a) The estimated population which takes time to get double is 63.36.
b) The estimated population which takes time to get triple is 100.42.
The growth equation is A(t) = [tex]A_0e^{kt}[/tex] where A(t) is the quantity at time t, A₀ is the initial quantity, k is a positive constant, and [tex]e^{(x)}[/tex] is the natural exponential function. For A₀ = 7.1E9 (7.1 billion) and k = 0.011 (1.1%):
Given formula:
A(t) = [tex]A_0 e^{kt}[/tex] --------------------------- (1)
A(t) = [tex]7.1E9e^{0.011t}[/tex] ----------------------------(2)
a) We have to find twice the population, or if A(t) = 2A₀. For doubles (or multiples of A₀₎, equation (1) can be written as
A(t) = [tex]A_0e^{0.11t}[/tex]
⇒ 2A₀ = [tex]A_0e^{0.11t}[/tex], (replaces A(t) = 2A₀)
⇒ 2 = [tex]e^{0.011t}[/tex],
⇒ ln(2) = ln(e0.011t ),
⇒ ln(2) = 0.011t,
⇒ ln(2)/0.011 = t
Therefore,
t = 63.36
b) Now we will find the number of years it will take the population to be triple of its size.
7.1 × 3 = [tex]7.1(1.011)^t[/tex]
⇒ [tex]\frac{7.1 * 3}{7.1}[/tex] = [tex]1.011^{t}[/tex]
⇒ 3 = [tex]1.011^{t}[/tex]
Now, Using the logarithm:
ln(3) = ln [tex](1.011)^{t}[/tex]
⇒ t = 100.42
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what is the the difference between a repeating decimal and a nonstop decimal on the rational numbers chart
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. Recurring numbers is another name for these figures. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
A repeating decimal can be a rational number, and any integer is a rational number since it can be expressed as a fraction by simply assigning it a denominator of 1. Then, by multiplying and dividing the decimal according to its place values, we can also state that a terminating decimal can be expressed as a fraction.
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(redo) A mistake was made in the steps shown to simplify the expression. which step includes the mistake?? EDMENTUM
The step in which there was a mistake in the simplification of the expression is given as follows:
A. Step 5.
How to simplify the expression?The expression in this problem is defined as follows:
(1 + 3²)/5 + |-10|/2
The first step is applying the absolute value of -10, which is the distance of -10 from the origin of 0, hence it is of 10 and the expression is given then by:
(1 + 3²)/5 + 10/2.
Then the square is applied to 3², as 3 x 3 = 9, hence:
(1 + 9)/5 + 10/2
The parenthesis takes precedence, hence:
10/5 + 10/2.
The first quotient takes precedence, hence:
2 + 10/2.
Then in Step 5 there was the mistake, as the quotient takes precedence over the addition, meaning that the expression should have been simplified as follows:
2 + 5 = 7.
This means that option A is correct.
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Identify the slope and y-intercept of each linear function's equation. X -3=4 slope = 1; y-intercept at -3 y=1-3x slope =-3; y-intercept at 1 y = 3x. - 1 slope =-1; y-intercept at 3 -x+3=y slope = 3; y-intercept at -1
Using slope-intercept form, the slope and y-intercept of the equation are 1 and - 7 respectively
Slope and Y-interceptThe slope-intercept formula is often used to calculate or identify the slope, the y-intercept, the x-intercept, or the equation of a straight line in the equation.
The slope of the line is defined as the rate of change of the y - axis to the change in the x - axis.
The formula is represented as;
m = Δy / Δx
where Δ represent the change
The y-intercept of a line is the point at which the line touches the y-axis of the graph.
With these information, we can write a slope-intercept form of a straight line which is given as;
y = mx + c
m = slopec = y-interceptIn the given question;
x - 3 = 4
Let's collect like terms
x - 3 - 4 = x - 7
The equation can be rewritten as y = x - 7
In this case, the slope is 1 and the y-intercept is - 7
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Try it #3
Pls help!
Find the biggest common factor between the ratio's two terms to write the ratio in its simplest form. The largest number that equally divides both numbers is known as the greatest common factor of two numbers.
How do you express a ratio in its simplest form?1 : 1/2 = 2 : 1
Add whole numbers to the values.
Create a fraction with the full number 1 as the denominator.
Next, we have:
1 : 1/2 = 1/1 : 1/2
Remove the denominators from fractions to convert them to integers.
We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.
1 1/3 : 4 4/7 = 7 : 24
There are now:
1 1/3 : 4 4/7 = 4/3 : 32/7
Remove the denominators from fractions to convert them to integers.
We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.
0.360 : 0.153 = 40 : 17
Add whole numbers to the values.
By multiplying both sides by 103 = 1000 to remove all three decimal places, you can convert any decimal values to integers.
Next, we have:
0.360 : 0.153 = 360 : 153
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PLEASE HELP WILL MAKR BRAINLIEST! Solve for y!!
Answer:
Below
Step-by-step explanation:
All of the angles are the same (their opposite sides are =)....it is an equilateral triangle
all of the angles sum to 180°
each angle is then 60°
5y+10 = 60
5y = 50
y = 10 °
Which equation is represented by the graph below
Answer: pls show list of equations
Step-by-step explanation:
write an equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4
An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.
What is Parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
12 = 4(9) + b
12 = 36 + b
b = -24
The equation will be y= 4x -24.
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k3-4j=12,wen k =8,j=2
With the Application of Arithmetic operators the value of given equation is 492.
what is Arithmetic operators?
an operator that works with groups and numbers in arithmetic. The prefix and the binary plus (+) and minus (-) symbols are the only arithmetic operators in AHDL that are supported for Boolean expressions.
solution:
sub k =8,j=2 in equation k^3-4j = 12
Therefore, (8)^3 - 4 (2) = 12
512 - 8 - 12 = 0
492 is the value.
Therefore the value of given equation is 492
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Complete Question:
What Is The Answer
k3 - 4j +12, when k=8, j=2
Solve the equation below. Only 1 term should be entered in each blank space.
Begin by reducing the fraction on the left by the greatest common factor and entering the new denominator
Since the terms on the left side of the equation are all divisible by that denominator, simplify the left side of the equation
Answer:
it's not easy but I'll try my best when I get the answer I'll come back thanks
Given MN is perpendicular to MP, PQ is perpendicular to MP, and NR is congruent to OR. Prove triangle NRP is congruent to triangle QRM
1. [tex]\overline{MN} \perp \overline{MP}[/tex], [tex]\overline{PQ} \perp \overline{MP}[/tex] (given)
2. [tex]\angle NMP[/tex] and [tex]\angle MPQ[/tex] are right angles (definition of perpendicular lines)
3. [tex]\angle NMP \cong \angle MPQ[/tex] (all right angles are congruent)
4. [tex]\overline{NR} \cong \overline{QR}[/tex] (given)
5. [tex]\angle NRM \cong \angle QRP[/tex] (vertical angles)
6. [tex]\triangle PRQ \cong \triangle MRN[/tex] (AAS)
7. [tex]\overline{MR} \cong \overline{RP}[/tex] (CPCTC)
8. [tex]\angle NRP \cong \angle MRQ[/tex] (vertical angles)
9. [tex]\triangle NRP \cong \triangle QRM[/tex] (SAS)
I need help with these
Answer:
[tex] = \frac{11}{10} \\ \\ [/tex]
this is the correct answer for first question
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 100 m, find Its area.
Answer:4
Step-by-step explanation:
rectangular prism 1 829 equals the conterpostiive
Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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Using composition of functions, determine if the two functions are inverses of each other. A. No, because the functions contain different operations. B. Yes, for all values x ≥ 0. C. No, because the composition does not result in an answer of x. D. Yes, because F(x) is equal to –G(x).
Yes, for all values x ≥ 0. If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other.
What is composition of functions?Composition of functions is a mathematical operation that involves combining two functions to form a new function. To determine if two functions are inverses of each other using composition of functions, we need to first define the two functions and then determine if the composition of the two functions is equal to the identity function (f(x) = x).If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other. In this case, the correct answer is B: Yes, for all values x ≥ 0.To learn more about composite functions refer :
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yes Are these polygons congruent? 1.5 cm 4 cm 3 cm no 2 cm
Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The
area of the patio is 350 ft2. Find the base. Round your answer to the nearest foot.
Hint : Use A = bh.
We may calculate our answer using fractions and the fact that the base is 18.3 feet.
What are fraction ?The components of a whole or group of items are represented by fractions. A fraction consists of two components.
The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.
According to our question-
The patio is 280 square feet in size. locate the base.
Height = 5x Area = 280 feet square
Base = 6x
The parallelogram A's area can be expressed mathematically as;
Base + height equals area.
A = b×h
the values of area, base, and height are substituted.
280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)
Given that the base is 6x,
swapping out x's value.
Base = 6x = 6(√(280/30))
Base=18.3 feet
18.3 ft tall is the base
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Answer:
At short 18.7 ft is the answer
In an exhibition, the cost of tickets for an adult is ₹5 more than thrice the cost of ticket for a child. Which equation relates the cost, , of adult ticket in terms of the cost, , of child ticket?
In an exhibition, the cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Equation relates the cost, y, of adult ticket in terms of the cost, x, of child ticket.
Cost of Adult ticket = y
cost of child ticket = x
cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.
=> cost of tickets for an adult = 5 + 3 (cost o f ticket for a child.)
=> y = 5 + 3x
=> y = 3x + 5
Equation is y = 3x + 5
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In the formula for average rate of change, what does the triangle in front of the x and y stand for? a. interval between x and y c. delta notation-change in y over change in x b. initial value of x and y d. the percent rate of change of y and x
The triangle in front of the x and y represents the ratio of the change in y to the change in x. Option C is the correct choice based on this interpretation.
The calculation involves determining the average rate of change between two given points, namely (x₁, y₁) and (x₂, y₂).
The average Rate of Change is given by, = ∆y / ∆x
where ∆y represents the change in the y-values [tex](y_2_-y_1)[/tex], and ∆x represents the change in the x-values [tex](x_2 - x_1)[/tex] between the two points on the function.
In the average rate of change formula, the triangle symbol (∆) preceding the x and y denotes the delta notation, which signifies "change in." More precisely, it indicates the change in y divided by the change in x.
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Find the inverse of the function f(x) = 3x + 2. State the answer in slope-intercept form.
suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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STEP BY STEP please help me asap please !!!???
Answer:
(A) 19 times, 16 people.
Step-by-step explanation:
There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.
The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.
Since the Caterpillar cannot run a fraction of a time, it must run 19 times.
There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.
Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.
Tell me if this helped :)
Hello can someone help me out with these two questions!?!?! This will help me a lot thank you! :D
The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The inequalities are,
2( x +6 ) > -6( x +1) +2
2x + 12 > -6x - 6 + 2
2x + 6x > -12 - 6 +2
8x > -16
x > -2
-3x - 1 ≥ 20
-3x ≥ 21
x ≥ -7
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75 points
Which statement is true about the relationship between the amount of plant food remaining and the number of days?
A. This relationship is not a function because only one amount of plant food remains each day.
B. This relationship is a function because only one amount of plant food remains each day.
C. This relationship is not a function because more than one amount of plant food remains each day.
D. This relationship is a function because more than one amount of plant food remains each day.
Answer:
Step-by-step explanation:
it is A/ this relationship is not a function because only one amount of plant food remains each day.
Answer:
it is A/ this relationship is not a function because only one amount of plant food remains each day.
Step-by-step explanation:
Which equation is linear?
-3
O y = 2+4
O y = 4x³ - 10
Oy= 3x (x - 2)
0y = 2-5
4
simplify the expression. be sure to show or explain how you arrived at your answer (-6i)(4i)
Answer:
hi no ugh I pero Eresi me gusta la
Find the value of a if the line line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x +a
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.
To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:
y = -x + 4
f(x) = x^2 - 5x + a
Then, we can substitute the equation for the function into the equation for the line:
-x + 4 = x^2 - 5x + a
We can then solve this equation for a by moving all the terms to one side:
-x + 4 - x^2 + 5x = a
-x^2 + 6x - 4 = a
We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.
The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:
2x - 5 = -1
2x = -6
x = -3
Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:
f(-3) = (-3)^2 - 5(-3) + a
f(-3) = 9 + 15 + a
f(-3) = 24 + a
Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:
y = -(-3) + 4
y = 3 + 4
y = 7
Substituting this back into the equation for the function, we get:
f(-3) = 24 + a = 7
a = 7 - 24
a = -17
Therefore, the value of a is -17.
what do you mean by tangent?
A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.
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Michael and Maria saw 6 cupcakes on the table. Michael ate 1/3 of the cupcakes. Maria ate 1/2 cupcakes. How many cupcakes are left on the table?
A:1 cupcake
B:1 1/2 cupcakes
C:4 2/5 cupcakes
D:2 cupcakes
Answer: The answer is C
Step-by-step explanation:
6- 1/3 - 1/2 = 4 2/5
By the way, you cannot make a negative number of donuts or pizzas.
Using x for the number of donuts produced each hour and y for the number of pizzas for each hour, choose the inequality/inequalities to represent this constraint.
The required inequality for the pizzas and donuts can be represented as, nx + ny > 0.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Number of donuts produced each hour = x,
And number of pizzas produced each hour = y.
Let for n hours, donuts and pizzas are produced.
So the inequality for the positive number of pizzas and donuts, the inequality can be presented as,
nx + ny > 0
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To represent the constraints, the inequalities are x ≤ n and y ≤ m.
What is an inequality?When two expressions or values are not equal to one another, this connection is referred to as "inequality" in mathematics.
Let you can make at most n numbers of donuts per hour.
If x represents the number of donuts produced per hour.
To write an inequality to represent this:
x ≤ n.
And also, you can make at most m number of pizzas per hour.
If represents the number of pizzas produced per hour.
To write an inequality to represent this:
y ≤ m.
You may use a variety of methods to eliminate the inequality, including multiplying or dividing each side by the same positive number, adding or subtracting the same amount from each side, and more. If either side is multiplied or divided by a negative value, the inequality sign must be reversed.
Therefore, the inequalities are x ≤ n and y ≤ m.
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When solving an equation, Tina gets to the last of line of her work and is left with "7=7." What does this mean?
A
The solution is 7.
B
There is infinite solutions.
C
There is only one solution.
D
There is no solution.
The last line of a solution is 7 = 7. It means there is infinite solutions.
What are types of solution of linear equation?
The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
The set of linear equations can have one of three different sorts of solutions. As follows:
1) unique solution
2) No solution
3) Infinite solutions
Given that the last line after solving an equation is 7 = 7.
Since the LHS and RHS of the equation is same thus it has infinite many solution.
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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?
Answer:D. y = 3/4x + 1
