One of the common terms for exponential decay is half-life, which refers to the period of time it takes for a quantity to fall by an exponential rate and halve its initial value.
What is meant by exponential decay function?In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. It can be written as [tex]y = a(1 - b)^x[/tex], where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.
The time it takes for a quantity to drop by an exponential rate to halve its initial value is known as the half-life, which is one of the popular words used to describe exponential decay.
Each 20 minutes there is 1/2 as much one hour is 3 half lives :
start 30 then 15 then 7.5 then 3.75 gm
30(1/2)3 = 3.75 gm
The complete question is;
Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left from a 30-gram sample after 1 hour.
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Amelia used 6 liters of gasoline to drive 48 kilometers. How many kilometers did Amelia drive per liter?
The square above has an area of 100. If Q is the
midpoint of AC and R is the midpoint of BD, what
is the area of the shaded area?
Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.
The definition of surface areaThe surface area of an object is an estimate of the entire amount of space it takes up. A three-dimensional shape surface area refers to the entire area surrounding it. The overall area of a muti shape is its surface area. The surface area of a cuboid can be calculated by adding the faces of each of its six rectangular sides. The following equation could be used to name the box's dimensions: Surface (SA) equals 2lh, 2lw, and 2hw. The surface area of a three-dimensional shape represents the overall area.
Here,
Square has an area of 100 a 2 = 100 a=10
QC=(1/2) AC=10/2=5,
BR=(1/2), and BD=10/2=5.
CD=AB=10=AC=BD
size of the triangle QCD is defined as: =(1/2)QCCD
= >(1/2)510=25.
size of the triangle ABR is =(1/2) ×AB×BR
=>( 1/2 ) ×10×5=25
Area of the darkened area equals area of square 2 area of triangles,
which is 100 (25+25)=50.
Area of the shaded area equals 50.
Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.
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The highest temperature ever recorded for a person with a fever who survived was 115 degrees. Alternatively, the lowest temperature ever recorded on a patient who survived was 56.7 degrees. If the average temperature is 98.6 degrees, which extreme temperature was furthest from the norm? How much further?
Answer:
The lowest temperature recorded is the furthest away from the average norm by 41.9 degrees.
Step-by-step explanation:
115-98.6= 16.4
98.6-56.7= 41.9
john wants to buy a bicycle worth R750 . how many hours should he work to earn R750
Answer: To determine how many hours John needs to work to earn R750, you would need to know his hourly wage. If John earns R50 per hour, he would need to work 15 hours to earn R750 (R750 / R50/hour = 15 hours). If his hourly wage is different, the number of hours he needs to work will be different.
Step-by-step explanation:
QS bisects PQR and m/PQR = 119°.
Find m/PQS and m/RQS.
Q
m/PQS = ?
m/RQS =
Therefore , the solution to the given problem of angles comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Define angles.
An angled structure in geometry is composed of two rays that converge at the vertex, or core, of the angle. These rays are referred to as the angle's faces. Depending upon where they are situated, two beams may be able to form any angle within a plane. The intersection of two planes also produces an angle. Diahedral angles are the name for them. Light beams or lines that share the same endpoint in plane geometry can have a wide variety of shapes or angles. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of the two rays is known as the vertex, or vertex of the angle.
Here,
QS cuts an angle. PQR, followed by ∠SQR = ∠ PQS and
∠PQS + ∠RQS = ∠PQR.
The equation then changes to
∠PQR = ∠PQS + ∠PQS
∠PQR = 2∠PQS
∠PQS equals ∠PQR/2
assuming∠ PQR = 119°
Replace in the resulting expression from the above;
∠PQS equals ∠PQR/2
∠PQS = 119/2
∠PQS = 59.5°
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Therefore , the solution to the given problem of angle comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
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125y - 5 -50y pls help lol
Answer:
The expression is a mathematical representation of an algebraic problem. The final form of the expression would be 75y -5 after combining like terms.
Here's the breakdown of the steps:
125y - 5 - 50y = (125-50)y -5 = 75y - 5
So the final simplified form of the expression is 75y -5.
At the independent record company where Chase works, the vinyl format has been experiencing a resurgence in popularity. Record sales are increasing by 6% each year. If 260,090 records were sold this year, what will annual sales be in 4 years?
If necessary, round your answer to the nearest whole number.
The annual sales is 322,511.6 in 4 years.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Record sales are increasing by 6% each year.
And, 260,090 records were sold this year.
Now, We have;
Record sales are increasing by 6% each year.
Hence, After 4 years;
The annual sales = 260,090 + 4 × 6% of 260,090
= 260,090 + 4 × 6/100 × 260,090
= 260,090 + 62,421.6
= 322,511.6
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Answer:328,358
Step-by-step explanation:
ANYONE GOOD AT MATH COME ON OVER AND HELP A FELLOW SLOW PERSON PLEASE WILL GIVE 30 POINTS!!!
The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x)) included is presented as follows;
[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]
f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different
What are composite functions?Composite functions are functions in which the input or argument are also functions.
The values of the composite functions based on the defined functions are found as follows;
f(x) = x² + 1, g(x) = -2·x + 5
Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;
f(x) = x² + 1
f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1
-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1
4·x² - 10·x - 10·x + 25 + 1 = 4·x² - 20·x + 26
When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = -2·x + 5
f(x) = x² + 1
g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5
g(f(x)) = -2·x² + 3
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;
f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4
2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16
f(g(x)) = 2·x² + 10·x + 16
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = x + 3
f(x) = 2·x² - 2·x + 4
g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7
g(f(x)) = 2·x² - 2·x + 7
When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;
f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]
g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4
g(f(x)) = 2·x - 4
The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.
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Pleaseeeee help me i need the full answer for everything single one please I WILL GIVE MORE POINTS
Answer:
Step-by-step explanation:
it depends on where each point is on each chart because they can't be blank
Use the distributive property to write an equivalent expression. Then
evaluate the expression.
(9+3)
Equivalent Expression
=
The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression 2/5(s + 20)
Using distributive property
2/5s+2/5*20
2/5s+2*4
2/5s+8
and (9+3)=12
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Right question:-
Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).
4. To which set of numbers does the number belong? (1 point)
√51
Orational numbers
O irrational numbers
O integers
Onatural numbers
Brandon wants to use the Distributive Property to figure this problem out. What should be his next step?
8 × (10 + 7)
Answer: (8*10) + (8*7)
Step-by-step explanation: This would be distributing the 8 to both numbers while still adding the two products
Answer: 136
Step-by-step explanation:
When you do distributive Property, you are multiplying everything right before the parenthesis, with everything inside the parenthesis.
8 x (10 + 7)
1. Multiply 8 by 10 to get 80
2. Multiply 8 by 7 to get 56
Now you have: (80 + 56)
3. Add the numbers
80 + 56 = 136
Determine the graph that represents a function. On a coordinate plane, a circle is shown that crosses the x-axis at (negative 5, 0), the y-axis at (0, 5), the x-axis at (5, 0), and the y-axis at (0, negative 5). On a coordinate plane, a parabola opens to the left. It crosses the y-axis at (0, 3) and (0, negative 3), and the x-axis at (9, 0). On a coordinate plane, a straight line with a positive slope crosses the y-axis at (0, negative 2) and the x-axis at (1.2, 0).
Answer: The graph that represents a function is the parabola that opens to the left.
This can be determined by the following characteristics of the graph:
It is a parabola because it opens to the left and has a vertex on the y-axis.
It crosses the y-axis at (0, 3) and (0, negative 3), which means that it is symmetric about the y-axis, and also it crosses the x-axis at (9, 0) which means that it is a function.
A circle is not a function because, for any value of x, there are two different values of y that can be plotted on the graph (i.e. the point (5,0) and (-5,0) produce two different y values)
A straight line with a positive slope is not a function because, for any value of x, there is only one value of y that can be plotted on the graph.
So the parabola is the graph that represents a function.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
i need help please i don’t get thus
According to the solving the lengths of right angle triangle using Pythagorean theorem x = 6, y = 3
How does the Pythagorean theorem work?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
According to the given information:The following is one way to perform the calculation. It may not be the best way.
c = b/cos(α)
= 6
a = √c2 - b2
= √62 - 5.192
= √9.0639
= 3.01063
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A decimal number is represented by (3 x 110) + (5 x 1100) + (8 x 11000).
Question 1
Which decimal is represented by the given expansion?
Responses
A 35.835.8
B 0.03850.0385
C 0.3580.358
D 3.58
8. Use the bar diagram to write an equation. Then
solve for x.
X
Total
7
X
5
X
Answer: 12, 16, 20, and 320.
Step-by-step explanation:
The value of x can be solved as follows, take note of the numbers you will need to drag to complete the equations:
4x + 12x = 320 (segment addition postulate)
16x = 320 (combining like terms)
x = 20 (dividing both sides by 16)
We would end up with the value of x, which equals 20.
Numbers that we end up using are: 12, 16, 20, and 320.
Make use of one of De Morgan's laws to write the given statement in an equivalent form.
She did not visit France and she did not visit Italy.
The statement "She did not visit France and she did not visit Italy" using De Morgan's laws will be C. She did not cost France if a only if she did not visit Italy.
What is De Morgan law about?The complement of the product of all terms is equal to the complement of each term added together. Similarly, the product of the complements of each term equals the complement of the sum of all the terms.
The intersection of their complements is the complement of the union of two sets, and the union of their complements is the complement of the intersection of two sets.
In conclusion, the correct option is C.
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The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
What is the value of y when x = 28?
The value of y when x = 28 in the proportional relationship is 112.
How to find the value of y in the proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
Therefore, let's find the constant of proportionality.
y = kx
14 = 3.5k
divide both sides by 3.5
k = 14 / 3.5
k = 4
Let's find the value of y when x = 28.
Hence,
y = 4x
y = 4 × 28
Therefore,
y = 112
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sometimes a change of variable can be used to convert a differential equation into a separable equation. one common change of variable technique is as follows. consider a differential equation of the form , where , and are constants. use the change of variable to rewrite the differential equation as a separable equation of the form . solve the initial value problem (a) help (formulas) (b) help (formulas)
The differential equation is [tex]y=\frac{-7t^2+22t-7}{7t-22}[/tex]
We are given the Initial value problem:
y'=(t=y)²-1, y(3)=4
Substitute the value z=t+y
When t=3 and y=4 then z=3+4=7
y'=z²+1
Differentiate z w.r.t t
[tex]\frac{dz}{dt} =1+y'[/tex]
Then, we get [tex]z'=1+z'-1=z^2[/tex]
z⁻²dz=dt
Integrate on both sides:
-1/zdz=t+c
z=-1/t=c
Substitute t=3 and z=7
Then, we get
7=-1/3+c
21+7c=-1
7c=-1-21=-22
c=-22/7
Substitute the value of C then we get:
z=-1/t-22/7
z=-7/7t-22
y=z-t
y=-7/7t-22-t
y=-7-7t²+22t/7t-22
y=-7t²+22t-7/7t-22.
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Scale factor from smaller to larger of THIS triangle
The scale factor in the image depicting a similar triangle is solved to be
1.4When are triangles said to be similar?The term similar triangles as used in geometry means that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence when the size of the triangles are in equal proportions and the size of the angles are equal then the triangles are said to be similar triangles
Examining the figure shows the scale factor is sought as follows
using side 28
let the scale factor form smaller to larger be k
k = length of larger side / length of smaller side
k = 28 / (28 - 8)
k = 28 / 20
k =1.4
The scale factor is 1.4
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(x'2-3x+5) dived (x-1)
The quotient of the division (x^2-3x+5) divided (x-1) is x - 2 with a remainder of 3
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
(x^2-3x+5) divided (x-1)
Using the long division method of quotient, we have
x - 1 | x^2 - 3x + 5
The division steps are as follows
x - 2
x - 1 | x^2 - 3x + 5
x^2 - x
------------------------------------------------
-2x + 5
-2x + 2
------------------------------------------------
3
Hence, the quotient is x - 2
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What is the equation of a circle with a radius of 4 and a center located at (2,3)
Answer:
x² + y² - 4x - 6y - 3 = 0
Step-by-step explanation:
Formula for equation of circle when the radius r and centre (a,b) is given:
(x-a)² + (y-b)² = r²
(x-2)² + (y-3)² = 4²
Expanding the brackets;
x² - 4x + 4 + y² - 6x + 9 = 16
x² + y² - 4x - 6x + 4 + 9 = 16
x² + y² - 4x - 6x + 13 = 16
x² + y² - 4x - 6x + 13 - 16 = 0
x² + y² - 4x - 6x - 3 = 0 Ans.
what is 2 over x to the power of 2 equivilent to
The equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
How to obtain the equivalent exponential expression?The expression for this problem is defined as follows:
(2/x)².
We have a fraction that is squared, meaning that both the numerator and the denominator are squared, hence:
2² = 4.x².This means that the equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
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Suppose f(x)=2x-8, evaluate f(7) =
Answer:
6
Step-by-step explanation:
f(x)=2x-8
f(7)=2(7)-8
f(7)=6
Answer:
Step-by-step explanation:
f(7)=2x-8
f(7) = (2)(7)-8
f(7) = 14-8
f(7) = 6
I am looking for a hard equation that equals to number 41.
Answer:
[tex]\bf x+23=64[/tex]
Step-by-step explanation:
you can try x+23=64
Let's solve it:-
[tex]\sf x+23=64[/tex]
Subtract 23 from both sides:-
[tex]\sf x+23-23=64-23[/tex]
[tex]\bf x=41[/tex]
__________________
Hope this's what you're looking for!
Have a great day!
Answer:
How about this:
290 / 8 * 2 - 31.5
Step-by-step explanation:
I dunno if that's hard enough, but there you go!
Suppose f(x)=−3x^2+ 6x +3 find f(-2) +f(2)
Answer:
-18
Step-by-step explanation:
In a triploid of genotype B/b/b, what proportion of gametes will be B? A) 1/2 B. 1/3 C.1/8
D. 1/4
E. 1/6
Answer:
I think it’s D
Step-by-step explanation:
trust
Zara part 2.4 pounds of grapes in the watermelon that cost $5.28. The total cost of the food was $7.32 which describes a way to determine X the price per pound for the grapes?
The way to determine x, which is the price per pound of the grapes is B. Subtract 5.28 from 7.32 and then divide the difference by 2.4.
How to find the price per pound ?To find the price per pound of the grapes, you first needed to find the price of the grapes alone, without the cost of the watermelons.
This price of the grapes can be found by the formula :
= Total cost of fruit - Cost of watermelon
= 7. 32 - 5. 28
= $ 2. 04
Then, you can find the cost of each pound of grapes by the formula :
= Cost of grapes / Pounds of grapes purchased
= 2. 04 / 2 . 40
= $ 0. 85
In summary, you can find the price per pound of the grapes when you Subtract 5.28 from 7.32 and then divide the difference by 2.4.
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The full question is:
Zara bought 2.4 pounds of grapes and a watermelon that cost $5.28. The total cost of the fruit was $7.32. Which describes a way to determine x, the price per pound for the grapes?
Divide 7.32 by 2.4 and then subtract 5.28 from the quotient. Subtract 5.28 from 7.32 and then divide the difference by 2.4. Solve for x in the equation 2.4x - 5.28 = 7.32. Solve for x in the equation 2.4 (x + 5.28) = 7.32.Enter the Correct 4 Character LETTER Code (Capital letters and no spaces) *
Please help
<3
Answer:
rawr :)
Step-by-step explanation:
PLEASE HELP ASAP!!!
I'd really appreciate the help, thanks in advance.
The questions below can be solved using the relation between angular size, physical size and distance. For the questions below, provide a complete solution with explanation.
1. Find the Sun's diameter. The sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. What is the sun's approximate physical diameter? Compare your
answer to the actual value of 1 390 000 km.
2. Find a Star's Diameter. The supergiant star Betelgeuse (in the constellation Orion) has a measured angular diameter of 0.040 arcsecond from Earth and a distance from Earth of 720 light-years. What is the actual diameter of Betelgeuse? Compare your answer to the size of our Sun and the Earth-Sun distance.
The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.
How to calculate the diameter?From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:
= 0.5π / 180
= 0.008727 radians
Distance from the sun = 150 × 10^6
The physical diameter of the sun will be:
= 150 × 10^6 × 0.008727
= 1309000km
The difference between the diameters will be:
= 1390000 - 1309000
= 8.1 × 10^4.
The percentage of difference will be:
= (8.1 * 10^4) / 1390000 × 100
= 5.8%
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