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3 years ago

14

A total of 768 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 more

2 answers:

sergejj [24]3 years ago

8 0

Answer:

Let x = the number of adult tickets sold

Let x + 61 = the number of student tickets sold

x + x + 61 = 761

2x = 700

x = 350

x + 61 = 411

Ymorist [56]3 years ago

8 0

Answer:

i could meane that only the adults bought 768 totel

Step-by-step explanation:

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Gayle is making gift bags and must tie 250 ribbons to them. If Gayle can tie 4 ribbons every 10 minutes, how long will it take G

mart [117]

Answer:

625 minutes

Step-by-step explanation:

Given that:

Time taken to tie 4 ribbons = 10 minutes

Number of ribbons to be tied = 250

To find:

Time taken to tie 250 ribbons.

Solution:

First of all, we need to find the time taken to tie one ribbon.

And then we can multiply it with 250 to find the time taken to tie all the 250 ribbons.

For finding the time to tie one ribbon, we need to divide the time taken to tie 4 ribbons with 4.

Time taken to tie 1 ribbon = $\frac{10}{4} = 2.5$ minutes

Time taken to tie 250 ribbons = 2.5 $\times$ 250 = <em>625 minutes</em>

4 0

3 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

3 years ago

Tara has 39 red pens she has to get 125 pens how many more pens does she need?

Crank

Answer: She needs 86 more pens

Step-by-step explanation: She starts off with 39 pens and she needs to get to 125 so you would subtract 39 from 125 and you would find the answer to how many more she needs.

4 0

3 years ago

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HELP! 8TH GRADE MATH PLS LOL

LekaFEV [45]

<h2><u>Given</u><u>:</u><u>-</u></h2>

${ \large{➢ \: \: \bf{x = - 8}}}$

<h2><u>Solution</u><u>:</u><u>-</u></h2>

${ \large{➢ \: \: \bf{ \dfrac{2y}{3} = 3 \times - 8 + 34}}}$

${ \large{➢ \: \: \bf{ \dfrac{2y}{3} = - 24 + 34}}}$

${ \large{ \bf{ ➢ \: \: \cancel{2}y = 3 \times { \cancel{(10)} {} \: \: ^{5} }}}}$

${ \large{ \therefore{ \bf{y = 15 \: \: Ans.}}}}$

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3 years ago

In each box, 20% of the total candies are grape flavored.

mrs_skeptik [129]

Answer:

9

Step-by-step explanation:

20 x 5 = 100

45/5 = 9

9 to 20 = 11

45 to 100 = 55

<u>55</u> = 5<--- Linear

11

(since the total answer is linear, the answer is right)

6 0

3 years ago

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