Answer:
11.4
Step-by-step explanation:
19.948-8.57=11.378
approximately 11.4
The correct number of significant figures is found as 1.1378 x 10⁻¹ .
Define the term significant figures?To demonstrate the accuracy of measurements and calculations in the fields of math, chemistry, and other sciences, significant figures are essential.
The following five rules can be used to assess whether a number is significant.
All non-zero digits, from 1 to 9, have meaning.Between nonzero numbers, all zeros have meaning.Zeros that come before or on the left of a non-zero digit have no meaning. These zeros are only stand-ins.When there is a decimal point, zeros following a nonzero digit are important.When there is no decimal point, zeros that follow a nonzero digit are not meaningful.The equation is given as:
= 19.948 - 8.57
On subtracting.
= 11.378
On converting in the significant figures:
= 1.1378 x 10⁻¹
Thus, the correct number of significant figures is found as 1.1378 x 10⁻¹ .
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On what interval is the parametric curve defined by x(t) = e^{-t} and y(t) = cos(t) for 0 ≤ t≤ π concave down?
A. (0, 3π/4)
B. (3π/4, π)
C. (0, π)
D. (0, π/2)
The parametric curve defined by x(t) = e^{-t} and y(t) = cos(t) for 0 ≤ t≤ π is concave down in the interval (c) (0, π) .
The Concavity of a parametric curve is determined by the second derivative of the curve.
To find the second derivative of a parametric curve, we need to differentiate each component of the curve with respect to the parameter t, then differentiate those expressions with respect to t again.
For x(t) = e^{-t} and y(t) = cos(t),
the first derivative w.r.t "t" is x'(t) = -e^{-t} and y'(t) = -Sin(t) ;
the second derivative with respect to t of x''(t) = e^{-t} and y''(t) = -Cos(t),
Since , y''(t) = -Cos(t) is negative over the interval (0, π), we can conclude that the curve is concave down over that interval.
Therefore, the curve is concave down over that interval (0, π).
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Malian bought a laptop with a 10% discount. She also bought a mouse for 13.99 and spent 621.49 before tax. Write an equation to find the original cost of the laptop.
Answer:
(621.49 x 0.1) + 13.99 = x
Step-by-step explanation:
I hope this helps
- 2/3 y - 3/5 X + 2/9 - 4/5 y + 1/3 X
-12X -- 66y + 10
_____________
45
comparing data collected on individuals' sales and individuals' attendance records would be an example of what type of data analysis? group of answer choices quantitative qualitative standard deviation concept
The answer is Quantitative because quantitative data mainly deals with the statistic and figures.
As given, Comparing data collected on individuals’ sales and individuals’ attendance records would be an example of what type of data analysis?
Quantitative data analysis involves the use of numerical data to discover patterns and relationships. In the example of comparing individuals' sales and attendance records, the data collected would be numerical and would be analyzed to determine the relationship between sales and attendance. This type of analysis often involves statistical techniques such as regression analysis, correlation analysis, and hypothesis testing. The goal is to gain insights and make informed decisions based on the numerical data, rather than just describing or summarizing it.
Answer is Quantitative.
Reason- Quantitative data mainly deals with the statistic and figures.
Thus, the answer is Quantitative because quantitative data mainly deals with the statistic and figures.
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The answer is Quantitative because quantitative data mainly deals with statistic and figures.
As given, Comparing data collected on individuals’ sales and individuals’ attendance records would be an example of what type of data analysis?
Quantitative data analysis involves the use of numerical data to discover patterns and relationships. In the example of comparing individuals' sales and attendance records, the data collected would be numerical and would be analyzed to determine the relationship between sales and attendance. This type of analysis often involves statistical techniques such as regression analysis, correlation analysis, and hypothesis testing. The goal is to gain insights and make informed decisions based on the numerical data, rather than just describing or summarizing it.
Answer is Quantitative.
Reason- Quantitative data mainly deals with statistic and figures.
Thus, the answer is Quantitative because quantitative data mainly deals with statistic and figures.
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Can someone please help me with this?
A: 28 degrees
B: 46 degrees
C: 17 degrees
D: 118 degrees
Answer:
A 28°
Step-by-step explanation:
we see that the sum of angle 1 and 62° must be 90° (right angle).
90 = 62 + angle 1
28° = angle 1
Giselle enjoys playing chess and Scrabble. She wants to play a total of at least 10 games (condition a) but she has only 6 hours to do it (condition b)
Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To determine the maximum number of games Giselle can play, we need to balance the time available with the number of games she wants to play. Let's assume that each game takes x hours to complete.
Condition a: 10 games = x * 10
Condition b: 6 hours = x * 10
From these two equations, we can solve for x, which represents the time it takes for Giselle to play one game. To do this, we'll divide both sides of the first equation by 10:
10 games / 10 = x * 10 / 10
x = 1 hour
So, it takes Giselle 1 hour to play one game. Knowing this, we can determine how many games she can play in the 6 hours she has available:
6 hours / 1 hour per game = 6 games
Therefore, Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
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Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To determine the maximum number of games Giselle can play, we need to balance the time available with the number of games she wants to play. Let's assume that each game takes x hours to complete.
Condition a: 10 games = x * 10
Condition b: 6 hours = x * 10
From these two equations, we can solve for x, which represents the time it takes for Giselle to play one game. To do this, we'll divide both sides of the first equation by 10:
10 games / 10 = x * 10 / 10
x = 1 hour
So, it takes Giselle 1 hour to play one game. Knowing this, we can determine how many games she can play in the 6 hours she has available:
6 hours / 1 hour per game = 6 games
Therefore, Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
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Jane needs a short-term loan to buy a new washing machine. She needs to borrow $1500 at 20% compounded annually and plans to have it paid off in 1 year. Jane writes the formula 1500(1. 2)t and finds out that this loan will cost her $1800. Which equation shows how Jane can rewrite the formula to find the annual percentage rate that would cost her the same amount if it compounded semi-annually?
A≈1500(1. 095)2t
A≈1500(1. 2)^1/2t
A≈1500(1. 095)^1/2t
A≈1500(1. 2)2t
The that shows how Jane can rewrite the formula to find the equivalent semi-annual interest rate is Option (a) A ≈ [tex]1500(1.095)^{2t}[/tex].
The formula [tex]1500(1.2)^t[/tex] shows the amount Jane will have to pay after t years if the loan is compounded annually at an interest rate of 20%. To find the equivalent semi-annual interest rate, we need to rewrite the formula so that it represents the amount she would have to pay if the interest was compounded semi-annually.
First, let's find the equivalent semi-annual interest rate. If the annual interest rate is 20%, the semi-annual interest rate would be:
[tex]r = 20\% / 2 = 10 \%[/tex]
Next, let's raise (1 + r) to the power of 2 to find the equivalent annual interest rate when compounded semi-annually:
[tex](1 + r)^2 = (1 + 10\%)^2 =( 1.1)^2 = 1.21[/tex]
So, the equivalent annual interest rate when compounded semi-annually is 21%.
Finally, let's substitute the equivalent semi-annual interest rate into the formula to find the amount Jane would have to pay if the interest was compounded semi-annually:
[tex]A = 1500(1 + r)^{2t} = 1500(1.095)^{2t}[/tex]
So, the equation that shows how Jane can rewrite the formula to find the equivalent semi-annual interest rate is:
A ≈ [tex]1500(1.095)^{2t}[/tex]
This equation represents the amount Jane would have to pay after t years if the loan is compounded semi-annually at an interest rate of 21%.
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How to Use the X-Intercept Calculator?
Press second, then CALC (above the TRACE key). Select option 2: 0You'll be required to enter an x-intercept guess, a left bound, and a right bound into the calculator.
What is the X-Intercept Calculator Used For? Press second, then CALC (above the TRACE key). Select option 2: 0You'll be required to enter an x-intercept guess, a left bound, and a right bound into the calculator.By dragging the cursor to the correct x-value with your left and right arrows, then pressing ENTER, you can enter them.When y = 0, we solve the equation for x to determine the x-intercept.The line crosses the x-axis at y=0, explaining this.If an equation isn't in the y = mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.With x = 0, solve for y to determine the y-intercept.To learn more about X-Intercept Calculator refer
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Determine the sum of the solutions to: 5x^2-16x+3=0
A. 3/5
B. 16
C. 8
D. 16/5
The sum of the two solutions is equal to 17/5.
How to find the solutions of the quadratic equation?Here we want to solve the quadratic equation:
5x^2 - 16x + 3 = 0
Using the quadratric formula, we will get the solutions:
[tex]x = \frac{16 \pm \sqrt{(-16)^2 - 4*3*5} }{2*5} \\\\x = \frac{16 \pm14 }{10}[/tex]
Then the two solutions of the quadratic equation are:
x = (16 + 14)/10 = 30/10 = 3
x = (16 - 14)/10 = 2/10 = 2/5
The sum is: 3 + 2/5 = 3 + 2/5 = 15/5 + 2/5 = 17/5
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Blake puts eight marbles in the bag cold puts nine marbles in the bag then Blake takes out seven marbles from the bag how many marbles are in the bag now
Answer: 10 marbles are still in the bag.
Step-by-step explanation:
(8+9)-7
17-7
10
Find the slope of this graph. Please help!! Will give brainliest!! :)
The slope of this graph is equal to 8/50 or 0.16.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (0, 150).Points on y-axis = (5.00, 29.00).Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (29.00 - 5.00)/(150 - 0)
Slope, m = 24/150
Slope, m = 8/50 or 0.16.
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in this situation is it possible that lim x → 1 f(x) exists? explain.
Yes, in this situation is it possible that lim x → 1 f(x) exists.
A horizontal/vertical oblique line that approaches 0 but never reaches it is known as an asymptote. Its distance from the graph of the function keeps becoming smaller.
What's the vertical asymptote rule?
Vertical asymptotes happen when a factor from a rational expression's denominator does not cancel out with a factor from the numerator.
The existence of a vertical asymptote occurs when a factor does not cancel, as opposed to creating a hole at that number. Using a dotted vertical line, the vertical asymptote is shown.
if f(x) has a vertical asymptote at x = 1,
it can be defined such that lim x→1− f(x) = 6,
lim x→1+ f(x) = 3,
and lim x→1 f(x) exists.
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how many terms does the sequence, 2, 5, 8, …, 332 have?
As per the details given, the sequence 2, 5, 8, …, 332 has 111 terms.
The formula for the nth term of an arithmetic series can be used to find the number of terms in the given sequence:
nth term = a + (n - 1) * d
Here,
nth term is the value of the term at position n
a is the first term of the sequence
n is the position of the term
d is the common difference between consecutive terms
In this case, the first term (a) is 2, and the common difference (d) is 3, as each term increases by 3.
We need to find the value of n when the nth term is 332. Plugging the values into the formula:
332 = 2 + (n - 1) * 3
Simplifying the equation:
330 = (n - 1) * 3
Dividing both sides by 3:
110 = n - 1
n = 111
Therefore, the sequence has 111 terms.
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What is 5/7 times 10/11 as a fraction in simplest form
Answer: 50/77
Step-by-step explanation:
write a (constant) function nats :: [integer] which produces an infinite list of all the natural numbers starting at 0. it is ok for this function if you do not use recursion.
A constant function is a function that returns the same output every time it is called, regardless of the input. In this case, we want to create a constant function that returns an infinite list of all the natural numbers starting at 0.
Here's an example of how you could implement the nats function in Haskell:
makefile
Copy code
nats :: [Integer]
nats = [0..]
The [0..] syntax creates an infinite list that starts with 0 and continues indefinitely. Every time the nats function is called, it returns this same infinite list, so it's considered a constant function.
Another way to write the nats function is to use the iterate function, which generates a list by repeatedly applying a function to an initial value.
makefile
Copy code
nats :: [Integer]
nats = iterate (+1) 0
In this case, iterate (+1) 0 generates a list by repeatedly adding 1 to 0. The first element of the list is 0, the second element is 0 + 1 = 1, the third element is 1 + 1 = 2, and so on. This generates an infinite list of all the natural numbers starting at 0, which is exactly what we want.
In either case, you can take any number of elements from the nats list by using the take function. For example, take 5 nats would return the first 5 elements of the nats list, which would be [0, 1, 2, 3, 4].
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What is a representative sample? What is its value? Choose the correct answer below A. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows descriptive B. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these C. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows inferential statistics D. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these statistics to be applied.
A representative sample is randomly selected from a population, and its unbiased nature allows for inferential statistics to be applied, making it a valuable tool for research.
Option C. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows inferential statistics to be applied.A representative sample is a sample that is randomly selected from a population, and that is representative of that population in terms of characteristics such as demographics, attitudes, and behaviors. This type of sample is valuable because it is unbiased, meaning that it does not favor any particular group within the population, and this allows for inferential statistics to be used to draw conclusions about the population as a whole.
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Scientists are preparing two satellites to be launched. The satellite, Space Explorer B, flies 43000 miles in 5 hours. The graph below represents the number of miles, y, that the satellite, Space Explorer A, flies in x hours.
Space Explorer B travels 8600 miles per hour 4800 miles per hour Space Explorer A.
How to compare Explorer A and Explorer B?
The slope, also known as gradient, in mathematics is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Space Explorer B, flies 43000 miles in 5 hours. The speed will be:
speed = 43000/5 = 8600 miles per hour
For Space Explorer A, we can find the speed from the slope of the graph. That is:
Speed = (38000-19000)/(10-5) = 19000/5 = 3800 miles per hour
Speed difference = 8600 - 3800 = 4800 miles per hour
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The vertices of a rectangle are at (−1, −5), (3, −5), (3, −7), and (−1, −7). What is the length of the shorter side of the rectangle? Enter your answer in the box
Answer:
4 units
Step-by-step explanation:
The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.
Answer: Your answer is 2
Step-by-step explanation: I did the k12 quiz here's proof
The kid went to the park to play 1/3 played on the eeaw 2/6 played on the lide and the remaining of the kid played occer what fraction of the kid played occer?
The fraction of the kid played soccer is 0
What is a fraction in math?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categories its types based on these two terms.Given data :
2/6 - 1/3 =
2 / 6 - 1*2 / 3*2
= 2/6 - 2/6 = 0/6 = 0
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A bicycle wheel has a diameter of 26 inches. What is the circumference?
Note: Use 3. 14 for pi (Tt) rather than the pi (Tt) key on a calculator,
*
The bicycle that has a diameter of 26 inches has a circumference of 81.64 inches
What is perimeter?The perimeter is the total length of the edge of a geometric figure.
To solve this geometry exercise the equation and procedure we will use is:
P = 2*pi*r
Where:
pi = constantr = radiusP = Length of a circleInformation about the problem:
pi = 3.14d = 26 inchesP = ?Applying the perimeter equation of a circumference, we have:
P = 2*pi*r
P = 2*3.14*(26 inches/2)
P = 3.14*26 inches
P = 81.64 inches
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Elliot make and ell key chain. Hi profit depend on what price he charge for a key chain. He write the expreion (x−10)(60−3x) to repreent hi profit baed on the price per key chain, x
The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.
The expression can be interpreted as follows:
x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.
60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.
So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.
In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.
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The expression (x - 10)(60 - 3x) represents Elliot's profit based on the price per key chain, where x is the price in dollars that Elliot charges for each key chain.
The expression can be interpreted as follows:
x - 10 represents the revenue Elliot makes from each key chain, as it's equal to the price per key chain minus the cost of materials for each key chain.
60 - 3x represents the number of key chains Elliot can make and sell, as it's equal to the maximum amount of money Elliot has minus the total cost of materials for all key chains.
So, (x - 10)(60 - 3x) represents Elliot's total profit, which is equal to the revenue from each key chain multiplied by the number of key chains Elliot can make and sell.
In other words, Elliot's profit is proportional to both the price he charges per key chain and the number of key chains he can sell at that price. The expression captures this relationship and can be used to determine Elliot's profit for different prices.
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what are the roots of 2x^4-26x^2-28
Answer: To find the roots of a polynomial equation, we can use various methods, such as factoring, synthetic division, or the quadratic formula. One common method to find the roots of a quartic polynomial (degree 4) is to use the factor theorem, which states that if a polynomial equation has a root "r", then "r" is a factor of the polynomial.
In this case, we can factor 2x^4-26x^2-28 as:
2x^4 - 26x^2 - 28 = 2(x^2 - 7)(x^2 + 4)
So, the roots of 2x^4-26x^2-28 are x = ±√7 and x = ±i√2.
These are the solutions to the equation 2x^4-26x^2-28 = 0.
Step-by-step explanation:
if x and y are independent random variables does it mean x^2 and y are also independent random variables?
No, the independence of x and y does not necessarily mean the independence of [tex]x^2[/tex] and y.
Independence means that the values of one random variable do not affect the values of the other random variable. In other words, knowing the value of one random variable does not give us any information about the value of the other random variable.
However, squaring a random variable changes its distribution and can affect its independence from another random variable.
For example, if x is a normally distributed random variable with a mean of 0 and a standard deviation of 1, then [tex]x^2[/tex] will follow a chi-squared distribution with 1 degree of freedom. The distribution of [tex]x^2[/tex] and y may not be independent, even though x and y are independent.
Hence, just because x and y are independent random variables does not mean that [tex]x^2[/tex] and y are also independent random variables. Independence must be established based on the joint distribution of the random variables.
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Determine if line AB is tangent to the circle.
22)
10.9
9.1
B
6
A
Yes we can say that the line AB of the given diagram is a tangent to the given circle.
How to find a tangent line to a circle?For the line to be tangent to the circle it means that the line must be perpendicular to the diameter line that divides the circle into 2. Thus, we will make use of Pythagoras theorem;
AB = √(10.9² - 9.1²)
AB = √(118.81 - 82.81)
AB = √36
AB = 6
This length of AB corresponds with the given length and as such AB is perpendicular to the line of length 9.1 and is therefore a tangent to the circle.
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suppose p and q are polynomial functions. if and q(0), find p(0).
The value of p(0) is the same as the value of q(0) since p and q are both polynomials.
Polynomials are mathematical expressions that are composed of variables and constants and involve only non-negative integer powers of the variables. In this case, p and q are both polynomials. This means that they have the same degree, or highest power of the variable, and the same coefficients. As a result, p(0) will have the same value as q(0). To find the value of p(0), substitute 0 into the function for p. This will give the value of p(0). For example, if p(x) = 3x2 + 2x + 1, then p(0) = 3(0)2 + 2(0) + 1 = 1. This means that p(0) = 1.
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Hi guys, really struggling with this question! any help would be greatly appreciated :)
Using the concept of PEDMAS, the simplified expression is equal to 12
What is Simplification of ExpressionSimplification of an algebraic expression involves transforming a given expression into a simpler equivalent expression while maintaining the same value. This can be done by combining like terms, applying the distributive property, using the properties of arithmetic operations, and combining constants. The goal is to write the expression in the most compact and understandable form.
In the question given, the expression is;
27^(1/3) * 16^(3/4) ÷ 8^(1/4) ÷ 2^(1/4)
simplifying the expression;
3 * 8 ÷ 4√8 ÷ 4√2
Applying the principle of PEDMAS here;
3 * 8 ÷ 4√8 ÷ 4√2 = 12
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The simplification of the given expression would be=225½
What is simplification of equations?The simplification of equations involves the replacement of ambiguous values with a simple value through the used of the various arithmetic operations.
(27⅓ × 16¾) ÷ (8¼ ÷ 16¾)
The about equations in the bracket are solved differently by changing the mixed fraction to a simple fraction:
= (27⅓ × 16¾)
= 82/3 × 67/4
The second bracket;
= (8¼ ÷ 16¾)
= 33/4 ÷ 67/4
= 4/33 × 67/4
Solving the both bracket through the following:
82/3 × 67/4 ÷ 4/33 × 67/4
The fraction 67/4 will cancel out each other;
= 82/3 ÷ 4/33
= 82/3 × 33/2
= 41×11/2
= 451/2
= 2251/2
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A town's population has been declining in recent years. The table shows the population since 1980. Is this data consistent with an exponential function? Explain. If so, predict the population for 2010 assuming the trend holds.
Year | Population
1980 | 5000
1990 | 4000
2000 | 3200
2010 | ____
The predicted population for 2010 is approximately 2782.7.
The data is consistent with an exponential function. An exponential function decays at a constant rate, which corresponds to the table's decreasing population trend.
To forecast the population for 2010, use the equation y = abx, where y is the population, an is the initial population, b is the decay factor, and x is the number of years elapsed. We can use the logarithm:
log(y2/y1) = log (b)
log(y2/y1) / log(x2/x1) = log (b)
Using data from 1980 to 1990:
log(4000/5000) / log(1990/1980) = log (b)
log(b) = -0.2231 b = 0.796
So the equation is: y = 5000 * 0.796x, where x is the number of years since 1980.
To find the population in 2010, enter x = 30:
y = 5000 * 0.796^30
y = 2782.7
So the predicted population for 2010 is approximately 2782.7.
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EASY 100 POINTS, WILL MARK BRAINLEST TO FIRST ANSWER,
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 3.25 + 0.3d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
A, 3.25; a kitten who is just born is predicted to weigh 3.25 ounces
B,0.3; a kitten who is just born is predicted to weigh 0.3 ounces
C, 3.25; for each additional day after the kitten is born, its weight is predicted to increase by 3.25 ounces
D, 0.3; for each additional day after the kitten is born, its weight is predicted to increase by 0.3 ounces
Answer:
The correct answer is A, 3.25; a kitten who is just born is predicted to weigh 3.25 ounces. This means that according to the line of fit, a kitten who is just born is predicted to weigh 3.25 ounces.
a sample of a radioactive substance decayed to 97% of its original amount after a year. (round your answers to two decimal places.) (a) what is the half-life of the substance? yr (b) how long would it take the sample to decay to 85% of its original amount?
a) The half-life of the substance is 22.76 years.
b) 5.34 years for the sample to decay to 85% of its original amount
A radioactive substance's half-life is the length of time it takes for half of its atoms to decay, while a drug's half-life is the amount of time it takes for half of its active ingredients to be either excreted by the body or broken down by it.
The amount of the radioactive substance after t years is modeled by the following equation:
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initial amount and r is the decay rate.
A sample of a radioactive substance decayed to 97% of its original amount after a year.
This means that:
[tex]P(1) = 0.97P(0)[/tex]
Then
[tex]P(t)=P(0)(1-r)^{t}[/tex]
[tex]0.97P(0)=P(0)(1-r)^{0}[/tex]
[tex]1-r=0.97[/tex]
So
[tex]P(t)=P(0)(0.97)^{t}[/tex]
(a) What is the half-life of the substance?
This is t for which P(t) = 0.5P(0). So
[tex]P(t)=P(0)(0.97t)^{t}[/tex]
[tex]0.5P(0)=P(0)(0.97t)^{t}[/tex]
[tex](0.97)^{t} =0.5[/tex]
㏒[tex](0.97)^{t}[/tex][tex]=[/tex] ㏒[tex]0.5[/tex]
[tex]t[/tex]㏒[tex]0.97[/tex][tex]=[/tex]㏒[tex]0.5[/tex]
[tex]t=\frac{log 0.5}{log 0.97}[/tex]
[tex]t=22.76[/tex]
The half-life of the substance is 22.76 years.
(b) How long would it take the sample to decay to 85% of its original amount?
This is t for which P(t) = 0.85P(0). So
[tex]P(t)=P(0)(0.97t)^{t}[/tex]
[tex]0.85P(0) = P(0)(0.97t)^{t}[/tex]
[tex](0.97)^{t} = 0.85[/tex]
[tex]log(0.97)^{t} = log 0.85[/tex]
[tex]tlog 0.97 = log0.85[/tex]
[tex]t=\frac{log0.85}{log0.97}[/tex]
[tex]t=5.34[/tex]
5.34 years for the sample to decay to 85% of its original amount.
To learn more about radioactive decay visit:
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is 40% bigger than 1/4
Answer:
40% is bigger
Step-by-step explanation:
40% ⇒ 40/100
1/4 ⇒ 25/100
40>25
∴ 40% is bigger