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2 years ago

5

A library contains 60,000 books. 14,000 are the subject of business. 22,000 are on healthcare and and 12,000 on psychology and l

aw . What percentage of the library books is on computing . If computing books make up two thirds of the remainder

1 answer:

PIT_PIT [208]2 years ago

5 0

Answer:

20%

Step-by-step explanation:

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A rectangular solid with a square base has a volume of 5832 cubic inches. (Let x represent the length of the sides of the square

Aleks04 [339]

Answer:

a) 18 in x 18 in x 18 in

b) $S = 1944\ in2$

Step-by-step explanation:

a) Let's call 's' the side of the square base and 'h' the height of the solid.

The surface area is given by the equation:

$S = 2s^2 + 4sh$

The volume of the solid is given by the equation:

$V = s^2h = 5832$

From the volume equation, we have that:

$h = 5832/s^2$

Then, using this value of h in the surface area equation, we have:

$S = 2s^2 + 4s(5832/s^2)$

$S = 2s^2 + 23328/s$

To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:

$dS/ds = 4s - 23328/s^2 = 0$

$4s = 23328/s^2$

$4s^3 = 23328$

$s^3 = 23328/4 = 5832$

$s = 18\ inches$

The height of the solid is:

$h = 5832/(18)^2 = 18\ inches$

b) The minimum surface area is:

$S = 2(18)^2 + 4(18)(18)$

$S = 1944\ in2$

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2 years ago

Sara wants to find the input value that produces the same output for the functions represented by the tables.

Korolek [52]

Answer:

The input value that produces the same output value in both charts is 2.

Step-by-step explanation:

You are given two functions $f(x)=-0.5x+2$ and $g(x)=2x-3$ with tables

$\begin{array}{cc}x&f(x)\\-3&3.5\\-2&3\\-1&2.5\\0&2\\1&1.5\\2&1\\3&0.5\end{array}$

and

$\begin{array}{cc}x&g(x)\\-3&\\-2&\\-1&\\0&\\1&\\2&\\3&\end{array}$

First, fill in the second table:

$g(-3)=2\cdot (-3)-3=-6-3=-9\\ \\g(-2)=2\cdot (-2)-3=-7\\ \\g(-1)=2\cdot (-1)-3=-5\\ \\g(0)=2\cdot 0-3=-3\\ \\g(1)=2\cdot 1-3=-1\\ \\g(2)=2\cdot 2-3=1\\ \\g(3)=2\cdot 3-3=3$

Hence, the second table is

$\begin{array}{cc}x&g(x)\\-3&-9\\-2&-7\\-1&-5\\0&-3\\1&-1\\2&1\\3&3\end{array}$

The input value that produces the same output value in both charts is 2.

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Step-by-step explanation:

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BAngle AOB is half as big as angle COB.

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