how much of a 2 gram sample of silver-105 would remain after 86 days? round to three decimal places
Answers
We know that the half life of this element is 41.3 days.
We have to find how much will remain of a sample of 2 grams after 86 days.
The half life of 41.3 days means that the mass after 41.3 days will become half of what it was.
We can express this as:
[tex]\frac{M(t+41.3)}{M(t)}=\frac{1}{2}[/tex]As this is represented with an exponential model like this:
[tex]M(t)=M(0)\cdot b^t[/tex]we can use the half-life to find the parameter b:
[tex]\begin{gathered} \frac{M(t+41.3)}{M(t)}=\frac{1}{2} \\ \frac{M(0)\cdot b^{t+41.3}}{M(0)\cdot b^t}=\frac{1}{2} \\ b^{t+41.3-t}=\frac{1}{2} \\ b^{41.3}=\frac{1}{2} \\ b=(\frac{1}{2})^{\frac{1}{41.3}} \end{gathered}[/tex]Then, knowing that the initial mass M(0) is 2 grams, we can express the final model as:
[tex]M(t)=2\cdot(\frac{1}{2})^{\frac{t}{41.3}}[/tex]We then can calculate the mass after t = 86 days as:
[tex]\begin{gathered} M(86)=2\cdot(\frac{1}{2})^{\frac{86}{41.3}} \\ M(86)\approx2\cdot0.236 \\ M(86)\approx0.472 \end{gathered}[/tex]Answer: the mass after 86 days will be 0.472 grams.
Related Questions
the equation of three lines are given below line 1:y=5/3x-6line 2:10x-6y=8line 3: 3y=5x+7for each pair of lines determine whether they are parallel perpendicular or neither line1 and line 2: parallel perpendicular or neither Line 1 and line 3:parallel perpendicular or neither line 2 to a line 3:parallel perpendicular or neither
Answers
line 1 = y = 5/3 x - 6
Find the slope of the line by comaring it with y = mx+ b
m= 5/3
Line 2
Write the equation in the form y =mx +b and find the slope m
10x - 6y = 8
6y = 10x - 8
Divide through by 6
y = 10/6 x - 8/6
y = 5/3 x - 4/3
m= 5/3
Line 3
3y = 5x + 7
Also write in the form y =mx + b and find the slope m
y = 5/3 x + 7/3
m = 5/3
Line 1 and line 2 are parallel since they have the same slope
Line 1 and 3 are parallel (they have the same slope)
Line 2 and 3 are parallel, they have the same slope
5. Write the division problem as a
multiplication equation with a
missing factor. The find the quotient.
2.1 /0.7
Answers
The quotient in this division problem is 3,4.
What is division problem?
There are three main parts to a division problem that are -the dividend, the divisor, and the quotient. The dividend is the number that will be the divided. The division is the number of (people )that the the number is being divided by among And The quotient is the answer.
a division is a process of a splitting a specific of amount into the equal parts.
Sol-
The formula is -
a/b=?
b×?=a
We can write a division statement as a multiplication statment
12/4=3
4×3=12
Thus
The quotients in this division problem are 3 and 4.
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Question content area top
Part 1
A box of cereal states that there are calories in a
-cup serving. What is the unit rate for calories per cup? How many calories are there in of the cereal?
Answers
The unit rate for calories per cup is 100 calories per cup.
There is 400 calories in 4 cup of cereal.
Given,
The amount of calories in 3/4 of the cup = 75 calories
We have to find the unit rate of calories per cup.That is,
Unit rate of calories = 75 / (3/4)
Unit rate of calories = 75 × (4/3)
Unit rate of calories = 25 × 4
Unit rate of calories = 100
There are 100 calories in a cup of cereals.
Now,
We have to find the calories in 4 cup of cereals.Calories in 4 cup = Calories in one cup × 4
Calories in 4 cup = 100 × 4
Calories in 4 cup = 400
So,
There are 400 calories in 4 cup of cereals.
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Which of the following statements is true about the graph shown?
The equation y = 4.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (3, 13.5).
The graph is incorrect and the line should go through the point (4.5, 4.5).
The graph does not show a proportional relationship.
Answers
Answer:
B. The graph is incorrect and the line should go through the point (3, 13.5)
Step-by-step explanation:
The equation is y = 4.5x
y = the y-axis/dependent variable
x = the x-axis/independent variable
4.5 x 1 = 4.5
4.5 x 2 = 9
4.5 x 3 = 13.5
Therefore the written ordered pairs would look like this.
(1, 4.5)
(2, 9)
(3, 13.5)
In the graph, (3, 13.5) is graphed as (13.5, 3) making the graph incorrect.
The statement which is true about the graph shown is that: the graph is incorrect and the line should go through the point (3, 13.5).
How to interpret the graph?Generally speaking, the graph of any linear function is always modeled by a straight line and it indicates a proportional relationship because it starts from the origin (0, 0).
Mathematically, a proportional relationship can be represented or modeled by the following linear equation:
y = kx
Where:
k represents the constant of proportionality.x and y represents the data points, variables, or coordinates.At data point (4.5, 4.5), we have:
y = 4.5x
y = 4.5(4.5)
y = 20.25 (incorrect).
At data point (3, 13.5), we have:
y = 4.5x
y = 4.5(3)
y = 13.35 (correct).
Therefore, we can logically deduce that this graph is incorrect because its line didn't pass through the data point (3, 13.5).
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How many pounds of N are in 2 tons of manure (4.8% N)?
Answers
Answer: 192 lbs
Total weight of manure = 2 tons
Step1: we need to converts tons to pounds
1 ton = 2000 lb
2 tons = x lb
Cross multiply
2 x 2000 = 1 * x
x = 2 x 2000
x = 4000 lbs
Therefore, 2 ton of manure = 4000 lbs of manure
We have 4.8% of N in the manure
Pounds of N = 4.8/100 x 4000
Pounds of N = 0.048 x 4000
Pounds of N = 192 lbs
The pounds of N in 2 tons of manure is 192 lbs
I want a line with equation y=mx+9 to pass through the point (10,10). What is m?
please please help
Answers
Answer:
y = 0.1x + 9Step-by-step explanation:
Given
Line y = mx + 9,Point (10 , 10).To find the slope plug in the coordinates of the given point, x = 10 and y = 10 and solve for m:
10 = 10m + 910m = 10 - 910m = 1m = 1/10m = 0.1The line is:
y = 0.1x + 9Are the proof and the identity valid? if not, what is the invalid step in the proofStep 1: x (9x+3) +3(x+3)=9x²+6x+9Step 2: =(3x+3)²Step 3: =(3(x+1))²Step 4: =9(x+1)²A) the proof is validB) step 2 is not validC) step 1 is not validD) step 3 is not valid
Answers
Are the proof and the identity valid? if not, what is the invalid step in the proof
Step 1: x (9x+3) +3(x+3)=9x²+6x+9
Step 2: =(3x+3)²
Step 3: =(3(x+1))²
Step 4: =9(x+1)²
A) the proof is valid
B) step 2 is not valid
C) step 1 is not valid
D) step 3 is not valid
Verify each step
step 1
x (9x+3) +3(x+3)
=9x^2+3x+3x+9
=9x^2+6x+9
step 1 is correct
step 2
Complete squares
9x^2+6x+9=0
Factor 9
9(x^2+6/9x)+9=0
9(x^2+2/3x)+9=0
9(x^2+2/3x+4/36-4/36)+9=0
9(x^2+2/3x+4/36)+9-1=0
9(x^2+2/3x+4/36)+8=0
9(x+2/6)^2=-8
therefore
step 2 is not valid6. A grocery store sells bags of oranges in two different sizes.
The 3-pound bags of oranges cost $4.
The 8-pound bags of oranges for $9.
Which oranges cost less per pound? Explain or show your reasoning.
(From Unit 2, Lesson 10.).
Answers
Explanation:
4/3= 1.33 pounds per bag
9/8 = 1.125 pounds per bag
Please show steps 1/2 divided by 1/2
Answers
To divide by a fraction is the same as multiplying by the reciprocal, which is (2/1), or just 2.
(1/2) x (2/1) = (2/2) = 1
multiply across and simplify
Which expression is equivalent to the following complex fraction?3.4X-12x-2-X-12(x-2)O-4x+7-4x+72(x-2)-4x+72(x2-2)21x2 - 2)-4x+7
Answers
Solution
For this case we can do the following:
[tex]\frac{3}{x-1}-4=\frac{3-4x+4}{x-1}[/tex][tex]2-\frac{2}{x-1}=\frac{2(x-1)-2}{x-1}[/tex]And if we simplify we got:
[tex]\frac{3-4x+4}{2(x-1)-2}=\frac{7-4x}{2x-2-2}=\frac{7-4x}{2x-4}=\frac{-4x+7}{2(x-2)}[/tex]Final answer would be:
-4x+7 /( 2(x-2))
which statement is true of this function f x equals 1/5 - 2
Answers
Its a decreasing function, and the y-intercept is NOT on (0, -2).
The correct option is A
(A) As the value of x increases, the value of f(x) moves towards a constant
what is 2 2/5 - 3 1/2
Answers
Does this work show that 8 is a solution to the equation s-3=11 and how?
Answers
Given -
s - 3 = 11
To Find -
Is s = 8 a solution or not?
Step-by-Step Explanation -
on Putting s = 8 in the above equation
8 - 3 = 11
5 = 11
Which is not true as 5 ≠ 11
Final Answer -
Option (D)
No, Because the last line of the work is not true. 5 and 11 are not equal
The cost of attending an amusement park is $15 for children and $35 for adults. On a particular day, the attendance at the amusement park is 25,000 attendees, and the total money earned by the park is $600,000. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
Answers
The number of children's tickets sold is 13750.
Let the number of children be x and the number of adults be y.
The total number of attendance at the amusement park is 25,000.
So we have an equation
x + y = 25000 ......(i)
The cost for children is $15 and the cost for adults is $35, and the total money earned by the park is $600,000.
So we have another equation,
15x + 35y = 600,000
3x + 7y = 120,000 ......(ii)
Multiplying equation (i) with 3 we get
3x + 3y = 75000
3x + 7y = 120,000
Now subtract both the equation we have,
4y = 45000
y = 11250
Now put the value of y in equation (i) we get
x + 11250 = 25000
x = 13750
Where x is the number of children's tickets sold.
Therefore the number of children's tickets sold is 13750.
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Triangle ABC is shown in this figure. 2 A B Which statement justifies that the sum of Angle 1 and Angle 2 is 180°? O All adjacent angles are supplementary. O Adjacent angles that form a linear pair are supplementary. O The sum of any interior and any exterior angle of a triangle is 180° 0 Each pair of interior and exterior angles that lie on a line is complementary
Answers
The answer is Adjacent angles that form a linear pair are supplementary.
November 1 Accepted a $4,000, 180-day, 6% note from Kelly White in granting a time extension on her past-due account receivable. December 31Adjusted the year-end accounts for the accrued interest earned on the White note. April 30White honored her note when presented for payment. Complete the table to calculate the interest amounts on December 31st and April 30th and use those calculated values to prepare your journal entries.
Answers
The interest amounts on December 31st and April 30th are $100, $33, and $67. Also, the journal entries are mentioned below.
What are Journal entries?A journal entry is an act of recording any transaction, whether one is economic or not.An accounting diary that displays the debit and credit balances of a corporation lists transactions. Multiple recordings, each of which is either a debit or a credit, may be included in the journal entry.The amount of the debits and credits must be equal in order for the journal entry to be declared balanced.Depreciation or bond amortization are examples of recurring items that can be recorded in journal entries.Accounts payable normally has its own sub-ledger that indirectly impacts the general ledger, and journal entries are frequently filed using a different module in accounting software.The Computation of the interest amount is shown below:-
Particulars Total through Through maturity Through maturity
Maturity Dec 31 Apr 30
Principal $4,000 $4,000 $4,000
Rate 5% 5% 5%
Time 180 ÷ 360 60 ÷ 360 120 ÷ 360
Total interest $100 $33 $67
2. The Journal entries are shown below:-
a. Notes receivable Dr, $4,000
To accounts receivable $4,000
(Being issuance of notes is recorded)
b. Interest receivable Dr, $33
To Interest revenue $33
(Being interest revenue is recorded)
c. Cash Dr, $4,100
To Notes receivable $4,000
To Interest revenue $67
To Interest receivable $33
(Being cash received is recorded)
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what’s the correct answer answer asap for brainlist
Answers
Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:
B: played by solo instrument with orchestral accompaniment.
A local Pet Shelter has 4 orange cats and 7 black cats. What is probability of selecting a black cat? Please enter your answer as a fraction.
Answers
The Solution:
Given:
We are asked to find the probability of selecting a black cat.
By formula,
[tex]Probability=\frac{number\text{ of required outcomes}}{total\text{ possible outcomes}}[/tex]Thus,
[tex]P(B)=\frac{number\text{ of black cats}}{total\text{ number of cats}}=\frac{7}{11}[/tex]Therefore, the correct answer is 7/11
(2580+2920+x)/3=3000
Answers
Answer:
x = 3500
Step-by-step explanation:
2580 + 2920 + x
------------------------ = 3000
3
5500 + x
------------------------ = 3000(3)
3(3)
5500 + x = 9000
-5500 -5500
------------------------------
x = 3500
I hope this helps!
The first aircraft has 65 more seats than the second aircraft. The third aircraft has 41 fewer seat than the second aircraft. If their total number of seats is 402, find the number of seats for each aircraft.
Answers
Solution:
Let A be the first aircraft
Let B be the second aircraft
Let C be the third aircraft
Here is the information that is given in the question:
The first aircraft has 65 more seats than the second aircraft:
A = B + 65
The third aircraft has 41 fewer seats than the second aircraft
C = B - 41
their total number of seats is 402
A + B + C = 402
Now substitute the values in the 1st and 2nd equations into the 3rd.
(B+65) + B + (B-41) = 402
this is equivalent to:
3B + (65-41) = 402
this is equivalent to:
3B + 24 = 402
this is equivalent to:
3B = 402 - 24 = 378
solving for B, we get:
[tex]B\text{ = }\frac{378}{3}=126[/tex]We can conclude that the correct answer is:
first aircraft A:
A = B + 65 = 126 + 65 = 191
that is:
A = 191
second aircraft:
B = 126
third aircraft:
C = B - 41 = 126 - 41 = 85
that is:
C = 85
what is this pleaseeee
Answers
The correct option C: y = (x + 2)(x -3)²(x - 1)² is function which correctly represents the given graph.
What is defined as the graphing?A diagram that depicts the relationship between quantities, particularly one in which lines, bars, as well as proportional areas portray how a quantity depends on it or changes with the other. A curve or line depicting a mathematical function or eq, usually drawn in Cartesian coordinates.In mathematics, a graph is characterized as a pictorial representation or diagram that organizes data or values.The graph's points frequently depict the connection between two or more variables.For the given graph;
Select one coordinate of the curve from the graph.
Point (0, 18); in which y is 18 for x = 0.
Now, go by option and put the value of x = 0 and find the correct value of y.
Option C: y = (x + 2)(x -3)²(x - 1)²
Put x = 0
y = (0 + 2)(0 -3)²(0 - 1)²
y = (2)(-3)²(- 1)²
y = 18
We, get the correct coordinates (0, 18).
Thus, the correct option is C, which satisfies the given graph.
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a cooler at picnic contain
Answers
we know that
the total cans are 100
number of cans of root beer=24
number of cans of orange soda=12
number of cans of cola=16
therefore
the probability is equal to
P=(24+12+16)/100
P=52/100
P=0.52 or P=52%
as fraction is 52/100=26/50=13/25
answer is 13/25I’m needing guidance solving this equation 9x-9=3x+7
Answers
GROUP THE LIKE TERMS FIRST.
[tex]9x - 3x = 7 + 9[/tex]
WHEN TERMS CROSS THE EQUAL SIGN THEY CHANGE SIGN.
[tex]6x = 16 \\ \frac{6x}{6} = \frac{16}{6} \\ x = \frac{16}{6} [/tex]
x can be simplified further
[tex]x = \frac{8}{3} [/tex]
HOPE THIS HELPS.
Answer:
The answer should be x=2.6
Step-by-step explanation:
9x-9=3x+7
-first you should move the numbers so you can get all your x values on one side and all your regular numbers on the other like this
9x-3x=7+9
-What i basically did was i passed the 3x from the right side to the left side of the equation, since in adding the 3x originaly, when i pass it to the left side itll be subtracting. then i passed my -9 to the right side of my equation, since i was subtracting originaly ill have to now switch it to adding
-after you do this you are going to want to want to combine like terms
6x=16
-then you are going to want to devide on both sides so you can get x alone
x=2.6
=MATHEMATICAL READINESSSummation of indexed dataThe following is a list of 14 measurements.38. -82. 19. 84. -37.93.-31, -73, -50.-65.-31. -85, -48Suppose that these 14 measurements are respectively laSum of Xi/ 50 with i going from 1 to 14Round your answer to at least two decimal places.
Answers
In order to calculate the sum we need to iterate over the "xi" variable going from 1 to 14 and adding all the data.
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop=1}\frac{x_i}{50}\text{ = }\frac{38\text{ - 82}+19+84-37.93-31-73-50-65-31-85-48}{50} \\ \sum ^{\infty}_{n\mathop{=}1}\frac{x_i}{50}\text{ = }\frac{-361.93}{50}\text{ = -7}.2386 \end{gathered}[/tex]The answer is approximately -7.24.
USChoose the definition for the function.1(-x + 2 x < 1 --x+ 2 x > 1C. Y = { x + 1x S1a.y=x+1--x+ 2 x51 d. y = { x+1b. y = x + 1-x + 2 x 2 16*x > 1Enter
Answers
Given data:
The given graph.
The equation of the line when x is less than or equal to 1 is,
x+1
he equation of the linne when x is greater than 1 is,
-x+2.
Thus, the correct option is (c).
Consider the following system of equations 4x + 6=24 and 2x + 3y=8 How many solutions does this system have? Justify your answer. Part B If we triple each side of the first equation 4x+6y=24, we have 12x+18y=72. Explain why the new system 12x+18y=72 and 2x+3y=8 has the same number of solutions as the original system.
Answers
For the given system of equations 4x + 6y=24 and 2x + 3y=8, there is no solution exists.
What is defined as the system of equations?When two or more equations are solved together in algebra, the solution should satisfy all of the equations with in system. The amount of equations must equal the amount of unknowns for a system to produce a unique solution. Even so, no solution is guaranteed. If there is a solution, the system has been consistent; otherwise, it is inconsistent.For the given system of equation,
4x + 6y =24 ......eq 1
and 2x + 3y = 8 ..... eq2
use elimination method.
Multiply eq 2 with 2 and subtract from eq 1.
0 = 16
But 0 ≠ 16, the system of equation becomes untrue.
As, the values o f the variables x and y are getting cancelled. So, the there is no solution existed for the given system.
Also,the ratio of 4x/2x = 2 and 6y/3y = 2 is same thus, no solution is possible for the system.
Now, when the we triple each side of the first equation 4x+6y=24, we have 12x+18y=72.
The new system 12x+18y=72 and 2x+3y=8
Then, also 12x/2x = 6 and 18y/3y = 6 is also same. Then, also the system of equation does not have any solution of the system.
Thus, the system of equation does not have any solution.
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HELP ASP show your work!!
Answers
The minimum number of friends for which Jump it Up is 7
A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).
Sky high pricing:
$50 for <=10 people and $5 per person after that
Jump it Up pricing:
Set up charges = $70
Per person charges = $2
Let p be the number of people
Formulating the equation we get:
50 + 5p = 70 + 2p
3p = 20
p = 6.66
or p =7
So, Jump it up will be less expensive for 7 friends
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ASAP PLEASE HURRY
What is the value of q − 8 if q = −18?
A. 26
B. -26
C. 10
D. -10
Answers
Answer:
-26
Step-by-step explanation:
Q = -18
-18 - 8
-26
Hope this helps! :)
What is the most precise name for quadrilateral ABCD with verticesA(-5, 7), B(6,-3), C(10, 2), and D(-1, 12)?A. rectangleB. rhombusC. squareD. parallelogram
Answers
Given that
The vertices of a quadrilateral are A(-5, 7), B(6,-3), C(10, 2), and D(-1, 12).
So we have to find the type of quadrilateral ABCD.
Explanation -
First, we have to find the length of each side AB, BC, CD, and DA.
We will use the distance formula to find the length of each side
[tex]\begin{gathered} T\text{he distance formula for point \lparen x}_1,y_1)\text{ and \lparen x}_2,y_2)\text{ is } \\ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Now we will find the sides by substituting the value,
[tex]\begin{gathered} For\text{ AB,} \\ AB=\sqrt{(6-(-5))^2+(-3-7)^2} \\ \\ AB=\sqrt{(6+5)^2+(-10)^2}=\sqrt{11^2+10^2}=\sqrt{121+100}=\sqrt{221} \\ \\ AB=\sqrt{221}\text{ units} \end{gathered}[/tex][tex]\begin{gathered} For\text{ BC,} \\ BC=\sqrt{(10-6)^2+(2-(-3))^2} \\ BC=\sqrt{4^2+(2+3)^2} \\ BC=\sqrt{16+25}=\sqrt{41} \\ BC=\sqrt{41}\text{ }units \end{gathered}[/tex][tex]\begin{gathered} For\text{ CD} \\ CD=\sqrt{(-1-10)\placeholder{⬚}^2+(12-2)\placeholder{⬚}^2} \\ CD=\sqrt{(-11)^2+(10)^2} \\ CD=\sqrt{121+100} \\ CD=\sqrt{221}\text{ units} \end{gathered}[/tex][tex]\begin{gathered} For\text{ DA,} \\ DA=\sqrt{(-1-(-5))^2+(12-7)^2} \\ DA=\sqrt{(-1+5)^2+5^2} \\ DA=\sqrt{4^2+5^2}=\sqrt{16+25} \\ DA=\sqrt{41}\text{ units} \end{gathered}[/tex]So we found that the opposite sides are equal. So it can be a parallelogram or a rectangle.
Now, we will check the triangular part ABC, by applying Pythagoras' theorem.
[tex]\begin{gathered} In\text{ trianlge ABC, } \\ AC=\sqrt{(10-(-5))^2+(2-7)^2}=\sqrt{(10+5)^2+(-5)^2} \\ AC=\sqrt{15^2+5^2} \\ AC=\sqrt{225+25}=\sqrt{250} \\ Now\text{ using pythagoras theorem we have,} \\ AC^2=AB^2+BC^2 \\ \sqrt{250}^2=\sqrt{221}^2+\sqrt{41}^2 \\ 250=221+41 \\ 250\ne262 \end{gathered}[/tex]So it is a parallelogram. Then option D is correct.
Final answer -
The final answer is a parallelogram.Find the altitude of rhombus whose area is 208 cm² and perimeter is 64 cm.
Answers
Given the area of a rhombus is 208 cm square and the perimeter of rhombus is 64 cm.
Recall that all the sides of the rhombus are equal.
Hence,
[tex]\begin{gathered} \text{perimeter}=4\times sides \\ 64=4\times\text{side} \\ 16cm=\text{side} \end{gathered}[/tex]Area of rhombus is :
[tex]\begin{gathered} area=base\times height \\ 208=16\times h \\ h=\frac{208}{16} \\ h=13\operatorname{cm} \end{gathered}[/tex]Hence the altitude of the Rhombus is 13 cm.