Answer:
P = 72.5 * e^(0.025t)
Step-by-step explanation:
Here's a step by step solution with all the details and calculus involved.
(a) Express P as a function in the form P = Poat.
Since the population is growing continuously at a rate of 2.5% per year, we can use the formula for continuous growth:
P = Po * e^(rt)
where Po is the initial population (72.5 million), r is the continuous growth rate (0.025), and t is the time elapsed in years since 2004.
The continuous growth rate, r, is related to the annual growth rate, g, by:
r = g / 100
So, the continuous growth rate is 0.025.
Substituting the values into the formula for continuous growth, we get:
P = 72.5 * e^(0.025t)
This is the expression for the population as a function of time in the form P = Poat.
(b) Express P as an exponential function using base e.
The exponential function using base e is already in the desired form. So, we can simply write:
P = 72.5 * e^(0.025t)
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How can using a 'Polygon Family Tree' help you to classify 2D figures into a hierarchy of sets and subsets?
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
What are plane figures?A figure that totally resides in one plane is referred to as a plane figure or a two-dimensional figure. Two-dimensional figures are drawn when you sketch, whether by hand or with a computer programme. Two-dimensional models of actual objects can be found in blueprints.
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
How do you classify 2D figures?Circles, triangles, squares, rectangles, pentagons, quadrilaterals, hexagons, octagons, and other basic 2D shapes include these. All shapes—aside from the circle—are categorized as polygons because they have sides. Regular polygons are those with equal sides and angles on all of their faces.
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Is the pair of events dependent or independent? Explain 14. You pick a number between 1000 and 5000. Then you flip a coin.
Answer:
Step-by-step explanation:
Here is a step-by-step explanation of the independence of the pair of events of choosing a number between 1000 and 5000 and flipping a coin:
Understanding the definition of independent events: Independent events are events that have no influence on each other. The outcome of one event does not affect the outcome of the other.
Event 1: Choose a number between 1000 and 5000: This event involves randomly selecting a number within the specified range.
Event 2: Flip a coin: This event involves flipping a coin and observing whether it lands on heads or tails.
Check for influence: To determine whether the events are independent, we need to check if the outcome of one event affects the outcome of the other. In this case, the outcome of the coin flip has no effect on the number you choose, and your choice of number has no effect on the outcome of the coin flip.
Conclusion: Since the outcome of one event does not affect the outcome of the other, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are considered independent.
So, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are independent events.
A sports trophy is in the shape of a cup
30 cm high. The winners are each given
copies of the cup, 7 cm high. One of the
copies holds 100 ml. What is the capacity of the trophy in liters?
The capacity of the trophy that us 30 cm high is 0.4286 liter
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
7 cm height cup holds 100 ml. Therefore:
7 cm = 100 ml
For a 30 cm height trophy:
30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml
1000 ml = 1 l
428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter
The capacity of the trophy is 0.4286 liter
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PLEASE HELP ME AS QUICK AS POSSIBLE !!
Answer:
1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0
Step-by-step explanation:
You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.
SimplificationThe expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.
[tex]\dfrac{1}{a^2+ab}+\dfrac{1}{ab+b^2}=\dfrac{1}{a^2+ab}\cdot\dfrac{b}{b}+\dfrac{1}{ab+b^2}\cdot\dfrac{a}{a}=\dfrac{b+a}{a^2b+ab^2}\\\\=\dfrac{a+b}{ab(a+b)}=\boxed{\dfrac{1}{ab}\quad a\ne0,b\ne0,(a+b)\ne0}[/tex]
The given conditions ensure the denominator(s) will not be zero.
Hual takes out a $3200 student loan at 6.4% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and
borrows another $12,400 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and
payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.6%. Find the total
amount of interest that will accrue until payments begin.
(a) Find the total amount of interest that will accrue for loan 1 (community college).
The total amount of interest that will accrue for loan 1 (community college) is $_____ Round your answer to two decimal
places, if necessary.
Part 2 of 3
A ALEKS-Erika Ramirez - Test 2-Chapter 7
(b) Find the total amount of interest that will accrue for loan 2 (state university).
The total amount of interest that will accrue for loan 2 (state university) is $____
Answer:
a) $4096 b) $1884,8 ■■ im not 100% sure
Step-by-step explanation:
a) 3200×0.064×2=$4096 in intrest
b) 12,400×0.076×2=$1884,8 in intrest
)) Of the 90 people who attended the Baybridge Middle School Winter Formal, 18 are
not students at Baybridge.
4) Shade the grid to show the fraction of the people who attended the formal who are not
students at Baybridge.
) What percent of the people who attended the Winter Formal are not students at
Baybridge Middle School? You can use your model to help.
Answer:
Step-by-step explanation:
To find the percent of the people who attended the Baybridge Middle School Winter Formal who are not students at Baybridge, we can use the following steps:
Find the fraction of non-student attendees: 18 attendees out of 90 total attendees can be represented as 18/90.
Convert the fraction to a decimal: 18/90 = 0.20, which can be rounded to 0.2.
Convert the decimal to a percentage: 0.2 * 100 = 20%.
So, 20% of the people who attended the Baybridge Middle School Winter Formal are not students at Baybridge.
Solve for x, each figure is a trapezoid
From the given trapezoid the value of the x is 1.
What is the trapezoid?
The sum of all the angles in a trapezoid is equal to 360°. The sum of the angles on the same side is equal to 180°.
We have,
Since a Trapizode has 360 Degrees total and since the sides are equal we can say that
180 = 66 + ∠R
∠R = 180 - 66
∠R = 114
so,
180 = 66 + (-2 + 116x)
180 = 66 - 2 + 116x
180 = 64 + 116x
180 - 64 = 116x
116 = 116x
x = 1
Therefore, from the given trapezoid the value of the x is 1.
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A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 18 centimeters. The height of the figure is 12 centimeters. The portion from the vertex to the perpendicular height is 4 centimeters. The portion from a point to a vertical line created by two vertices is 3 centimeters.
Which of the following represents the total area of the figure?
222 cm2
240 cm2
258 cm2
294 cm2
The total area of the figure is 258cm². Thus, option 3 is corect.
Given:
shorter side: 18 centimeters
perpendicular height : 4 centimeters
portion from a point to a vertical line created by two vertices : 3centimeters
height : 12 centimeters
from figure we know that, it is the vertex's height as well as the length of the sides to multiply together and we also have to divide since there is 5 sides
So , after multiplying the vertex height and sides and dividing it by the 5 , we get 258 cm²
Hence , the total area of the figure is 258cm².
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Solve the formula A=1/2h (a+b) for b 
Your friend wants to write code for Linux computer systems and says, “Why do I need to install Linux? I never open it and use it the way I do my browser.” How would you explain to your friend the difference between an operating system like Linux and an application like their web browser? In your answer, discuss how both Linux and at least one other operating system function, comparing those to an application like a browser.
Answer:
That's not math. Please classify your question correctly.
Write the simplest polynomial function with the given zeros: -2 , 2 , 3
Step-by-step explanation:
Zeros is another term for X intercepts.
We'd right the simplest form as (x-/+a), a being the zero
Just remember when you do that, change the signs. It shows -2, +2, +3. That becomes +2, -2, -3
Following that simple form, we get
[tex](x + 2)(x - 2)(x - 3)[/tex]
In the division example at the right A and B represent
different digits. What is the sum of A and B if the
remainder is zero?
In the division example at the right A and B represent different digits. The sum of A and B if the remainder is zero is 8.
What is Division?
This is one of the four basic mathematical operations and it is the process of splitting a number or an amount into equal parts.
The table shows all possible answers for A÷B with no remainder when digits from 1-9 for A and B are considered.
Since A is not equal to B such as A=6, B=2, divides it with no remainder. Therefore the sum of A and B is 8, so the cell (6,2) contains 8.
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Explain how to find 20% of 160
Answer: 20% of 160 is 32.
Step-by-step explanation:
The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.
To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.
Let us now find the 20% of 160.
20% = 0.2
percentage = 160 × 0.2
= 32
12. "The sum of 9 and the product of a number and -7 is -19
Answer:
Step-by-step explanation:
We can use algebra to solve for the unknown number. Let's call the number "x".
The equation can be written as:
9 + x * (-7) = -19
Expanding the product on the left side:
9 + -7x = -19
Subtracting 9 from both sides:
-7x = -28
Dividing both sides by -7:
x = 4
So the number x is 4.
This is a two-part question:
1. Jack's gasoline-powered model airplane travels in a circle while the cord is held. How far does it travel in 5 full circles if the cord is 15 ft.?
2. Last Saturday Jack flew his airplane 100 times around a circle with a cord of 50 ft. If Jack increases the length of the cord by 10 ft and fly it for 100 circles, how much further will the plane travel?
1. The plane travelled a distance of 471.239 ft
2. The plane would travel further by 6283.185 ft
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]
Part 1:
Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times
The total distance travelled by plane is [tex]15*2\pi *15[/tex]
[tex]=150\pi[/tex]
= 471.239 ft
Part 2:
Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.
The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])
If he increases the length by 10 ft, The cord will now be 60 ft.
The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])
Now,
100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])
= 100 * (2*(60-50))*[tex]\pi[/tex])
= 100 * 2 * 10 * [tex]\pi[/tex]
= 2000 * [tex]\pi[/tex]
= 6283.185 ft
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Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements.
If there are no possible solutions, submit an empty answer.
Answer: 2 hours babysitting
Step-by-step explanation:
18 x 9 = 162
180-162= 18
meaning he'd have to work 2 hours babysitting to get to meet his requirement.
hours used = 11
hours left= 3
which of the following statements are equivalent to the statement "the price increased by 1/2 if what it was before"
Answer:
The question is incomplete
Answer:
It was 1/3 before
Step-by-step explanation:
Expression
9x - 2 + 16x + 8 - x + 10
What are the coefficients in this expression?
The coefficients in the expression "9x - 2 + 16x + 8 - x + 10" are the numerical values that multiply the variables. In this expression, the coefficients are 9, -2, 16, 8, -1, and 10.
So, the expression can be written as:
9x + 16x - x + 10 = 24x + 10
where 9, -2, 16, 8, -1, and 10 are the coefficients of the expression.
Answer:
The coefficients in this expression would be 10, -2, 8, -1, 10, 9, 16
Step-by-step explanation:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
2-81
When graphing the function f(x)= x2-11x+18
window for determining the domain and range of the function?
O Xmin: -10, Xmax: 10
Ymin: –10, Ymax: 10
O Xmin: -5, Xmax: 5
Ymin: –5, Ymax: 5
Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10
O Xmin: -10, Xmax: 0
Ymin –10 Ymax: 0
on your graphing calculator, what is the most appropriate viewing
The most appropriate viewing range for the quadratic function is given as follows:
Xmin 0, Xmax 10.YMin - 15, Ymax, 15.How to obtain the viewing range?The quadratic function for this problem is defined as follows:
f(x) = x² - 11x + 18.
The function can be factored as follows:
f(x) = (x - 2)(x - 9).
Hence the roots are:
x - 2 = 0 -> x = 2.x - 9 = 0 -> x = 9.Meaning that the viewing range should include x = 2 and x = 9.
The coefficients of the function are:
a = 1, b = -11, c = 18.
Hence the x-coordinate of the vertex is of:
x = -b/2a
x = 11/2
x = 5.5.
Hence the minimum value of the function is the y-coordinate of the vertex, given as follows:
y = 5.5² - 11(5.5) + 18
y = -12.25.
Meaning that Ymin should be less than -12.25.
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A tailor charges a basic fee of $20 plus $4 per letter to sew an athlete's name on the back of a jacket. Write a linear equation that will find the cost c to have a name containing x letters
The equation will be;
c = 20 + 4x
What are Linear Equations?Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.
A linear equation that will find the cost c to have a name containing x letters will be;
c = $20 + 4x
where c = cost
$20 = basic fee
x = number of letters
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The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answer:
Step-by-step explanation:
B
Need help with this Question pls
Step-by-step explanation:
a. £5,37
b.£2,07
c.£15,70
Please verify my answer. I am not sure if it is correct.
now, we're making the assumption we're simply doing an identity proof, so
[tex]sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}[/tex]
PLS HELP ANSWER QUICKLY PLS
Answer:
10
Step-by-step explanation:
a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
c = 10
Rewrite in simplest terms: (5x + 5y) - (-x + 10y)
Answer:
6x - 5y
Step-by-step explanation:
( remove the unnecessary parentheses)
= 5x + 5y + x - 10y
= 6x + 5y - 10y
= 6x + 5y
at a movie theater, tickets cost 15$ for adults and 8$ for children. a group of 28 movie goers cost 308$. how many adults and how many children are in the group?
The number of adult and children in the group is given as follows:
Adult: 12.Children: 16.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: number of adults.Variable y: number of children.There were a total of 28 people, hence:
x + y = 28
y = 28 - x.
They spent a total of $308, hence:
15x + 8y = 308.
Replacing the second equation into the first, the value of x is given as follows:
15x + 8(28 - x) = 308
7x = 84
x = 84/7
x = 12.
Then the value of y is given as follows:
y = 28 - x = 28 - 12 = 16.
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PLS HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the solution to the equation given the replacement set?
25 - 3r = 10; {3, 4, 5, 6,}
Responses
3
4
5
6
Answer:
r = 5
Step-by-step explanation:
25 - 3r = 10 ( subtract 25 from both sides )
- 3r = - 15 ( divide both sides by - 3 )
r = 5
the solution from the replacement set is 5
Mann Park is the shape of a triangle.
On a map, it has borders that measure 5 inches inches, 7 inches
and 9 inches. If the shortest border of Mann Park is
1000 meters long, how long in meters, is its longest
border?
The longest border of the Mann's park is 228.6 meter.
What is Triangle inequality theorem ?The Triangle Inequality It is a basic principle of geometry that the lengths of any two sides of a triangle must add up to more than the length of the third side. In other words, the longest side of any triangle must be shorter than the total length of the other two sides.
In this case, the shortest side of Mann Park measures 5 inches, and the two longer sides measure 7 inches and 9 inches.
So, the sum of the lengths of the two longer sides is:
' 7 inches + 9 inches = 16 inches.
Since 5 inches is less than 16 inches, we know that the 5-inch side is the shortest side, and the 9-inch side is the longest side.
One inch is approximately equal to 0.0254 meters, so we have:
= 9 inches x 0.0254 meters/inch
= 0.2286 meters
Since the shortest side is 1000 meters long, the longest side is:
= 1000 meters x 0.2286 meters/inch
= 228.6 meters long.
Therefore, the longest border of Mann Park is approximately 228.6 meters long.
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If x = logb2 and y = log b5, express log b100 in terms of x and y.
logb100=____?
Using logarithm expressing log b100 in terms of x and y is logb100 = 2y + x
What is the logarithm of a number?The logarithm of a number x to base a written as logₐy is such that when a is raised to the power of x,it equals y.
How to express logb100 in terms of x and y?Since
x = logb2 and y = log b5,We desire to express logb100 in terms of x and y.
So, we proceed as follows.
We have logb100, re-writing this, we have
logb100 = logb(25 × 2)
Now, applying the addition law of logarithm which states that
logab = loga + logb.
So, we have that
logb100 = logb(25 × 2)
logb100 = logb25 + logb2
= logb5² + logb2
Now applying the power rule of logarithm which states that logaⁿ = nloga
So,
logb100 = logb5² + logb2
= 2logb5 + logb2
= 2y + x
So, logb100 = 2y + x
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15. "Twice a number, increased by 13, is -21.“
Answer:
Step-by-step explanation:
(X=the number)
2x+13=-21
(-21)-13=34
34x2=68
