From the logistic population differential equation for approximate the growth of the world population , which is given here as [tex]P = L/1+ e^{-k(x-x_{0} )[/tex]
The general form of the logistic population equation is given as [tex]dP/dt = kP(1- P/L)[/tex]. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve. 4 x + 6 < − 6
The solution to the inequality 4x + 6 ∠ -6 is x ∠ -3
What is an inequality?inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.
4x + 6 ∠ -6
taking 6 to the right hand side of the inequality
4x < -6 -6
4x < -12
divide both sides by 4
x < -12/4
x < -3
In conclusion, x < -3 is the solution to the Algebraic expression above.
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Rewrite the following equation in slope-intercept form.
y − 8 = 2(x + 6)
Enrique predicts that he can make additional money from sales of accessories and service for computer products sold by his store. The table at the right shows predicted percent returns for such sales. For example, if the store makes x dollars selling computer products, Enrique predicts the store with make 0.05x dollars from selling accessories. Part A In January and February of this year, the store made $2,500 from sales of accesories and services. Let x represent the amount the store with make from sales of computer products from March through December. Write an equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year. If Enrique predicts sales from accessories and services for the entire year will be $5,000, about how much money must be made from computer product sales from March through December? Explain.
The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
Given that:
Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.
The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.
The following steps can be used in order to determine the equation that represents the predicted amount y:
Step 1 - According to the given data, the store makes x dollars selling computer products.
Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.
Step 3 - So, the linear equation that represents the given situation is:
y = 0.05x + 2500
Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
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is y=4x-8, continuous or discrete?
The equation y = 4x - 8 is discrete
What are discrete data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.
While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
The difference between discrete and continuous dataThe main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.
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Choose ALL answers that describe the quadrilateral UVWX if UV = 31,
VW = 67, WX = 45, XU = 56, m/U = 146°, m/V = 54°, m/W = 95°,
and m/X = 65°.
Parallelogram
□ Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.
What is meant by the term Quadrilateral? A polygon comprising four sides, 4 angles, and 4 vertices is called a quadrilateral.There are some aspects that all quadrilaterals share. These attributes are:There have been four of them.There have been four of them.360° is the summation of all interior angles.There have been two diagonals in them.For the given values in the question;
In the quadrilateral UVWX
Sides are;UV = 31,VW = 67, WX = 45, XU = 56, Angles are-m/U = 146°, m/V = 54°, m/W = 95°,and m/X = 65°.As, none of the sides are equal to other and none of the angles are equal to the other.
Thus, the this information shows the values are given for quadrilateral.
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The owner of a small store buys coats for $40.00 each. Answer parts a and b. a. She sells the coats for $72.00 each. What percent of the purchase price is the sale price? The sale price is 180% of the purchase price. b. The owner increases the sale price by the same percent that you found in part a when she buys jackets for $25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260? Explain your answer. The owner must buy how many jackets?
The percent of the purchase price that the sales price is 80%.
The number of jackets that should sold so that total sales can be at least $260 is 6.
What is the percent of sales price and the number of jackets to be sold?The equation that can be used to determine the percent of the purchase price the sales price is:
Percent = (sale price / purchase price) - 1
($72 / $40) - 1 = 0.80 = 80%
The sales price of the $25 jackets if prices are increased by 80%
Sales price = (1 + percent) x purchase price
(1 + 0.8) x $25
1.8 x $25 = $45
The number of jackets to sell so that total jacket sales can be at least $260 is:
(sales price per jacket x number of jackets) ≥ $260
($45 x j) ≥ $260
$45j ≥ $260
j ≥ $260 / $45
j ≥ 5.8 ≈ 6
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 11
Green 8
Yellow 4
Purple 19
The probability that the next spin will land on red or green or purple is 75%
Given , A spinner is divided into five colored sections that are not of equal size
Color Frequency
Red 18
Blue 11
Green 8
Yellow 4
Purple 19
Total spin recorded = 18+11+8+4+19
=60
Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple
P(A) = 18/60 = 0.3
P(B) = 8/60 = 0.134
P(C) = 19/60 = 0.32
Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)
P(A∪BC) = 0.3 + 0.134 + 0.32 =0.754
= 0.754 × 100 = 75%
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 700 liters in the pond to start.
Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.
An equation relating W to T is given by W = 700 + 25T. Also, a graph of this linear equation is shown in the image attached below.
How to write an equation relating W to T?In order to write an equation relating W to T, we would define the variables that represents the amount of water in the pond (in liters) and the number of minutes this water has been added as follows:
Let the variable W represent the amount of water in the pond (in liters).Let the variable T represent the number of minutes that water has been added.The initial volume of water is given by:
700
The volume of water added to this pool would be given by:
25T
Therefore, the total volume of water added to this pool is given by:
W = 700 + 25T
Next, we would determine the points for the graph of this equation:
At T = 0, we have:
W = 700 + 25(0)
W = 700 ⇒ (0, 700)
At T = 1, we have:
W = 700 + 25(1)
W = 725 ⇒ (1, 725)
At T = 2, we have:
W = 700 + 25(2)
W = 750 ⇒ (2, 750)
At T = 3, we have:
W = 700 + 25(3)
W = 775 ⇒ (3, 775)
At T = 4, we have:
W = 700 + 25(4)
W = 800 ⇒ (4, 800)
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Determine the coordinates of the preimage given the image below and the composition of a rotation 180 about the origin and a translation 3
units up.
The coordinates of the preimage given in the image below and the composition of a rotation 180 about the origin and a translation 3 units up are: (2, -3), (3, 1), and (-5, 0).
What is a rotation?In Geometry, the rotation of a geometric figure 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
From the graph of the image of triangle A'B'C', we have the following coordinates and they would be reversed to obtain the coordinate of triangle ABC before a translation:
(-x, -y) → (x, y)
Points at A' = (-2, 5) → Points at A = (2, -5)
Points at B' = (-3, 1) → Points at B = (3, -1)
Points at C' = (5, 2) → Points at C = (-5, -2)
Next, we would apply a translation of 3 units up:
Points at A = (2, -5) → (2, -5 + 2) = (2, -3)
Points at B = (3, -1) → (3, -1 + 2) = (3, 1)
Points at C = (-5, -2) → (-5, -2 + 2) = (-5, 0)
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solve for b: 84,250=b(1.008)120
Answer: 696.511
Step-by-step explanation:
84,250 = b(1.008)120
84250 = 120.96b
b = 696.511
f(x)=5+7x-9x^2+4^3 state the end behavior of f(x). Explain (x). Explain or show your reasoning.
The end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,
as x → -∞, f(x) → -∞
as x → ∞, f(x) → -∞
In this question, we have been given a polynomial function
f(x) = 5 + 7x - 9x^2 + 4^3
We need to state the end behavior of f(x).
The graph of f(x) is as shown below.
We can observe that as x tends to -∞, f(x) → -∞
Also, as x → ∞, f(x) → -∞
We know that the end behavior of polynomial function is determined by the degree of the polynomial and the leading coefficient.
For given polynomial function, the degree of this polynomial is 2.
The leading coefficient is -9
We know that for polynomial function of even degree, the ends of the function graph point in the same direction.
Therefore, the end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,
as x → -∞, f(x) → -∞
as x → ∞, f(x) → -∞
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the square root of $x$ is greater than 3 and less than 4. how many integer values of $x$ satisfy this condition?
6 integers that satisfy the given condition are 10,11,12,13,14,15.
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
we have the number X
Of which the square root is greater than 3 and less than 4
so,
[tex]3 < \sqrt{X} < 4[/tex]
on squaring both sides
[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]
[tex]9 < X < 16[/tex]
so the integer that satisfies the condition is 10,11,12,13,14,15.
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Answer:
6
Step-by-step explanation:
Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.
Antoinette spends 3 hours reading each day.
What is the total amount of time (in hours) that
Antoinette spent reading after 6 days?
Answer:
The answer is 18 hours
Step-by-step explanation:
3 hours x 6 days
3x6 = 18
Write the equation of
the circle with diameter
endpoints of (17, -3) and
(-13,3). PLEASE HELP
The equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936
What is meant by a circle?A circle is a form made up of all points on a plane that are at the same distance from the center. In other words, it is the curve that a moving point in a plane creates to keep its distance from a specific point constant. The radius is the separation between any point on a circle and its center. The radius must typically be a positive integer. Degenerate cases include circles with displaystyle r=0 and r=0. Unless otherwise stated, this article discusses circles in Euclidean geometry, specifically the Euclidean plane.
A circle is a straight forward closed curve that splits the plane into its inner and outside. In regular use, the
The equation of a circle is given as,
(x-a)²+(y-b)=r²
Here, the center of the circle is (a ,b) and r is the radius of the circle
The circle's center can be located first. The middle point of the line segment serves as the center of the circle since the two locations from the issue are the endpoints of a diameter.
Given two end points, how do you calculate a line's midpoint? You may use the formula below.
M=((x1+x2)/2, (y1+y2)/2)
Here, M denotes the mid-point
The points are taken as (x1, y1), (x2, y2)
M=((17-13)/2, (-3+3)/2)
M=(2,0)
Now, the center of the circle is (2,0)
We have to calculate the distance
d= √(x₁-x₂)²+(y₁-y₂)²
d= √(17+13)²+(-3-3)²
d=√900+36
d=√936
Therefore, the radius of the circle is √936
Now, the equation of the circle is,
(x-2)²+(y-0)²= (√936)²
(x-2)²+y²=936
Therefore, the equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936
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What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ?
Enter your answer by filling in the boxes.
(
,
)
The coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) is; (x, y) = (-1, 2)
What are the coordinates of the triangle centroid?Centroid of a Triangle states that the center of the triangle can be calculated as the point of intersection of all the three medians of that same triangle, and that this median is a line drawn right from the midpoint of one side to the opposite vertex.
We are given the coordinate of the vertices of the triangle as;
X(−4, 0) , Y(−1, 4) , and Z(2, 2)
Now, the formula to find the coordinates of the centroid of the triangle is; (x, y) = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3
Thus, the coordinates of the Centroid is;
(x, y) = (-4 + (-1) + (2))/3, (0 + 4 + 2)/3
(x, y) = (-1, 2)
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Casey's Mail Manufacturing is a company that produces chain mail. Their most popular product is saw-cut metal links that hobbyists can use to make their own creations. The company recently spent $100 on advertising, which they hope to make back quickly. The wire used to produce one gram of links costs $2, but the finished links sell for $3 per gram. Eventually, the company will make back its investment and break even. How many grams of links must be sold?
In order to a breakpoint or the total cost = total investment company must need to sell 100 grams of links.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's suppose the number of links that are needed to solve for a breakpoint is x.
Cost of x number of links with the rate of $2/gram = 2x
Total cost = total selling
100 + 2x = 3x
3x - 2x = 100
x = $100
Hence "In order to break even point or the total cost = total investment company must need to sell 100 grams of links".
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What is the sum of all the even numbers between 105 and 351?
What is the difference between the sum of all the even numbers between 305 and
609 and the sum of all the odd numbers between 304 and 608?
The sum of even numbers between 105 and 351 is 28,044 .
What is arithmetic progression ?An additive or arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.
Calculationeven numbers between 105 and 351
the series will start like
106 , 108 , 110 , .................................. , 346 , 348 , 350
this is a arithmetic progression
a = 106 d = 2 l = 350
we need to find n
350 = 106 + ( n - 1 ) 2
350 - 106 = (n -1 ) 2
244/2 = n -1
n = 123
now sum = 123/2 ( 106 + 350)
= 28,044
so the sum of even numbers between 105 and 351 is 28,044 .
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an environmental agency is analyzing soil samples from 50 farms for lead contamination. eight of the farms have dangerously high levels of lead. ten farms are randomly selected from the sample. using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?
Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.
Permutation and Combination
Combination is a mathematical way to arranging the set of values randomly.
ⁿCᵣ = n! / r! (n-r)!
we have given that ,
total number of farms for lead contamination = 50
Number of farms have dangerously high level of lead = 8
so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42
We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .
Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28
Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈
= 42! / 8! 34! = 42×41×---×35/8×7×----×1
= 118013185
The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .
= 118030185× 28 = 3,304,845,180
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1. 3x^2-7=31
2. 2x^2+18=0
3. 4x^2-26=-50
4. 2x^2+36=x^2
The quadratic equations are solved and answered below -
What is a equation?An equation is a mathematical statement showing the equivalence of two mathematical expressions. Example -
3x + 5 = 8
Given is -
3x² - 7 = 31
2x² + 18 = 0
4x² - 26 = - 50
2x² + 36 = x²
We have -
3x² - 7 = 31
3x² = 38
x² = 38/3
x² = 12.67
x = ±3.56
2x² + 18 = 0
2x² = - 18
x² = -9
x = ±3i
4x² - 26 = - 50
4x² = - 24
x² = -6
x = ±√6i
2x² + 36 = x²
x² = - 36
x = ±√6 i
Therefore, the quadratic equations are solved above.
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The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. x= 0 1 2 3 4 5, P(x)= 0.1666 0.3275 0.2875 0.1489 0.0382 0.0313. The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? Compute the theoretical mean of the random variable X for the given probability distribution. (Round to three decimal places as needed.)
For a single game, the mean and the standard deviation of the number of hits is given as follows:
Mean: 1.659 hits.Standard deviation: 1.209 hits.For 25 games, the mean and the standard deviation are:
Mean: 1.659 hits.Standard deviation: 0.242 hits.For 50 games, the mean and the standard deviation are:
Mean: 1.659 hits.Standard deviation: 0.171 hits.This shows that as the number of trials increase, the standard error reduces.
How to obtain the mean and the standard deviation of a discrete distribution?The mean is given by the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 0 x 0.1666 + 1 x 0.3275 + 2 x 0.2875 + 3 x 0.1489 + 4 x 0.0382 + 5 x 0.0313 = 1.659 hits.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values, hence:
S(X) = sqrt((0-1.659)² x 0.1666 + (1-1.659)² x 0.3275 + (2-1.659)² x 0.2875 + (3-1.659)² x 0.1489 + (4-1.659)² x 0.0382 + (5-1.659)² x 0.0313) = 1.209.
Central Limit TheoremFor the repetition of n experiments, we have that the mean remains constant, while the standard deviation is given as follows:
s = S(X)/sqrt(n).
Meaning that it is divided by the square root of the sample size.
Hence, for 25 games, the standard deviation is:
S(X) = 1.209/sqrt(25) = 0.242.
For 50 games, the standard deviation is:
S(X) = 1.209/sqrt(50) = 0.171.
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four people (john, paul, george, and ringo) are seated in a row on a bench. the number of ways to order the four people so that john is next to paul is 12. how many ways are there to order the four people on the bench so that john is not next to paul?
The Number of ways that four people can be seated on the bench so that john is not next to paul is 12
Permutations :
In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.
The arrangement of n items in r ways is given by
ⁿPr = n! /(n-r)!Here we have
4 people (John, Paul, George, and Ringo) are seated in a row on a bench
Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24
The number of ways of seating the four people so that john is next to paul is 12
Then the number of ways the four people on the bench so that john is not next to paul can find as given below
= Total No of ways, 4 can be seated - No of ways that john next to paul
= 24 - 12 = 12
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A single bathc of your mother resipe for slalsa call for 3 tomatos. 1/4 cup cilantro,1/2 onion, and spices. you are having a party and need 5 batches of salsa how many cups of onions do you need?
To produce five constructive batches of salsa, 2.5 cups of onion will be needed.
What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.
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the coordinates of point are (-3,5). what are the coordinates of point B, which is a reflection of point A across the x-axis?
Answer:
Step-by-step explanation:
3 as the x axis and -5 for the y axis
A statement that two numbers or expressions are equal is a(n)
A statement that two numbers or expressions are equal is an equation.
What is an equation?An equation is a mathematical expression that states that two expressions are equal. An equation's solution is the value that, when substituted for the variable, makes the equation true. To accomplish our goal, we employ two equality principles: the addition principle and the multiplication principle.
An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
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a marine biologist wants to estimate the mean size of the barnacle semibalanus balnoides on a stretch of rocky shoreline. to do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. this is an example of
Option B is the correct choice
A marine biologist measured the size of each barnacle in twenty 10 by 10 square inch areas that were chosen at random. Cluster sampling is illustrated by this.
For a study that is a population into clusters, such as districts or schools, researchers will divide the population into multiple groups (clusters) and will then randomly select some of these clusters as your sample. Ideally, each cluster should be a miniature reflection of the population as a whole.
In order to determine the average size of the barnacles Semibalanus balconies along a section of rocky shoreline, a marine biologist is conducting this study. To do this, he measured the size of every barnacle in each of the twenty 10 by 10 square inch plots that were randomly chosen. Cluster sampling is illustrated by this. (Option B)
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COMPLETE QUESTION:
A marine biologist wants to estimate the mean size of the barnacle Semibalanus balconies on a stretch of rocky shoreline. To do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. This is an example of
a. convenience sampling.
b. cluster sampling.
c. stratified random sampling.
d. simple random sampling.
e. voluntary sampling.
Write an equation of the line that passes through (1,6) and is parallel to the line shown.
Answer:
[tex]y=2x+4[/tex]
Step-by-step explanation:
The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].
Parallel lines have the same slope, so the equation is:
[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]
Rebekah deposited $1500 in a savings account that pays simple annual
interest. After 21 months, she earns $131.25. What is the interest rate
for her account?
The rate of interest for Rebekah's account is 5.25%
Given,
The principal amount deposited by Rebekah, P = $1500
The time period of the deposit, T = 21 months = 5/3 years
The simple interest she got after 21 months, SI = $131.25
We have to find the rate of interest, R;
Simple Interest;
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Here,
Simple interest, SI = PRT/100
131.25 = (1500 × R × 5/3) / 100
131.25 = 15R × 5/3
131.25 = 25R
R = 131.25/25
R = 5.25%
That is,
The rate of interest for Rebekah's account is 5.25%
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611.2 times 0.0061 with steps please
well, there's no great mystery when it comes to getting a product from decimals. Now, we have 611.2 and 0.0061, let's for a second take off the decimal point and simply multipy 6112 times 00061
6112 * 00061 = 372832
ok....... hmmm now let's see 611.2 had 1 decimal, whilst 0.0061 had hmm 4 decimals, let's add them up, that's 1 + 4 = 5 decimals total from both amounts, that simply means that our 372832 needs to have 5 decimals as well, so that makes it 3.72832.
I need the abswer to 20005+56258
76263
Step-by-step explanation:
[tex] \: \: \: 20005[/tex]
[tex] + 56258[/tex]
___________
[tex] = 76263[/tex]
You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how
much will be left after 45 minutes?
grams
Answer:
1,070 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: 8,560 ÷ 2 = 4,280 g
2nd half-life: 4,280 ÷ 2 = 2,140 g
3rd half-life: 2,140 ÷ 2 = 1,070 g
