research experiments, a sample is a representation of the whole. Any result which holds for a random sample should hold for the total population and vice versa.

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3 years ago

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What is ZI? Can you specify? thanks

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