the half life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount . The half-life of the radioactive gas radon is approximately 3.8 days. The initial amount of radon used in an experiment is 75 grams. if N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives N in terms of t.
b. How much gas radon approximately remains after 3.8 days?
c. approximately when will the amount of radon remaining be 10 grams?

Answer:

It should be B

Step-by-step explanation:

2 2 -1 2 - -3 2 (2+-1)

1. Always do what's in parentheses

so we know that 1 is a negative and 2 is bigger than that number so you would just subtract normally.

2 2 -1 2 - -3 2 -1

Then get all exponents done.

4 -1 - 9-1

3-9-1

-6-1

Which should give u -5

The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

The difference formula in trignometry for the sine funciton is given as,

[tex]\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)[/tex]

The trignometric equation given in the problem is,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)[/tex]

Compare this equation with the above eqution, we get,

[tex]A=80^o\\B=20^o[/tex]

Thus, this equation can be written as,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}[/tex]

Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

Learn more about the difference formula in trignometry here;

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Answer:

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The given expression can be solved as shown below.

(2,3) - 3(1,1)

Multiply 3 in the second vector,

= (2,3) - (3,3)

Subtracting vectors

= (2-3, 3-3)

= (-1, 0)

Hence, the value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ5

Answer:

1376.1 ft^3

Step-by-step explanation:

The volume of a sphere formula: V=4/3πr^3

r = 6.9 ft

V = 4/3 * π * (6.9^3) = 1,376.055

to the nearest tenth it's 1376.1 ft^3

Answer:

Your answer would be:
3,384 books are left in the library

If each patron has 6 books, and there are 564 patrons:

564 x 6 = 3,384 books left

In conclusion, there are 3,384 books left in the library.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]

Answer:

See below.

Step-by-step explanation:

The answer would be 2 3/4.

The third tick represents 3/4, and this is between 2 and 3.

-hope it helps

Answer:

My guess is 2 3/4

Step-by-step explanation:

Sorry if i'm wrong, if im right can i have brainliest? So explanation is that the plotted point on the number line is c so that will make the numerator is id.k the difference between them the top of the number would be three because c is ploted on c and id.k how to get 4.

Answer:

43 ffhfhfhfhfhfhchchchchchc

Answer:

It will take 225 days for Evie's chicken to lay 45 eggs

Step-by-step explanation:

The amount of change Lucy receives if she paid with few $20 bills is $12.84

Total cost of pants = $21.79 × 4

= $87.16

If the total cost of the pants exceeds $80, then she paid with 5 $20 bills

5 $20 bills = $100

Her change = $100 - $87.16

= $12.84

Learn more about cost:

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Answer:

13

Step-by-step explanation:

7j=91

91/7=j

13

hope that helps:)

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.

  Cos = Adjacent/Hypotenuse

__

In the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...

  cos(A) = AB/AC

  cos(A) = 3/5

__

The right angle in the triangle is angle B. The cosine of a right angle is 0.

  cos(B) = 0

__

The side adjacent to angle C is CB, so its cosine is ...

  cos(C) = CB/AC

  cos(C) = 4/5

Answer:

cos <ABC=0

cos <BAC=3/5

cos<ACB=4/5

GIVE 5 STARS IF YOU DO RSM!!!

Answer:

1.

+4

number: 11

2.

x × 3

number: 48

3.

+5

number 46

4.

÷2

number: 19

5.

-1.5

number: 19.5

6.

-0.2

number: 31.2

Answer:

[tex]\displaystyle 3286[/tex]

Explanation:

Just multiply 62 and 53 to get 3286.

I am joyous to assist you at any time.

Step-by-step explanation:

3x + 4 + 2x +7

= 3x + 2x + 4 + 7

= 5x + 11

Answer:

7 units

Step-by-step explanation:

(Background info, skip if not interested or needed for you)

The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

a and b being sides of a right triangle, c being the hypotenuse.

When we are solving for distance we are solving for c essentially.

[tex]c[/tex] = [tex]\sqrt{a^2 + b^2}[/tex]

Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.

(solutions)

So essentially distance is:

[tex]d = \sqrt{(x_2 - x_1)^2+ (y_2-y_1)^2 }[/tex]

Now we just use the values given to us, and sub in the x and y values respectively.

(-2,4) [tex]x_1 = -2, y_1 = 4[/tex]

(5,4)[tex]x_2 = 5, y_2 = 4[/tex]

plug these values in:

[tex]d = \sqrt{((5) - (-2))^2+ (4-4)^2 } = \sqrt{(7)^2+ (0)^2 } = \sqrt{7^2 } = 7[/tex]

Therefore the distance is 7 units.

Step-by-step explanation:

Factors of 36 are {1,2,3,4,6,9,12,18,36}

.

Factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}

Common factors are }1,2,3,4,6,12} .

greatest Common Factor is 12 .

Answer:

sin = opp / hyp

cos = Adj / hyp

tan = opp / adj

7. cos 41 = x / 86

8. sin x = 5/13

9. cos x = 9/37

10. tan 61 = x/28

11. sin 41 = x/65

12. tan x = 79/84

Step-by-step explanation:

circles are 360⁰ and lines are 180⁰

Answer:

i think the answer will be = 8 × 10^2

Answer:

made a mistake in step 3

Step-by-step explanation:

there, he should have gotten y=5-2x which is then translated to y=-2x+5

this means the y-intercept is correct, but the slope is actually -2

The amount of plastic covering needed to cover the window is 25.71.

The window consists of a semi circle and a rectangle. The circumference and the perimeter of the semi circle and a rectangle has to be determined.

Circumference of the semi circle = 1/2πd + d

Where:

π = 3.14

d = diameter = 3

1/2 x 3.14 x 3 + 3 = 7.71

Perimeter of the rectangle = 2(length + width)

2x (6 + 3) = 18

18 + 7.71 = 25.71

Please find attached an image of the window. To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029

Answer:

and

Step-by-step explanation:

we have

-----> equation A

------> equation B

we know that

The solution of the system of equations is equal to the intersection point of both graphs

Using a graphing tool  

see the attached figure

There are two intersection points

Therefore

The system of equations has two solutions

The solutions of the system of equations are the points  and

Answer:

[tex]588mm^3[/tex]

Step-by-step explanation:

Each side of the blue pyramid is 3 times the size of the red pyramid.

Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.

First, we know that angle B is congruent to angle E.

2x + 40 = 5x + 10

2x + 30 = 5x

30 = 3x

x = 10

Angle B and Angle E = 60 degrees

Angle C = 14 degrees

Remember that the interior angles of a triangle always add up to 180 degrees. Now that we know 2 of the 3 angles of these triangles, and because they are congruent, all that's left to do is find Angle A/D by setting up a simple equation.

60 + 14 + D = 180

74 + D = 180

D = 106

Angle D = 106 degrees

Hope this helps!

Answer:

Step-by-step explanation:

<E = <A                property of congruency.

<A = 5x + 10        Comes from the fact that <A and <E are equal.

Three angles of the triangle are given. They add to 180 degrees.

2x + 40 + x + 4 + 5x + 10 = 180         Combine like terms

8x + 54 = 180                                     Subtract 54 from both sides.

8x + 54 - 54 = 180 - 54                      Combine  

8x = 126                                              Divide by 8

8x/8 = 126/8

x = 15.75

<B = <D                                               Congruency and parallel lines

<D = 2x + 40                                       Substitute for x

<D = 2*15.75  +  40                             Combine

<D = 31.5 + 40

<D = 71.5

Answer:

2 is the next number in the sequence

Step-by-step explanation:

in this pattern, you go down by one decimal spot ( zero)

this is a geometric sequence since there is a common ratio between each term.

Step-by-step explanation:

4.5 s, 324 ft

Explanation:

The object is projected upward with an initial velocity of

v_0 = 144 ft/sv

0

=144ft/s

The equation that describes its height at time t is

s(t) = -16t^2 + 144 ts(t)=−16t

2

+144t (1)

where t, the time, is measured in seconds.

In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):

v(t) = s'(t) = -32t +144v(t)=s

′

(t)=−32t+144 (2)

At the maximum heigth, the vertical velocity is zero:

v(t) = 0

Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:

\begin{gathered}0=-32t+144\\t=\frac{144}{32}=4.5 s\end{gathered}

0=−32t+144

t=

32

144

=4.5s

And by substituting this value into eq.(1), we also find the maximum height:

s(t) = -16(4.5)^2+144(4.5)=324 fts(t)=−16(4.5)

2

+144(4.5)=324ft

[tex]5~~,~~\stackrel{5(6)}{30}~~,~~\stackrel{30(6)}{180}~~,~~\stackrel{180(6)}{1080}~~,~~\stackrel{1080(6)}{6480}~\hfill \boxed{f(x)=x_{n-1}(6)}[/tex]

now, that's recursive, we can also write it in explicit as [tex]5(6)^x[/tex]