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3 years ago

What is the mean of the dot plot???

Mathematics

1 answer:

vichka [17]3 years ago

7 0

Answer:

19.5 (Rounded: 20)

Step-by-step explanation:

In math, the mean is every number added together, then divided by the amount of numbers. For example, 1,2,5,4,8 would have a median of 4.

<em>(1 + 2 + 4 + 5 + 8 = 20 ÷ 5 = 4)</em>

Your dot plot has 14 total numbers, meaning that you add up all the numbers and divide by 14.

16 + 17 + 17 + 17 + 17 + 19 + 19 + 19 + 19 + 21 + 22 + 22 + 23 + 25 = 273

273 ÷ 14 = 19.5

If you don't need to round, 19.5 is correct. However, if you need to round my best guess is 20. Good luck!

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3 years ago

AC=8x-14 and EC=2x+11, solve for x

dimaraw [331]

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3 years ago

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

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Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

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∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

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⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

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2 years ago

What is the mean of the dot plot???​

What is the mean of the dot plot???