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3 years ago

If twelve inches correspond to 30.48 centimeters, how many centimeters are there in thirty inches?

Mathematics

1 answer:

GenaCL600 [577]3 years ago

4 0

Answer:

76.2 cm

Step-by-step explanation:

Do 30.48 / 12 to find the amount of centimeters per inch. 30.48 / 12 = 2.54

So, for ever inch, there are 2.54 cm. Now to find the amount of centimeters in thirty inches, do 2.54 x 30 = 76.2.

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What is 28- 12.5% decrease???

OLEGan [10]

Ok so I assume
28 and decreased by 12.5%

percent means partst out of 100 so
12.5%=12.5/100=0.125
first find 12.5% of 28 then subtract
0.125 times 28=3.5
decrease
28-3.5=24.5

answer is 24.5

3 0

3 years ago

505.45 55% of what amount

Nana76 [90]

Answer: 919

Step-by-step explanation: I set up a cross multiplication equation. I set 55 over 100 equal to 505.45 over X. I cross multiplied and did 505.45 times 100, which is 50,545. I then did 50,545 divided by 55 to get the answer of 919.

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3 years ago

Pardon my dear aunt Sally

Tatiana [17]

If that's a way to remember PEMDAS, then it's Please Excuse My Dear Aunt Sally.

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3 years ago

What is the range of the graph

natta225 [31]

Answer:

You're correct the answer is B) $-5 \leq y \leq -1$

Step-by-step explanation:

The key behind this problem is think about the function $\sqrt[3]{x}$ and think what happen when you plug in values in it.

So we're going to try with some simply values for evaluate

$\sqrt[3]{-8} = -2$

$\sqrt[3]-1} = -1$

$\sqrt[3]{0} = 0$

$\sqrt[3]{1} = 1$

$\sqrt[3]{8} = 2$

How you can see when plug in a negative number the function return a negative number, but when you plug in a positive number the function return a positive number (this isn't a proof of this happen in each value of the given interval, but is a good way of demonstrate the relation). This means that when you plug in a value this value is greater than the value of before, so the function is increasing it's outputs.

Now this is good because that's mean that the limits of the range are the limits of the domain evaluates in the function (because the smaller input give us the smaller output and the same with the greater). But the given function have different operation in it, so you have to interpret this operations of this way:

When you have a negative value in the $x$ like in this occasion ( $\sqrt[3]{-x}$ ) the function reflex it's values with respect to the y axis (image put the functions in a mirror a draw the given image in the same cartesian plane).
And you have a -3 this is move each value of the function 3 units down.

So with this information you evaluate each limit of the domain $\{-8, 8\}$ in the function and get the limits for the range.

$f(-8) = \sqrt[3]{-(-8)} -3= \sqrt[3]{8} -3 = 2 -3 = -1$

$f(8) = \sqrt[3]{-8} -3= -2 -3 = -5$

So the range of the function in the given interval is equal to $\{-1, -5\}$ in the interval notation is equal to $-5 \leq y \leq -1$

4 0

2 years ago

Question 1

anastassius [24]

Answer:

a ) Surface Area ⇒ 222 cm^2, Volume ⇒ 180 cm^3

b ) Surface Area ⇒ 372 cm^2, Volume ⇒ 360 cm^3

c ) Surface Area Increase ⇒ ( About ) 67.56 %, Volume Increase ⇒ 100 %

Step-by-step explanation:

a ) Consider dividing the figure into parts, first solving for the area of the base, using the attachment below for guidance;

As you can see, in the picture I have made it so that the base is nested in a rectangle with dimensions 8 by 5. Calculating the area of this rectangle, subtracting the area of a square with dimensions 2 by 2 cm, we can derive the area of the base in a much quicker manner;

$Area of Base - ( 8 cm * 5 cm ) - ( 2 cm* 2 cm ) = 40 square cm - 4 square cm = \\Solution; Base = 36 square cm$

Now let us imagine adding the another dimensions to this two dimensional base. That would make a 3 - d prism, with surface area equivalent to mini rectangles and squares with a common dimension being the length of the height; 5 cm

$Area of 1 Square = 5 cm * 5 cm = 25 square cm,\\Area of 2 Square = 25 square cm,\\Area of 1 Rectangle = 3 cm * 5 cm = 15 square cm,\\Area of 2 Rectangle = 15 square cm,\\Area of 3 Rectangle = 2 cm * 5 cm = 10 square cm,\\Area of 4 Rectangle = 10 square cm,\\Area of 5 Rectangle = 10 square cm,\\Area of 6 Rectangle = 8 cm * 5 cm = 40 square cm\\Area of Base 2 = 36 square cm,\\\\Surface Area of Figure = 25 + 25 + 15 + 15 + 10 + 10 + 10 + 40 + 36 + 36 = 222 square cm\\Volume = 36 square cm * 5 cm = 180cubiccm$

b ) We have calculated the area of the base before, now let us solve for all the " mini shapes " given a new height of 10 cm;

$Area of Rectangle 1 = 5 cm * 10 cm = 50 cm^2,\\Area of Rectangle 2 = 50 cm^2,\\Area of Rectangle 3 = 3 cm* 10 cm = 30 cm^2,\\Area of Rectangle 4 = 30 cm^2,\\Area of Rectangle 5 = 2 cm * 10 cm = 20 cm^2,\\Area of Rectangle 6 = 20 cm^2,\\Area of Rectangle 7 = 20 cm^2,\\Area of Rectangle 8 = 8 cm * 10 cm = 80 cm^2,\\\\Surface Area of Figure = 50 + 50 + 30 + 30 + 20 + 20 + 20 + 80 + 36 + 36 = 372 cm^2\\Volume of Figure = 36 cm^2 * 10 cm = 360 cubic cm$

c ) <em>Solution; Increase of Surface Area ⇒ ( About ) 67.56 %, Increase of Volume ⇒ 100 %</em>

8 0

3 years ago