15 days
Step-by-step explanation:
The half-life equation is given as
[tex]m(t) = m(0)e^{-0.073t}[/tex] (1)
where m(0) is the initial mass of radioactive iodine at t = 0. To solve for the time t, let's put the exponential part on the left-hand side:
[tex]e^{-0.073t} = \dfrac{m(t)}{m(0)}[/tex]
Taking the natural logarithm of both sides to get
[tex]\ln{e^{-0.073t}} = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex] (2)
Recall the following properties of logarithms:
[tex]\ln{A}^b = b\ln{A}[/tex]
[tex]\ln{e} = 1[/tex]
We can rewrite Eqn(2) as
[tex]-0.073t = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Solving for t, we get
[tex]t = -\dfrac{1}{0.073}\ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Since m(0) = 15 gm and m(t) = 5 gm, then the amount of time that elapses to reduce the mass down to 5 gm is
[tex]t = -\dfrac{1}{0.073}\ln\left(\dfrac{5\:\text{g}}{15\:\text{g}}\right)[/tex]
[tex]\:\:\:\:\:= 15\:\text{days}[/tex]
Bart learned that the first stage of a type of rocket had a burn time that was 28.5 seconds longer than the burn time during the second stage. The total burn time for both stages was 150.3 seconds. What was they burn time for the first stage?
Answer:
60.9
Step-by-step explanation:
im prob not crct
Which expressions are equivalent to (13x+x−53x)−(−43x+2) ?
Answer:
4x+2
Step-by-step explanation:
(13x+x−53x)−(−43x+2)
Group all the same variables on each side.
(-39x)-(-43x+2)
-39x+43x+2
4x+2
Hope this helps :)
Answer: x-2 & -2-x+2x
Step-by-step explanation:
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m
Hello
just a second
people reading this please complete because you will help me a lot.
I am an Indian girl my name is Lamer and am 13 years old.
I Just got this new device after working at a farm for 2 years.
I used to use brainly at my friend device she had money to buy brainly plus.
I cant please help me get points so I can get good marks and my dad let me complete my education instead of getting married.
Is this correct way to solve the problem?
5(2x-2)=30
10x-1030
10x=30+10
10x=40
(-10x)=(40)
x=-4
help me plz
Answer:
10x=40
x=40/10
x=4
4 is the answers, not -4
Step-by-step explanation:
pls mark as brainliest
Help quick 20points please please
Answer:
AB = 23.6
BC = 18.5
CD = 23.6
DA = 18.5
Step-by-step explanation:
4.
Both sets of opposite sides are parallel, so this is a parallelogram.
In parallelogram ABCD:
AB≅CD
AD≅BC
Knowing that, you can write 2 equations with the given information:
[tex]2a-20.4=a+1.6\\a-3.5=18.5[/tex]
You can solve whichever one you want, but I'll do both to be sure.
[tex]2a-20.4=a+1.6\\2a=a+1.6+20.4\\2a-a=1.6+20.4\\a=22[/tex]
Now for the second one:
[tex]a-3.5=18.5\\a=18.5+3.5\\a=22[/tex]
a = 22, so now you can solve for the side lengths.
[tex]2(22)-20.4=23.6\\22-3.5=18.5\\22+1.6=23.6\\18.5=18.5[/tex]
4 4/6 + 3 7/8 = ? ........................................
Answer:
[tex]8\frac{13}{24\\}[/tex]
Step-by-step explanation:
[tex]4\frac{4}{6}+3\frac{7}{8}[/tex]
[tex]\frac{28}{6}+\frac{31}{8}=\frac{205}{24}=8\frac{13}{24}[/tex]
Two trains travelling along parallel tracks in the same direction do 50 km/h and 100 km/h on average. The faster train starts 2 hours later than the slower. After how many kilometres will the faster train catch up?
Answer:
200 kmStep-by-step explanation:
Let the faster train catches the slower one after x hours.
The distance the trains travel is same:
50(x + 2) = 100x50x + 100 = 100x50x = 100x = 2The distance is:
50*(2 + 2) = 100*2 = 200 km3/8 is found between which pair of fractions on a number line
Answer:
2/8 and 4/8
Step-by-step explanation:
Answer:
2/8,4/8 or 1/4,1/2
Step-by-step explanation:
3+1=4 3-1=2
2/8=1/4
4/8=1/2
6+7+8+...+(n+5) find the sum.
Answer:
n + 26
Step-by-step explanation:
first you have to simplify
6 + 7 +8 + n + 5
then combine the like terms
6 + 7 + 8 + n + 5
(n) + ( 6 + 7 + 8 + 5)
= n + 26
hope this helps
What is the degree of each polynomial?
(x^2 - y)^2 Degree _______
8x^4-5x^7+4c^5 Degree ______
x^2y^3/3+2x^3+8x^3 Degree ______
x^4 +2x^3-6x^4-17 Degree ______
-x^2+7x-4x Degree _____
x^7+y^8+x^7-y^8 Degree_____
Answer:
A- 4
B- 5
C- 8
D- 4
E- 2
F- 7
I'm 99% sure these are right!! I hope this helps :(
A line has a slope of 5 and passes through the point (1,5). What is its equation in
slope-intercept form?
Answer:
[tex]y=5x[/tex]
Step-by-step explanation:
Insert the information into the point-slope formula to find slope-intercept form.
[tex]y-y_1=m(x-x_1)\\\\y-5=5(x-1)\\\\y-5=5x-5\\\\y=5x[/tex]
Translate the English phrase into an algebraic expression: the sum of the quotient of 3 and 2m, and the product of 8 and
m.
Enter all quotients as fractions,
Answer:
[tex]\frac{3}{2m}[/tex]+8m
Answer:
the sum of quotient of 3 and 2m and the product of 8 and m is
(3/2m +8m)
A 16" × 16" square tray can hold at most 9 bagels placed side by side, as shown below. At most how many bagels can a 32" × 32" square tray hold if bagels are placed side by side?\
Answer:
At most it can hold 18 bagels
Step-by-step explanation:
So we can make this an equation
16 · 16 square tray = 9 bagels on top of it
We just doubled both sides of it
giving us 32 · 32 square tray = 18 bagels can be held.
Write an equation of the line that passes through (−2,3) and (0,8).
An equation is y=
.
Answer:
Step-by-step explanation:
y = mx + b
b is the y intercept and occurs where x = 0. One of our select points has an x value of 0, therefore b = 8
m is the slope and is found as the change in y over the change in x
m = Δy/Δx = (8 - 3) / (0 - (-2)) = 5/2
y = 5x/2 + 8
P(E') = P(F) = 0.6 and P(E n F) = 0.24:
a. Write down P(E).
b. Explain how you know E and F:
i are independent
ii are not mutually exclusive
c Find P(E u F').
Answer:
(4- x)(x - 4) = 16 - x2 help me sir please
A right triangle is shown in the graph. Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points) Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points) Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)
Answer:
Part A, write out the equation by subtracting the vertex from x and y, then set it equal to the radius square. All of this information is given in the picture. Then the domain is all the x's and the range is all the y's starting at the center and going out 10 in each direction since 10 is the radius.
Step-by-step explanation:
Use the circle formula that you learned in lesson 3.02 using the given points. Remember this quiz was open note and your formula should be in your notes. Also, it should be familiar to you from Geometry and middle school math where you first learned about circles:)
BRINLEST WIL BE GIVIN
Answer:
[tex]\huge\boxed{-0.001a^{n+1}}[/tex]
Step-by-step explanation:
[tex]-0.001a^{3n+3}=-0.001a^{3(n+1)}=(-0.001a^{n+1})^3\\\\\text{Used}\\\\a(b+c)=ab+ac\qquad\text{distributive property}\\\\(a^n)^m=a^{n\cdot m}[/tex]
Shawn has $20.00 to spend. He wants to save $5.00. He buys two ice creams for $1.65 each, what is the maximum number of packets of chocolate can he buy at a cost of $3.45 for each packet and still have at least $5.00 left over
(solve as an inequality)
Answer:
3
Step-by-step explanation:
3.45x+2*1.65+5>=20
3.45x+8.3>=20
3.45x>=11.7
after rounding
x>=3
Samantha has 7/3 cups of ice cream to make milk shake.Each shake uses 1/8 cup of ice cream. How many milk shakes can she make?
When the input of the function is -1, What is the output of the function?
Answer:
2
Step-by-step explanation:
The graph clearly shows that when x = -1, y = 2.
Thus, the output of this function is 2.
Estimate the difference of $19 320 and $9 876?
Answer:
$9444 Is the difference
Step-by-step explanation:
$19,320 - $9876 = 9444$
(Hope this helps can I pls have brainlist (crown)☺️)
Brainiest fastest answer no link or bot or I report you I report you if you report me
I did this really quick so I hope all the answers are right, and double check them if you have time just in case
3x + 3y = 9
-3x + 2y = 1
Answer:
X=1
Y=2
Step-by-step explanation:
put 1 in for X
3(1)+3(y)=9
-3(1)+2(y)=1
now put 2 for Y
3(2)+3(2)=9
-3(1)+2(2)=1
3•1= 3
3•2=6
3+6=9
-3•1=-3
2•2=4
-3+4=1
ANSWER USING STEPS: find the inverse function of y=-5x-7
the inverse of y is =x+7
Step-by-step explanation:
y=5x-7
then solve for x
5x=y+7
x=(y+7)/5
then exchange x with y
y=(x+7)/5
The inverse of the given function is expressed as:
-(x + 7)/5
How to find the inverse of the function?The given function is expressed as:
y = -5x - 7
Replacing y with x and vice versa gives us:
x = -5y - 7
Add 7 to both sides gives:
x + 7 = -5y
divide both sides by -5 gives us:
-(x + 7)/5 = y
Thus, we conclude that the inverse of the given function is expressed as:
-(x + 7)/5
Read more about Inverse of Function at: https://brainly.com/question/3831584
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Please show how you solved the problem.
4a - 14 = 7a - 8
4a - 14 = 7a - 8
4a - 7a = 14 -8
-3a = 6
a = 2
ok done. Thank to me :>
Answer:
a= -2
Step-by-step explanation:
4a -14 = 7a -8
Subtract 7a from both sides
-3a -14= -8
Add 14 to both sides of equation
-3a = -8 +14
Add -8 and 14
-3a = 6
Divide each term by -3
a = -2
plssssssssssss answer for brainiest
Answer:
E = 120
F = 60
G = 120
H = 60
Step-by-step explanation:
0.7619047619 as a fraction?
which one
1. 1/16
2. 16/21
3. 2
4. 4
Answer:
16/21
Step-by-step explanation:
Use the following function rule to find f(3) f(x)=3(4)^x+2
Answer:
3f×16=36
Step-by-step explanation:
f(x)=2x×fx
(substitute
=3f×16
=36f
"HKA
Erloka borrowed money from her brother to buy a new phone, and is paying off a fixed amount
each week
Answer:
$76
Step-by-step explanation:
28. Marta Sanchez purchased a sweater for $15.67, a pair of socks for $2.13, and a bracelet for $6.78. For all
purchases she must pay the state sales tax of 7.5% and the county tax of 0.5%. What is the tax on her
purchases?
Answer:
$ 1.94
Hope I helped