The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 90% of the lead to decay? (Round your answer to two decimal places.)
Answer:
It will take 10.96 hours for 90% of the lead to decay.
Step-by-step explanation:
The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t
This means that the amount can be modeled by the following function:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate.
Has a half-life of 3.3 hours.
This means that [tex]A(3.3) = 0.5A(0)[/tex]. We use this to find r.
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.5A(0) = A(0)e^{-3.3r}[/tex]
[tex]e^{-3.3r} = 0.5[/tex]
[tex]\ln{e^{-3.3r}} = \ln{0.5}[/tex]
[tex]-3.3r = \ln{0.5}[/tex]
[tex]r = - \frac{\ln{0.5}}{3.3}[/tex]
[tex]r = 0.21[/tex]
So
[tex]A(t) = A(0)e^{-0.21t}[/tex]
How long will it take for 90% of the lead to decay?
This is t for which [tex]A(t) = 0.1A(0)[/tex], that is, 100 - 90 = 10% of the initial amount.
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.21t}[/tex]
[tex]e^{-0.21t} = 0.1[/tex]
[tex]\ln{e^{-0.21t}} = \ln{0.1}[/tex]
[tex]-0.21t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.21}[/tex]
[tex]t = 10.96[/tex]
It will take 10.96 hours for 90% of the lead to decay.
Х?
When a side of the triangle is 55°
Answer:
70
Step-by-step explanation:
180 - 55 -55 = 70
Mike read 18 books. This was 4 fewer than twice the number that Jeff
read. How many books did Jeff read?
Answer:
i think 13
Step-by-step explanation:
AHH IM SORRY!!Twenty-four out of forty pies at the bake sale are chocolate pies. What percent is chocolate.
Answers
24%
40%
60%
75%
Ik I should be figuring it out on my own but my brain is fried
Answer:
60%
Step-by-step explanation:
Answer The Question for Brainliest
Answer:
turn it 90 degrees, hope this helps
Step-by-step explanation:
Answer:
so go to the 120 degree line and make sure the line is straight across from zero and thin dray a line going from 120 down to the bottom of where the zero is
Step-by-step explanation:
A park ranger wants to know the average time it takes hikers to hike a trail. There is an average of 1,245 hikers on the trail in a year. How can he find a reasonable estimate for the amount of time it takes to hike the trail? A time any hiker on the trail and use that time
B time himself on the trail and use that time
C time 100 hikers and average their times
D time 3 hikers and average their times
Answer:
B
Step-by-step explanation:
the reason why is a bigger sample size and a different types of people in a 100 than 3 or than himself
A helicopter is planning a route in a straight line from the top of Mount Whitney to Death Valley. (These two locations are in California and are the highest and lowest points respectively in the continental United States. They are only about 85 miles apart.) The helicopter will start at the top of Mount Whitney at an elevation of 14,505 feet and fly to the Badwater Basin (282 feet BELOW sea level). During its flight, the helicopter descends at a rate of 493 feet per minute, and the trip will take about 30 minutes.
Write an equation that relates the helicopter's elevation (E) to the travel time (t).
Question 3 options:
E=−493t+14787
t=14505−493E
E=14505−493t
E=282+14505t
The linear function that relates the helicopter's elevation (E) to the travel time (t) is:
E = −493t+14787What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
The helicopter descends at a rate of 493 feet per minute, hence [tex]m = -493[/tex].It flies from an elevation of 14,505 feet to an elevation of 282 feet BELOW sea level, hence the distance it travels in feet is [tex]b = 14505 + 282 = 14787[/tex]Hence, the model is:
E=−493t+14787You can learn more about linear functions at https://brainly.com/question/13967935
Answer:
E=−493t+14787
Step-by-step explanation:
just got it right on the test
Joey pays $35.85 each month for his new stereo what does he pay each year
Answer:
$430.20
Step-by-step explanation:
35.85 x 12= 430.20
HELP ME PLEASE!!!!!!!!!!!
Answer:
9.y=Mx+b
Y= 2/5x+4
10. y=Mx+b
Y=4x-5
Step-by-step explanation:
Answer:
9) [tex]y=\frac{2}{5} x+4[/tex]
10) [tex]y=4x-5[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, or the value of y when the line crosses the y-axis.
Question 9
[tex]y=mx+b[/tex]
The question tells us that the slope of the line is [tex]\frac{2}{5}[/tex]. Because the slope is [tex]m[/tex], plug [tex]\frac{2}{5}[/tex] into the equation as [tex]m[/tex].
[tex]y=\frac{2}{5} x+b[/tex]
Then, it tells us that the y-intercept is (0,4). Recall that the y-intercept is the value of y when the line crosses the y-axis. The value of y in the point (0,4) is 4. Because the y-intercept is [tex]b[/tex], plug 4 into the equation as [tex]b[/tex].
[tex]y=\frac{2}{5} x+4[/tex]
Question 10
[tex]y=mx+b[/tex]
First, we must calculate the slope using the slope equation:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] when the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
The given points are (0,-5) and (2,3). Plug those into the equation.
[tex]\frac{3-(-5)}{2-0}[/tex]
Two negatives make a positive
[tex]= \frac{3+5}{2-0}\\= \frac{8}{2} \\= 4[/tex]
Therefore, the slope of the line is 4. Plug 4 into the original equation as [tex]m[/tex].
[tex]y=4x+b[/tex]
Now, we can find the y-intercept by simply looking at the graph. The line crosses the y-axis at the point (0,-5). Therefore, the y-intercept is -5. Plug -5 into the equation as [tex]b[/tex].
[tex]y=4x+(-5)\\y=4x-5[/tex]
I hope this helps!
You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the
(h,k)
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y -k)² = r²
(x+ 3)² + (y + 9)² = 144
(x+ 3)² + (y + 9)² = 12²
h = -3 ; k = -9
A carpenter leans a 20-foot ladder against a building so that an angle of 60° is formed between the ladder and the ground. How many feet away from the
building is the bottom of the ladder?
O 10/3ft
O 20 ft
O 20V2 ft
O 10 ft
Answer:
The foot of the ladder is
10
feet away from the base of the wall.
Step-by-step explanation:
The distance between building and the bottom of the ladder is option (D) 10 ft
What is Trigonometric function?In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given,
Length of the ladder = 20 foot
Angle between the ladder and the ground = 60 degrees
Draw the figure using the given data
We know,
cos θ = Adjacent side / Hypotenuse
cos 60 = [tex]\frac{x}{20}[/tex]
x = 20 × cos 60
x = 10 ft
Hence, the distance between building and the bottom of the ladder is option (D) 10 ft
Learn more about Trigonometric function here
https://brainly.com/question/6904750
#SPJ2
Blake bought a new set of golf clubs. He found them at Golf Pro for $270. If the store is offering 20% off how much are the new clubs?
Answer:
216
Step-by-step explanation: 270-20%= 216
What's the slope of the line in the graph above?
Question 9 options:
A)
–3∕5
B)
–5∕3
C)
5∕3
D)
3∕5
Answer:
C.5/3
Step-by-step explanation:
5 up and 3 to the side
Answer:
C is correct
Step-by-step explanation:
Please answer all these questions for me for day 4.
Help me please if you can
Answer:
<D=<J
Step-by-step explanation:
The first answer is the only correct statement. In geometry, congruent angles are shown through the number of arcs on the vertex of an angle. For example, if two different angles both had three arcs on the vertex, then those two angles are congruent. In this figure, both <D and <J have 4 arcs, which means they are congruent. Additionally, both angles are opposite of a line that measures 25 inches. If two angles are opposite of congruent lines, then the angles are also congruent.
AM I RIGHT PLEASE HELP will mark BRAINLIEST
Answer:
Yes
Step-by-step explanation:
BC ll EF
It’s due late tonight can some pls help me pass
Answer:
Table A
Step-by-step explanation:
plugging the x values into the rule f(x)=-2x gets you
f(-3)= 6
f(-1)= 2
f(1)= -2
f(3)= -6
A billiard ball bounces off the sides of a rectangular billiards table in such a way that 1= 23,
24 = 26, and Z3 and 24 are complementary. If m_1 = 27°, find the measure of all the other angles.
1
3
2
m/2 = =
4
m23 =
5
6
m24 =
m25 =
m26 =
Looking out for me balcony the angle of elevation to the top of the next building is approximately 22° in the English depression to the bottom of the building approximately 29° if the building is 200 feet away how tall is the building?
I will give brainliest to whoever solves it right. hint its not 80.7 feet
Answer:
Step-by-step explanation:
[tex]\tan22=h_1/200,\ \tan29=h_2/200
h_2+h_1=200(\tan29+\tan22)
H\approx 191.667ft
H\approx 191’ 8”
Need help please only searious answers.
Answer:
answer 3
Step-by-step explanation:
Hope this helps you out
The sum of eight and twice a number is 42
Answer:
8 + 2n = 42
Step-by-step explanation:
the sum of eight: ___+ 8
and twice(2) a number(could be any variable but for now i choose n): 2n + 8
is 42 (literally mean it equals 42): 2n + 8 = 42
50 points! I need help fast! Random answers will be reported! I will mark brainliest to the correct answer :)
Answer:
1) yes, SAS
2) No, there is no SSA theorem
Step-by-step explanation:
1) PR is shared between the two triangles so you know by Side-Angle-Side
Find the sum to 40 terms of the arithmetic sequence below. Please show your
work.
14+23+32
Answer:
7580
Step-by-step explanation:
The formula for the sum of an arithmatic sequence is
[tex]\frac{n}{2} (a_{1} + a_{n})[/tex],
where n = total number of terms (in this case 40)
[tex]a_{1}[/tex]= the first term (in this case 14)
and [tex]a_{2}[/tex] = the last term (we will need to find this)
to find the last term, we can use this formula:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
where d is the difference between each term (in this case 9, because 23 - 14 = 9, and 32 - 23 = 9)
thus, [tex]a_{n}[/tex] = 14 + (40 - 1)9 = 14 + 39*9 = 14 + 351 = 365
plug this back into the first formula to get
Σ = [tex]\frac{40}{2}[/tex] (14 + 365) = 20(379) = 7580
Pls help me I will give brainliest
Answer:
Step-by-step explanation:
a^8/c
Answer:
a8
b
10
/c
a^8/c
Step-by-step explanation:
Can I pls get the Brainlist
Find three consecutive integers such that that product of the first and third is one
less than 22 times the second integer.
Answer:
n = the first
n + 1 = the 2nd
n + 2 = the 3rd
n(n + 2) - (n + 1) = 10(n + 2) + 1
n2 + 2n - n - 1 = 10n + 20 + 1
n2 - 9n - 22 = 0
(n - 11)(n + 2) = 0
If two factors = 0, at least one must = 0.
n - 11 = 0
n = 11
11,12,13
n + 2 = 0
n = -2
-2,-1,0
X-3y=15 and y=-3x+4 determine if the lines are parallel,perpendicular,or neither
Answer:
neither parallel or perpendicular.
Step-by-step explanation:
Answer:
3 x + y = 16
Step-by-step explanation:
The Question is in the attachment below
Answer:
Step-by-step explanation:
It is J I’m pretty sure
30 is 60% of
due today
Answer:
30 is 60% of 50.
Step-by-step explanation:
30 ÷ 60% = 50
What is the domain of the function V(x)+1.
Answer:
3th one
Step-by-step explanation:
Answer:
i am not completely sure, im a bit rusty on this, but if im correct the answer is Option 1. I hope you get it right :)
Step-by-step explanation:
The highest degree of academic achievement in the American education system is a __________ degree.
A.
bachelor’s
B.
doctorate
C.
master’s
D.
secondary