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riadik2000 [5.3K]
4 years ago
7

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half of its initial m

ass. Starting with 195 g of radioactive isotope how much will be left after five lives? round to the nearest gram
Mathematics
1 answer:
Dovator [93]4 years ago
4 0
1st half life: 195/2 = 97.5 g
2nd half life: 97.5/2 = 48.75 g
3rd half life: 48.7/2 = 24.375 g
4th half life: 24.375/2 = 12.1875 g
5th half life: 12.1875/2 = 6.09375 g

or you can do
195(2)^(-5) = 6.09375
** rounded to nearest gram = 6 g

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A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than
Volgvan

Answer:

Length = 8 inches

Width = 4 inches

Height = 6 inches

Step-by-step explanation:

Volume of the box = 192 cubic inches

Volume of a box = length × width × height

Let

Width = x

Length = 2x

Height = x + 2

Volume of a box = length × width × height

192 = 2x * x * (x + 2)

192 = 2x^2 (x + 2)

192 = 2x^3 + 4x^2

Divide through by 2

96 = x^3 + 2x^2

Subtract 96 from both sides

x ^3 + 2x^2 - 96 = 0

Factorise

(x - 4) (x^2 + 6x + 24) = 0

x^2 + 6x + 24 has no real x-value

So,

Divide both sides by (x^2 + 6x + 24).

0 ÷ (x^2 + 6x + 24) = 0

So,

(x - 4) = 0

x = 4

Width = x = 4 inches

Length = 2x

= 2(4)

= 8 inches

Height = x + 2

= 4 + 2

= 6 inches

Check:

Volume of a box = length × width × height

= (8 * 4 * 6) inches

= 192 inches

4 0
3 years ago
Which line segment is parallel to GE?<br><br> DH<br> KI<br> FG<br> HI
son4ous [18]

The right answer is KI


This is a square prism. The bases of this type of prism are squares. In square prisms the opposite sides and angles are congruent. In this problem, we need to find which line segment is parallel to GE, so the right answer is KI as solved in the Figure bellow. Recall that parallel lines are lines that have the same distance apart called equidistant.

7 0
3 years ago
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Divide $500 in the ratio 1:4
dezoksy [38]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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In the figure shown the value of a is equal to
Vikentia [17]

Answer:

a = 7.2

Step-by-step explanation:

The figure has been re-labelled and attached to this response.

From the figure, the larger right triangle DAB and the small right triangle BCA are similar. This is because;

i. They have two corresponding congruent angles which are<em> the right angle</em>

and <em>angle B</em>

Therefore, we can say that;

\frac{|DB|}{|BA|} = \frac{|AB|}{|BC|}

\frac{13}{a} = \frac{a}{4}

<em>Cross multiply</em>

a x a = 13 x 4

a² = 52

a = √52

a = 7.2

Note: The figure showing the similar triangles has also been attached to this response.

6 0
3 years ago
A sector of a circle of radius is 15Cm, and angle 216 degrees is bent to form a cone. What is base radius of the cone and the ve
-Dominant- [34]

Answer:

Step-by-step explanation:

Radius r = 15

Circumference = 2πr = 30π cm

Circumference of cone = arc length of sector

= 30π × 216°/360°

= 18π cm

Radius of base of cone = 18π/(2π) = 9 cm

Slant height of cone = radius of circle = 15 cm

Height of cone = √(15² - 9²) = 12 cm

3 0
3 years ago
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