The half-life of this radioactive element is approximately 2 years.
We have,
The decay of a radioactive element follows an exponential decay model of the form:
[tex]N = N_0 e^{-kt}[/tex]
where:
N0 is the initial concentration of the radioactive element
N is the concentration after time t
k is the decay constant
We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:
N/N0 = 1/32
Taking the natural logarithm of both sides and rearranging, we get:
ln(N/N0) = ln(1/32) = -3.465
Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:
t1/2 = ln(2) / k
We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:
ln(N/N0) = -kt
-3.465 = -k x 10
k = 0.3465
Substituting this value of k into the formula for half-life, we get:
t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.
Therefore,
The half-life of this radioactive element is approximately 2 years.
Learn mroe about half-life here:
https://brainly.com/question/24710827
#SPJ1
What is the answer to this question
The maximum profit that can be made is $1737.82
What is an equation?An equation is an expression showing the relationship between numbers and variables using mathematical operators.
The profit function is the difference between the revenue and cost of a commodity. Given that:
Revenue, R(x) = 700x - 11.3x²
Cost, C(x) = 8068 - 34.25x
Profit, P(x) = Revenue - Cost
P(x) = (700x - 11.3x²) - (8068 - 34.25x)
P(x) = 665.75x - 11.3x² - 8068
The maximum profit is at P'(x) = 0; hence:
P'(x) = 665.75 - 22.6x
665.75 - 22.6x = 0
22.6x = 665.75
x = 29.45
P(29.45) = 665.75(29.45) - 11.3(29.45)² - 8068
P(29.45) = 1737.82
The profit to be made is $1737.82
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
An hourglass is 6ft wide and 4 ft tall on top. On bottom the hourglass is 6ft wide and 2 feet tall. It can hold 2000 pounds. if the water takes exactly one year to pass through the hourglass, how much water pass through to the bottom each day? What is the linear function of the water passing through the hourglass?
The linear equation outlining the entire volume of water (y) which has coursed through the hourglass following x days. is
y = 5.48xThe volume of water passed each which is the slope is
5.48How to find the amount of water passing through the glass each dayTo ascertain the amount of water that is passing through the hourglass daily:
where:
Total water capacity: 2000 pounds
Time: 365 days
Water transpiring every day = Total water capacity / Time
Water pervading each day ≈ 200 / 365
Water pervading each day ≈ 5.48 pounds/day
the linear function of the water traveling through the hourglass.
Making x the number of days and y being the total quantity of water which has crossed through the hourglass after x days--as the fluid fluxes at a constant velocity--thus a linear relationship between x and y can be determined.
Every single day (x), the hourglass moves 5.48 pounds of water. This reveals the linear representation of:
y = 5.48x
Learn more about linear function at
https://brainly.com/question/4025726
#SPJ1
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
solvesolveslvesolbesolve
The maximum value of z = 28. I occurs at (x, y) = 4
How to go about this ?To solve thhis linear programming problem, we can use the graphical method..
Graph the feasible region defined by the constraints.....
x >= 0 and y >= 0 represent the non-negative quadrants.
x + y < = 8 represents the area below the line passing through ( 8, 0) and (0, 8).
x + y >= 2 represents the area above the line passing through ( 2 , 0) and (0 , 2).
Identify the corner points of the feasible region .....
(0, 2)
( 2, 0)
( 4, 4)
( 8, 0 )
Calculate tthe objective function at each corner point....
z(0, 2 ) = 3(0) + 4(2) = 8
z (2, 0 ) = 3(2) + 4(0) = 6
z(4, 4 ) = 3(4) + 4(4) = 28
z ( 8, 0) = 3(8) + 4(0) = 24
Determine the maximum value of the objective function and the values of x and y that give this maximum value
The maximum value of z is 28, which occurs at the corner point (4, 4).
So we c can be stated as follows --
Maximum value of z = 28
x = 4
y = 4
Learn more about maximum value:
https://brainly.com/question/14316282
#SPJ1
The radius of a circle with area A is approximately $\sqrt{\frac{A}{3}}$
. The area of a circular mouse pad is 45 square inches. Estimate its radius to the nearest tenth.
in.
The radius of the circular mouse is 3.7 inches.
How to find the radius of a circle?The area of the circular mouse pad 45 square inches. Therefore, the radius of the circle can be found as follows:
area of the circle = πr²
where
r = radiusTherefore,
area of the circular mouse = 3.14 × r²
45 = 3.14r²
divide both sides by 3.14
r² = 45 / 3.14
r² = 14.3312101911
square root both sides
r = √14.331210911
r = 3.78565714243
r = 3.7 inches
learn more on radius here: https://brainly.com/question/27668188
#SPJ1
1. Joe has a chocolate box whose shape resembles a rectangular prism. Its length is 6 in, height is 2 in and width is 4 in. Find the volume of the box.
length= 5 in , width= 4 in, height= 3 in
Answer:
48 square inches
Step-by-step explanation:
lxwxh
6x4x2
What is the value of z in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
Answer:
z = 12.52 in.
Step-by-step explanation:
Because this is a right triangle, we can solve for z using on the trigonometric ratios.
If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.
Thus, we can use the cosine ratio which is
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
Now, we can plug everything into the formula and solve for z, the hypotenuse:
[tex]cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52[/tex]
perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
The width of the worktable is 32 inches, and the length of the worktable is 82 inches.
Let's assume that the width of the worktable is "w" inches.
We are given that the length is 18 inches more than twice the width, which can be expressed as:
Length = 2w + 18
The perimeter of the worktable is the sum of the lengths of all four sides.
We know that the perimeter of the worktable is 228 inches, so we can write an equation:
Perimeter = 2 × (Length + Width)
228 = 2 × (2w + 18 + w)
228 = 2 × (3w + 18)
Dividing both sides by 2:
114 = 3w + 18
Subtracting 18 from both sides:
96 = 3w
Dividing both sides by 3:
w = 32
So, the width of the worktable is 32 inches.
Now we can use this value to find the length:
Length = 2w + 18
Length = 2 × 32 + 18
Length = 82
So, the length of the worktable is 82 inches.
To learn more about width here:
https://brainly.com/question/13342613
#SPJ1
Can someone explain how to get the answer to…if 7p-4=8 what is the value of p?
The value of p in the equation 7p - 4 = 8 is p = 12/7
Solving for what is the value of p?From the question, we have the following parameters that can be used in our computation:
7p - 4 = 8
Add 4 to both sides
So, we have
7p = 12
Divide both sides by 7
So, we have
p = 12/7
Hence, the solution is p = 12/7
Read more about expression ta
https://brainly.com/question/15775046
#SPJ1
PLEASE PLEASE HELP DUE IN A FEW HOURS ILL GIVE U ANYTHING
What age represents the median of this data? (1 point)
4. What age(s) represent the mode? (1 point)
5. Beth is 63 years old. She loves to bike. She decides to look at other clubs to join. Why do you think she didn’t want to join this club? Explain your answer using the stem-and-leaf plot above. (1 point)
Are there any outliers in this data? If so, what age(s) are they? (Hint: you’ll need to find the quartiles first. Show your work.) (4 points)
Beth could not join the club because the highest age which is allowed here is only 55 years
We know that;
A statistical expression obtained from a list of data that refers an abnormal gap from other values.
And, The statistical rules that instruct us to divides the data or observation values into four parts.
After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.
the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.
hence, Beth did not join the club because her age was above the highest age that allowed in this club.
To know more about Stem Leaf diagram visit:
brainly.com/question/29479023
#SPJ1
Write an explicit formula for an, the nth term of the sequence 36, 32, 28, ....
WORTH 20
Answer:
an = 36 + -4(n - 1)
Step-by-step explanation:
Explicit formula:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
an = nth terma1 = first termd = common differenceHere, we are given the following:
Sequence: 36, 32, 28The first term is 36
To get to the next term, 4 is subtracted from the previous term so the common difference is -4.
So we have:
First term(a1) = 36Common difference = -4By plugging this into [tex]a_n=a_1+(n-1)d[/tex]
We acquire : [tex]a_n=36+(n-1)(-4)[/tex]
Find the area of this semi-circle with diameter, d = 20cm.
Give your answer rounded to 2 DP.
The area of the semicircle is 157. 00 cm
How to determine the area of the semi-circleTo determine the area of the semi-circle, we need to consider the formua.
the formula for calculating the area of a semi-circle is expressed with the equation;
A = 1/2π²
Such that the parameters of the formula are;
A is the area of the semi-circler is the radius of the semi-circleπ takes the constant value of 3.14It is important to note that
Formula for diameter is expressed as
Diameter = 2radius
Radius = 10cm
Substitute the values
Area = 1/2× 3.14 × 100
Multiply the values
Area = 157 cm²
Learn more about area at: https://brainly.com/question/25292087
#SPJ1
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
To learn more about Scatter Plot visit:
brainly.com/question/6592115
#SPJ1
Write the inductive hypothesis for this statement
The inductive hypothesis is P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + {6(a +1) +1} = (a + 1) {3(a + 1) + 4} is true for all (a+1) = n for the statement Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
The statement is given as,
Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
For n =1 we get,
P₁ : 6(1) + 1 =7
and, 1{3(1) + 4} = 7
Hence, 6n+ 1 = n(3n + 4) is true for n= 1.
Therefore assume that Pₐ is true for some a = n, we get,
Pₐ : 7 + 13 +19 +... + (6a +1 ) = a(3a + 4)
Let, n =a+1 , we get,
P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + (6a +1) + {6(a +1) +1}
= Pₐ + (6a+ 7)
= a(3a + 4) + 6a + 7
= 3a² + 4a + 6a + 7
= 3a² +10a + 7
= 3a² + 7a + 3a + 7
= a( 3a + 7) + 1(3a + 7)
= (a + 1) ( 3a + 7)
= (a + 1) {3(a + 1) + 4}
Hence, (a +1) is true for all (a+1) = n by mathematical induction principle. Thus, the inductive hypothesis is true.
To know more about inductive hypothesis here
https://brainly.com/question/29584620
#SPJ1
On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}
The domain is all real numbers.
The range is {y|y ≤ 16}.
Option B is the correct answer.
We have,
The given parabola opens downwards and has a vertex at (-1,16).
So,
The parabola has a maximum value at y = 16.
Also, the y-intercept of the parabola is (0,15), which is below the vertex, and the parabola intersects the x-axis at (-5,0) and (3,0).
We can use the factored form of the equation of a parabola to find its equation in this case.
The factored form is:
y = a(x - h)² + k
where (h,k) is the vertex and "a" determines whether the parabola opens upwards or downwards.
Since the parabola opens downwards, "a" is negative.
Also, we know that the vertex is (-1,16), so we have:
y = a(x + 1)² + 16
To find "a", we can use one of the x-intercepts, say (-5,0).
Substituting these values into the equation gives:
0 = a(-5 + 1)² + 16
0 = 16a
a = 0
This indicates that the parabola is actually a line passing through (0,15) and (3,0). Therefore, the equation of the parabola is:
y = -x² - 2x + 15
The domain of this function is all real numbers because there are no restrictions on the values of x that can be plugged into the equation.
However, the range of the function is limited by the maximum value of y, which is 16.
Since the parabola opens downwards, all y values less than or equal to 16 are attainable.
Therefore, the domain is all real numbers, and the range is {y | y ≤ 16}.
Therefore,
The domain is all real numbers.
The range is {y|y ≤ 16}.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
The percentage of pennies in the roll is A = 30 %
Given data ,
Let the percentage of pennies in the roll made before 1985 be A
Now , the total number of pennies be = 50 pennies
And , the number of pennies made before 1985 is = 15 pennies
So , the percentage is A = ( 15 / 50 ) x 100
On simplifying the equation , we get
A = 3/10 x 100
A = 30 %
Hence , the percentage is 30 %
To learn more about percentage click :
https://brainly.com/question/12861068
#SPJ1
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
The total cost that Ellie would pay with 4 snacks is $59.
The total cost that Ellie would pay with x snacks is $29 + $5x.
What is the total cost?The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.
The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.
Total cost = total cost of the tickets + total cost of the snacks
= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)
= (13 x 3) + ($5 x 4)
$39 + $20 = $59
Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39 + $5x
To learn more about cost, please check: brainly.com/question/25717996
#SPJ1
i need the answer of this 9th grade question
The amount of fabric used to make the number cube is given as follows:
C. 294 cm².
How to obtain the amount of fabric?The amount of fabric used to make the number cube is represented by the surface area of the number cube.
The surface area of a cube of side length a is given by the equation presented as follows:
S = 6a².
The side length for this problem is given as follows:
a = 7 cm.
Hence the surface area of the cube is calculated as follows:
S = 6 x 7²
S = 294 cm².
More can be learned about the surface area of a cube at https://brainly.com/question/26403859
#SPJ1
Let v = - 8i+2j, and w=-i-5j. Find 6w + 9v.
6w +9v = (Type your answer in terms of i and j.)
..
The value of the given expression in terms of i and j is -78i-12j.
Given that, v = - 8i+2j and w = -i-5j.
We need to find the value of 6w+9v.
Substitute v = - 8i+2j and w = -i-5j in 6w+9v, we get
6(-i-5j)+9(-8i+2j)
= -6i-30j-72i+18j
= -78i-12j
Therefore, the value of the given expression in terms of i and j is -78i-12j.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ1
Select the correct answer. Which statement correctly describes this expression?\left|x^3\right|+5 A. the sum of the absolute value of three times a number and 5 B. 5 more than the absolute value of the cube of a number C. the cube of the sum of a number and 5 D. the absolute value of three times a number added to 5
The expression |x³| + 5 is 5 more than the absolute value of the cube of a number.
Option B is the correct answer.
We have,
The expression |x³| represents the absolute value of the cube of a number x.
This means that no matter what value x takes (positive, negative or zero), the result of the expression will always be positive.
For example, if x = 2, then |x³| = |2³| = |8| = 8.
If x = -2, then |x³| = |-2³| = |-8| = 8.
Adding 5 to the absolute value of the cube of x means adding 5 to the positive number that resulted from |x³|.
So, if we take the examples from above, if x = 2, then the expression becomes |2³| + 5 = 8 + 5 = 13.
If x = -2, then the expression becomes |-2³| + 5 = 8 + 5 = 13.
Therefore,
The expression |x³| + 5 is 5 more than the absolute value of the cube of a number.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Triangle A and B are similar. Triangle A is shown below. The shortest side of triangle B is 10cm. What is the length of the other two sides?
Using the concept of similar triangles, the length of the other two sides of triangle B are: 20 cm and 25 cm
How to find the lengths of similar triangles?Similar triangles are defined as triangles that possess the same shape, but then their sizes may very well vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.
Since the shortest side of triangle B is 10cm, it means that it corresponds to the shortest side of triangle A which is 8 cm.
Thus:
Ratio of corresponding sides of B:A = 10/8
Thus:
Second side of triangle B: (10/8) = (x/16)
x = 160/8
x = 20 cm
Third side of triangle B: 10/8 = y/20
y = 200/8
y = 25 cm
Read more about Lengths of similar triangles at: https://brainly.com/question/11920446
#SPJ1
Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his
friends standing? Round to the nearest foot.
Write a polynomial function with the given zeros and their correspond possible answers. f(x) = Zeros 0 -6 -7 Mult. 1 3 1
[tex] - 13(t - 7) {6(t + 1) {8(t - 2)}^{?} }^{?} [/tex]
The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions have zeroes 0, - 6, - 7 with multiplicity 1, 3, 1
Hence, We can formulate;
The value of a polynomial function with the given zeros would be,
⇒ f (x) = (x - 0)¹ (x - (- 6))³ (x - (- 7))¹
⇒ f (x) = x (x + 6)³ (x + 7)
⇒ f (x) = x (x + 7) (x + 6)³
Thus, The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
Kevin wants to save $600 to buy a TV. He saves $17 each week. The amount, A (in dollars), that he still needs after w weeks is given by the following function.
A (w)=600-17w
Answer the following questions.
(a) If Kevin still needs $277, how many weeks has he been saving?
weeks
(b) How much money does Kevin still need after 5 weeks?
$?
Answer:
A) Kevin has been saving money for 19 weeks.
B) Kevin still needs $515.
Step-by-step explanation:
A) 277=600-17x /-600
-17=-323 /÷(-17)
x=19
B) x=600-17×5
x=600-85
x= 515
What is the slope of the line that passes through the points (2,-4) and (5,2)
Answer:
2.
Step-by-step explanation:
To find the slope of the line that passes through the points (2,-4) and (5,2), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (2,-4) and (x2, y2) = (5,2)
slope = (2 - (-4)) / (5 - 2)
slope = 6 / 3
slope = 2
Therefore, the slope of the line that passes through the points (2,-4) and (5,2) is 2.
This is the graph of a function in the form f(x)=a•b^x what’s the function
Answer:
Step-by-step explanation:
The function f(x) = a * b^x represents exponential growth or decay. The value of a represents the starting value or y-intercept, while the value of b represents the growth or decay factor. If b is greater than 1, the function represents exponential growth, while if b is between 0 and 1, the function represents exponential decay.
To determine the values of a and b from a graph, we need to look for specific features. The y-intercept represents the value of a, so we can read it directly from the graph. The growth or decay factor b can be found by examining the slope of the graph. If the graph is increasing, then b is greater than 1, and if it is decreasing, then b is between 0 and 1.
if u are given the midpoint of a segment and one endpoint find the other endpoint (6,2) (1,3)
The other endpoint is (11, 1).
We have,
Midpoint = (6, 2) and endpoint = (1, 3).
and, ratio of m: n = 1 :1
Using section formula
6 = ( 1 + a) / (1+1)
6 = (1+a)/2
1 + a = 12
a = 11
and, 2 = (3 + b) / (1+1)
2 = (b + 3) /2
b +3 = 4
b = 1
Thus. the other endpoint is (11, 1).
Learn more about Section Formula here:
https://brainly.com/question/30242630
#SPJ1
What the answer for radius huryyyyyyyyyy pleaseeee
Answer: 12.6
Step-by-step explanation:
150/360*2*pi*r=10.
divide to get r alone
what’s the answer? To solve the law of cosine I don’t understand this math I rly need help.
The length of u to the nearest centimeter is about 30 cm.
We are given that;'
s = 730 cm, t = 270 cm and U=125°.
Now,
The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:
c2=a2+b2−2abcosC
To find c = u. Plugging in the values, we get:
u2=7302+2702−2×730×270×cos125°
Using a calculator, we get:
u2≈912.9
Taking the square root of both sides, we get:
u≈30.21
Rounding to the nearest centimeter, we get:
u≈30cm
Therefore, by the law of cosine the answer will be 30 cm.
To know more about law of cosine visit;
https://brainly.com/question/16886213?referrer=searchResults
#SPJ1
What are the angles of rotation for a regular
pentagon? (Select all that apply)
a) 60
B) 72
c)90
d) 144
e) 180
f)216
g) 360
Answer:
c,,e,b,f
Step-by-step explanation: