1) The x-intercepts of the function [tex]\( f(x) = x^2 + 2x - 8 \)[/tex]are [tex]\( x = -4 \)[/tex]and [tex]\( x = 2 \).[/tex]
2) The y-intercept of the function [tex]\( f(x) = x^2 + 2x - 8 \) is \( y = -8 \).[/tex]
3) The equation of the axis of symmetry is [tex]\( x = -1 \).[/tex]
4) The vertex of the function [tex]\( f(x) = x^2 + 2x - 8 \) is \( (-1, -9) \).[/tex]
5) The graph of the function is a parabola opening upwards with the vertex at [tex]\( (-1, -9) \).[/tex]
Explanation:1) To find the x-intercepts, set [tex]\( f(x) = 0 \)[/tex] and solve for x. The quadratic equation [tex]\( x^2 + 2x - 8 = 0 \)[/tex] factors into [tex]\( (x - 2)(x + 4) = 0 \),[/tex] yielding x-intercepts of [tex]\( x = -4 \)[/tex] and [tex]\( x = 2 \).[/tex]
2) To find the y-intercept, set \( x = 0 \) in the function. \( f(0) = 0^2 + 2(0) - 8 = -8 \), so the y-intercept is [tex]\( y = -8 \).[/tex]
3) The axis of symmetry for a quadratic function in the form [tex]\( f(x) = ax^2 + bx + c \)[/tex] is given by [tex]\( x = \frac{-b}{2a} \).[/tex] For [tex]\( f(x) = x^2 + 2x - 8 \)[/tex], the axis of symmetry is [tex]\( x = -1 \).[/tex]
4) The vertex of a quadratic function in the form [tex]\( f(x) = ax^2 + bx + c \) is located at \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]Substituting [tex]\( x = -1 \)[/tex] into the function, we find that the vertex is [tex]\( (-1, -9) \).[/tex]
5) The graph of the function is a parabola that opens upwards, consistent with the positive coefficient of the [tex]\( x^2 \)[/tex] term. The vertex at (-1, -9) is the lowest point on the graph, and the parabola extends upward indefinitely from there.
if 3n is an odd number, which of the following is an even number?
(a) 3n-1
(b) 3n+2
(c) 3n-2
(d) 3n +2n
Answer:
Option (a).
Step-by-step explanation:
It is given that 3n is an odd number.
We need to find an even number from the given options.
Even numbers: Which are divisible by 2.
Odd numbers: Which are not divisible by 2.
We need know that the numbers are alternatively even and odd.
If we add or subtract 1 from an odd number, we always get an even number.
If we add or subtract 2 from an odd number, we always get an odd number.
3n is an odd number. So,
3n-1 is an odd number.
3n+2 is an even number.
3n+2 is an even number.
3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.
Therefore, the correct option is (a).
The volume of a gas "V" varies inversely with the pressure "P" put on it. If the volume is 360cm³ under a pressure of 20 kgcm2, then what pressure is needed for it to have a volume of 480cm³?
Answer:
[tex]15\,\,kg/cm^2[/tex]
Step-by-step explanation:
Given:
The volume of a gas "V" varies inversely with the pressure "P" put on it.
Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]
To find:
pressure when volume is 480 [tex]cm^3[/tex]
Solution:
As of a gas "V" varies inversely with the pressure "P" put on it,
[tex]V=\frac{k}{P}[/tex]
Here, k is a constant
As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]
[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]
So,
[tex]V=\frac{7200}{P}[/tex]
Put [tex]V=480[/tex]
[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]
Find the profit function for the given marginal profit and initial condition. Marginal Profit Initial Condition dP dx = −20x + 290 P(5) = $670 P(x) =
Answer:
[tex]P(x) = -10x^2+290x-530[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dP}{dx} = -20x + 290[/tex]
Initial condition:
[tex]P(5) = $670[/tex]
Solving the given differential equation, we get,
[tex]\dfrac{dP}{dx} = -20x + 290\\\\dP=(-20x + 290)dx\\\text{Integrating both sides}\\\\\displaystyle\int dP = \int (-20x + 290)dx\\\\P(x) = -20\dfrac{x^2}{2} + 290x + C\\\\\text{where C is constant of integration}\\P(x) = -10x^2+290x + C\\P(5) = 670\\670 = -10(5)^2+290(5) + C\\670 = 1200 + C\\\Rightarrow C = -530\\P(x) = -10x^2+290x-530[/tex]
is the required profit function.
To determine the profit function, integrate the given marginal profit function. After integration, apply the initial condition to find the integration constant. The final profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
Explanation:The subject matter of this question is calculus, specifically how to determine the profit function based from the given marginal profit and initial condition. To determine the profit function, you need to integrate the marginal profit function. The marginal profit is given as dP/dx = -20x + 290. When you integrate this, you will get [tex]P(x) = -10x^2 + 290x + C[/tex], where C is an integration constant that we determine using the initial condition P(5) = 670.
To do this, substitute 5 into x in the equation and set P(x) equal to[tex]670: 670 = -10*5^2 + 290*5 + C.[/tex] Solving for C, you will find that C equals -60. So the profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
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f(4)= ______
-11
-2
1
30
if g(x) = 2, x = _______
0
2
5
30
Answer:
f(4) = -11
If g(x) = 2 then x = 0
Step-by-step explanation:
here it asks to determine graphically, so we need to use the provided graph:
f(4) = -11 ( just notice the y-coordinate of the point of x-coordination 4)
If g(x) = 2 then x = 0 (just notice the x-coordinate of the point of y-coordination 2)
what is the area of a circle if the diameter is 16 millimetres
Answer:
201.1 mm²
Step-by-step explanation:
given that the diameter is 16mm,
radius = diameter ÷ 2 = 16÷2 = 8 mm
area of a circle is given by
A = πr², where
π=3.142
r = radius = 8 mm
Substituting these into the equation,
A = πr²
= 3.142 (8)²
= 201.088 mm²
= 201.1 mm² (rounded to nearest tenth)
NEED ANSWER ASAP WILL GIVE BRAINLIEST!!!!!!!
A teacher had 1 apple, he gave 1 to his student. How many apples does the teacher have and how much apples does his student have?
Answer:
Teacher has 0 . Student has 1 apple
Step-by-step explanation:
PLEASE hurry !!!!!! y = 24x^2-14x+5
Answer:
(0.3,3)
Step-by-step explanation:
That is the vertex.
"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."
The rate of the passenger train is 100 miles per hour.
Given:
1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.
2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.
We can set up equations based on the distances traveled and the rates:
1. For the passenger train:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]
Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]
So, the rate of the passenger train is 100 miles per hour.
Witch expression has a product of 32.76?
Answer:
20.00+12.76 would give you that sum
Step-by-step explanation:
Answer:
0.00+12.76 would give you that sum
Step-by-step explanation:
Pls BRAINLIEST
Which are ways to decompose the composite figure into simpler shapes that you have area formulas for? Check all that apply
Answer:
A,B and C
Step-by-step explanation:
Answer
a,b,c are the correct answer
Step-by-step explanation:
hope it helps you my luvs
Nicole shines a light from a window of a lighthouse on a cliff 250 feet above the water level. Nick 10 feet above the water level in a ship off shore, finds that the angle of elevation of the light is 3°. Find the length of the line of sight (light beam) from the ship to Nicole.
We want to find the length of the light beam from the ship to Nicole.
We will see that the solution is 4,585.76 ft.
We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:
250ft - 10ft = 240ft
And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.
Then we can use the relation:
Sin(θ) = (opposite cathetus)/(hypotenuse)
Solving it for the hypotenuse we get:
hypotenuse = (opposite cathetus)/sin(θ)
Replacing by the values that we know, we get:
hypotenuse = 240ft/sin(3°) = 4,585.76 ft
The length of the line of sight is 4,585.76 ft
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To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.
Explanation:To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:
tan(3°) = 250 / d
Simplifying this equation, we have:
d = 250 / tan(3°)
Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:
d ~ 8424.78 feet
So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.
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Any jogs 1/3 of a mile in 1/5 of an hour while john takes 1/30 of an hour to jog 1/5 of an mile if they continued at this rate who would jog farther in one hour and by how much?
Answer:
At the end of one hour, John would be ahead of Anny by 4.33 miles
Step-by-step explanation:
In this question, we are to state who jogs Farther between these. 2 persons per hour.
Any jogs 1/3 of a mile in 1/5 of an hour, what this means that he jogs one-third of a mile in 1/5 * 60 in 12 minutes
John however jogs 1/5 miles in 1/30 of hour. This means he jugs one-fifth of a mile in 1/30 * 60 in 2 minutes
Let’s go back to Any
if Any jogs 1/3 in 12 minutes, then the whole lap will be completed in 36 minutes
Thus if he can jog 1 mile in 36 minutes, then in 60 minutes he would have jogged 1.67 miles
If he Jogs 1/5 in 2 minutes, this mean that the whole lap of 1 mile would be completed in 10 minutes
Thus if he can jug 1 mile in 10 minutes, then in 60 minutes, he will be able to jug a whopping 6 miles
This shows that John is actually faster than Any.
By how much distance? that would be 6 - 1.67 = 4.33 miles
Mrs. Benton selects one student's work to display on a bulletin board each week. Each student's name is placed in a bag from which Mrs. Benton draws a name. What is the probability that an eighth grade student will NOT be selected? A) 3 /10 B) 2/ 5 C) 1 /2 D) 2/ 3
Answer:
1/2
Step-by-step explanation:
What is the domain of the function y = StartRoot x EndRoot?
Answer:
C
Step-by-step explanation:
0 is less than or equal to x is less than infinity. PERIODT.
The domain of the function y = √x will be [0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = √x
The graph of the function is similar to the rightward parabola, the function is not defined for the negative value of x, because the function becomes imaginary.
For the domain of the function, the value of x should be greater than equal to zero.
Because the value under the square root should be greater than or equal to zero.
Then the domain of the function y = √x will be
x ≥ 0
Thus, the domain of the function y = √x will be [0, ∞).
The graph of the function is given below.
More about the domain and range link is given below.
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what is the range for this set of data 38,17,55,40
a)2
B)38
C)39
D)72
Answer:
b.38
Step-by-step explanation:
An open-top box is to be made from a 70-centimeter by 96-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume? Enter the area of the square and do not include any units in your answer. Enter an improper fraction if necessary.
Answer:
[tex]177 \frac{7}{9} cm^2[/tex]
Step-by-step explanation:
Length of the Plastic Sheet= 96cm
Width of the plastic Sheet =70cm
If a square of side x is cut from each corner of the plastic sheet to form the box.
Length of the box=96-2x
Width of the box=70-2x
Height of the box =x
Volume of the box = LWH
Volume=(96-2x)(70-2x)x
The maximum volume of the box is obtained at the point where the derivative is zero.
[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]
Setting the derivative to 0.
[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]
Since we are looking for the minimum value of x,
[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]
determine if the listed line is tangent to the circle
Answer:
SEG KL is not a tangent coz Pythagoras theorem doesn't apply hereSEG GH is not a tangent coz Pythagoras theorem doesn't apply hereSEG GF is not a tangent coz Pythagoras theorem doesn't apply hereSEG FG is not a tangent coz Pythagoras theorem doesn't apply hereSEG XY is a tangent Pythagoras theorem apply here 24²+7²=25²SEG XY is not a tangent coz Pythagoras theorem doesn't apply hereWhich statements are true? Check all that apply.
The radius of the cone is 9 units.
The height of the cone is 15 units.
The height of the cone is 12 units.
The volume of the cone is represented by the
expression 17(15)?(9).
The volume of the cone is represented by the
expression 1.9(9)2(12)
Answer: ACE
The radius of the cone is 9 units
The height of the cone is 12 units
The volume of the cone is represented by the expression 1/3 pie (9)2(12)
Step-by-step explanation:
6g=48 g=? Please hell
Answer:
g = 8
Step-by-step explanation:
We're going to isolate g to find out what it equals, so we have to divide both sides by 6.
6g=48
__ __
6 6
g = 8
The solution to the equation 6g = 48 is g = 8.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
6g = 48
By dividing both sides of the equation by 6, we have:
g = 48/6
g = 8
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Ten people at two local restaurants were randomly surveyed and asked to rate their experience, with “1” representing very poor and “10” representing very good. The data is shown in the dot plots. Find the mean for each set of data. Blue Terrace: Paradiso Grill:
Answer:
Blue Terrace: 6.1
Paradiso Grill: 6.3
Step-by-step explanation This is the right answer
Answer:
6.1 and 6.3
Step-by-step explanation:
A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the desert for vacation. How many individuals were surveyed in total? How many people are planning on going to the mountains for their vacation?
Answer:
140 individuals were surveyed
42 people are planning on going to the mountains
Step-by-step explanation:
The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.
If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:
[tex]21=n*0.15\\n=140\ individuals[/tex]
140 individuals were surveyed
Since 30% responded "the mountains", the number of people planning on going to the mountains is:
[tex]m = 140*0.30\\m=42\ people[/tex]
42 people are planning on going to the mountains
PLEASEEEEEW ANSWERRRRRRRRR QUICKKKKKMM
Answer:
multiply all the numbers
Step-by-step explanation:
Victor has already taken 4 pages of notes on his own, and he will take 2 pages during each hour of class. Write an equation that shows the relationship between the time in class h and the number of pages p.
Write your answer as an equation with p first, followed by an equals sign
Answer:
The answer is p = 4 + 2h .
Step-by-step explanation:
It is given that Victor has already taken 4 pages and he will take 2 pages per hour of class. So you have to make an equation of p in terms of h :
Let p be pages,
Let h be hours,
p = 4 + (2×h)
p = 4 + 2h
what is 3y takeaway y
Answer:
y = 1/3
Step-by-step explanation:
The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104
Answer:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
We select a sample of n = 50 and we want to find the probability that:
[tex]P(\bar X >104)[/tex]
Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} [/tex]
And using this formula we got:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
From an upstairs window, I can see my neighbor’s fence. The angle of depression is 7 degrees. If my window is 15 ft off the ground, how far is my neighbor’s fence from my house?
Answer:
1.84ft
Step-by-step explanation:
From the figure attached,
AB = Height of the window = 15ft
Let the distance between the base of the housr and the fence 'C' = xft
If the angle of depression = 7°
Then angle of elevation of the top of the fence from the house = 7°
Now from right triangle ABC,
tan7° = x/15
x = tan7°×15
x = 0.1227×15
x = 1.84ft
Therefore, distance of the house from the fence is 1.84ft
What is the coefficient of x in the following expression?
1 - 10x + 4y
Evaluate the following expression for x = 15.
LaTeX: \frac{1}{5}1 5x - 12
Answer:
(1) The coefficient of x in this expression is -10.
(2) The value of the expression for x = 15 is -9.
Step-by-step explanation:
(1)
A coefficient is a numerical value that is placed before a variable or is multiplied by the variable in an algebraic equation.
For example, in the algebraic equation 4x² + 5y the coefficient of variable y is 5.
The expression given is:
1 - 10 x + 4 y
The coefficient of x in this expression is -10.
(2)
The expression provided is:
[tex]f(x)=\frac{1}{5}x - 12[/tex]
Compute the value of the expression for x = 15 as follows:
[tex]f(x)=\frac{1}{5}x - 12\\=(\frac{1}{5}\times 15) - 12\\=3-12\\=-9[/tex]
Thus, the value of the expression for x = 15 is -9.
Tickets to the school play cost $4.00 for adults and $2.00 for students. If 85 people attend the show, and the receipts totaled $268, how many students attended the show?
Answer:I think it is 226
Step-by-step explanation:
85/2= 42.5 then 268 - 42.5= 225.5 then round it and you get 226
Circle A and circle B are similar. A. What is the similarity ratio of circle A to circle B? B. What is the circumference of each circle? Leave answers in terms of . C. What is the ratio of the Circumference of circle B to the Circumference of circle A? Simplify your ratio.
Answer: A) 5/2
B) 10pi for A and 4pi for B
C) 5/2
Step-by-step explanation:
Please find the attached file for the solution
Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 154 grams?
Answer:
It would take 27.5 minutes the element to decay to 154 grams.
Step-by-step explanation:
The decay equation:
[tex]\frac {dN}{dt}\propto -N[/tex]
[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]
[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]
Integrating both sides
[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]
[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]
When t=0, N=[tex]N_0[/tex] = initial amount
[tex]ln|N_0|=-\lambda .0+c[/tex]
[tex]\Rightarrow c=ln|N_0|[/tex]
[tex]ln|N|=-\lambda t+ln|N_0|[/tex]
[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]
Decay equation:
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
Given that, the half life of of element X is 11 minutes.
For half life, [tex]N=\frac12 N_0[/tex], t= 11 min.
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]
[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]
[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]
[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]
[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex] [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]
N=154 grams, [tex]N_0[/tex] = 870 grams, t=?
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]
=27.5 minutes
It would take 27.5 minutes the element to decay to 154 grams.
Answer:
60.6 minutes
Step-by-step explanation:
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