Approximately 70.79 grams of radium will be present in 500 years.
To determine the amount of radium that will be present in 500 years, we can use the concept of radioactive decay and the half-life of radium.
The half-life of a radioactive substance is the amount of time it takes for half of the initial quantity to decay. In this case, the half-life of radium is given as 1690 years.
To calculate the amount of radium that will be present in 500 years, we can divide the elapsed time by the half-life and then use the exponential decay formula:
N(t) = N₀ * (1/2)^(t / T),
where N(t) represents the amount of radium present at time t, N₀ represents the initial amount of radium, T represents the half-life, and t represents the elapsed time.
Given that the initial amount of radium is 90 grams, the half-life is 1690 years, and we want to find the amount present in 500 years, we have:
N(500) = 90 grams * (1/2)^(500 / 1690).
To calculate this expression, we can use a calculator or a computer software. Evaluating the expression, we find:
N(500) ≈ 90 grams * (1/2)^(0.2959) ≈ 90 grams * 0.7866 ≈ 70.79 grams.
Therefore, approximately 70.79 grams of radium will be present in 500 years.
It's important to note that radioactive decay is a random process, and the half-life represents the average time it takes for half of the substance to decay. The actual amount of radium present in 500 years may vary due to the random nature of radioactive decay.
By using the exponential decay formula and the given half-life of radium, we can estimate the amount of radium that will be present in 500 years as approximately 70.79 grams.
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у
80
The graph of quadratic function
is shown on the grid.
What is a solution to r(x) = 0?
60
40
A -50
20
B 4
х
-4
4
8
12
- 16 -12 -8
16
C 14
-20
D-60
vo
-60
-80
Answer:
C 14
Step-by-step explanation:
Please help me will mark brainliet
Answer:
The degree of the term is 5
Don't forget to mark me as brainliest
Both antibiotics were prescribed in high dosage slow release capsules. The function C(x)=5log(x+1)+10 models the concentration of levofloxacin in mol/L over a time x, in hours. The function D(x) = 10log(x+1)+5 models the concentration of metronidazole in mol/L over a time x in hours. a) Which of the two drugs has a higher initial concentration in the blood stream? Justify your answer with an explanation. (2K, A) b) Determine when C(x) = D(x) algebraically and state what this represents in this situation. (6K, A, T) c) If Mathews is instructed to take both antibiotics at once the concentration levels could be modeled by the function(C+D)(x). How would the graph of (C+D)(x) differ from the individual graphs of C(x) and D(x)? Explain. (2T)
a) The initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x))
b) There is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
a) The initial concentration of a drug in the bloodstream can be determined by evaluating the functions C(x) and D(x) at x = 0. Plugging in x = 0 into both functions, we find that C(0) = 5log(0 + 1) + 10 = 5log(1) + 10 = 5(0) + 10 = 10, and D(0) = 10log(0 + 1) + 5 = 10log(1) + 5 = 10(0) + 5 = 5. Therefore, the initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x)).
b) To find when C(x) = D(x), we set the two functions equal to each other and solve for x: 5log(x + 1) + 10 = 10log(x + 1) + 5. Subtracting 10log(x + 1) from both sides, we get 5log(x + 1) - 10log(x + 1) = 5. Simplifying, we have -5log(x + 1) = 5. Dividing by -5, we find log(x + 1) = -1. This equation can be rewritten in exponential form as 10^(-1) = x + 1, which simplifies to 0.1 = x + 1. Subtracting 1 from both sides, we get x = -0.9. However, since time cannot be negative, there is no solution to the equation. Therefore, there is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would represent the combined concentration levels of both antibiotics when taken together. It would differ from the individual graphs of C(x) and D(x) by showing a higher overall concentration. Since (C+D)(x) is the sum of the two individual functions, the resulting graph would be the sum of their concentrations at each point in time. This means that at any given time, the concentration of the combined antibiotics would be the sum of the concentrations of levofloxacin and metronidazole at that time. The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
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PLEASE HELP!!
In a geometric sequence, a2=2, a3=12, and a4=72. Which equation can be used to find the nth term of the sequence, an?
an=2⋅10n−1
an=6⋅2n−1
an=13⋅6n−1
an=2n−1
Ik this is late, but people who are looking for the answer can see this.
Answer:
an =1/3*6^n-1
Step-by-step explanation:
You should plug in 2 for n in each equation, which, the correct one should give you 2. Then, to make sure, you plug in 3 in the equations that gave you 2.
Example:
an = 1/3 * 6 ^n-1
Plug in 2.
an = 1/3 * 6 ^2-1
an = 1/3 * 6 ^1
1/3 * 6 = 2
Step 2.
an = 1/3 * 6 ^3-1
an = 1/3 * 6 ^2
1/3 * 36 = 12
Hope this helps.
The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In a geometric sequence,
⇒ a₂ = 2, a₃ = 12 and a₄ = 72
Now, From option 3;
The equation is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
Put n = 2
⇒ a (2) = 1/3 × 6²⁻¹
⇒ a (2) = 1/3 × 6
⇒ a (2) = 2
Hence, This is the correct equation which can be used to find the nth term of the sequence, an.
Thus, The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
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Plz help I’ll give brainliest
1. y= -5
2. m=0
3. I dont know
1. 3x+4y=-20
x=0
3×0+4y=-20
0+4y=-20
y=-5
2. m=y/x
m=0/1
m= 0
3. Sorry
help please 100 point
Answer:
Solution given:
we have
<A+<B=exterior <C[sum of two opposite interior angle of a triangle is equal to the exterior angle in a triangle]
So
3x-13+ 2x+4=116°
5x-9=116°
5x=116°+9°
x=125/5
x=25
Now
<A=3×25-13=62°
<B=2×25+4=54°
Answer:
[tex]3x - 13 + 2x + 4 = 166 \\ 5x - 9 = 116 \\ 5x = 166 + 9 \\ 5x = 125 \\ x = \frac{125}{5} \\ x = 25 \\ \\ a = 3 \times 25 - 13 = 62 \\ b = 2 \times 25 + 4 = 54[/tex]
Luke now takes 20 cards numbered 1 to 20. Show how the cards can
be paired to give an LCM of 60.
Answer:
Step-by-step explanation:
The pair members cannot be multiplied. Look at the last numbers that are prime starting with eleven
What are you going to pair these primes with
11 13 17 19
So they must be added (or maybe subtracted).
1 19
2 18
3 17
4 16
5 15
6 14
7 13
8 12
9 11
and 20 which no matter how you do this, there will be 1 card left over.
Each of them adds to 20 so the LCM is 20
If Ann travels 50 meters North, 200 meters East and 150 meters South, what is her total distance travelled ? A. 150 meters B.400 meters C. 250 meters D. 0 meter
Answer:
400 meters
Step-by-step explanation:
50 + 200 + 150 = 400
Name the decimal and fraction for R on the number line.
Click the icon to view the number lines.
The decimal is 1.
The fraction is
A cylinder has a radius of 4 units and a height of 7 units. What is the volume in cubic units
Answer:
The answer is 352 cubic units
Can someone please help me with this question
Answer
180 - x
Step-by-step explanation:
opposite angles of a quadrilateral inscribed in a circle are supplementary
Answer:
180-x !!!
Step-by-step explanation:
i had some time to think about it
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do
you know?
Answer:
Step-by-step explanation:
but is their any answer choices
$17.99 with an 11.25% tax
Answer:
it's 2.0
hope that helps
What is the point-slope form of a line with slope
(-3, 6)?
nun
that contains the point
A. y- 3 = (x+3)
B. y+6 = {(x+3)
O C. y- 6 = - 3(x+ 3)
O D. y-6 = {(x+3)
Alyssa walked 1.34 fewer miles than Emily. Alyssa walked 7.45 miles. How many miles did Emily walk?
7(2x+3)-x(14-y)
[tex]7(2x + 3y) - x(14 - y)[/tex]
Answer:
[tex]y(x+21)[/tex]
Step-by-step explanation:
[tex]7(2x+3y)-x(14-y)\\=14x+21y-14x+xy\\= 21y+xy\\= y(x+21)[/tex]
helpppp please
On a map, 2 inches represent an actual distance of 28 miles. If the actual distance
between two cities is 322 miles, how many inches apart will the two cities be on the
map?
644 inches
23 inches
2 inches
28 inches
Ethel had 4 feet of ribbion she used 1 1/2 feet for a craft project how many feet of ribbon does she have left
Please Please help me
Answer:
1. 30
Step-by-step explanation:
First, place the numbers from least to greatest.
11,13,23,37,45,58
Then, find the middle number (or two middle numbers).
In this case, the middle numbers are 23 and 37.
Third, we find the mean of these numbers.
23+37=60
60/2=30
So your answer is 30.
Repeat this method for the other problems.
Please help asap. This is khan acadamy
Answer:
xr 30 degrees
Step-by-step explanation:
the angles always add up to 180 sooo
53+97=150
180-150=30
there's how u solve these kinds of problems
hope this helps
PLSSSSSSSSSSSSSS HELPPP FOR REAL SOMEBODDYY REWARD BRAINLIEST!!!!!!!!!!!!!!!!!
Answer:
1. x = 3
2. (1, 0)
3. x = 3, -2
4. 144
5. -3 + 4√3
Step-by-step explanation:
Triangle ABC was reflected across an axis.
A. State what axis it was reflected across
B. Give the ordered pairs of the reflected triangle
Graph a line that has a slope of 5/2 and includes the point (-2, -7)
PLEASE ANSWER THIS ASAP
Answer:
Option D
is the correct....
Pharoah Limited purchased a computer for $8,600 on January 1, 2020. Straight-line depreciation is used for the computer, based on a five-year life and a $900 residual value. In 2022, the estimates are revised. Pharoah now expects the computer will be used until December 31, 2023, when it can be sold for $700. Calculate the 2022 depreciation expense.
The depreciation expense for 2022, based on the purchase price for the computer of $8,600, the revised estimate in 2022, using the straight-line method is $2,410 per year
What is the straight line depreciation method?The straight-line depreciation method is method for calculating the depreciation of an asset in which the value of the asset is uniformly reduced within each period until the salvage value of asset is reached.
The depreciation on the computer = $8,600 - $900 = $7,700
The annual depreciation rate for the computer in the first two years, using the straight line depreciation method is; $7,700/5 = $1,540 per year
The depreciation of the computer by the end of 2021 = 2 × $1,540 = $3,080
Therefore, the net book value of the computer at the end of 2021 = $8,600 - $3,080 = $5520
The estimates are revised with Pharoah expecting to use the computer until December 2022, to sell for $700, therefore;
The revised depreciable amount for the computer = $5,520 - 700 = $4,820
The revised depreciation rate for the years, 2022 and 2023 is therefore;
Depreciation = $4,820/2 = $2,410 per year
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Determine the equation of the circle graphed below
The equation of the circle graphed below is (x - 2)² + (y + 3)² = 25.
To determine the equation of a circle, we need the center and the radius of the circle. In the graph below, the center appears to be at (2, -3) and the radius appears to be 5.
Therefore, we can use the standard equation of a circle,
which is (x - h)² + (y - k)² = r²,
where (h, k) is the center of the circle and r is the radius.
Substituting the values of the center and radius, we obtain the equation of the circle as follows:(x - 2)² + (y + 3)² = 25
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Bernard works for a business that sells and repairs tires. He can repair tires in an hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Answer:
3 tires per hour
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired per day = 24 tires
Number of time used to repair tire per day = 8 hours
What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired in one hour = Number of tires repaired per day / Number of time used to repair tire per day
= 24 tires / 8 hours
= 3 tires per hour
The unit rate for the number of tires repaired in one hour is 3 tires per hour
Express the following in form, where p and q are integers and q≠ . (0.1282828) find the answer please and thank you
Answer: [tex]\dfrac{127}{990}[/tex].
Step-by-step explanation:
Let x=0.1282828...
Multiply 10 on both sides , we get
10 x = 1.282828... (i)
Now multiply 100 on both sides , we get
1000x=128.2828... (ii)
Eliminate (i) from (ii), we get
[tex]990x=127\\x=\dfrac{127}{990}[/tex]
Hence, the required [tex]\dfrac{p}{q}[/tex] form: [tex]\dfrac{127}{990}[/tex].
4. A Tesla dealership is having a sale on their cars. This week you can save 15% off
the total price. If the retail price of the Tesla is $30,190, what is the discount?
Answer:
25,661.5
Step-by-step explanation:
30160x15%=4528.50
30160-4528.50=25,661.50
Is j+j+j+j and j with the power of four equivalent?
Answer:
No, they are not equivalent.
Step-by-step explanation:
j + j + j + j = 4j
j^4
Let's say j = 2
4j = 8
j^4 = 16
Answer:
NO
Step-by-step explanation:
j+j+j+j
remember multiplication is repeated addition!
j+j+j+j = 4j
THIS IS DIFFERENT! powers are repeated MULTIPLICATION.
j^4 = j to the power of 4 = j * j * j * j, NOT j+j+j+j !!!!!