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3 years ago

5

to make a greeting card Bryce use 1/8 sheet of red paper 3/8 sheet of green paper and 7/8 sheet of white paper how many sheets o

f paper did Bryce use?

2 answers:

morpeh [17]3 years ago

6 0

He used 1.3 sheets of paper, or 1 and 3/8 of a sheet.

Marina86 [1]3 years ago

6 0

You add 1/8 to 3/8 to get 4/8, then you add 7/8 to get 11/8, as a mixed number that is 1 and 3/8 of paper

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PSYCHO15rus [73]

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3 years ago

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Vladimir [108]

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3 years ago

You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

$Radius = 6cm$

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

$V = 432\pi$

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

$V = \pi r^2h\\$

Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

$A=2\pi (\frac{432}{r})+2\pi r^2$

Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

$\frac{432}{r^2} = 2r$

Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

$r = 6$

Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

$h = \frac{432}{36}$

$h = 12$

Hence, the dimension that requires the least amount of material is when

$Height = 12cm$

$Radius = 6cm$

3 0

3 years ago

Uma rede de supermercados fornece a seus clientes um cartão de crédito cuja identificação é formada por 3 letras distintas (dent

Vitek1552 [10]

Answer:

The correct option is (A) 33,600.

Step-by-step explanation:

The question is:

A supermarket chain provides its customers with a credit card whose identification is formed by 3 different letters (among 26), followed by 4 different digits. A given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1. The total number of distinct cards offered by such supermarket chain for that city is A) 33600 B) 37800 C) 43200 D ) 58500 E) 67600

Solution:

The general format of the credit cards provided by a supermarket chain is as follows:

<u>X</u> <u>X</u> <u>X</u> <u>#</u> <u>#</u> <u>#</u> <u>#</u>

Here, <em>X</em> represents letters and # represents numbers.

All the three letters have to different and all the four numbers have to different, i.e. no repetition allowed.

It is provided that a given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1.

Then the general format of this cities credit cards is as follows:

<u>X</u> <u>X</u> <u>L</u> <u>#</u> <u>#</u> <u>1</u> <u>0</u>

Now there are two spaces left for letters and 2 for numbers.

As there are no repetition allowed the two letter spaces can be filled by:

Number of ways to select 2 letters = 25 × 24 = 600

And the number of ways to select two numbers when there is no repetition allowed is:

Number of ways to select 2 numbers = 8 × 7 = 56

Compute the total number credit cards available at the supermarket as follows:

Total number credit cards = 600 × 56 = 33600

Thus, the total number of distinct cards offered by such supermarket chain for that city is 33,600.

The correct option is (A).

3 0

3 years ago

PLEASE HELP FAST 100 EASY POINTS WILL MARK BRAINLEST!!!

spin [16.1K]

Answer:

$y=-1x+8 \\or\\y=-x+8$

Step-by-step explanation:

Okay so we know that line on the triangle DEF that's parallel to the line BC is EF. This because they have the same slope and we can prove that while solving for slope-intercept form.

First we figure out our points for both the lines:

BC: $B=(-2,4) \\C=(1,1)$

EF: $E=(4,4)\\F=(6,2)$

Now that we have our points we can use the slope formula to prove these two line have the same slope and are therefore parallel to eachother:

$\frac{y_1-y_2}{x_1-x_2}$ = Slope Formula

BC = $\frac{4-1}{-2-1} =\frac{3}{-3} =\frac{-3}{3} =-1$

EF = $\frac{4-2}{4-6} =\frac{2}{-2}=\frac{-2}{2}= -1$

So now we proved that both of these lines have a slope of -1. Then we can use the slope intercept formula and one of the points from the line EF to find the y-intercept of the of line EF:

Let's use point = $(4,4)$

$y=4,m=-1,x=4,b=?$

$y=mx+b\\4=-1(4)+b\\4=-4+b\\(+4) 4=-4+b(+4)\\8=b$

We used the formula and found that the y-intercept was $(0,8)$ , so now we plug in all of our answers:

$y=-1x+8$

This is the complete answer but if you wanted to simplify it more you could write it as $y=-x+8$ , cause as long as you make the x negative in the equation it will always be as if you multiplied it by -1.

7 0

2 years ago