consider a certain type of nucleus that has a decay rate constant of 0.0250 min-1. calculate the time required for the sample to decay to one-fourth of its initial value.
It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
In the given statement is:
λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus
To solve this problem, we use
N(t) = [tex]N_{0}[/tex]e^-λt
and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set
N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]
We can substitute this in the decay equation:
0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt
Cancel the like terms
0.25 = e ^-λt
Take the natural logarithm of both sides:
㏑(0.25) =㏑(e^-λt)
㏑(0.25)= -λt
Solve for the time t:
t = - ㏑(0.25)/λ
Substitute the given rate constant :
t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]
t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]
t = 55.452mins
It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
Learn more about the Decay of Nucleus at:
https://brainly.com/question/14667624
#SPJ4
Which linear function represents the line giving by the point slope equation y-2=4(x-3)
The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Also note that f(x) = y
Isolate the y then add 2 from both sides:
y - 2 = 4(x-3)
y - 2+ 2 = 4(x-3)+2
y = 4(x-3) + 2
Note that the equation is : y = 4(x-3) + 2
Now Distribute 4 to all terms within the parenthesis
y = 4(x-3) + 2
y = 4x - 12 + 2
Simplify. Combine like terms
y = 4x - 10 ; or f(x) = 4x - 10.
Hence, The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10
Learn more about slope;
https://brainly.com/question/11249395
#SPJ1
What is the slope of the line that passes through the points (5, -6) and (9, -6) Write your answer in simplest form.
Answer:
slope=y2-y1/x2-x1
=-6-(-6)/9-6
=0/3
any fraction in which numerator is 0 is 0.
HELPPPP!! Each of 8 students reported the number of movies they saw in the past year. Here is what they reported. 6,14,14,16,14,18,15,6
Based on the number of movies that each of the 8 students saw in the past year, the mean number of movies is 12.875 movies
How to find the mean?To find the mean of a distribution of numbers such as the number of movies seen in the past year, sum up the number of movies watched and then divide it by the number of students.
The mean number of movies watched by the students is therefore:
= Sum of movies watched / Number of students
= (6 + 14 + 14 + 16 + 14 + 18 + 15 + 6) / 8 students
= 103 / 8
= 12.875 movies
Rest of the question is:
Find the mean number of movies that the students saw.
Find out more on the mean at https://brainly.com/question/20118982
#SPJ1
a bucket holds 10 liters.about how many gallons does the buket hold?round to the nearest tenth,if necessary
For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.
What is termed as units and unit conversion?A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.
Before performing any arithmetic operations on 2 variables, we should always convert all of their values to a common unit.Unit conversion is the process of converting one unit of measurement to another measurement unit for the same amount by multiplying/dividing by conversion factors.Scientific notation is used to express the units, which are then converted into numerical based on the quantities.Now, per the given question;
The total amount a bucket contains is 10 litres.
Noe, the conversion of litres in gallons is given as;
1 litres = 0.26 gallons.
Thus, 10 litres = 10×0.264
= 2.64 gallons.
Therefore, the bucket will contain 2.64 gallons.
To know more about the units and unit conversion, here
https://brainly.com/question/13016491
#SPJ9
for how many bases between two and nine inclusive does the representation of $576 {10}$ have a final digit of 1?
Answer:
Step-by-step explanation:
Convert 576 from base 10 to following bases:
first of all convert 576 from base 10 to base 2 we got this
1001000000_2
now then convert 576 from base 10 to base 3 we got this
210100_3
now then convert 576 from base 10 to base 4 we got this
21000_4
now then convert 576 from base 10 to base 5 we got this
4301_5
now then convert 576 from base 10 to base 6 we got this
2400_6
now then convert 576 from base 10 to base 7 we got this
1452_7
now then convert 576 from base 10 to base 8 we got this
1100_8
now then convert 576 from base 10 to base 9
710_9
Only in base 5 does it end in 1.
referred by www.web2.0calc.com
So only in base 5 does it end in final digit of 1.
A Binary operation can be considered as a function whose input is two elements of the same set S and whose output also is an element of S. S . Two elements a and b of S can be written as a pair (a, b) of elements in S.
So first of all convert 576 from base 10 to following bases:
first of all convert 576 from base 10 to base 2 we will get this 1001000000_2
Then convert 576 from base 10 to base 3 we will get this 210100_3
Then convert 576 from base 10 to base 4 we will get this 21000_4
Then convert 576 from base 10 to base 5 we will get this 4301_5
Then convert 576 from base 10 to base 6 we will get this 2400_6
Then convert 576 from base 10 to base 7 we will get this 1452_7
Then convert 576 from base 10 to base 8 we will get this 1100_8
Then convert 576 from base 10 to base 9 we will get this 710_9
Therefore only in base 5 does it end in final digit of 1.
Learn more about bases on brainly.com/question/485375
SPJ4
A farmer sells an average of 15 3/5 bushels of corn each day. What integer represents the charge in bushels of corn in his inventory after 6 days?
well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.
[tex]\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}[/tex]
Please Help
Thanks In advance
Answer:
U = 4
Step-by-step explanation:
We take 3/9 and simplify it, making 1/3.
We multiply both by 12 to eliminate denominators, so the new numbers are 4 and U.
U = 4
WILL GIVE U BRAINLIEST
Answer: ( -2, 4)
Step-by-step explanation:
What is 4(3-x)+10 what does that equal
Answer:
22 - 4x
Step-by-step explanation:
4(3-x) + 10 Distribute the 4
4(3) - 4x +10
12 - 4x +10
22 - 4x
What is the relationship of the edge length of the cube
to its volume?
Volume is equal to [tex]a^{3}[/tex] where an is the width or length of its edges.
The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes [tex]centimetres^{3}[/tex], [tex]metres^{3}[/tex], [tex]inches^{3}[/tex], [tex]feet^{3}[/tex], etc.
A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.
If a cube's length, breadth, and height are equal to "a," then;
Cube volume = a[tex]\times[/tex]a[tex]\times[/tex]a.
Therefore, Volume of cube is [tex]a^{3}[/tex] where a is the length of the edge.
To learn more about cube visit: https://brainly.com/question/28134860
#SPJ9
In 1975, a person earning minimum wage made $80 for a 40-hour work week. what was the minimum wage per hour in 1975?
The minimum wage per hour = $2
Here we need to find the value of minimum wage per hour in 1975
As is given that the earning minimum wage is $80 for working 40 hours.
40-hour work gives = $80
1-hour work gives = $80/40
= $2
Therefore the minimum wage per hour in 1975 is $2
To know more about the wages and time refer to the link given below:
https://brainly.com/question/1622389
#SPJ4
------------------------------------------------------------------------
Answer:
A) The percentage of the bacteria increasing each hour is 15% per hour
B) When t=0 the population of bacteria is 3000 bacteria
C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)
Step-by-step explanation:
A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%
B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.
C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.
Yossi has a square-shaped garage with 52 square meters of floor space plans to build an addition that will increase the floor space by 50%. What will be the length of one side of the new garage?
The length of the new garage will be approximately 8.83 meters.
The length is referred as the side of a rectangle or a square. Ideally we use length to measure the larger side of a rectangle, but for a square all sides are equal and so can be called length.
The are of a square is given by the square of any side .
Given the area of the square is 52 square meters.
The new are of the square is 50% more.
Increased amount = 50% of 52 = 26 meters²
New area of square = 52 + 26 meters² = 78 meters²
Now we know that the area of a square is given by (side)² .
Therefore (side)²= 78
or, side = √78
or, side = 8.8317...
or, side ≈ 8.83 meters
Therefore the length of the new garage is approximately 8.83 meters.
To learn more about length visit:
https://brainly.com/question/2042017
#SPJ1
Determine whether the ordered pair (9, 10) is a solution of y = 2x −8.
Answer:
false
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
to determine if (9, 10 ) is a solution, substitute x = 9 into the equation and if y = 10 then it is a solution.
y = 2(9) - 8 = 18 - 8 = 10
then (9, 10 ) is a solution of the equation
Select all the polynomials that have (x - 4) as a factor.
a
x3 - 13x - 12
b
x3 + 8x2 + 19x + 12
c
x3 + 6x + 5x -12
d
x3 - x2 - 10x - 8
e
x2 - 4
Polynomials which have (x-4) as a factor are a. x³ - 13x - 12 = 0 and c. x³ + 6x + 5x - 12 = 0.
What is a polynomial ?An algebraic equation having two or more than two terms is called a polynomial.
According to the given question we have determine which of the following polynomials have (x-4) as a factor.
One way is factoring each of these polynomials.
Another way is given x - 4 is a factor,
∴ x - 4 = 0
x = 4 must satisfy the polynomial which has a factor of (x-4).
Now we have to replace x with 4 in each of the given polynomials and if LHS = RHS then (x -4) is a factor.
a. x³ - 13x - 12 = 0
(4)³ - 13(4) - 12 = 0
64 - 52 - 12 = 0
64 - 64 = 0. (LHS = RHS).
b. x³ + 8x² + 19x + 12 = 0
(4)³ + 8(4)² + 19(4) + 12 ≠0
Here you don't need to calculate further because in LHS sum of these terms won't be zero.
c. x³ + 6x + 5x - 12 = 0.
x³ + 11x - 12 = 0.
64 + 44 - 12 ≠ 0.
d. x³ - x² - 10x - 8 = 0.
64 - 16 - 40 - 8 = 0.
64 - 64 = 0, (LHS = RHS).
e. x² - 4
16 - 4 ≠ 0.
learn more about polynomials here :
https://brainly.com/question/11536910
#SPJ1
What number is halfway between -46.3
and 46.31?i
The number that is halfway between the numbers -46.3 and 46.31 will be 46.305.
We are given the two numbers:
- 46.30 and 46.31
Now, we need to find a number that is halfway between the given numbers.
For this, we need to find the mid point between the two numbers that is given to us.
Mid point is calculated as:
| x | + | y | / 2
Substituting the values in the expression, we get that:
46.3 + 46.31 / 2
= 92.61 / 2
= 46.305
Therefore, we get that, the number that is halfway between the numbers -46.3 and 46.31 will be 46.305.
Learn more about mid point here:
https://brainly.com/question/5566419
#SPJ9
If A= [-2 14 9] and B= [0 -6 10], the A-3B=?
Answer:
(-2, 32, -21)
Step-by-step explanation:
You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)
a researcher wants to know how the residents of a town feel about constructing a new road through the town
Write the function rule for the function shown below reflected in the given axis. f(x) = 4x; x-axis Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)? g(x) =
The function rule for g(x) is g(x) = -4x
How to determine the function rule for g(x)?The function is given as
f(x) = 4x
The transformation is given as reflection across the x-axis
The rule of this transformation is
(x, y) = (x, -y)
So, we have
g(x) = -f(x)
This gives
g(x) = -4x
Hence, the function rule for g(x) is g(x) = -4x
Read more about function transformation at:
https://brainly.com/question/4025726
#SPJ1
Point B is on line segment AC. Given AB = 3x, BC = 4x + 8, and
AC = 5x + 10, determine the numerical length of AC.
Answer: AC
Submit Answer
B
attem
Answer:
AC = 15
AB = 3
BC = 12
Step-by-step explanation:
AB + BC = AC
3x + (4x + 8) = 5x + 10
3x + 4x - 5x = 10 - 8
2x = 2
x = 1
AC = 5x + 10 = 5(1) + 10 = 15
AB = 3x = 3
Bc = 4x + 8 = 12
a real estate agent believes that the value of houses in the neighborhood she works in has increased from last year. to test this claim, she randomly selects houses in this neighborhood and compares their estimated market value in the current year to their estimated market value in the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market value of the previous year from the market value of the current year. assume that the values are normally distributed. using a test statistic of t≈7.496, the significance level α
The hypothesis is called the alternative hypothesis test.
According to the statement
We have to explain about the alternative hypothesis.
So, For this purpose, we know that the
The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.
From the given information:
she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.
Then
the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.
Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.
So, The hypothesis is called the alternative hypothesis test.
Learn more about alternative hypothesis here
https://brainly.com/question/15980493
#SPJ4
-10 plus - 3/4
Hurry please!
Graph the image of V(0, -2) after a rotation 180° clockwise around the origin.
Greetings from Brasil...
For rotation, we can use the expression:
V(X; Y) → V'(Xcos θ - Ysen θ; Xsen θ + Ycos θ)Let rotate 180° - specifically for this angle, 180°, either counterclockwise or clockwise
SEN 180 = 0 and COS 180 = - 1
V(X; Y) → V'(- X; - Y)
V(0; - 2) → V'(0; - (- 2))
V'(0; 2)___________________________________
see more:
https://brainly.com/question/28470508
The sum of a number and its half is 27. Find the number.
Let the number be y
Answer:
Step-by-step explanation:
the number is y
you are told
y+0.5y=27
Therefore,
1.5y = 27.
If you divide by 1.5 on both sides, you'll get 18 which is your answer.
18+9=27
Find the constant of variation where y varies directly as x if y = 30 when x = 8. Write your answer
as a decimal.
The value of constant v is 3.75 if y varies directly as x and when
x = 8 and y = 30.
Let v be any constant.
According to the given question.
y varries directly as x.
⇒ y ∝ x
⇒ y = vx (beacuse v is constant)
Here, it is give that x = 8 and y = 30.
Thereofre, the value of constant v when y = 30 and x = 8 is given by
y = vx
⇒ 30 = v(8)
⇒ 30/8 = v
⇒ v = 3.75
Hence, the value of constant v is 3.75 if y varies directly as x and when
x = 8 and y = 30.
Find out more information about constant here:
https://brainly.com/question/14993324
#SPJ1
6) I used 4 packages of printer paper during 10 months. At this rate, how many packages
will I use for the year? (Hint: change months to years)
4.8 packages will need for the use of one year.
No. of used packages of printer paper during 10 months = 4 Packages
As we know that there is 12 months in a year,
To determine the number of packages need for the year, first we have to find the number of package is being use in one month.
S0, No. of used package in 1 month = 4/10 = 0.4 Package
Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.
No. of packages for the use of one year = 12 × 0.4
= 4.8 Packages
To learn more about Packages visit :
https://brainly.com/question/14965351
#SPJ9
Help I don’t know any of this please
Cho tam giác ABC vuông tại a đường cao AH biết AB = 6 cm và diện tích tam giác ABC bằng 24 cm². Tính độ dài các đoạn thẳng AC BC AH
Answer:
AC = 8
BC = 10
AH = 4.8
Step-by-step explanation:
A = 1/2(AB)(AC)
24 = 1/2(6)(AC)
AC = (24)(2)/(6) = 8
BC^2 = AB^2 + AC^2 = 6^2 + 8^2 = 36 + 64 = 100
BC = 10
A = 1/2(AH)(BC)
24 = 1/2(AH)(10)
AH = (24)(2)/(10) = 48/10 = 4.8
Riley bought 1.52 pounds of raisins and 1.08 pounds of prunes for $6.50. The raisins and prunes cost the same price per pound. What is the price per pound for the dried fruit? Show all work .
Answer:
$2.08 per pound
Step-by-step explanation:
1.52+1.08= 2.6pound
6.50/2.6=$2.5 per 2.6 Ibs
(turn the pound to a whole number)
2.6/2= 1.3 so 2,6/1.3= 2Ibs
(what you do to one side must be done to the other)
$2.5/1.3 =2.08