Answer:
a=671000
Step-by-step explanation:
woah
The formula for the number of internet host computers as an exponential function of t is: n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t) and the values of a and k in the model are k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million
a. To find the values of a and k, we can use the information given in the question. Let n(0) be the number of host computers in July 1998, which is 35.3 million. Let n(7) be the number of host computers in July 2005, which is 352.1 million. We can use these values to solve for a and k.
n(0) = a × e^(k0) = a
n(7) = a × e^(k7)
Dividing the second equation by the first equation, we get:
n(7) / n(0) = e^(k×7)
Taking the natural logarithm of both sides, we get:
ln(n(7) / n(0)) = k×7
Therefore, k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million.
Therefore, the formula for the number of internet host computers as an exponential function of t is:
n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t)
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Identify the transformation from the original to the image.
Original ABCD: A(-2, 5), B(1, 4), C(1, 1), D(-2, -1)
Image A'B'C'D': A'(5, 2), B'(4, -1), C'(1,-1), D'(-1,2)
A. Dilation B. Reflection C. Rotation D. Translation
The sum of one-fifth of a non-negative integer and one-third of another non-negative integer is 1. What is the maximum value of the sum of these 2 non-negative integers.
Answer: 7, and it occurs when x = 5 and y = 2
Step-by-step explanation:
1/5 x + 1/3 y = 1 (Equation 1)
x + y = ? (Equation 2)
We want to find the maximum value of x + y, so we need to maximize each of the variables x and y subject to the constraint given in Equation 1.
To solve for one of the variables, we can isolate it in terms of the other variable. Let's solve for y:
1/5 x + 1/3 y = 1
1/3 y = 1 - 1/5 x
y = 3(1 - 1/5 x)
Now we can substitute this expression for y into Equation 2:
x + y = x + 3(1 - 1/5 x)
Expanding the expression, we get:
x + y = x + 3 - 3/5 x
x + y = 3 + 2/5 x
So we can see that x + y is a linear function of x with slope 2/5 and y-intercept 3. To maximize x + y, we want to maximize x. However, x is a non-negative integer, so the maximum value of x occurs when x = 5 (since any larger value would result in a fraction in the expression for y).
Therefore, the maximum value of x + y is:
x + y = 3 + 2/5 x
x + y = 3 + 2/5 (5)
x + y = 5 + 2
x + y = 7
So the maximum value of the sum of these two non-negative integers is 7, and it occurs when x = 5 and y = 2.
HS HONORS GEOMETRY graph
PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
According to the information of the graph the correct sentences are: D. Dilate ABC by a scale factor of 1/2 centered at the right angle, and E. Dilate ABC by a scale factor of 2 centered at the right angle.
How to find the correct sentences?To show that two triangles are similar, we need to demonstrate that they have the same shape but not necessarily the same size. This can be done using similarity transformations such as dilation, rotation, and reflection. Statements A, B, and C involve rotations which would change the shape of the triangle, therefore they do not demonstrate similarity.
On the other hand, statement D suggests dilating triangle ABC by a scale factor of 1/2 centered at the right angle. This transformation will change the size of the triangle but maintain the same shape, which is a property of similar triangles. Similarly, statement E suggests dilating triangle ABC by a scale factor of 2 centered at the right angle, which again maintains the same shape but changes the size. Therefore, statements D and E demonstrate that triangle ABC and triangle LMN are similar.
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TIMED PLS HELP - GIVING MOST PTS I CAN
Rounding to the nearest tenth, the measure of UV is 7.1.
What is angle?An angle is a measure of space between two lines or planes. It is measured in degrees, using a protractor, and can range from 0 to 360. Angles can be either acute, obtuse, right, straight, reflex, or full. Acute angles are angles that measure less than 90 degrees, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, straight angles measure 180 degrees, reflex angles measure more than 180 degrees, and full angles measure 360 degrees.
To find the measure of UV in ∆ UVW, we will use the law of cosines. The law of cosines states that [tex]c^{2} =a^{2} +b^{2} -2ab cos C[/tex], where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and C is the angle opposite side c. In this case, side c is UV, a is UW, b is VW, and C is ∠ W.
Plugging in the given values, we get:
[tex]U^{2}V^{2}[/tex] = [tex]9^{2} + 12^{2} - 2 *9* 12 cos *35[/tex]
[tex]U^{2} V^{2}[/tex] = 81 + 83.44 – 162.08 cos 35°
[tex]U^{2} V^{2}[/tex] = 164.44 – 114.45
[tex]U^{2} V^{2}[/tex] = 49.99
Taking the square root of both sides, we get:
UV = 7.086
Rounding to the nearest tenth, the measure of UV is 7.1.
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Find the surface area of each triangular prism.
Also don't mind my writing on the paper
The surface area of the given triangular prism is approximately 58.26 square units.
what is triangular prism?
A triangular prism is a three-dimensional geometric shape that consists of two congruent parallel triangles as its bases and three rectangular faces that connect the corresponding sides of the two triangles.
In the given question,
To find the surface area of a triangular prism, we need to add the area of all the faces of the prism. A triangular prism has two congruent triangular bases and three rectangular lateral faces.
First, let's calculate the area of the triangular bases. We can use the formula for the area of a triangle:
Area of a triangle = (1/2) * base * height
In this case, the base of the triangle is 5 and the height is 6. To find the height, we need to use the Pythagorean theorem because we are given the slant height of the triangular prism, which is the hypotenuse of the right triangle formed by the base, the height, and the slant height. The Pythagorean theorem is:
slant height² = base² + height²
Substituting the given values, we get:
6.5² = 5² + height²
42.25 = 25 + height²
height² = 17.25
height = √17.25 ≈ 4.15
Now we can calculate the area of each triangular base:
Area of a triangular base = (1/2) * base * height
Area of each triangular base = (1/2) * 5 * 4.15
Area of each triangular base ≈ 10.38
Next, we need to calculate the area of each rectangular lateral face. The length of each lateral face is the same as the base of the triangle, which is 5, and the width is the same as the width of the prism, which is 2.5. The height of each lateral face is the same as the height of the prism, which is 6. Therefore, the area of each rectangular lateral face is:
Area of a rectangular lateral face = length * width
Area of each rectangular lateral face = 5 * 2.5
Area of each rectangular lateral face = 12.5
Finally, we can find the total surface area of the prism by adding up the areas of the two triangular bases and the three rectangular lateral faces:
Total surface area = 2 * area of a triangular base + 3 * area of a rectangular lateral face
Total surface area ≈ 20.76 + 37.5
Total surface area ≈ 58.26
Therefore, the surface area of the given triangular prism is approximately 58.26 square units.
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Find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x-3y-3z=-3. Vector Form: < , , 5> + t < , , -3> Parametric form (parameter t, and passing through P when t = 0):
x=x(t)=
y=y(t)=
z=z(t)=
The parametric equation of the line is given by; x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
Find the parametric equation of the line?To find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x - 3y - 3z = -3, the following
Write the equation of the plane.5x - 3y - 3z = -3 is the given equation
Find a vector that is orthogonal to the planeThis can be done by finding the normal vector of the plane. Using the coefficients of x, y, and z in the equation of the plane. A normal vector of the plane is obtained and simplified:<5,-3,-3>.
Find the vector equation of the line.
Let L be the line through P(-2, 2, 5) and orthogonal to the plane. A direction vector of the line, v is the normal vector of the plane (which is <5,-3,-3>), a point P(-2, 2, 5) on the line can be used to obtain the vector equation of the line:
Parametric form (parameter t, and passing through P when t = 0):x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
The vector form:<-2, 2, 5> + t<5,-3,-3> The parametric equation of the line is given by; x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
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onsider an economy with three industries: I1, I2, and I3. Consumer demand is currently
‚ 100 units from I1,
‚ 75 units from I2,
‚ 200 units from I3.
Also suppose that
‚ for every unit that I1 produces, it needs 0.5 units from I2 and 0.1 units from I3;
‚ for every unit that I2 produces, it needs 0.25 units from I1 and 0.2 units from I3;
‚ for every unit that I3 produces, it needs 0.3 units from I1 and 0.4 units from I2
Set up a system of equations
We have the following system of equations:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
Define the term equation?Statement gives the equality of different mathematical expressions is called as an equation.
Let x₁, x₂, and x₃ be the outputs of I₁, I₂, and I₃, respectively. Then the total production must satisfy the following system of equations:
For I₁:
I₁ itself produces x₁ unitsIt requires 0.5 units of I₂ for every unit, so it requires 0.5x₂ unitsIt requires 0.1 units of I₃ for every unit, so it requires 0.1x₃ unitsTherefore, total demand from I₁ is x₁ + 0.5x₂ + 0.1x₃ = 100For I₂:
I₂ itself produces x₂ unitsIt requires 0.25 units of I₁ for every unit, so it requires 0.25x₁ unitsIt requires 0.2 units of I₃ for every unit , so it requires 0.2x₃ unitsTherefore, total demand from I₂ is x₂ + 0.25x₁ + 0.2x₃ = 75For I3:
I₃ itself produces x₃ unitsIt requires 0.3 units of I₁ for every unit, so it requires 0.3x₁ unitsIt requires 0.4 units of I₂ for every unit, so it requires 0.4x₂ unitsTherefore, total demand from I₃ is x₃ + 0.3x₁ + 0.4x₂ = 200Therefore, the system equations are:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
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James is using a groupon that provides him 10% off of a purchase of $29 or more at an ice cream shop. His total comes to $38.50. Which
calculation below could be used to determine how much he will pay in total (select all that apply)?
A 38.5-0.9(38.5)
B 38.5 -0.1(38.5)
C 1.1(38.5)
D 0.9(38.5)
E 0.1(38.5)
Options A and B are both correct. Options C, D, and E are not correct, as they do not take into account the discount that James is receiving.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Equation:The correct calculations to determine how much James will pay in total are:
First, we need to calculate how much 10% of $38.50 is:
10% of $38.50 = 0.1 × $38.50 = $3.85
So, James will receive a discount of $3.85.
To determine how much James will pay in total, we can use either of the following calculations:
A. James' total cost after the 10% discount would be: 38.5 - 0.9(38.5) = 38.5 - 34.65 = $3.85
B. The 10% discount on the total cost can be calculated as 0.1(38.5) = $3.85, which can be subtracted from the total cost to get James' final cost as 38.5 - 3.85 = $34.65
C. James' final cost after the 10% discount would be 1.1(38.5) = $42.35, which is not the correct answer as it does not take into account the discount.
D. James' total cost after the 10% discount would be: 0.9(38.5) = $34.65, which is the correct answer.
E. The calculation 0.1(38.5) = $3.85 represents the amount of the discount, and is not the final cost.
Therefore, options A and B are both correct. Options C, D, and E are not correct, as they do not take into account the discount that James is receiving.
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Number 12 please help
The two-column proofs that line segments AC ≅ EC are shown below
The complete proof that AC ≅ ECGiven that
AB || DE
BC ≅ DC
The proof is as follows
Statement Reason
AB || DE and BC ≅ DC Given
AB ≅ DE CPCTC
AC ≅ EC CPCTC (proved)
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1)If 24 kids Sharded and 1789 kids went to a taco bell in 24 hours how many kid sharded in total?
2.a)1638 men cheated on their wife in one week how many men cheated on their wife’s in 7 weeks?
2.b) 47 percent of the men that cheated on their wife’s in 7 weeks have cheated many times before, how many men have cheated before?
1) Given that 1789 children visited a Taco Bell in 24 hours. We can calculate the number of students who went every hour by dividing this number by the number of hours:
[tex]1789 / 24 = 74.54\\\frac{1789}{24} = 74.54[/tex]
We get 75 students each hour, rounded up to the nearest whole number.
If 24 children shared, we can calculate the total number of children who shared by multiplying the number of hours by the number of children shared every hour:
24 x 75 = 1800
As a result, 1800 children shared.
How many men cheated on their wives in 7 weeks?2)If 1638 men cheated on their wives in one week, multiplying by 7 gives us the number of men who cheated on their wives in seven weeks:
1638 x 7 = 11,466
As a result, 11,466 men cheated on their wives in just 7 weeks.
How many men have cheated before?c) If 47% of the men who cheated on their spouses in 7 weeks cheated numerous times before, we can calculate the number of men who cheated previously by multiplying the total number of men who cheated by the proportion of men who cheated previously:
11,466 x 0.47 = 5,390.02
Rounding to the nearest whole number, we get 5,390 men who have cheated in the past.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
What is inequality?Inequality refers to the state of being unequal, or not having equal access to resources, opportunities, or privileges. Inequality can manifest in many different ways, including but not limited to income inequality, wealth inequality, social inequality, gender inequality, racial inequality, and educational inequality.
Inequality can be caused by a variety of factors, including systemic discrimination, unequal distribution of resources, and societal structures that favor certain groups over others. It can have a significant impact on individuals and communities, leading to disparities in health, education, economic opportunities, and overall well-being. Addressing inequality requires a multifaceted approach that involves policies and initiatives aimed at promoting equal access to resources, opportunities, and rights for all individuals.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
To solve the inequality3(8 – 4x) < 6(x – 5)[tex]3(8 - 4x) < 6(x – 5)[/tex], we first simplify both sides of the inequality:
[tex]3(8-4x) < 6(x -5)[/tex]
[tex]24 - 12x < 6x - 30[/tex]
[tex]54 < 18x[/tex]
[tex]3 < x[/tex]
So, the solution set for the inequality is x > 3. We represent this on a number line by placing an open circle at 3 and drawing a bold line pointing to the right to indicate all the values of x that satisfy the inequality. Therefore, the correct answer is:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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Answer:
it's 3
Step-by-step explanation:
Gwen is making a circular garden that has a diamete of 10 feet. She is looking to buy fencing for the garden. How many feet if fencing will she need?
what is illegal to include in a sales letter? check all that apply. satisfied customer names unauthorized use of a celebrity name misleading statements free sample trials
Unauthorized use of celebrity name and misleading statements are illegal to include in a sales letter.
A sales letter comprises a format that follows a certain set of instruction that should always be implemented to form an ideal sales letter, this set of instruction are as follows
Start with a catchy headline to gasp the attention of the reader.Explain in layman's language the need and the scope of this intervention through a letterAvoid false statistics and misleading statements to provide evidence to make the reader inclined.Offer the reader something crucial and only available for a limited period of time.Furthermore, a sales letter provides a basic layout of the needs of the writer and how they can help in providing aid for the needs of the reader.
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please help meeeeeeee
Step-by-step explanation:
For a RIGHT triangle , remember S-O-H-C-A-H-T-O-A ?
Cos (Φ) = Adjacent leg / Hypotenuse
so cos D = sqrt (78) / DF = sqrt (78) / 28
What’s Name the vertex of the angle (Don’t say a complaint answer)
The common end point I believe :)
please help me die today
Answer:
[tex]A = 212.1 \text{ cm}^2[/tex]
Step-by-step explanation:
We can identify the bases of the trapezoid as:
9cm and 21.3 cm
(notice how they are parallel)
We know the height is 14 cm.
Using these values, we can solve for the trapezoid's area.
[tex]A = \dfrac{1}{2}(b_1 + b_2) \cdot h[/tex]
↓ plugging in the values
[tex]A = \dfrac{1}{2}(9 + 21.3) \cdot 14[/tex]
↓ simplifying the parentheses
[tex]A = \dfrac{1}{2}(30.3) \cdot 14[/tex]
↓ multiplying 14 and (1/2)
[tex]A = 7 \cdot 30.3[/tex]
↓ multiplying
[tex]A = 212.1 \text{ cm}^2[/tex]
PLSS due by tomorrow I will give all my points
can you add the question?
Add a picture of the question.
James returned home from a trip and opened the door if m<1 is 46 what is the measure of its complementary angle
A. 44
B. 54
C. 134
D. 224
when you do it please label is as "the title:" then put the numbers from the first box in so i don't get it confused
To better understand your question, it is important to identify the key terms and concepts that are being used.
Title: Understanding Terms in a Question
1. . Look for specific words or phrases that relate to the topic at hand, and try to understand their meaning within the context of the question.
2. It can also be helpful to break the question down into smaller parts or sub-questions, and focus on each one individually.
3. If you are unsure about the meaning of a particular term, do some research or consult a dictionary or other reference source.
4. By taking the time to understand the terms and concepts in a question, you can improve your ability to answer it accurately and effectively.
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How can I find the value to x? I’m struggling!!
Answer:
x ≈ 51°
Step-by-step explanation:
Use trigonometry:
[tex] \sin(x°) = \frac{7}{9} [/tex]
Use the reverse (SHIFT, sin (7/9)) function on your calculator to find x:
x ≈ 51°
Triangle PQR is translated to triangle P'Q'R'.What are the co-ordinates of Q' and R'?
Triangle PQR is translated to triangle P'Q'R'. (-3,3) and (-1,1) are the co-ordinates of Q' and R'.
The co-ordinates of Q' and R' when triangle PQR is translated to triangle P'Q'R' are (-3,3) and (-1,1), respectively.
A translation is a type of transformation where a shape is moved from one position to another.
However, the shape is not rotated, resized, or reflected in a translation.
Instead, it is moved in a straight line from one position to another.
A translation in a two-dimensional plane is specified by a vector, which specifies the distance and direction of the translation.
The co-ordinates of Q' and R' when triangle PQR is translated to triangle P'Q'R' are (-3,3) and (-1,1), respectively.
To determine these co-ordinates, we can use the following steps:
Determine the vector of the translation.
To do this, we find the difference between the corresponding vertices of the two triangles.
Here, we can take PQ as the base.
So, P'Q' = QRQR
= PQP' = P + (-1,2)
= (-2,3)Q'
= Q + (-1,2)
= (-3,3)R'
= R + (-1,2)
= (-1,1).
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HELPP 100 POINTS WILL GIVE BRAINLIEST
Answer:
a = 3
b = 8
c = 4
Step-by-step explanation:
We can identify the coefficients a, b, and c by comparing the equation with the standard form of a quadratic equation:
ax^2 + bx + c = 0
(always use this for these kinds of problems)
So, in the given equation:
The coefficient of x^2 is a = 3
The coefficient of x is b = 8
The constant term is c = 4
Given only a compass and straightedge, Greeks believed that many constructions were impossible to complete.
True or False?
The answer of the given question based on compass and Straight edge construction is , option (b) False.
What is Pentagon?A pentagon is a geometric shape that has five straight sides and five angles. It is a polygon, which means it is a closed shape made up of straight line segments. The word "pentagon" come from Greek word "penta" meaning "five" and "gonia" meaning "angle".
There are several types of pentagons, including regular and irregular pentagons. A regular pentagon has five equal sides and angles, while an irregular pentagon has sides and angles of different lengths and measures.
False.
The Greeks believed that all constructions could be made with only a compass and straightedge, but some constructions were more difficult than others. In fact, they were able to make remarkable geometric constructions using only these two tools, such as trisecting an angle, duplicating a cube, and constructing a regular pentagon. However, in the 19th century, the discovery of new mathematical methods showed that some constructions, like squaring the circle, were actually impossible to complete with just a compass and straightedge.
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write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0
-4x1 – 4x2 – 8x3 = 0
-3x2 – 9x3 = 0
[ x1 ]
Where the solution set is x = [ x2 ]
[ x3 ]
X = x3 _____
The solution set can be written in parametric vector form as: [tex]X = x3 [-1 0 1]^T + x2 [-2 1 0]^T[/tex]
How we get the solution of homogeneous system?We can rewrite the system of equations in matrix form as AX = 0, where [tex]A =[2 2 4]\\[-4 -4 -8]\\[0 -3 -9][/tex]
[tex]X = [x1 x2 x3]^T[/tex]
To solve for the solution set, we can row reduce the augmented matrix [tex][A|0].\\[2 2 4|0]\\[-4 -4 -8|0]\\[0 -3 -9|0][/tex]
[tex]R2 < - R2 + 2R1 and R3 < - R3 - 3R1[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 -3 -9|0][/tex]
[tex]R3 < - -1/3 R3[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - R1 - R2[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - 1/2 R1 and R2 < - 1/2 R2[/tex] to obtain:[tex][1 1 2|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
Therefore, the system has two free variables, x2 and x3, while x1 is a pivot variable. where x2 and x3 are arbitrary constants.
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A group of friends worked together at a lemonade stand. They earned $8.00 in all. Each friend was paid 20% of the total earnings. How much did each friend earn?
Answer: i would say $1.60 because 20% of $8.00 is $1.60
Each friend earned an amount of $1.6.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Given that,
A group of friends worked together at a lemonade stand.
They earned $8.00 in all.
Each friend was paid 20% of the total earnings.
Total earnings = $8
Each friend earn = 20% × 8
= (20/100) × 8
= 0.2 × 8
= 1.6
Hence the amount each friend earned is $1.6.
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Biologist a lake with 500 fish and estimated the carrying capacity to be 6100 the number of fish grew to 740 in the first year.
Find an equation for the number of fish P(t) after t years.
How many years will it take for the population to increase to 3050
In light of this, it will take roughly 2.25 years for the populace to reach 3050,that shows growth rate. The equation to calculate the number of fishes in a pond after t years would be equal to t = -ln (0.12125) / r
What is the growth rate?The logistic development model can be used to calculate an equation for the growth rate of fish P(t) after t years:
Where[tex]: P(t) = K / (1 plus A e(-rt))[/tex]
[tex]r[/tex]= growth rate, where[tex]K =[/tex] carrying capacity [tex]= 6100 A =[/tex] starting population[tex]= 500[/tex]
T equals time in years
Using the given data, we can determine the increase rate:
In the first year, the quantity of fish increased from[tex]500 to 740:[/tex]
[tex]740 = 6100 / (1 + A e^(-r1))[/tex]
We arrive at [tex]A e(-r*1) = 8.24324[/tex] after solving for [tex]A e(-r).[/tex]
Given that P(t) must lie half way between A and K in order for there to be a maximal growth rate, the carrying capacity is [tex]6100:[/tex]
[tex]3050 = (6100 + 500) / 2 = 3300[/tex]
As a result, if [tex]P(t) = 3300,[/tex] we have:
[tex]3300 = 6100 / (1 + A e^(-rt))[/tex]
We arrive at [tex]A e(-rt) = 1.84848[/tex] after solving for [tex]A e(-rt).[/tex]
The following is the result of substituting the numbers of [tex]A e(-r*1)[/tex] and [tex]A e(-rt)[/tex] into the equation for P(t):
We can put into an expression and solve for t to determine how long it will take for the population to reach [tex]3050:[/tex]
[tex]3050 = 6100 / (1 + 8.24324 e^(-rt))[/tex]
[tex]e(-rt) = 0.12125 -rt = ln = 1 + 8.24324 e(-rt) = 2(0.12125)[/tex]
[tex]t = -ln(0.12125) / r[/tex]
Although we are unsure of r's precise value, we do know that [tex]A e(-rt) = 1.84848.[/tex]
at[tex]t = 3300, P(t).[/tex] When we enter these numbers into the solution, we obtain:
[tex]1.84848 = A e^(-r1)[/tex]
[tex]A = 1.84848 / e^(-r1)[/tex]
We obtain the following equation for t by substituting this value of A:[tex]t = -ln(0.12125) / r t = -ln(0.12125) / ln(1.84848 / e(-r*1))[/tex]
The precise value of r is not required to provide an answer, but we can solve for it using a numerical approach like trial and error or a graphing method.
The logistic development model can be used to calculate an equation for the quantity of fish P(t) after t years:
Where: [tex]P(t) = K / (1 plus A e(-rt))[/tex]
r = growth rate, where K = carrying capacity =[tex]6100 A[/tex] = starting population [tex]= 500[/tex]
T equals time in years
Using the given data, we can determine the increase rate:
In the first year, the quantity of fish increased from 500 to 740:
[tex]740 = 6100 / (1 + A e^(-r1))[/tex]
We arrive at A e(-r*1) = 8.24324 after solving for A e(-r).
Given that P(t) must lie half way between A and K in order for there to be a maximal growth rate, the carrying capacity is 6100:
[tex]3050 = (6100 + 500) / 2 = 3300[/tex]
As a result, if P(t) = 3300, we have:
[tex]3300 = 6100 / (1 + A e^(-rt))[/tex]
We arrive at c[tex]A e(-rt) = 1.84848[/tex] after solving for [tex]A e(-rt).[/tex]
The following is the result of substituting the numbers of A e(-r*1) and A e(-rt) into the equation for P(t):
[tex]P(t) = 6100 / (1 + 8.24324 e^(-rt))[/tex]
We can put P(t) = 3050 into an expression and solve for t to determine how long it will take for the population to reach 3050:
[tex]3050 = 6100 / (1 + 8.24324 e^(-rt))[/tex]
[tex]e(-rt) = 0.12125 -rt = ln = 1 + 8.24324 e(-rt) = 2(0.12125)[/tex]
[tex]t = -ln(0.12125) / r[/tex]
Although we are unsure of r's precise value, we do know that[tex]A e(-rt) = 1.84848.[/tex]
a[tex]t t = 3300, P(t).[/tex] When we enter these numbers into the solution, we obtain:
[tex]1.84848 = A e^(-r1)[/tex]
[tex]A = 1.84848 / e^(-r1)[/tex]
We obtain the following equation for t by substituting this value of A:[tex]t = -ln(0.12125) / r t = -ln(0.12125) / ln(1.84848 / e(-r*1))[/tex]
Assuming r = 0.1 as a sample growth rate, we obtain[tex]t = -ln (0.12125) / ln (1.84848 / e(-0.1*1))[/tex]
The precise value of r is not required to provide an answer, but we can solve for it using a numerical approach like trial and error or a graphing calculator. By assuming a growth rate, we can calculate how long it will take for the populace to reach 3050. Assuming r = 0.1 as a sample growth rate, we obtain[tex]t = -ln(0.12125) / ln(1.84848 / e(-0.1*1))[/tex]
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Is 5c + 5c already simplified
Answer:
10c
Step-by-step explanation:
When we have similar terms we can add or subtract them together.
Combine terms is like grouping similar terms together.
Accordingly, let us solve the given question.
5c + 5c
Combine the like terms to simplify the answer.
10c
activation functions: sigmoid 4 points possible (graded) recall that there are several different possible choices of activation functions . let's get more familiar with them and their gradients. what is the derivative of the sigmoid function, ? please write your answer in terms of and :
The derivative of the sigmoid function is f(x) × (1 - f(x)).Answer: f(x) × (1 - f(x)).
As per the question, we are supposed to determine the derivative of the sigmoid function.
The sigmoid function is given as,
[tex]f(x) = 1 / (1 + e^-x)[/tex]
To determine the derivative of the sigmoid function, we first find out the derivative of f(x) with respect to x using the quotient rule,
[tex]f'(x) = d/dx [ 1 / (1 + e^-x) ][/tex]
[tex]f'(x) = [ (d/dx)[1] × (1 + e^-x) - 1 × (d/dx)[1 + e^-x] ] / [ (1 + e^-x)^2 ][/tex]
[tex]f'(x) = [ 0 × (1 + e^-x) - (-e^-x) ] / [ (1 + e^-x)^2 ][/tex]
[tex]f'(x) = e^-x / (1 + e^-x)^2[/tex]
Now we are supposed to write the answer in terms of f(x),
[tex]f'(x) = e^-x / (1 + e^-x)^2f(x) = 1 / (1 + e^-x)[/tex]
Substituting f(x) in the above equation,
f'(x) = f(x) × (1 - f(x))
Therefore, the derivative of the sigmoid function is f(x) × (1 - f(x)).Answer: f(x) × (1 - f(x)).
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A spinner has five equal sections marked 1-5. What is the probability of not landing on four?
Answer: 4/5
Step-by-step explanation:
Five equal sides = 5
4 is just one side, so = 1
Not landing in 4 = 4/5
Answer: 4/5 or 80%
Step-by-step explanation:
Since the spinner has five equal sections, each numbered 1 through 5, the probability of landing on any particular number is 1/5.
To find the probability of not landing on 4, we need to add up the probabilities of landing on all the other numbers and subtract that sum from 1 (since the sum of all possible outcomes must equal 1).
The probability of landing on 4 is 1/5, so the probability of not landing on 4 is:
1 - 1/5 = 4/5
Therefore, the probability of not landing on 4 is 4/5 or 0.8, which is equivalent to an 80% chance.
Hope this helped!
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Therefore, f(11) can either be -16 or 20, depending on whether we use the recursive or explicit rule.
What is graph?In mathematics, a graph is a visual representation of the relationship between two or more variables. It is a collection of points (or vertices) that are connected by lines or curves (called edges) to show the relationships between them. Graphs are commonly used in many different fields of study, including mathematics, science, engineering, and social sciences, to represent and analyze data, identify patterns, and make predictions.
Here,
We can observe that this is an arithmetic sequence, where each term is obtained by adding a constant difference to the previous term. To find the recursive rule, we can use the formula:
f(n) = f(n-1) + d
where f(n-1) is the previous term, d is the common difference, and f(n) is the nth term. Using the given values, we can find that the common difference is d = -6. So the recursive rule for the sequence is:
f(1) = 80
f(n) = f(n-1) - 6
To find the explicit rule, we can use the formula:
f(n) = a + (n-1)d
where a is the first term, d is the common difference, and n is the term number.
Using the first two terms, we can find that:
a = 80
d = -6
So the explicit rule for the sequence is:
f(n) = 80 - 6(n-1)
To find f(11), we can substitute n = 11 into either the recursive or explicit rule:
Using the recursive rule:
f(11) = f(10) - 6
= (f(9) - 6) - 6
= (f(8) - 12) - 6
= (f(7) - 18) - 6
= (f(6) - 24) - 6
= (f(5) - 30) - 6
= (20 - 30) - 6
= -16
Using the explicit rule:
f(11) = 80 - 6(11-1)
= 80 - 6(10)
= 20
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