A radioactive element has a half-life of 18 years. We start with 40mg. Assuming the decay is occurring continuously, the appropriate model is...
Identity P0.
Solve for k.
What amount of the element remains after 10 years?
When with 10mg be remaining?
Answers
1) The decay constant is 0.0385
2) The amount after ten years is 27.2 mg
3) The time taken for 10 mg to remain is 36 years.
What is the half life of a radioactive isotope?We know that;
P = Poe^-kt
Given that the half life is 18 years;
20=40e^-18k
20/40=e^-18k
0.5 =e^-18k
ln0.5 = -18k
k = -0.693/-18k
k = 0.0385
After 10 years we have;
P = 40e^-10(0.0385)
P = 27.2 mg
10 mg will remain when;
10 = 40e^-0.0385t
10/40 =e^-0.0385t
0.25 = e^-0.0385t
ln0.25 = -0.0385t
t = -1.386/-0.0385
t = 36 years
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Related Questions
9. The prices of sweat shirts at five different stores are $6, $12, $11, $15, and $18. The mean price is $12.40 and the median price is $12. Identify the outlier and describe how the mean and median for this data set are affected by it.
Answers
The outlier in this data set is the sweatshirt priced at $18 since it is significantly higher than the rest of the prices.
How does the outlier affect the mean and median for the data set?The mean is affected more by outliers than the median.
In the provided data, the mean is higher than the median, which suggests that there may be an outlier pulling the average up. The outlier value of $18 is causing the mean to be higher.
If we remove the outlier value of $18, the mean price would be (6+12+11+15)/4 = $11, which is lower than the original mean of $12.40.
On the other hand, the median would remain the same since it is not affected by extreme values.
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If y= 2x +3, What is Y=(-5) + 3=
Answers
The value of the expression is -4
What is a function?
A function can simply be explained as an equation, law, rule or expression that tends to show the relationship between two distinct variables.
These variables are called the independent variables and dependent variables.
From the information given, we have the function as;
y= 2x +3
First, let's determine the function y(-5)
Substitute the values of x as -5 in the function;
y(-5) = 2(-5) + 3
expand the bracket
y(-5) = -10 + 3
Add the values
y(-5) = -7
Then, we get;
y(-5)+ 3
-7 + 3
-4
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14. Sarah makes and sells candles. She spends $80 on supplies, and she sells
each candle for $6. Write an expression that represents her profit for
selling c candles.
Answers
Answer: hmm this question is based on 6-80 and if you calulate the sum and difference it is -74
find f(g(4)) and g(f(4)) given f(x)=2x-3 and g(x)=5x^2-4x+1
Answers
Answer:
g(f(4)) = 106.
Step-by-step explanation:
To find f(g(4)), we first need to find
g(4):g(4) = 5(4)^2 - 4(4) + 1 = 80 - 16 + 1 = 65
Now that we know g(4) is 65, we can find
f(g(4)):f(g(4)) = f(65) = 2(65) - 3 = 127
Therefore,
f(g(4)) = 127.
To find g(f(4)), we first need to find f(4):f(4) = 2(4) - 3 = 5
Now that we know f(4) is 5, we can find g(f(4)):
g(f(4)) = g(5) = 5(5)^2 - 4(5) + 1 = 125 - 20 + 1 = 106
Therefore, g(f(4)) = 106.
Pls help
The shape below contains a rectangle and four semi circles.
Answers
The perimeter of the shape is 13π
The area of the shape is 48.125π square units
What are the perimeter and area of the shapes?The perimeter of the shape is calculated as follows:
The perimeter of shape = perimeter of the two semicircles of radius 2 + perimeter of the two semicircles of radius 4.5The perimeter of a semicircle = πr
The perimeter of shape = 2 * π * 2 + 2 * π * 4.5
The perimeter of shape = 13π
The area of the shape = area of the two semicircles of radius 2 + area of the two semicircles of radius 4.5 + area of the rectangle
Area of semicircle = πr²/2
The area of the shape = π * 2²/2 + π(4.5)²/2 + 4 * 9
The area of the shape = 48.125π square units
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The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 11654 and the sum of squares of regression (SSR) was 11405.0.
Answers
The value of R² (coefficient of determination) is 0.0214
We know that the formula for the coefficient of determination is,
R² = 1 - (SSR / SST)
where, R² is the coefficient of determination
SST is the total sum of squares
SSR is the sum of squares of regression
Here, the total sum of squares (SST) = 11654
and the sum of squares of regression (SSR) = 11405
Using above formula,
R² = 1 - (SSR / SST)
R² = 1 - (11405 / 11654 )
R² = 1 - 0.9786
R² = 0.0214
This is the required value.
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Find the complete question below.
Find the difference between 6c² +3c+9 and 3c-5.
Answers
Please someone help me. i really dont get this. If you help i give 40 POINTS Please help me
Answers
Answer:
Only Carla's
Step-by-step explanation:
I believe the answer is only Carla's because even though the left side is factored, there is still an 8 on the right side. To apply the zero product property rule, the equation needs to equal 0
Meanwhile Carla's works because then the equation would be x²=9 which we can easily take the square root of
Answer: Only Carla
Step-by-step explanation:
Only Carla
Carla said:
(x+1)(x-1)=8 FOIL
x²-1=8
x²=9
x=±3
Jordan said:
He will use 0 property rule but the factored portion must =0 It equals 8, so you can't use that property.
Gary has 24 quarters, 16 dimes, and 32 pennies. Write a ratio that compares the combined number of dimes and pennies to the number of quarters
Answers
Brainlist pls
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 2 ft by 2 ft by 12.5 ft. If the container is entirely full and, on average, its contents weigh 0.22 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answers
Answer:
38.81 pounds
Step-by-step explanation:
Considering the definition of right rectangular prism and its volume, the total weight of the contents is 38.81 pounds.
Right rectangular prism
A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
Volume of right rectangular prism
To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.
That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.
Volume of the container
In this case, you know that:
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
7.5 ft× 11.5 ft× 3 ft= 258.75 ft³
Then, the total weight of the contents is calculated as:
258.75 ft³× 0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds
Finally, the total weight of the contents is 38.81 pounds.
-x^2(x-4)
simplify the equation
Answers
Answer:
-x³ + 4x²
Step-by-step explanation:
-x^2(x-4)
Distribute
-x³ + 4x²
So, the answer is -x³ + 4x²
Cual es el volumen, en cm cúbicos, de un prisma rectangular con una altura de 3 cm, un ancho de 2 cm y una longitud de 18 cm ?
Answers
El volumen de un prisma rectangular se calcula multiplicando la altura por el ancho y por la longitud. En este caso, el volumen sería:
Volumen = 3 cm x 2 cm x 18 cm = 108 cm³
Por lo tanto, el volumen del prisma rectangular es de 108 cm³.
Answer:
El volumen en cm cúbicos es 108 cm cúbicos (o a la tercera potencia). La fórmula utilizada para encontrar el volumen es largo por ancho por alto.
Help me please! if a conditional statement is written in the form “If p then q”, how is the converse of the conditional statement is written?
A) If not q then p
B) If q then p
C) If not p then q
D) If not p then not q
Answers
The converse statement is of the conditional “If p then q” is the one in option B.
if q then p.
How can we identify the converse statement?For two given propositions p and q, a conditional statement is written as:
"if p, then q"
So, if the proposition p is true, also is the proposition q.
The converse statement just changes the order of the two propositions ( if the proposition q is true, also is the proposition p), then here start with q and end with p, so the converse statement is:
if q then p.
The correct option is B.
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A bag contains 3 black balls, 2 blue balls, and 3 green balls. A
random sample of 4 balls is selected. Given that x is the number of
black balls. y is the number of blue balls.
a) Find the joint probability function f(x, y)
b) Find the joint probability distribution of f(x, y)
Answers
The requreid, the joint probability function f(x, y) is:
f(0,0) = 3/14
f(0,1) = 9/28
f(0,2) = 3/28
f(1,0) = 9/28
f(1,1) = 9/28
f(2,0) = 3/14
f(2,1) = 3/14
f(3,0) = 1/14
To evaluate the joint probability function f(x, y), we need to determine the probability of selecting x black balls and y blue balls out of a sample of 4 balls. We can do this using the hypergeometric probability distribution formula:
f(x,y) = P(X = x, Y = y) = (C(3, x) * C(2, y) * C(3, 4-x-y)) / C(8, 4)
where C(n, k) represents the number of combinations of k items chosen from a set of n items.
Plugging in the values, we get:
f(0,0) = (C(3,0) * C(2,0) * C(3,4-0-0)) / C(8,4) = 3/14
f(0,1) = (C(3,0) * C(2,1) * C(3,4-0-1)) / C(8,4) = 9/28
f(0,2) = (C(3,0) * C(2,2) * C(3,4-0-2)) / C(8,4) = 3/28
f(1,0) = (C(3,1) * C(2,0) * C(3,4-1-0)) / C(8,4) = 9/28
f(1,1) = (C(3,1) * C(2,1) * C(3,4-1-1)) / C(8,4) = 9/28
f(2,0) = (C(3,2) * C(2,0) * C(3,4-2-0)) / C(8,4) = 3/14
f(2,1) = (C(3,2) * C(2,1) * C(3,4-2-1)) / C(8,4) = 3/14
f(3,0) = (C(3,3) * C(2,0) * C(3,4-3-0)) / C(8,4) = 1/14
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The rim of a basketball hoop is 10 feet high. When Chase stretches his hand, it is 88 inches high. How many feet does Chase have to jump to be able to touch the rim?
Answers
Chase has to jump 2.67 feet to touch the rim.
The rim of the basketball hoop is 10 feet high, which is equal to 120 inches .
Chase's hand can reach 88 inches high.
To find out how many feet Chase has to jump to touch the rim, we need to subtract his reach from the height of the rim:
120 inches (height of rim) - 88 inches (Chase's reach) = 32 inches
So Chase has to jump 32 inches to touch the rim. To convert this to feet, we can divide by the number of inches in a foot:
32 inches ÷ 12 inches/foot = 2.67 feet
Therefore, Chase has to jump 2.67 feet to touch the rim.
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n - 29 = -53
What is n????
Answers
You do -53+29 to get -24
(1/3)k=-4=7
what's k
Answers
The value of the variable k is 33
What are algebraic expressions?Algebraic expressions are simply described as the expressions that consist of variables, terms, coefficients, constants and factors.
These expressions also consist of certain mathematical operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationFrom the information given, we have that;
(1/3)k - 4=7
collect the like terns
1/3k = 7 + 4
Add the values
1/3k = 11
cross multiply the values, we have;
k = 11(3)
Multiply the values
k = 33
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This question here. Thank you in advance
Answers
Answer:
Step-by-step explanation:
211
welcome hun
Lesson 7 Practice Problems
(1.A crew has paved of 3/4 a mile of road. If they have completed 50% of the work, how
long is the road they are paving? Where did the 2 come from
Answers
Solve these 4 problems
Answers
The perimeter and the area of each composite figure are, respectively:
Case 1: p = 77.6 cm, A = 304 cm²
Case 2: p = 25.1 ft, A = 28 ft²
Case 3: p = 42 mi, A = 52.5 mi²
Case 4: p = 56.5 in, A = 179.424 in²
How to determine the perimeter and the area of a figure
In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:
Triangle
A = 0.5 · b · h
Rectangle
A = b · h
Where:
A - Areab - Baseh - HeightNow we find the perimeter and the area of each figure:
Case 1
p = 2 · (18.8 cm) + 2 · (20 cm)
p = 77.6 cm
A = (15.2 cm) · (20 cm)
A = 304 cm²
Case 2
p = 10 ft + 8.1 ft + 7 ft
p = 25.1 ft
A = 0.5 · (10 ft) · (5.6 ft)
A = 28 ft²
Case 3
p = 17.5 mi + 6 mi + 18.5 mi
p = 42 mi
A = 0.5 · (17.5 mi) · (6 mi)
A = 52.5 mi²
Case 4
p = 20 in + 13.9 in + 15 in + 7.6 in
p = 56.5 in
A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)
A = 98.8 in² + 31.982 in² + 48.642 in²
A = 179.424 in²
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Determine whether the ordered pair is a solution to the given equation.
(−4, 24); y = −6x
Answers
Answer: Yes, (-4, 24) is a solution to the given equation.
Step-by-step explanation:
24 = -6(-4)
24 = 24
Which expression is NOT equivalent to 24 + 12
Group of answer choices
3(8+4)
2(12+10)
2(12+6)
6(4+2)
Answers
The vertices of a triangle are at (0,0), (8,8) and (4,12). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x ?
Answers
The volume of the figure that was created by the triangle being rotated, would be 94. 83 units ³
How to find the volume ?When a triangle is rotated about y = x, a right circular cone is created. The formula is:
= π r² h / 3
We need to find the height and radius. The coordinates for the right circular cone are:
(0,0) - (0,0)
(8,8) - (8,8)
(4,12) - (12,4)
Using this, we find that the radius is 4 units. The height can be found by using any point such as ( 12, 4).
= √ ( ( 12 - 8) ² + ( 4 - 8 ) ²)
= 5. 66 units
The volume would therefore be:
= π x 4² x 5. 66 / 3
= 94. 83 units ³
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To find the total number of people sitting in the full rows, Mandy multiplied 142 by 10 and 142 by 2 and then added the products. Does Mandy’s method make sense? Use what you know about multiplication to explain why or why not.
Answers
Mandy's solution makes sense since it entails multiplying the total number of persons in those entire rows (142) by the number of people in each row (ten).
How does multiplication apply?Similarly, multiplying the total number of people in the remaining seats (142) by the number of people in each row (2) yields the total number of people in the remaining seats. The total number of persons in the theater is calculated by adding these two components.
This is a viable use of multiplication's distributive property, in which we break down a multiplication issue into simpler products and then add them up. As a result, Mandy's approach is a viable method for determining the total number of people in the theater.
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help see photo on simple interest
Answers
The principal amount was £1260, and the annual interest rate is 5.5%.
Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.
SI = principal × rate × time / 100
So,
P + 5pr = £1606.50
P = £1606.50 - 5pr............(i)
P + 6pr = £1675.80
P = £1675.80 - 6pr.........(ii)
Therefore,
£1606.50 - 5pr = £1675.80 - 6pr
Pr = 69.3
Put the value of pr in eq(i)
P + 5(69.3) = 1606.50
P = 1606.5 - 346.5
P = 1260
Now,
(1260)r = 69.3
r = 0.055
The annual interest is 5.5%
Hence, the principal amount was £1260, and the annual interest rate is 5.5%.
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17. The diameter of a cylinder is 7 yards. The height
is 12 yards. What is the volume, in terms of and
to the nearest cubic yard, of the cylinder?.7.GR.2.3
Answers
The volume of the cylinder that has a diameter of 7 yards and a height of 12 yards is: 147π cubic yard.
What is the Volume of a Cylinder?The volume of a cylinder can be determined by applying the volume formula which is given as:
Volume (V) = πr²h,
where "r" is the radius of the cylinder
"h" is the height of the cylinder
π is a constant
Given the following:
Diameter of cylinder = 7 yards, thus, radius (r) = 7/2 = 3.5 yards
Height (h) = 12 yards
Plug in the values:
Volume of the cylinder = π * 3.5² * 12 = 147π cubic yard.
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suppose sin(A)=2/5 use the trig identity sin^2(A)+cos^2(A)=1 to find sin (A) in quadrant IV
Answers
The trigonometry identity value of sin(A) is -2/5
Solving the trigonometry identityFrom the question, we have the following parameters that can be used in our computation:
sin(A) = 2/5 sin^2(A) + cos^2(A) = 1 The angle A is in Quadrant IVThe value of sin(A) has already been given
However, because the angle A is in Quadrant IV, the value of the trigonometry identity would be negative (sine are negative in the 4th quadrants)
So, we have
sin(A) = -2/5
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Claude Monet's Impression: Sunrise (1872) is considered a(n) _____painting because it was completed out-of-doors.
plein-air
alfresco
alla prima
sfumato
Answers
Answer:
the answer
Step-by-step explanation:
plein-air painting
5 ft:25 ft to fraction in its simplest form
Answers
Answer:
The answer is 1/5
Step-by-step explanation:
5ft:25ft=5ft/25ft=1/5
Answer:
1/2
Step-by-step explanation:
A rectangle has an area of 54 square inches and a length of 6 inches. What is the width, in inches, of the rectangle?
Answers
Answer:
width = 9 in
Step-by-step explanation:
Area = A = length x width = w x l
w = A/l = 54 in²/6 in = 9 in