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2 years ago

5

a shelf holds 3 novels, 2 biographies, and 1 history book. two students in turn choose a book at radom. what is the probability

that the students choose both biographies?

1 answer:

shepuryov [24]2 years ago

3 0

1/2 choose biographies

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Suppose you are given a cube made of magnesium (mg) metal of edge length 2.15 cm. (a) calculate the number of mg atoms in the cu

SVETLANKA909090 [29]

solution:

a) To calculate the volume of cube of edge 1.0cm

Volume= (edge)³

=(100cm) ³

= 1cm³

To find the mass of MG atoms

Density = mass/volume

Mass of mg = 1.74g/cm³ x 1cm³

= 1.74g

To find the number of mg atoms,

Molar mass of mg = 24.31g

24.31g mg contain 6.022 x 10²³ atoms of mg

1.74g mg contain = 6.022 x 10²³mg atoms/24.31g mg x 1.74g mg

= 0.4310 x 10²³mg atoms

= 4.31 x 10²² mg atoms

B) to find the volume occupied by mg atoms

Total volume of cube = 1 cm³

Volume occupied by mg atoms

= 74% of 1cm³

=74/100 x 1cm³= 0.74cm³

To find the volume of 1 mg atom

4.31 x 10²² mg atoms occupy 0.74 cm³

1 atom will occupy 0.74cm³

1 atom will occupy = 0.74cm³/4.31 x 10²²mg atoms x 1mg atom

volume of 1 mg atom = 0.1716 x 10⁻²²cm²

Volume of 1 mg atom = 4/3 π³ in the form of sphere.

4/3πr³ = 0.1716 x 10⁻²²cm³

R³ = 0.1716 x 10⁻²²cm³x 4/3 x 7/22

R³ = 0.04095 x 10⁻²²cm³

R = 0.1599 x 10⁻⁷cm

1 = 10⁻¹⁰cm

= 0.1599 x 10⁻⁷cm

= 1pm/1 x 10⁻¹⁰cm x 0.1599 x 10-7cm

= 1.599 x 10² pm

R= 1.6 x 10²pm

3 0

2 years ago

Softa [21]

Answer: The customer should buy Giana’s jewelry box.

Step-by-step explanation:

The jewelry boxes are rectangular prisms, in order to find the box that would hold the most amount of jewelry we need to find the volumes of each box.

V= l.w.h

Katherine’s box: 5x5x5= 125

Giana’s box: 10x12x2= 240

Jackson’s box: 10x5x4= 200

3 0

3 years ago

Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$

Now, cross multiply.

$4b-8=b^2-2b$

$b^2-6b+8=0$

Solve for b. Factor using the numbers -4 and -2.

$=(b-4)(b-2)=0$

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

4 0

2 years ago

Help me please <br> PLEASEEE

vodka [1.7K]

So you can do 1/2 and then divide it by 1/8.

To divide by a fraction, multiply by its reciprocal.
So;
1/2 / 1/8 = 1/2•8/1

1/2• 8 = 8/2
8/2= 4

So he can fill 4 mugs!!!

Brainliest if i helped!

7 0

3 years ago

Read 2 more answers

Find y<br>Solve the simultaneous <br>equations<br><br><br>3x + 2y = 27 3x - Y = 9<br>

lutik1710 [3]

Answer:

$y = 6$

Step-by-step explanation:

To find $y$ , we need to eliminate $x$ in this system of equations:

$3\cdot x + 2\cdot y = 27$ (1)

$3\cdot x - y = 9$ (2)

From (1) and (2):

$x = \frac{27-2\cdot y}{3}$

$x = \frac{9+y}{3}$

Then, we equalize both expressions and solve for $y$ :

$\frac{27-2\cdot y}{3} = \frac{9+y}{3}$

$27-2\cdot y = 9 + y$

$3\cdot y = 18$

$y = 6$

6 0

3 years ago