The length of PS is 34 inches. Points P,Q,S are points on a line, so that PQ is 6 in, The ratio PQ:QR is 3:4 and The ratio QR:RS is 2:5.
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
The length of PQ is 6 in. The ratio PQ:QR is 3:4, hence:
PQ = PR * (3/7)
6 = PR * (3/7)
PR = 14 inches
QR = PR * (4/7)
QR = 14 * 4/7
QR = 8 inches
The ratio QR:RS is 2:5, hence:
QR = QS * (2/7)
8 = QS * 2/7
QS = 28 inches
Points P,Q,S appear in that order on a line. Therefore:
PS = PQ + QS
PS = 6 + 28
PS = 34 inches
The length of PS is 34 inches.
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fsUse the conversion 8 km/h = 5 mph to convert 32 m/s into mph. If your answer is a decimal, give it to 1 d.p.
Answer:
72mph
Step-by-step explanation:
To convert km/hr into m/s, simply multiply the speed value by 5/18
To convert 8Km/hr to m/s, multiply 8 by 5/18 or divide by 3.6
8 x 5/18 = 2.22m/s
You can say that 2.22m/s = 5mph since 8km/hr = 5mph
If 2.2m/s =5mph, 1m/s = 5mph/ 2.2 (Divide both sides by 2.2)
Then 32m/s = 5mph/2.2 x 32
2.25 x 32 = 72 mph
Using the conversion, 32 m/s is equivalent to 72 mph.
We have,
To convert 32 m/s to mph using the conversion factor 8 km/h = 5 mph,
We can follow these steps:
- Convert 32 m/s to km/h by multiplying by the conversion factor:
32 m/s x (3.6 km/h / 1 m/s) = 115.2 km/h
- Convert 115.2 km/h to mph using the conversion factor 8 km/h = 5 mph:
115.2 km/h x (5 mph / 8 km/h) = 72 mph
Therefore,
Using the conversion, 32 m/s is equivalent to 72 mph.
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The mean of 50 observations was 250. Later it was found that the number 152 was wrongly copied as 102 for the computation of mean. Find the correct mean.
Answer:
[tex](250*50-102)+152[\tex]
The correct mean of the 50 observations is 249.96.
To find the correct mean, we need to adjust the value that was wrongly copied. The difference between 152 and 102 is 50, so the corrected total of the 50 observations would be:
Corrected total = (original total - 102) + 152
= [tex](250*50-102)+152[/tex]
= [tex]12498[/tex]
Therefore, the correct mean of the 50 observations is:
Correct mean = Corrected total / Number of observations
= [tex]12498 / 50[/tex]
= 249.96
Hence, the correct mean of the 50 observations is 249.96.
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PLEASE SHOW WORK!!!!!!!!!
The midpoint of the line segment is (-2, 2). The correct answer is F. (-2, 2).
What is the equation of the line?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
((x1 + x2)/2, (y1 + y2)/2)
Using this formula, we can find the midpoint of the line segment that has endpoints (-10,-4) and (6,8):
Midpoint = ((-10 + 6)/2, (-4 + 8)/2) = (-2, 2)
Therefore, the midpoint of the line segment is (-2, 2). The correct answer is F. (-2, 2).
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4) What is the value of v?
Answer:
v = 110
Step-by-step explanation:
The big line is a 180 degree line. We need to find the value of the missing side so we take 70 degrees and subtract it from the total angle 180 degrees. That leaves us 110 degrees, so v = 110 degrees.
One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 2 hours and the second pump works for 3 hours.
Answer:
1/2 of the pool is filled, and in the second situation, the entire pool is filled.
Step-by-step explanation:
Let's start by finding the hourly filling rate of each pump. The first pump can fill the pool in 4 hours, so its hourly rate is 1/4 of the pool. The second pump can fill the pool in 6 hours, so its hourly rate is 1/6 of the pool.
For the first situation, the first pump works for 2 hours, so it fills 2/4 or 1/2 of the pool. The second pump does not work in this situation, so it fills 0 of the pool. Therefore, the total amount of the pool filled is 1/2.
For the second situation, the first pump works for 2 hours and fills 1/2 of the pool. The second pump works for 3 hours and fills 3/6 or 1/2 of the pool. Therefore, the total amount of the pool filled is 1/2 + 1/2 = 1.
So, in the first situation, 1/2 of the pool is filled, and in the second situation, the entire pool is filled.
1 point) (a) Find the discriminant of the equation 5x−9x²+6=0Discriminant =(b) Use the discriminant to say whether the equation has two (distinct) solutions, one solution, or no solutions.The equation has
Using the discriminant of the given equation 5x - 9x² + 6 = 0 which is 241, we can say that the the equation has two real and distinct solutions.
The mentioned equation is 5x - 9x² + 6 = 0. Now we have to find the discriminant of the equation.
Discriminant: ax² + bx + c = 0 is b² - 4ac. The discriminant is used to determine the nature of the roots of the quadratic equation. It can be categorized as the following: If b² - 4ac > 0, the quadratic equation has two real and distinct roots.If b² - 4ac = 0, the quadratic equation has one real and repeated root.If b² - 4ac < 0, the quadratic equation has no real roots or two complex roots.
In the given equation 5x - 9x² + 6 = 0, the coefficients are as follows:
a = -9, b = 5, and c = 6.
Now, we can find the discriminant: Discriminant = b² - 4ac= (5)² - 4(-9)(6)= 25 + 216= 241.
Thus, the discriminant of the given equation is 241. As the discriminant is greater than 0, the quadratic equation has two real and distinct roots.
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Please help me answer my homework in the image question 5
Answer:
C) trapezoid
Step-by-step explanation:
See attached image. The shape formed from the lines is a trapezoid, for the reasons listed.
Find the sum or type
"impossible"
[3 -8] +[4 -5 -6]
These matrices have various dimensions, making it difficult to determine their total. Because of this, the sum of these matrices is either undefinable or unattainable.
Due to their various dimensions, it is difficult to find the sum of these matrices.
One row and three columns make up the second matrix, whereas two rows and one column make up the first matrix. Two matrices can only be added if they share the same dimensions. To be more precise, two matrices can only be added if they have the same number of rows and columns.
The matrices [3 -8] and [4 -5 -6] cannot be added together since they have different numbers of rows and columns. Because of this, the sum of these matrices is either undefinable or unattainable.
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Trapezoids 1 and 2 are similar. The perimeter of Trapezoid 1 is 240 centimeters and the perimeter of Trapezoid 2 is 150 centimeters. What is the ratio x:y ?
The answer of the given question based on perimeter of trapezoid the ratio will be x:y is 8:5.
What is Trapezoid?A trapezoid is quadrilateral with at least one pair of the parallel sides. The parallel sides are called bases of trapezoid, and non-parallel sides are called legs.
Let's denote the lengths of the four sides of Trapezoid 1 as a, b, c, and d, and the lengths of the corresponding sides of Trapezoid 2 as m, n, p, and q, respectively. Then we have:
a + b + c + d = 240 (perimeter of Trapezoid 1)
m + n + p + q = 150 (perimeter of Trapezoid 2)
Since Trapezoid 1 and Trapezoid 2 are similar, we can write:
m = ax
n = bx
p = cy
q = dy
where x and y are the ratios of the longer and shorter bases of Trapezoid 1 to Trapezoid 2, respectively.
Substituting these expressions into the equations for the perimeters of the trapezoids, we get:
a(x+y) + b(x+y) + c(x+y) + d(x+y) = 240
(ax+bx+cy+dy) = 150
Simplifying these equations, we get:
(a+b+c+d)(x+y) = 240
(a+b+c+d)(x+y)(x/y) = 150
by Dividing second equation by first, we will get:
x/y = 240/150 = 8/5
Therefore, the ratio x:y is 8:5.
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The first equation in the system models the height, h, of a falling volleyball as a function of time, t. The second equation models the height, h, of the hands of a player jumping up to spike the ball as a function of time, t. Which statement describes the situation modeled by this system?
StartLayout Enlarged Left-Brace 1st Row h = 14 minus 16 t squared 2nd Row h = 7 + 24 t minus 16 t squared EndLayout
The volleyball is 7 feet above the ground at the instant the player begins her jump.
The volleyball is 14 feet above the ground at the instant the player begins her jump.
The volleyball is 16 feet above the ground at the instant the player begins her jump.
The volleyball is 24 feet above the ground at the instant the player begins her jump.
Answer:
The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Step-by-step explanation:
Here we have two situation of system of models.
[tex]\text{The height (h) of a falling volleyball as function of time (t):h}(t)=14-16t^2[/tex]
[tex]\text{The height (h) of the hands of a player as function of time (t):h}(t)=7-24t-16t^2[/tex]
We need to find the height of ball above the ground at the instant the player begins jump.
At t=0, player begins jump.
We put t=0 into [tex]h(t)=7+24t-16t^2[/tex]
Height of player hand at t=0 , h=7 feet.
Now we will set t=0 for first model.
[tex]h(0)=14-16\times0^2 \ = > 14[/tex]
Thus, The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Answer: B
Step-by-step explanation:
EDGE 2023
i really need help on this please
The value of r(s(4)) is -33.
What is a function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.
To find the value of r(s(4)), we first need to find the value of s(4), and then use that as the input for the function r.
To find s(4), we substitute x = 4 into the expression for s(x):
s(4) = 3(4) - 1 = 12 - 1 = 11
Now that we have the value of s(4), we can use it as the input for the function r:
r(s(4)) = r(11) = -3(11) = -33
Therefore, the value of r(s(4)) is -33.
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'If vector a =k times vector b, what is the angle between a and b where k is a scalar quantity?,
Angle between vector a and vector b is 0 degrees or 180 degrees.
What is vector?
A vector is a quantity that not only indicates magnitude but also indicates how an object is moving or where it is in relation to another point or item. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
What is scalar quantity?
Physical quantities with merely magnitude and no direction are referred to as scalar quantities. These physical quantities can be explained just by their numerical value without any further guidance. These physical values can be added according to the basic algebraic rules, and in this case, only their magnitudes are added.
GIVEN:
If vector a is equal to k (scalar quantity)times vector b.
then vector a and vector b are parallel to each other.
The angle between two parallel vectors is 0 degrees or 180 degrees.
So, the angle between vector a and vector b is
0 degrees or 180 degrees.
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The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function f(x)equalsnegative 3. 439 x Superscript 4 Baseline plus 35. 952 x cubed minus 99. 139 x squared plus 41. 541 x plus 178. 192 where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 1999
The number of bald eagles in the state in the winter of 1999 is 273.909, where The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function.
by the given information the equation is
[tex]f(x) = -3.439(x)^4 + 35.952(x)^3 - 99.139(x)^2 + 41.541(x) + 178.192[/tex]
where x = number of years since 1996
The given quartic function must be changed to x = 3 in order to determine the number of bald eagles in the state during the winter of 1999:
[tex]f(3) = -3.439(3)^4 + 35.952(3)^3 - 99.139(3)^2 + 41.541(3) + 178.192[/tex]
When we condense this expression, we get:
f(3) = -3.439(81) + 35.952(27) - 99.139(9) + 41.541(3) + 178.192
f(3) = -1107.759 + 970.104 - 892.251 + 124.623 + 178.192
f(3) = 273.909
Hence, in the winter of 1999, there were roughly 273.909 bald eagles in the state.
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1.
2.
Solve the system of equations using elimination.
3x + by=18
-3x+4y=218
(3x+6y=18
1-3x+4y= 2
10g = 20
10 10
-3+9/21=2
- 3+by=2
x=2
y=2
(2,2)
Verify the solution from question 1 algebraically using substitution,
The system of equations solved by elimination has its solution to be (2, 2)
How to solve the system of equations using elimination.From the question, we have the following parameters that can be used in our computation:
-3x + 4y = 2
3x + 6y = 18
When the above equations are added, the variable x is eliminated
Using the above as a guide, we have the following:
4y + 6y = 2 + 18
Evaluate
10y = 20
So, we have
y = 2
Recall that
-3x + 4y = 2
So, we have
-3x + 8 = 2
Evaluate
-3x = -6
Divide
x = 2
Hence, the solution is (2, 2)
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Question two, please help
2/10
Determine the lateral area of a triangular prism with a height of 20 centimeters (cm) and whose base is a right triangle with side lengths of 8cm,15cm, and 17cm. 416cm^(2) 675cm^(2) 731cm^(2) 800cm^(2)
A right triangle at the base of the a spherical structure with such a height of twenty centimeters (cm) has a lateral area of [tex]= 416 cm^2[/tex].
What distinguishes a triangular prism?There are 6 vertices, 9 edges, and 5 faces in a triangular prism. It contains 3 rectangle faces as addition to a pair of triangle-shaped faces. It is a polyhedron. The two triangle-shaped bases are parallel to one another.
How can we recognise a prism?A three-dimensional form with flat sides is referred to as a prism. It features two identically shaped and sized ends. From one end of the form to the other, it shares a comparable cross-section.
The triangle base's perimeter must be determined. The length of all 3 sides are added to determine the perimeter:
[tex]8 + 15 + 17 = 40[/tex]
The lateral area is,
[tex]2(8 * 20) + 2(15 * 20) + 2(17 * 20)[/tex]
[tex]= 416 cm^2[/tex]
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Which set of points includes all of the solutions for y = five halves times x plus three halves?
line going through negative 1 comma negative 1 and 1 comma 4
(x, five halves times x plus three halves) for all real numbers
(−1, −1), (0, 1. 5), (1, 4)
(x, y) for all real numbers
(−3, −6), (−2, −3. 5), (0, 1. 5), (2, 6. 5), (3, 9)
The set of points that includes all of the solutions for [tex]y = 5/2x + 3/2[/tex] is [tex](x, 5/2x + 3/2)[/tex] for all real numbers.
The set of points that includes all of the solutions for the given equation is [tex](x, 5/2x + 3/2)[/tex] for all real numbers. This is because any point on this line will satisfy the equation [tex]y = 5/2x + 3/2[/tex], which means that any solution to the equation will be included in this set of points.
Alternatively, we can find the equation of the line passing through the points (-1, -1) and (1, 4) and confirm that it is the same as the equation [tex]y = 5/2x + 3/2[/tex].
Using the two-point form of a linear equation, the slope of the line passing through the two points is:
[tex]m = (y2 - y1) / (x2 - x1) = (4 - (-1)) / (1 - (-1)) = 5/2[/tex]
Using the point-slope form of a linear equation with the slope and one of the points:
[tex]y - y1 = m(x - x1)[/tex]
[tex]y - (-1) = (5/2)(x - (-1))[/tex]
[tex]y + 1 = (5/2)(x + 1)[/tex]
[tex]y = (5/2)x + (5/2) - 1[/tex]
[tex]y = (5/2)x + (3/2)[/tex]
This is the same equation as [tex]y = 5/2x + 3/2[/tex], so we know that the set of points that includes all of the solutions is [tex](x, 5/2x + 3/2)[/tex] for all real numbers.
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Spencer is researching the cost to rent office space in the Brookton Office Center. Office space is rented based on
the square footage of an office's floor area. A linear relationship exists between the square footage of the floor and
the yearly cost to rent that square footage, as shown in the table below.
Brookton Office Center
Yearly Rental Costs
Square
Footage
500
600
800
1,200
Yearly
Rental
Cost
$9,250
$11,100
$14,800
$22,200
Spencer budgeted $20,720 for his yearly office rental cost. The office space can be customized to the size needed.
What is the maximum amount of square footage he can rent in the Brookton Office Center?
Answer:
Step-by-step explanation:
Find the height of a cone with a radius of 12 inches and a volume of 1,281.12 cubic inches.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ V=1281.12 \end{cases} \implies 1281.12=\cfrac{\pi (12)^2 h}{3} \\\\\\ (3)(1281.12)=144\pi h\implies \cfrac{(3)(1281.12)}{144\pi }=h\implies 8.50\approx h[/tex]
what is the HCF of 144 and 360
A beg of corn can feed 100 chickens for 12 days . For how many days would the same bag feed 80 chickens
Answer:
9.6 days
Step-by-step explanation:
100 chickens, 12 days
find the days for 10 chickens: 1.2 days (to get 10 you have to divide 100 by ten, so divide 12 by ten too)
times by 8 to get the days for 80 chickens: 9.6 days
Answer: Let's assume that the bag of corn contains "C" units of corn. We know that this amount of corn can feed 100 chickens for 12 days.
To determine how long the same bag of corn would feed 80 chickens, we can use the following proportion:
(Corn units)/(chickens * days) = (Corn units)/(chickens * days)
We can set up two ratios, one for the original situation and one for the new situation, and then cross-multiply to solve for the unknown value:
C/100 * 12 = C/80 * d
where "d" is the number of days that the same bag of corn would feed 80 chickens.
Simplifying the equation, we get:
C/10 = C/80 * d
Multiplying both sides by 80, we get:
8C = Cd
Dividing both sides by "C", we get:
8 = d
Therefore, the same bag of corn would feed 80 chickens for 8 days.
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I need to know the answer asap
256 is the lateral surface area.
What's the lateral surface area?
Side indicates the side of commodity. thus, lateral surface area is set up by chancing the face area of the sides of the object.
This is done by chancing the border of the base and multiplying it by the height of any three- dimensional figure.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 16 cm
The formula for lateral surface area of triangular prism is
LSA = (perimeter)(length)
On substituting the above values,
LSA = (5 + 6 + 5)(16)
= (16)(16)
= 256
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find arc length of the partial circle
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (8)}{180}\implies s=4\pi[/tex]
Find the arc length of the partial circle
Answer: 3π
Step-by-step explanation:
360 - 90 = 270°
Perimeter of full circle = πd = 4π
Arc length = [tex]\frac{270}{360}[/tex] × 4π = 3π
Urgent help is needed
The volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
What is hemisphere ?
A hemisphere is a three-dimensional geometric shape that consists of half of a sphere. It is formed by slicing a sphere into two equal parts along a plane that passes through its center. The term "hemisphere" comes from the Greek words "hemi," meaning half, and "sphaira," meaning sphere.
A hemisphere has a curved surface that is a portion of a sphere's surface, as well as a flat circular base that is formed by the plane of the cut. The diameter of the base is equal to the diameter of the original sphere, and the radius is half of the diameter.
To find the volume of the hemisphere, we first need to know its formula. A hemisphere is half of a sphere, so its volume is half of the volume of a sphere with the same radius.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume and r is the radius.
Since the hemisphere has diameter 9, its radius is half of the diameter, which is:
r = 9/2 = 4.5
Substituting the value of r in the formula for the volume of a sphere, we get:
V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 152.087
Since the hemisphere is half of a sphere with radius 4.5, its volume is half of the volume of that sphere, which is:
V_hemisphere = (1/2)V_sphere
V_hemisphere = (1/2)(4/3)π(4.5)³
V_hemisphere = 76.0435
Therefore, the volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
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Mike's Bakery recently spent a total of $392 on new equipment, and their average hourly operating costs are $9. Their average hourly receipts are $10. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?
For Mike's Bakery the total expenses will be $3528 and the total receipts will be $3920 and it will take 392 hours.
Let number of hours the bakery needs to operate in order to make back the amount it invested in equipment be = "h".
To find "h", we need to find the profit per hour,
The profit per hour is = difference between hourly receipts and hourly operating costs;
Profit per hour = Hourly receipts - Hourly operating costs
Profit per hour = $10 - $9
Profit per hour = $1
The total profit required to make back the $392 investment is = $392,
We know that,
⇒ Total profit = (Profit per hour) × (Number of hours)
⇒ $392 = $1 × h
⇒ h = $392/$1
⇒ h = 392
So, bakery needs to operate for 392 hours to make back the amount it invested in equipment.
To calculate the total expenses and receipts, we can use the following formulas:
⇒ Total expenses = (Operating costs) × (Number of hours)
⇒ Total expenses = $9 × 392
⇒ Total expenses = $3528
⇒ Total receipts = (Hourly receipts) × (Number of hours)
⇒ Total receipts = $10 × 392
⇒ Total receipts = $3920
Therefore, the total expenses is $3528 and total receipts is $3920.
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Two storage sheds are to have the same area. One is square and one is regtangular. The rectangular she is 4 meters wide and 16 meters long
As per the given question, the length of the square shed is 8 meters.
Length of the sheet = 4m
Width of the sheet = 16m
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Since a rectangle's opposite sides are both equal and parallel, a parallelogram is another name for this geometric shape.
Using the formula for the area of the rectangle -
Area = Length x Width
Now,
Let the length of the square shed be x, therefore -
x² = 4(16) = 64
x = √64
= 8
Complete Question:
Two storage sheds are to have the same area. One is square and one is rectangular. The rectangular she is 4 meters wide and 16 meters long. What is the length of the square shed?
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MULTIVARIATE STATISTICS
(a) What are the two ways in which the exploratory factor
analysis (EFA) can be useful?
(b) Differentiate between principal component method
and factor analysis
(a) The exploratory factor analysis (EFA) can be useful in two ways: Dimensional Reduction: The dimensionality of a set of data can be reduced by exploratory factor analysis. Rather than dealing with several variables, it identifies the basic factors that describe the data set. This can be achieved by extracting factor information that shows the covariance structure of the variables that underlie the observations. Investigation of latent variables: Exploratory factor analysis can be used to determine whether an underlying dimension, such as depression or anxiety, underlies a collection of observable variables, such as feelings of depression, nervousness, or irritability. Latent variables are those that cannot be observed directly. (b) Factor analysis and principal component analysis are two techniques for data reduction that are frequently confused. The principal component analysis, on the other hand, is a technique that creates uncorrelated variables to replace the original variables. It can be viewed as a special case of factor analysis in which all of the extracted factors are used. It includes the raw data's total variance, which is defined by a few components. Principal component analysis is a method of data reduction that extracts uncorrelated factors from the original variables. The correlation structure of the original variables is utilized in factor analysis to define the underlying factors.
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Find the values of the variables and the measures of the indicated angles.
Answer:
115°
Step-by-step explanation:
You want the measure of angle S opposite angle (4x+5)° in an inscribed quadrilateral in which the other two angles are (5x-2)° and (7x+2)°.
Inscribed quadrilateralThe measure of an inscribed angle is half the measure of the arc it intercepts.
Two opposite angles in an inscribed quadrilateral intercept arcs that total the full circle. Since the sum of double those angles is 360°, the sum of opposite angles of an inscribed quadrilateral is 180°—they are supplementary.
We can use this to find the value of x:
(5x -2)° +(7x +2)° = 180°
12x = 180 . . . . . . simplify
x = 15 . . . . . . . divide by 12
Now, the angle opposite S can be found to be ...
(4x +5)° = (4·15 +5)° = 65°
Angle S is the supplement of this:
S = 180° -65°
S = 115°
In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was 300 grams
and mass was decreasing by 6% per day. Determine the mass of the radioactive
sample at the beginning of the 16th day of the experiment. Round to the nearest tenth
(if necessary).
Answer:
To solve this problem, we can use the formula for exponential decay:
m = m0(1 - r)^t
where:
m0 = initial mass (300 grams)
r = decay rate (6% per day, or 0.06)
t = time in days
We want to find the mass at the beginning of the 16th day, so t = 15:
m = 300(1 - 0.06)^15
m ≈ 107.4
Therefore, the mass of the radioactive sample at the beginning of the 16th day of the experiment is approximately 107.4 grams.