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3 years ago

Is 10 thousands, 5 hundreds greater than or less than 1,050 tens

Mathematics

2 answers:

Olegator [25]3 years ago

4 0

Its greater than 1,050 tens.

elixir [45]3 years ago

3 0

It greater because 1050 is smaller than 10,500

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Find the median of the set of data. <br><br> 4, 16, 7, 10, 15, 11, 13, 20

Rainbow [258]

The median is twelve [12].

8 0

3 years ago

Read 2 more answers

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

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3 years ago

How many three-digit positive integers <img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle"

Anastaziya [24]

Answer:

Step-by-step explanation:

Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.

As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.

_____

The equation reduces, mod 23, to ...

10x = 11

Its solutions are x = 23n +8.

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2 years ago

What is the interest rate $2,200 at 7.5% for 3 1/4 years

Phoenix [80]

Answer:

$536.25

Step-by-step explanation:

First, you need to find what 7.5% of $2,200 is,

(2200/100)7.5=165

then to find how much interest has accumulated over 3 1/4 year you need to multiply the one-year interest rate by the 3.25

(165)3.25=536.25

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3 years ago

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr^2. Find the instantaneous rate of change of the surface area

8090 [49]

Instantaneous rate of change = S'(r) = 8πr
S'(8) = 8π(8) = 64π

Therefore, the instantaneoud rate of change of the <span>surface area with respect to the radius r at r = 8</span> is 64π

7 0

3 years ago