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Irina18 [472]
3 years ago
5

Alphabet cutouts come in packages of 6 sheets for $8. How much does Tanesha spend on alphabet cutouts if she need 72 sheets?

Mathematics
2 answers:
ad-work [718]3 years ago
6 0

Answer:

$96

Step-by-step explanation:

Let's set up a proportion using the following setup.

cost/sheets=cost/sheets

It costs $8 for 6 sheets.

$8 / 6 sheets= cost/sheets

We don't know how much it costs for 72 sheets. Therefore, we can say it costs $x for 72 sheets.

$8 / 6 sheets= $x / 72 sheets

8/6=x/72

We want to find out what x is. Therefore, we need to get x by itself.

x is being divided by 72. The inverse of division is multiplication. Multiply both sides by 72.

72*(8/6)=(x/2)*72

72*8/6=x

95.9999998=x

Round to the nearest dollar.

The 9 in the tenth place tells us to round 95 to 96.

96=x

She needs $96 for 72 sheets of alphabet cutouts.

Darina [25.2K]3 years ago
4 0

Hey there! :)

Answer:

$96 spent.

Step-by-step explanation:

Set up a proportion to determine the amount spend for 72 sheets. Express it in sheets/amount spent:

\frac{6}{8} = \frac{72}{x}

Cross multiply:

6 · x = 8 · 72

6x = 576

Divide:

x = $96 spent for 72 sheets.

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I know it's not a 3 digit number, but it's impossible to make a 3 digit number in your specifications.

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2 years ago
A candy box is made from a piece of cardboard that measures 23 by 13 inches. Squares of equal size will be cut out of each corne
wolverine [178]

Answer:

2.67 inches.

Step-by-step explanation:

Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).

The formula for a rectangular box = L × B × W

= (23 -2y)(13-2y) (y)

= (299 - 46y - 26y + 4y²)y

= 299y - 72y² + 4y³

Now for the maximum volume:

dV/dy = 0

This implies that:

299y - 72y² + 4y³ = 299 - 144y + 12y² = 0

By using the quadratic formula; we have :

= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}

where;

a = 12; b = -144 and c = 299

= \dfrac{-(-144) \pm \sqrt{(-144)^2 -4(12)(299)}}{2(12)}

= \dfrac{144 \pm \sqrt{20736 -14352}}{24}

= \dfrac{144 \pm \sqrt{6384}}{24}

= \dfrac{144 \pm79.90}{24}

= \dfrac{144 + 79.90}{24} \ \  OR  \ \   \dfrac{144 - 79.90}{24}

= 9.33 \ \  OR  \ \ 2.67

Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33

Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.

3 0
3 years ago
A cereal box is 9 1 2 inches long, 5 1 2 inches wide, and 12 inches high. What is the volume of the box?
lara31 [8.8K]

Answer

5603328

Step by step explanation:

Hey! Rmemeber length x width x height!

Multiply: 9 1 2 x 5 1 2 x 12

Answer= 5603328

And thats it! If it is wrong you must have put the wrong numbers in, I dont get why their spaces though....

Have a good day!!

6 0
2 years ago
Describe several real world situations can be modeled by equations of the form Y equals MX plus be or Y equals MX explain how th
lara [203]

The linear equation represents y = mx + b describes several real world situations such as

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<u>Step-by-step explanation</u>:

Linear equations  y = mx + b.  

m is your rate of change.

b is your constant. This is the initial value of y. The value of y when x is 0.

Finally, y is the thing that depends on x.

Oh right, examples:  

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total cost = 25(cartridges I buy) + 100 or y = 25x + 100

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amount left on card = -$1(songs bought) + 100 or y = -x +100

5 0
3 years ago
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