Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
Exponential function:
A decaying exponential function is modeled by:
⇒ A (t) = A (0) (1 - r)ⁿ
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
In this problem:
In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000
Emissions will decrease 2.5% in each successive year, hence r = 0.026
Then, the equation for the amount emitted each year is:
⇒ A (t) = A (0) (1 - r)ⁿ
⇒ A (t) = 80000 (1 - 0.025)ⁿ
⇒ A (t) = 80,000 (0.975)ⁿ
The total amount emitted over the course of the 11 year period is:
T = ∫ 0 to 11 ( A (t) ) dt
Hence:
T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt
Applying the Fundamental Theorem of Calculus:
T = 763,968 kilotons
Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
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Hello please I don't understand this exercise..
In an orthonormal frame (o; i; j), we give the points A(3; 1), B(1; 2) and the line (AC) with equation 2x-y-5=0.
1) Determine the equation of the line (AB).
2)a) Show that the direction vectors AB and AB of the lines (AC) and (AB) are orthogonal.
b) Then determine the coordinates of C.
The equation of the line AB,with slope of -1/2 is y = (-1/2)x + 7/2. We then use the dot product to show that the direction vectors of the lines AB and AC are orthogonal, and the coordinates of point C is (6,7).
In an orthonormal frame (o; i; j), the points A and B are given as A(3;1) and B(1;2), and the line (AC) is given by the equation 2x-y-5=0.
To determine the equation of line (AB), we need to find the slope (or gradient) of the line passing through A and B. We can find this by using the formula
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the values of A and B, we get
slope = (2 - 1) / (1 - 3) = -1/2
Now that we have the slope, we can use the point-slope form of a line to find the equation of line (AB). Let (x,y) be any point on the line, then we have
y - 1 = (-1/2)(x - 3)
Simplifying, we get
y = (-1/2)x + 7/2
So the equation of line (AB) is y = (-1/2)x + 7/2.
To show that the direction vectors AB and AC of the lines (AB) and (AC) are orthogonal, we need to find the direction vectors of these lines and show that their dot product is zero. The direction vector of a line is just the vector that "points" in the direction of the line. To find it, we can take any two points on the line and subtract their coordinates to get a vector.
For line (AC), we can take A and C as two points on the line. Since we don't know the coordinates of C yet, we can solve the equation of line (AC) for x to get
x = (y + 5) / 2
Now substituting x by the above expression in the coordinates of point A we get
C((y + 5)/2, y)
Thus, the direction vector of line (AC) is
AC = C - A = ((y + 5)/2 - 3, y - 1) = (y/2 - 7/2, y - 1)
Similarly, we can take A and B as two points on the line (AB) to get the direction vector of line (AB):
AB = B - A = (1-3, 2-1) = (-2, 1)
Now, the dot product of AB and AC is
AB · AC = (-2)(y/2 - 7/2) + (1)(y - 1) = -y + 7
We can see that the dot product is zero when y=7. Hence, direction vectors AB and AC are orthogonal at point C(3,7).
To determine the coordinates of C, we substitute y=7 in the equation of line (AC) we obtained earlier
2x - y - 5 = 0
2x - 7 - 5 = 0
2x = 12
x = 6
Therefore, C has coordinates (6,7).
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14 15. A composite figure is created from a cylinder and a cone like in the image below. Use the informative given in the image to find the volume of the composite figure. Select the closest estimate for the volume of the figure. 15 7 feet h
The volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.
How to evaluate for the volume of the composite figureWe shall calculate for the volumes of the cone and the cylinder, the sum of each volume will give the volume of the composite figure
The cone have;
radius = 7 ft
height = 34ft - 16ft = 18ft
Volume of the cone = 1/3 × 22/7 × 7ft × 7ft × 18ft
Volume of the cone = (22 × 7 × 6) ft³
Volume of the cone = 924 ft³
The cylinder have;
radius = 7 ft
height = 16 ft
Volume of the cylinder = 22/7 × 7ft × 7ft × 16ft
Volume of the cylinder = (22 × 7 × 16) ft³
Volume of the cylinder = 2464 ft³
Volume of the composite figure = 924 ft³ + 2464 ft³
Volume of the composite figure = 3388 ft³
Therefore, the volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.
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Write the equation of a line parallel to 2y = x – 3 and that passes through point (-4,3) in slope intercept form.
Answer:
The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
Step-by-step explanation:
To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.
2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.
The slope of this line is 1/2.
Since we want a line parallel to this line, the slope of the new line will also be 1/2.
Next, we can use the point-slope form of a line to write the equation of the new line.
Point-slope form: y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we get:
y - 3 = (1/2)(x - (-4))
Simplifying, we get:
y - 3 = (1/2)x + 2
Adding 3 to both sides, we get the final equation in slope-intercept form:
y = (1/2)x + 5
Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
someone pls help i really need help with this
Answer:
50° F
Step-by-step explanation:
35 - -15= 50
Check
-15 + 50 = 35
And 35 - 50 = -15
is 1 over 16 the same as 16 A: Yes B.NO
Answer:
1 over 16 is not the same as 16.
1 over 16 is a fraction, which means that it represents a part of a whole. It can be written as 1/16, which means one part out of a total of sixteen equal parts.
On the other hand, 16 is a whole number, which represents a quantity of sixteen units.
So, 1/16 is not equal to 16.
Step-by-step explanation:
what are the coordinates of each point after quadrillateral MNPQ is trans;ated 2units right and 5 units down
The coordinates of each point after the quadrilateral MNPQ is translated 2 units right and 5 units down are:
M' = (x1 + 2, y1 - 5)
N' = (x2 + 2, y2 - 5)
P' = (x3 + 2, y3 - 5)
Q' = (x4 + 2, y4 - 5)
How to calculate the coordinates?To calculate the coordinates, we shall assume that the coordinates of the points of the quadrilateral MNPQ are:
M = (x1, y1)
N = (x2, y2)
P = (x3, y3)
Q = (x4, y4)
Next, we translate the quadrilateral 2 units right and 5 units down by adding 2 to the x-coordinate and subtracting 5 from the y-coordinate of each point.
The new coordinates of the points after the translation will be:
M' = (x1 + 2, y1 - 5)
N' = (x2 + 2, y2 - 5)
P' = (x3 + 2, y3 - 5)
Q' = (x4 + 2, y4 - 5)
Therefore, the coordinates of each point after the quadrilateral is translated 2 units right and 5 units down are:
M' = (x1 + 2, y1 - 5)
N' = (x2 + 2, y2 - 5)
P' = (x3 + 2, y3 - 5)
Q' = (x4 + 2, y4 - 5)
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Question completion:
Although part of your question is missing, you might be referring to the below question:
What are the coordinates of each point after quadrilateral MNPQ is translated 2 units right and 5 units down?
Use the unit circle to find exact value of the trig function
sin(135°)
Guys can someone help me with these 2 problems please that's the matrix
The solution of the matrix is [tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]
A matrix is a rectangular array of numbers arranged in rows and columns. The size of a matrix is given by its dimensions, which indicate the number of rows and columns in the matrix. In this question, both matrices G and F have 4 rows and 5 columns, so we say that they are 4x5 matrices.
Scalar multiplication is performed by multiplying each element of a matrix by a scalar, which is simply a number.
Now, to find the value of 4G + 2F, we need to perform scalar multiplication on each matrix and then add the results. We get:
[tex]4G = 4 * \begin{bmatrix}8 &-5 &-8& -2 &-10 \\-6& -7 &1 &9 &2 \\4& 6 &3 &7 &5 \\-4&-3 &0 &-10 & -9\end{bmatrix}\\= \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 & -36\end{bmatrix}[/tex]
[tex]2F = 2 * \begin{bmatrix}1 &8 &-2& -5 &9 \\-9& 10 &6 &-3 &0 \\4& 5 &-4 &3 &7 \\2&-10 &-6 &-1 & -8\end{bmatrix}= \begin{bmatrix}2 &16 &-4& -10 &18 \\-18& 20 &12 &-6 &0\\8& 10 &-8 &6 &14 \\4&-20 &-12 &-2 & -16\end{bmatrix}[/tex]
Now, we can perform matrix addition on 4G and 2F to get:
[tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]
Therefore, the value of 4G + 2F is the 4x5 matrix given above.
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Which of the following statements about the number line
is true?
A. Number lines can't help you compare numerals.
B. Numbers get larger as you move to the left on the
number line.
C. Numbers get smaller as you move to the left on the
number line.
D. Number lines end with the number 10.
Solve for x. Round to the nearest tenth, if necessary.
50 points
Answer: 8.7
Step-by-step explanation:
Given:
hypotenuse = 9
Angle x =75
opposite of angle = x
Solution:
From SOH CAH TOA, use SOH
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] > substitute
sin 75 = [tex]\frac{x}{9}[/tex] > multiply both sides by 9
9*sin 75 =x
x=8.7
Kyle has three times as much money in his savings account as Hayden Hayden has twice as much money in his savings account as Jeremy combine Kyle Hayden and Jeremy have a total of 612 how much money does Kyle have in his account
Kyle has $306 in his account so, right answer is Option D.
Let Kyle's money = x
Hayden's money = y
Jeremy's money = z
Given that Kyle has three times as much money in his savings account as Hayden.
x = 3y .....Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y ..... Eqn 2
Now Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 .....Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
6y = 612
y = 106
Putting in Eqn 1;
x = 306
Thus, Kyle has $306 in his account.
The right answer is Option D.
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3. Write the following using exponential notation:
(5.
5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7)
Answer:
5.5.5.5.5.5.5.5.5 in exponential notation is 5^9
7.7.7.7.7.7.7.7.7.7.7.7.7.7 in exponential notation is 7^13
Therefore, (5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7) in exponential notation is:
5^9 * 7^13
Examine the steps below. Between which two lines was a mistake made?
A.
between line 1 and line 2
B.
between line 2 and line 3
C.
between line 3 and line 4
D.
between line 4 and line 5
Answer:
A and D
Step-by-step explanation:
A- when multiplying -5 and -3 it should be positive 15.
D- when dividing 3 they just outta nowhere forgot about the negative, it should've been -5
Given that the coefficient of x⁵ in the expansion of (1+kx)⁵ is -672 find the value of k
The value of k that satisfies the given condition is approximately 0.4041.
In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:
C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵
where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.
So, we have the equation:
k⁵ * C(5,k) = -672
We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:
k⁵ * C(5,5-k) = -672
Expanding C(5,5-k), we get:
k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672
Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.
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Please help Thanks
there is a FRACTION symbol two variable symbols y and x
I need to write an equation
The required equation of line is y = 2x
What is equation of line?A straight line's equation is y=mx+c, where m denotes the gradient and c denotes the height at which the line crosses the y-intercept, also known as the y-axis.
According to question:Given points:
(1,2) and (2,4)
then
[tex]Slope of line = \frac{4-2}{2-1}= 2[/tex]
then
y-2 = 2(x-1)
y = 2x - 2 + 2
y = 2x
Thus, required equation of line is y = 2x
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Total score:
of 15 points
(Score for Question 1: of 5 points)
1. The diagram shown is two intersecting lines. The measure of 22 is 29
2
(a) What is the measure of 24? How do you know? Explain your answer in complete sentences.
(b) Suppose the measure of 3 can be represented by (3x - 8)*. What equation can be written to solve for the value of x?
(c) What is the value of x? Show all work.
Answer:
•(Score for Question 2: _ of 5 points)
2. Draw a right triangle with side lengths of 6, 8, and 10 units. For full credit, be sure to include appropriate labels and symbols where necessary. © Stride, Inc. All rights reserved. No reproduction without written consent of Stride, Inc.
Answer:
•Score for Question 3:
_ of 5 points)
3. At a park, a statue has a ring-shaped brick path around it. The outer edge of the brick path is a circle with a radius of 13 m. The inner edge of the brick path is a circle with a radius of 8 m.
Brick path
13 m
8 m
Statue
(a) Write and simplify an expression for the exact area of the brick path. Show all work.
(b) Find the approximate area of the brick path. Use 3.14 to approximate r. Show all work.
The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53
The right angle using the given lengths is attachedThe exact area is 105π square meters and the approximate area is 330 square metersThe two intersecting linesGiven that, we have
∠2 = 29°
(a)
Angles 2 and 4 are vertical angles
So, we have
∠4 = 29°
(b) and (c)
We have
∠3 = (3x - 8)°
Angles 3 and 4 are angles on a straight line
So, we have the equation to be
3x - 8 + 29 = 180
Solving for x, we have
3x = 159
Divide by 3
x = 53
This means that the equation is 3x = 159 and the value of x is 53
The right angle with the given lengthsIn this section, we have the following side lengths
Lengths = 6, 8 and 10
This means that
Side lengths = 6 and 8
Hypotenuse = 10
Next, we create the right angle using the given lengths of the legs and the hypotenuse
Calculating the area of the brick pathHere, we have
R = 13
r = 8
The exact area is calculated as
A = π(R² - r²)
So, we have
A = π(13² - 8²)
Evaluate
A = 105π
For the approximate area, we have
A = 105 * 22/7
A = 330
This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters
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3x^6 • 5x^-2 simplified
Answer:
First, you distribute the 3 into the brackets,
3(x - 2) + 5x
=3(x) + 3(-2) + 5x
=3x - 6 + 5x
Adding the like terms, 3x and 5x, gives you
=8x - 6
Step-by-step explanation:
Please help fast. Thanks! (:
The value of variable y from the system of vertical angles is equal to 125.
How to find the values of a variable associated with system of vertical anglesIn this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:
x + 20 = 3 · x - 50
2 · x = 70
x = 35
Then, by definition of supplementary angles:
(x + 20) + y = 180
55 + y = 180
y = 125
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Make x the subject of m= n+ 1 + x/p
Answer:
Step-by-step explanation:
m = n + 1 + x/p
First, we can start by subtracting (n+1) from both sides:
m - (n+1) = x/p
Then, we can multiply both sides by p to isolate x:
p(m - (n+1)) = x
So the final answer is:
x = p(m - (n+1))
A cube has shaded shapes on three of its faces. Here is a net of the cube. Draw in the two missing shaded shapes.
The appropriate diagram to illustrate the cube is given.
What is a cube?A cube is a three-dimensional shape featureing six equal square faces, with its edges and vertices being of congruent length. It counts as one of the five platonic solids distinguished by all of its features having matching sizes.
The cube can be perceived as a special instance of a rectangular parallelepiped where all six are perfectly square in shape. In order to calculate the volume of such an ordinary cube, the number of its edge needs to be multiplied by itself thrice (V = a³).
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The pair of polygons is similar. Find the missing side measure
The missing side measure is equal to: A. 14.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)
By substituting the given parameters into the formula for scale factor, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
4/5.6 = 10/x
4x = 56
x = 56/4
x = 14
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 29 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects?
Answer:
Step-by-step explanation:
This problem can be solved using the binomial distribution, which gives the probability of obtaining a certain number of successes in a fixed number of independent trials.
Let p be the probability that a single ibuprofen tablet has a defect, which is given as 15% or 0.15. Then, the probability that a single ibuprofen tablet does not have a defect is 1 - p = 0.85.
The acceptance sampling plan requires that at most one tablet does not meet the required specifications out of 29 tablets. This means that the shipment will be accepted if there are 0 or 1 defective tablets in the sample of 29.
The probability of getting exactly k defective tablets in a sample of n tablets is given by the binomial probability formula:
P(k) = (n choose k) * p^k * (1 - p)^(n - k)
where (n choose k) = n! / (k! * (n - k)!) is the number of ways to choose k defective tablets out of n, and ! denotes the factorial function.
To find the probability that the whole shipment will be accepted, we need to find the probability that there are 0 or 1 defective tablets in the sample of 29:
P(0 or 1 defects) = P(0 defects) + P(1 defect)
= (29 choose 0) * 0.15^0 * 0.85^29 + (29 choose 1) * 0.15^1 * 0.85^28
≈ 0.1098
Therefore, the probability that the whole shipment will be accepted is approximately 0.1098 or 10.98%
what is the interquartile range of this data set? enter answer in box
Answer:
do it by yourself what you do while teacher is teaching
Reasoning What is the height of the square pyramid? Use pencil and paper. Once you know which length represents the hypotenuse, does it matter which length you substitute for a and which length you substitute for b? Explain.
The height of the square pyramid is 35.5 in.
From the given figure we can see that the figure is a pyramid.
The base of the pyramid is a square.
The each side of base square i = 24.8 in.
The slant height is = 37.6 in.
So the right angle formed in between prism has hypotenuse = 37.6 in.
one of the rest two sides = 24.8/2 = 12.4 in.
So another side is the height of the pyramid. Let that side be = x in.
By Pythagoras Theorem we get,
(12.4)² + x² = (37.6)²
153.76 + x² = 1413.76
x² = 1413.76 - 153.76
x² = 1260
x = 35.5 (rounding off to nearest tenth and neglecting the negative value obtained from square root as length cannot be negative.)
Hence the height of the square pyramid is 35.5 in.
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To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
The given scenario is Biased, since those who chose to respond may be systematically different than those who chose not to respond. So, the correct answer is C).
The sampling method is biased, since those who chose to respond may be systematically different than those who chose not to respond. This is known as non-response bias, where the opinions and characteristics of those who choose not to respond to the survey may differ from those who choose to respond.
Additionally, only one higher education institution per state was selected, which may not be representative of all institutions within the state. Therefore, the sample may not accurately reflect the population of students in the United States who pay for their higher education. So, the correct option is C).
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--The given question is incomplete, the complete question is given
" To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.
Is the sampling method biased or unbiased and why?
Unbiased, since a random sample was selected
Unbiased, since a large sample was selected
Biased, since those who chose to respond may be systematically different than those who chose not to respond
Biased, since all higher education institutions are represented
Unbiased, since a questionnaire was used
Biased, since every state will be represented in the sample"--
The mass of 12 packets of flour and 8 packets of salt is 19 kg. When 7 packets of flour are removed, the mass became 9.9 kg. Find the mass of each packet of salt in kilogram.
Answer:
1.235 kg
Step-by-step explanation:
Let's assume that each packet of flour and salt weighs the same.
When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.
Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.
Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:
19 kg - 9.12 kg = 9.88 kg
Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:
9.88 kg ÷ 8 = 1.235 kg
Therefore, each packet of salt weighs approximately 1.235 kg.
What does |23| mean?
please I need help in this one
Answer: 55
Step-by-step explanation:
Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
g(x)
(Table)
0 1 2 3 4
1/2 1 2 4 8
A.They have the same y-intercept.
B.They have the same asymptote.
c. They have the same range.
D.They have the same domain.
The functions have the following characteristics:
A. They have the same y-intercept.
D. They have the same domain.
How to compare the graphs of the functionsWhen a function f(x) is transformed by multiplying its input by a constant "a", it results in a new function g(x) = f(ax). In this case, f(x) = 2x, so when we multiply x by a constant "a", we get g(x) = f(ax) = 2ax.
Therefore, the functions f(x) = 2x and g(x) = 2ax have the same y-intercept (0,0) and the same domain (-∞, +∞).
The range of g(x) is determined by the value of "a", which is different from the range of f(x), so option C is not correct. Asymptotes are not relevant for linear functions, so option B is not correct.
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When Sarah opens a map of her neighborhood on her cell phone, she notices that the park near her house is 0.5 cm wide. She zooms in until it is 3 times as large. If the park is 15 m wide, what is the scale of her zoomed-in map?
A 10cm=1 m
B 1cm= 10 m
C 1cm= 30 m
D 3cm= 10m
The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.
To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.
Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.
15 m = 1500 cm
Next, we can set up a proportion:
0.5 cm / x = 1500 cm / (3x)
where x is the scale of the zoomed-in map.
Simplifying the proportion, we get:
0.5(3x) = 1500
1.5x = 1500
x = 1000
Therefore, the answer is (B) 1cm = 10 m.
To learn more about scale click on,
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