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2 years ago

I didnt mean to click on the 31.50 but what is the answer ?

Mathematics

2 answers:

Viktor [21]2 years ago

8 0

If you add all of them together you get 11.25
Then times it by 6 and that’s 67.5 then add the zero and that gets you 67.50 and that’s your answer

Genrish500 [490]2 years ago

4 0

Answer:

D. $67.50

Step-by-step explanation:

A ticket costs $5.25, a drink costs $2.00, and a popcorn costs 4.00. Each person in the group buys all of these. So we know that each person is paying:

4.00 + 2.00 + 5.25 = 11.25

Since there are 6 people in the group we can multiply that by 6:

11.25 * 6 = 67.50

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Equation at the end of step 2 :

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The right denominator is : 9

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Calculating Multipliers :

3.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

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Denote the Right Multiplier by Right_M

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—————————————————— = —————

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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".

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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)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

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).

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12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 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.

Volume(v)= $(30-2x)\times (16-2x)\times x$

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

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

∴ Volume(v)= 725.93 inches³

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