a. The expression of the amount of phosphorus-32 remaining as a function of time t is A(t) = [tex]6.6\left(\frac{1}{2}\right)^{t / 14}[/tex].
b. The time when 1 gram remaining is 38.1145 days.
What is the half-life?The half-life is the amount of time it takes for half of a unstable nuclei to decay. Each substance has its own half-life.
Now, as per the question;
Exponential growth is given by the formula;
[tex]A(t)=A_0(1+r)^t[/tex]
Where,
A(t) = amount at time t.
A₀ = Initial amount of the nuclei (= 6.6)
r = rate of increasing( = -1/2; as decay is always negative)
t = time (= t/14)
Part a. Calculate the expression for the amount of phosphorus-32 remaining as a function of time t as-
Substituting all the values in the equation;
[tex]\begin{aligned}&A(t)=6.6\left(1+\left(-\frac{1}{2}\right)\right)^{t / 14} \\&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
This is the requires expression.
Part b. Calculate the time there be 1 gram remaining as;
This time can be written as A(t) = 1.
Substitute the value in the equation.
[tex]\begin{aligned}&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14} \\&1=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
[tex]\left(\frac{1}{2}\right)^{t / 14}=\frac{10}{66}[/tex]
Further solving;
t = 38.1145 days.
Thus, the time taken by phosphorus-32 to remain as 1 gram is 38.1145 days.
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f(x) = -x+5, solve for x when f (x) =-10
Answer:
x=15
Step-by-step explanation:
-x+5
-15+5
= 10
14
Starting with the number 0 and counting left
to right,
0
35
5
40
10
45
Date:
15 20 25 30
50
55
60
65
write the first number
write the fourth number
write the ninth number
Answer:
first number: 0
fourth number: 15
ninth number: 40
Write an expression that computes the difference of the variables ending_time and starting_time .
ending_time - starting_time is expression that computes the difference of the variables ending_time and starting_time.
What does a variable schedule mean?
There is an alternative to the standard 8-hour workday, five days a week work schedule: a variable work hours program. It is a program that provides staff members more freedom and control over their time, both at work and at home.What is an example of variable schedule?
A variable-ratio schedule is a partial reinforcement schedule used in operant conditioning when a response is reinforced after a variable number of responses. Using this plan, a constant, high rate of reaction is produced. Games of chance and lotteries are two excellent examples of rewards with variable-ratio schedules.An expression that computes the difference of the variables ending_time and starting_time = ending_time - starting_time
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five less than twice a number is 7 algebraic expression
nina goes to the neighborhood store to buy 14 rolls of paper towels. if she pays $20.02 in all for the purchase, how much does one roll of paper towels cost?
Answer:
$1.43
Step-by-step explanation:
To find how much one roll of paper towels cost, we have to divide the total purchase ($20.02) by the number of paper towel rolls (14).
20.02 ÷ 14
= $1.43
One paper towel roll costs $1.43
Have a lovely rest of your day! :)
You want to make 20 plates and have 30 bags of shredded cheese. How can you determine how much cheese to put on each plate so that each plate has the same amount of shredded cheese?
The amount of cheese in each plate = 1.5x
There are 30 bags of shredded cheese.
Let 'x' be the quantity of cheese in each bag. Then,
The total quantity of cheese in 30 bags = 30x
Number of plates = 20 plates
We need to determine the quantity of cheese put on each plate so that each plate has the same amount of shredded cheese.
For this we just need to divide the total amount of shredded cheese by the number of plates.
The equal amount of cheese in each of 20 plates = 30x/20
= 3x/2
= 1.5x
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Shortest
3.09 miles
3.75 miles
3.9 miles
3.5 miles
3.05 miles
Longest
Answer:
Okie Dokie
Step-by-step explanation:
short to long
3.05 < 3.09 < 3.5 < 3.75 < 3.9
The shortest distance is 3.05 miles, while the Longest is 3.9 miles.
What is the value in ordering number according to their measure?
Ordering numbers according to their measure allows us to arrange them in increasing or decreasing order, providing a systematic way to compare and analyze their magnitudes.
Arranging the given distances from shortest to longest -
3.05 miles
3.09 miles
3.5 miles
3.75 miles
3.9 miles
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Write an expression that represents the total owed for 4 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $35?
Answer:
4c + 35
Step-by-step explanation:
What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35
please help me with this problem
Answer:
The equivalent fraction of 6/9 is 4/6
Melissa rents out her barn for weddings and special events. She charges $550 for the space plus $10 per hour for utilities. The equation that represents this situation is y=10+550
Complete the following statements.
The variable,x, in this context is defined as [Drop Down 1]. The parameter is the coefficient of x, which is [Drop Down 2], and is [Drop Down 3]. The constant [Drop Down 4] is [Drop Down 5]. The variable that is the output in this context is [Drop Down 6] and represents [Drop Down 7].
drop down 1:
the hourly rate
the base fee to rent
the number of hours the barn is rented
the total amount charged to rent the barn for a certain number of hours
drop down 2:
y
10
550
drop down 3:
the hourly rate
the base fee to rent
the number of hours the barn is rented
the total amount charged to rent the barn for a certain number of hours
drop down 4:
y
10
550
drop down 5:
the hourly rate
the base fee to rent
the number of hours the barn is rented
the total amount charged to rent the barn for a certain number of hours
drop down 6:
y
10
550
drop down 7:
the hourly rate
the base fee to rent
the number of hours the barn is rented
the total amount charged to rent the barn for a certain number of hours
Answers:
Choice C) the number of hours the barn is rentedChoice B) 10Choice A) the hourly rateChoice C) 550Choice B) the base fee to rentChoice A) The variable yChoice D) total amount charged========================================================
Explanation:
The equation is y = 10x+550
If x = 0, then it leads to y = 550. This is the smallest amount paid, and it's the base fee. Think of it like the fee to get in the door. This is the y intercept of the equation.
On top of this base fee is the $10 per hour fee for utilities. Each time an hour goes by, add on another extra $10. So we attached x to this to reflect what's going on. This is the slope of the equation, aka rate of change.
It might be helpful to compare y = mx+b to y = 10x+550
m = 10 = slope = how things change
b = 550 = y intercept = starting point
----------
Example:
Let's say you rented the barn for 2 hours.
That means x = 2 and 10x = 10*2 = 20 extra dollars is added on top of the base fee of $550
total = 20+550 = 570
This is what the steps could look like when plugging in x = 2
y = 10x+550
y = 10*2 + 550
y = 20 + 550
y = 570
Therefore, renting the barn for x = 2 hours leads to a total cost of y = 570 dollars.
Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 9x2 y2 and the parabolic cylinder y = 2x2
The vector function is, r(t) = [tex]\bold{ < t,2t^2,9t^2+4t^4 > }[/tex]
Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.
First surface is the paraboloid, [tex]z=9x^2+y^2[/tex]
Second equation is of the parabolic cylinder, [tex]y=2x^2[/tex]
Now to find the intersection of these surfaces, we change these equations into its parametrical representations.
Let x = t
Then, from the equation of parabolic cylinder, [tex]y=2t^2[/tex].
Now substituting x and y into the equation of the paraboloid, we get,
[tex]z=9t^2+(2t^2)^2 = 9t^2+4t^4[/tex]
Now the vector function, r(t) = <x, y, z>
So r(t) = [tex]\bold{ < t,2t^2,9t^2+4t^4 > }[/tex]
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There are two squares with the same side lengths scaled copies of one another explain your reasoning
A square is a rectangle with equal lengths on each side. The two squares with the same length side will be lengths scaled copies of one another.
A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
As it is known that two squares are always similar to each other which is because all the angles of a square are always 90°. Therefore, any two squares are always similar to each other.
Now, as it is given that the two square have the same length sides. Therefore, the two squares with the same length side will be lengths scaled copies of one another. This is because all the sides are equal and all the angles are equal.
Hence, the two squares with the same length side will be lengths scaled copies of one another.
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Solve for e: E/e = (R + r)/r
The equation solved for e gives e = rE/(R + r)
Subject of formulaFrom the question, we are to solve for e. That is, we are to make e the subject of the given formula.
The given formula is
E/e = (R + r)/r
First cross multiply
E/e = (R + r)/r
e(R + r) = rE
Now, divide both sides of the equation by (R + r)
That is,
e(R + r)/ (R + r) = rE/ (R + r)
Thus,
e = rE/ (R + r)
Hence, the equation solved for e gives e = rE/(R + r)
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HELP EASY LOOKING FOR ANSWERS TO NUMBER FOUR
Answer:
Step-by-step explanation:
it should be Venus
hmmm. im thinking its venus
is y=10^2 linear or no linear
Answer: it is linear
Step-by-step explanation:
y = 10^2
y = 100
horizontal line going through y = 100
I don’t understand can someone help
Answer:
I plugged in your equation into Desmos and here are 5 points
Step-by-step explanation:
(-6,7)
(-5,6)
(-4,5)
(-3,6)
(-2,7)
*PLS HELP*
Suppose a and b give the populations of two states where a > b. Compare the expressions and tell
which of the given pair is greater or if the expressions are equal.
a-b
5
(select)
b
5
a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5×102nm thick, how many square meters will the oil slick cover?
The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².
What is meant by volume?Volume is defined as the amount of three-dimensional space enclosed by a closed surface.
The liter (L) is the metric system's base volume unit, with several extended volume units also available. There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.Now, as per the given question;
First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:
15×42 gal = 630 gal
This volume must be converted to square meters:
V = 630 gal × (0.00379 m³/ gal
V = 2.4 m³
The thickness (height) of a oil film in meters is required:
h = 250 nm × (m/10⁻⁹nm)
h = 2.5 × 10⁻⁷m
The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.
A = V/h
A = 2.4 m³/2.5 × 10⁻⁷m
A = 9.6 × 10⁶ m²
Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².
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find the perimeter of the polygon with vertices U (-2,4) V (3,4) and W (3,-4)
So the perimeter of the polygon with vertices U (-2,4) V (3,4) and W (3,-4) is Perimeter = 22.434
Perimeter of any close shape is the total length of the boundary of any closed shape.
We have been given vertices of polygon that are U (-2,4) V (3,4) and W (3,-4)
To find the perimeter we need to find the length of all three sides, and we do that by finding the distance between the points that form the sides:
The formula for the distance between two points is:
[tex]$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$[/tex]
side UV:
[tex]$U V=\sqrt{(-2-3)^2+(4-4)^2}=5$[/tex]
side VW:
[tex]$V W=\sqrt{(3-3)^2+(4-(-4))^2}=8$[/tex]
side UW:
[tex]$U W=\sqrt{(-2-3)^2+(4-(-4))^2}=9.434$[/tex]
So the perimeter is:
P=UV+VW+UW
[tex]$P=5+8+9.434=22.434$[/tex]
So the perimeter is: 22.434
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Which of the following shows double the sum of 8 and 4?
a. 2 *8 +4
b. 2(8 + 4)
C. 2*8-4
d. 2(8-4)
Answer:
C
Step-by-step explanation:
Error Analysis ( PLS I NEED THIS ANSWERD TODAY! :(
Mr.Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of bracelets Mr.Gonzales could buy. Solve the equation to determine the number of bracelets Mr.Gonzales could buy.
Show your work.
42.50 - 29= 13.5
13.5÷4.50=3
Answer: 3
Solve the problem correctly.
Explain, in complete sentences, the error(s) made. In your explanation, make sure to include how you can fix there error(s), how you could have checked that the answer was incorrect, and diagram/drawing yo explain your thinking.
The maximum number of bracelets Mr.Gonzales could buy is 3
How to write an equation to determine x, the maximum number of bracelets Mr.Gonzales could buyThe given parameters are:
Budget = $42.50
Shirt = $29
Bracelet = $4.50 each
Represent the number of bracelets with x
So, we have
Shirt + Bracelet * x = Budget
This gives
29 + 4.50x = 42.50
Evaluate the like terms
4.50x = 13.5
Divide both sides b 4.50
x = 3
Hence, the maximum number of bracelets Mr.Gonzales could buy is 3
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Miranda bought a square frame that has an area of 30 square inches.What is the approximate side length of the frame to the nearest tenth?
Answer:
6in lenght
Step-by-step explanation:
cause 30in square = 5 multiplied by 6 = 30
Find the sum of 2.53 x 1019 and 3.197 x 1017. 2.56197 x 1019 3.2223 x 1019 2.56197 x 1036 3.2223 x 1036
17716.09385 is sum of multiplication .
What does multiply mean?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.= 2.53 x 1019 + 3.197 x 1017 + 2.56197 x 1019 + 3.2223 x 1019 + 2.56197 x 1036 + 3.2223 x 1036
= 2578.07 + 3251.349 + 2610.64743 + 3283.5237 + 2654.20092 + 3338.3028
= 17716.09385
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Answer:
180
Step-by-step explanation:
Because its true
Nigel and Mia are searching for a treasure chest under water. The straight line distance between them is 100 meters.
A triangle has points Nigel, Mia, and Treasure Chest. The distance from Nigel to Mia is 100 meters. The angle between Treasure Chest, Nigel, and Mia is 65 degrees. The angle between Nigel, Mia, and Treasure Chest is 80 degrees.
Given the angles in the diagram, who is closer to the treasure chest and why?
Nigel is closer because his distance to the chest is opposite the larger angle.
Mia is closer because her distance to the chest is opposite the smaller angle.
Nigel is closer because his distance from the chest is 100 meters.
Mia is closer because her distance from the chest is 100 meters.
Answer:Mia is closer because her distance to the chest is opposite the smaller angle. Nigel is closer because his distance from the chest is 100 meters
Step-by-step explanation:
Answer:
B. Mia is closer because her distance to the chest is opposite the smaller angle.
Step-by-step explanation:
The answer is
B. Mia is closer because her distance to the chest is opposite the smaller angle.
Your welcome <3
The expression 162 models the distance, in feet, that an object falls during the first t seconds after being (1 point)
dropped. Find the distance the object falls in 2 seconds.
O 24 feet
O 64 feet
O 32 feet
O 16 feet
Answer:
64 Feet.
Step-by-step explanation:
First find the expression that describes the distance at t seconds. Which will be 16t^2
Now the distance is t=2.
So...
=16t^2
=16(2)^2
=64.
rewrite the following statements less formally, without using variables. determine, as best as you can, whether the statements are true or false
All of the statements are True when the expressions are evaluated using appropriate illustrations.
What are Real numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.STATEMENT: 1
Real numbers have both rational and irrational values and can thus be manipulated using arithmetic operators like addition.
As a result, the statement is correct.
[tex]1+\frac{1}{2}=1 \frac{1}{2}[/tex]
STATEMENT: 2
Real numbers can be expressed or raised to the power of another number in a variety of ways, including being squared.
2² = 4; (1/3)² = 1/9STATEMENT: 3
All positive integers have a squared value that is greater than or equal to the value.
n = 2; n² = 2² = 44 > 2STATEMENT: 4
A sum's absolute value is always less than or equal to the sum of two numbers' absolute values.
a = 3 ; b = - 4|a + b | = |3-4| ≤ |-3|+|4||-1| ≤ 3 + 4-1 ≤ 7Therefore, all of the statements are True when the expressions are evaluated using appropriate illustrations.
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The complete question is given below:
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.
a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
What are the coordinates of the point on the
directed line segment from (4, 3) to (9, 8) that
partitions the segment into a ratio of 2 to 3?
The required coordinates are (6, 5).
Let A denotes the point (4, 3), and B denotes the point (9, 8).
Let C denote the point which divides the line segment AB in the ratio of 2:3.
The distance between A(4, 3) and B(9, 8) is given by
AB = √{(x₂ - x₁)² + (y₂ -y₁)²}
= √{(9 - 4)² + (8 - 3)²
= √{5² + 5²}
= √(2×5²)
= 5√2
We have AC + BC = AB
AC and BC are in the ratio 2:3.
Therefore 2x + 3x = AB
⇒5x = 5√2
⇒x = √2.
Therefore, AC = 2√2 and BC = 3√2.
Using the distance formula,
AC = √{(x - 4)² + (y - 3)²}
⇒ 2√2 = √{(x - 4)² + (y - 3)²}
⇒ √(2² + 2²) = √{(x - 4)² + (y - 3)²} (taking the 2 inside the square root.)
⇒ x - 4 = 2 ⇒ x = 6
⇒ y - 3 = 2 ⇒ y = 5.
Therefore the required coordinates are (6, 5).
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________ is a statistical measure of how much scores in a sample vary around the mean. multiple choice normal distribution standard deviation frequency accuracy
Standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Therefore, the standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
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The sum of 5 times a number m and 12 is equal to 27
The value of m is 3
How to calculate the value of m ?The expression can be written as follows
The sum of 5 times a number m and 12 is equal to 27
5m + 12 = 27
collect the like terms
5m= 27-12
5m= 15
Divide both sides by the coefficient of m which is 5
5m/5 = 15/5
m= 3
Hence the value of m is 3
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The solution to a system of equations is (2,-4).one equation in the system is 2x+y=0.explain how you can find a second equation for the system.then find a second equation.solve by system of equations to justify your answer
The second equation is 3x + y = 2.
Let the other equation be of the form ax + by = c, where a, b and c are constants.
Given equation is 2x + y = 0
We have, a₁ = 2 and a₂ = 1
And b₁ = a and b₂ = b
Since, both equations have a unique solution,
∴ a₁ ÷ b₁ ≠ a₂ ÷ b₂
2 ÷ a ≠ 1 ÷ b
2b ≠ a … (1)
Also, (2, -4) is the solution of the equations, so it will satisfy the equations
2a - 4b = c
b = (2a - c)/4
Let c=2
b = (2a - 2) ÷ 4
b = 1
Now we can take any value for a and b which satisfy eq.(1)
Let a=3
b = (2(3) - 2) ÷ 4
b = 1
Thus, a = 3 and b=1 satisfy eq.(1)
Hence the second equation is 3x + y = 2
The equations are justified by keeping the values -
2x+y=0 ... (2)
3x+y=2 ... (3)
From eq.(2),
y=-2x
Putting value of y in eq. (3), we get,
3x+(-2x)=2
3x-2x=2
x=2
Now, putting x=2 in eq.(2)
2(2)+y=0
y=-4
Hence, the solution is justified.
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