A substance with a half life is decaying exponentially. If there are initially 12grams of the substance and after 70 minutes there are 7 grams, after how many minutes will there be 2 grams remaining?
Answer:
Step-by-step explanation:
Use the half life formula
[tex]N=N_0e^{kt}[/tex] where N is the amount after decay, No is the initial amount, e is Euler's number, k is the decay constant, and t is the time in minutes. For us, the first equation looks like this:
[tex]7=12e^{k(70)}[/tex] and we will solve that for k and then use that value of k in the second equation to find time.
Begin by dividing 7 by 12 to get
[tex]\frac{7}{12}=e^{k(70)}[/tex] Now take the natural log of both sides since the natural log and that e are inverses. The e then disappears:
[tex]ln(\frac{7}{12})=k(70)[/tex]
Plug the left side into your calculator and then set it equal to the right side, giving us:
[tex]-.5389965007=70k[/tex]
Divide both sides by 70 to get the k value of
k = -.00769995
Now the second equation looks like this:
[tex]2=12e^{(-.00769995)t[/tex] where t is our only unknown now that we know k.
Begin by dividing both sides by 12 to get
[tex]\frac{1}{6}=e^{-.00769995t[/tex] and take the natural log of both sides again to eliminate the e:
[tex]ln(\frac{1}{6})=-.00769995t[/tex]
Take care of the left side on your calculator to get
-1.791759469 = -.00769995t and divide both sides by -.00769995 to get
t = 232.697 minutes
What is 3/8+11/16
In metric tape
Answer:
Step-by-step explanation:
3/8=0.375
11/16=0.6875
0.375+0.6875=1.0625
Suppose you roll a fair die. Let X be the value of the roll. What is the Moment Generating Function of X?
Answer:
μ₁`= 1/6
μ₂= 5/36
Step-by-step explanation:
The rolling of a fair die is described by the binomial distribution, as the
the probability of success remains constant for all trials, p.the successive trials are all independent the experiment is repeated a fixed number of times there are two outcomes success, p, and failure ,q.The moment generating function of the binomial distribution is derived as below
M₀(t) = E (e^tx)
= ∑ (e^tx) (nCx)pˣ (q^n-x)
= ∑ (e^tx) (nCx)(pe^t)ˣ (q^n-x)
= (q+pe^t)^n
the expansion of the binomial is purely algebraic and needs not to be interpreted in terms of probabilities.
We get the moments by differentiating the M₀(t) once, twice with respect to t and putting t= 0
μ₁`= E (x) = [ d/dt (q+pe^t)^n] t= 0
= np
μ₂`= E (x)² =[ d²/dt² (q+pe^t)^n] t= 0
= np +n(n-1)p²
μ₂=μ₂`-μ₁` =npq
in similar way the higher moments are obtained.
μ₁`=1(1/6)= 1/6
μ₂= 1(1/6)5/6
= 5/36
Help me out please i have an E im scared to fail
Answer:
The answer is x= 3
Step-by-step explanation:
hope this helps
Answer:
i think 48
Step-by-step explanation:
Find the measures BC and AC.
B
6.4
A
X
2.3
C
BC =
AC =
Answer:
AC = 4.6
Step-by-step explanation:
since AX and XC are equal amd XC= 2.3
so AC = 2*2.3
Answer:
4.6
Step-by-step explanation:
Estimate each quoitient 2449÷8
Answer:
Quotient=306
Step-by-step explanation:
2449÷8
Quotient=306 remainder=1
A number line going from 0 to 3 in increments of 3.
Divide: 2 ÷ 1
2
2
16
8
4
Answer:
2 divided by 1/2 is 4.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
did it on edge
Fabiola is reviewing for the Algebra 1 End-of-Course exam. She made this graph
representing a system of inequalities.
Circle the ordered pairs below that represent solutions to the system of
inequalities.
(−6, 3) (−3, 3) (0, 3) (0, 0) (6, 0)
(−6, −6) (−3, −6) (−6, 6) (−4, 2) (3, −3)
Answer
(-6. 3) (-6, 6) (-4, 2)
Step-by-step explanation:
the solution is the dark area between the two lines.
the only trick would be if one of the points fell on the dotted line.
all points on the dotted line are not included but all points on the solid line are included.
how do you solve this?
Answer:
Horizontal component = 9.6
Step-by-step explanation:
Recall that the horizontal component is given by the cosine projection;
[tex]v_x=|v_0| * cos(\theta)[/tex]
which in our case (using the fact that in each degree of angle one has 60 minutes of angle, and therefore 30 minutes of angles is the same as 0.5 degrees) becomes:
[tex]v_x=12.6 * cos(40.5^o)=9.5811[/tex]
And rounding to the nearest tenth as requested, we have:
[tex]v_x=9.6[/tex]
Find a center of mass of a thin plate of density delta equals 5δ=5 bounded by the lines y equals xy=x and x equals 0x=0 and the parabola y equals 20 minus x squaredy=20−x2 in the first quadran
Answer:
center of mass
X = [tex]\frac{my}{m} = \frac{28}{19}[/tex]
Y = [tex]\frac{mx}{m} = \frac{872}{95}[/tex]
Step-by-step explanation:
y = x and x = 0
parabola ; y = 20 - x^2
attached below is the detailed solution
M = [tex]\frac{152}{3}[/tex]б
Mx = [tex]\frac{6976}{15}[/tex]б
My = [tex]\frac{224}{3}[/tex]б
X = [tex]\frac{my}{m} = \frac{28}{19}[/tex]
Y = [tex]\frac{mx}{m} = \frac{872}{95}[/tex]
Find an equation of the plane that passes through the point (1, 3, 4) and cuts off the smallest volume in the first octant.
Answer:
12x +4y + 3z=36
Step-by-step explanation:
The equation of plane is given by
z-zo = a(x-xo) + b(y-yo)
pass through (1,3,4)
Z -4 = a(x -1) +b(y-3)
The question is asking us to optimize a and b. To minimize the volume V both a and b should be negative as the normal vector should be towards the negative x and y direction so that a finite tetrahedron can be formed in the first octant.
we need x , y and z intercepts o define volume
x intercept( y, z =0) = [tex]\frac{a+3b-4}{a}[/tex]
y intercept (x, z =0) = [tex]\frac{a+3b-4}{b}[/tex]
z intercept ( x, y =0) = -(a+3b-4)
Base = [tex]\frac{(a+3b-4)^2}{2ab}[/tex]
Volume = [tex]\frac{1}{3}*base*height[/tex]
Volume(a, b) = [tex]\frac{-(a+3b-4)^3}{6ab}[/tex]
now we differentiate partially in terms to a and b the volume to minimize and get a and b.
ΔV(a, b) = [tex]\frac{-1}{6}(\frac{3(a+3b-4)^2ab-b(a+3b-4)^3}{a^2b^2}[/tex] ,[tex]\frac{-1}{6}(\frac{9(a+3b-4)^2ab-a(a+3b-4)^3}{a^2b^2}[/tex] = 0
Taking the first part of differential it will give
b(a+3b-4) [3a -(a+3b -4)] =0
(a+3b-4) [tex]\neq 0[/tex] because the volume will become zero if this becomes true
2a -3b = -4 ..................(1)
similarly the second part of the differential will give
a-6b=4 ................(2)
on solving 1 and 2 we get
a = -4 and b = -4/3
so the equation will be
Z -4 = -4(x -1) - 4/3*(y-3)
final equation
12x +4y + 3z=36
I need some help with this ( check the link). My eyes are not good with 3D shapes like these so, I need some help with this one.
Answer:
Step-by-step explanation:
1). Plane parallel to the plane WXT → Plane ZYU
2). Segments parallel to VU → ST and ZY
3). Two segments parallel to SW → VZ and TX
4). Two segments skew to XY → VS and VU
5). Two segments skew to VZ → UT and WX
Select equivalent or not equivalent for each pair of expressions
Answer:
Equivalent, equivalent, not equivalent.
Step-by-step explanation:
The answers for the first two are equal, but the last one doesn't have equal answers.
additon and subtraction and the whole no
Answer:
dont get it
Step-by-step explanation:
The question is specific enough for an answer.
Whoever answers correctly gets brainlist
Answer:
So now D would be at (-4 , 2)
Step-by-step explanation:
From D, you can calculate every other letter’s location. Yeah.
Answer:
Please mark me as brainliest!
Step-by-step explanation:
The coordinates:
D: ( 2,6 )
A: ( 2, 1 )
B: ( 5, 1 )
C: ( 5, 6 )
You want to translate this down 4 units and left 6 units.
So what you would do is this:
Formula = ( x - 6 , y - 4 )
D: ( -4, 2 )
A: ( -4, -3 )
B: ( -1, -3 )
C: ( -1, 2 )
the sum of 5th and 9th terms of AP is 72 and the sum of 7th and 12th term is 97 find AP
Answer:
The AP is 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61 ....
Step-by-step explanation:
The nth term = a1 + d(n - 1)
Sum of 5th and 9th terms
= a1 + 4d + a1 + 8d = 72
2a1 + 12d = 72.............(1)
Similarly:
a1 + 6d + a1 + 11d = 97
2a1 + 17d = 97..............(2)
Subtracting equation (1) from equation (2):
5d = 25
d = 5.
and , using equation (1), the first term
a1 = (72 - 12(5)) / 2
= 12/2
= 6.
sarah is looking at her online banking account summary and sees a money transfer for -$80.
which of the following best describes -$80
A. $40 spent
B. $40 received
C. $80 spent
D. $80 received
Answer:
C
Step-by-step explanation:
She spent $80
X+5 Y-6 means that the figure is
Answer:
The figure is translating right 5 and down 6
Step-by-step explanation:
X and Y both represent axis on a coordinate grid. x+5 simply means adding 5 to a value. In other words, on a coordinate grid, an increase in the value means you are going right, the lower the farther left. Same for the y axis, the higher the more you are increasing vertically, the lower the value the lower the point is.
which of the following choices is equivalent to the expression below?
can someone explain how to do it?
USE THE PHOTO. .............
Answer:
1st and 4th
Step-by-step explanation:
goodluck!
Find the total cost if you paid $45 for a pizza order plus a 15% tip. Round your answer to the nearest cent.
Answer:
6.75, if you round it i guess 6.80
Step-by-step explanation:
HELP ME!! What is the number of terms in this expression?
m/5+4⋅6
Answer:
eek, m/5+120??
Step-by-step explanation:
Answer:
I cant find the answer
Step-by-step explanation:
I searched and searched but no answer
please tell fast plzzzzzz
Answer:
5:15
Step-by-step explanation:
Quater means 15 and passed means 15 passed 5
y= -5x + 12
y = -5x – 7
Answer:
19
Step-by-step explanation:
1. y= -5x + 12
y= -5x – 7
2. -5x + 12
-(-5x – 7)
3. -5x + 12
5x + 7
0 +19
4. 19
Given
f(x) = −5x9 − x8 + 3x3 − 8
and
g(x) = −5x9 − 5x3 − 5x2 + 5,
find and simplify
f(x) − g(x).
Answer:
f(x) - g(x) = -x⁸ + 8x³ + 5x² - 13
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Combining like termsStep-by-step explanation:
Step 1: Define
f(x) = -5x⁹ - x⁸ + 3x³ - 8
g(x) = -5x⁹ - 5x³ - 5x² + 5
Step 2: Find f(x) - g(x)
Substitute: f(x) - g(x) = -5x⁹ - x⁸ + 3x³ - 8 - (-5x⁹ - 5x³ - 5x² + 5)Distribute -1: f(x) - g(x) = -5x⁹ - x⁸ + 3x³ - 8 + 5x⁹ + 5x³ + 5x² - 5CBT (x⁹): f(x) - g(x) = -x⁸ + 3x³ - 8 + 5x³ + 5x² - 5CBT (x³): f(x) - g(x) = -x⁸ + 8x³ - 8 + 5x² - 5CBT (Z): f(x) - g(x) = -x⁸ + 8x³ + 5x² - 13And we have our final answer!
A child fills a bucket with sand so that the bucket and sand together weigh 10 lbs, lifts it 2 feet up and then walks along the beach, holding the bucket at a constant height of 2 ft above the ground. How much work is done on the bucket after the child has walked 100 ft?
Total weight, w = 10 lbs.
Height of the bucket, h = 2 feet.
Distance walked, d = 100 ft.
Now, work done in moving the bucket at a height of 2 feet.
W = mgh
W = 2× 32.17×100
W = 6434 lbs ft²/s²
Work done in moving bucket in horizontal direction is zero because it is perpendicular to the force.
Therefore, work done is 6434 lbs ft²/s² .
Hence, this is the required solution.
Jenny makes food for her hummingbird feeders
for fun: 17 + -3 - 3
Answer:
11 or I'm just bad at math
Quadrilateral ABCD shown below, is translated 3 units to the left to create quadrilateral A'BCD
B
D
Which statement is true?
If the area of the triangle is 20cm, what is the missing height?
Answer:
The answer for height is 20
Step-by-step explanation:
