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Answer:

The substance half-life is of 4.98 days.

Step-by-step explanation:

Equation for an amount of a decaying substance:

The equation for the amount of a substance that decay exponentially has the following format:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which k is the decay rate, as a decimal.

k-value of 0.1392.

This means that:

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

Find the substance's half life, in days.

This is t for which [tex]A(t) = 0.5A(0)[/tex]. So

[tex]A(t) = A(0)e^{-0.1392t}[/tex]

[tex]0.5A(0) = A(0)e^{-0.1392t}[/tex]

[tex]e^{-0.1392t} = 0.5[/tex]

[tex]\ln{e^{-0.1392t}} = \ln{0.5}[/tex]

[tex]-0.1392t = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.1392}[/tex]

[tex]t = 4.98[/tex]

The substance half-life is of 4.98 days.

Answer:

180

Step-by-step explanation:

90 + 4x + 7x - 20 equals to 180

Answer:

B. 50

Step-by-step explanation:

Answer:  sorry i dont know this

Step-by-step explanation:

Answer:

To make a "clean getaway"

Step-by-step explanation:

haha, nice one :D

Decimal form is 3.96811878

Answer:

the angle shown is a straight angle value of which is equal to 180°

3x + 30. 6 = 180

3x = 180 - 30. 6

3x = 149.4

Answer:

Step-by-step explanation:

A=bh A=7*8 A=56units^2

Answer:

34

Step-by-step explanation:

i think its 34

Answer:

256

Step-by-step explanation:

4^4^4 = 4^(4^4) = 4^256

so written in base 4, there will be 256 zeroes after a 1.

This translates to approximately 154 digits in decimal.

Just like 2^2^2 =  2^4

there will be four zeroes after a 1.

2^2^2=2^(2^2) = 2^4 = 16 = 10000 (16 in base 2).

Answer: [tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given

There are 9 chips numbered 1 to 9 placed in a box

Margie selected one chip from the box

If the chip is multiple of 3 then the chip can be 3, 6, or 9

So, the probability associated with this is

[tex]\Rightarrow P=\dfrac{\text{favorable}}{\text{Total}}\\\\\Rightarrow P=\dfrac{3}{9}\\\\\Rightarrow P=\dfrac{1}{3}[/tex]

Answer:

25 hours

Step-by-step explanation:

first you ask yourself that :

if it takes just 10 hrs to make $80 , would it take more or less hours to make $200.

The answer is it will take more hours to make $200,

Based on this idea established: we say if it's giving more then less would divide.

so therefore:

we have

[tex] \frac{200}{80} \times 10 [/tex]

finally we have 25 hours.

Thanks

Answer:

16

Step-by-step explanation:

AB = BC    

32[tex]\sqrt{2}[/tex] = [tex]\sqrt{2 *AB^{2} } \\ => AB = 32 = BC\\x= BC/2 => x = 32/ 2 = 16[/tex]

Answer:

She swims 9m in one second

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

hey

Answer:

I thing answer is no. D .....

Answer:

1. Right Triangle

2. Right Triangle

3. Not a Right Triangle

4. Not a Right Triangle

Answer:

6 cm

Step-by-step explanation:

Given :

base is 9cm, Height is 4cm, and Length is 12cm.

Volume of triangular prism :

V = 1/2 * base * height * length

V = 1/2 * 9 * 4 * 12

V = 9 * 2 * 12

V = 216 cm³

Volume of a cube = a³

Where , a = side length

If 216cm³ is melted to form a cube

Then ;

a = 216^1/3

a = 6 cm

Answer:

BRO I HAVE THE SAME QUESTION FOR MY TEST....

ITS BIASED IM REALLLLY SURE

Step-by-step explanation:

Answer:

226

Step-by-step explanation:

Area of rectangle:

x+6=17

x=11

11+6=17

11+3=14

17×14=238

Area of triangle:

[tex] \frac{1}{2} \times b \times h[/tex]

Use phytagoras theorem to find the base of the triangle:

c²=a²+b²

5²=4²+b²

25=16+b²

b²=25-16

b²=9

b=√9

b=3 (only the half)

b=6 (the whole base)

[tex] \frac{1}{2} \times 6 \times 4[/tex]

3×4

12

Shades region:

238-12

=226

Answer:

43.9823

Step-by-step explanation:

[tex]Arc length = 2\pi r(\frac{0}{360} )\\ = 2\pi 12(\frac{210}{360} )[/tex]

Answer:

g(x) = 12*x^2 + 8

Step-by-step explanation:

For a function f(x), a vertical stretch of scale factor k is defined as:

g(x) = k*f(x)

In this case, we know that f(x) = 3*x^2 + 2

And the function g(x) is the function f(x) vertically stretched by a factor of 4, then we have k = 4

and:

g(x) = 4*f(x)

Replacing by the actual function, we get

g(x) = 4*(3*x^2 + 2)

g(x) = 4*3*x^2 + 4*2

g(x) = 12*x^2 + 8

Yes, this parabola is a function because it passes the vertical line test!

The vertical line test is a test where you move left to right over a graph, and look to see if there are any instances where the vertical line touches two points at the same time. If not, then the graph is a function!

Hope this helps!! :)

Answer:

857.766cm^3

Step-by-step explanation:

Given data

Lenght = 3m

Internal radius r = 3m

External radius R= 10m

Volume of pipe= πr^2h

Volume of metal= External - Internal

Volume= πR^2h-πr^2h

Volume= πh(R^2-r^2)

Volume= 3.142*3(10^2-3^2)

Volume= 3.142*3(100-9)

Volume= 9.426*(91)

Volume= 857.766cm^3

Hence the volume of the metal is 857.766cm^3

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1

Answer:

The answer to the problem is 15.

Answer:

0.25 and 25% are equivalent

Step-by-step explanation:

Answer:

4³=4*4*4 is a required expanded form.

Answer:

3(p - 5) + 2s should be the correct answer!

Step-by-step explanation:

3 henna powder, and you get $5 off each henna powder so equation is 3(p - 5)

2 bottle so, 2s

add them up and get the answer

Anyways, hope this helped!

Answer:

Step-by-step explanation:

90 = 10x+30

60 = 10x

6 = x

Answer:

Step-by-step explanation:

6^4*612/6^7

6^4*6^12-7

6^4*6^5

6^4+5

6^9