The marginal product of capital is 3000 units of output when 5 units of capital and 10 units of labor are employed.
The marginal product of capital (MPK) is defined as the additional output that results from adding one more unit of capital while holding other inputs constant.
To find the MPK when 5 units of capital and 10 units of labor are employed, we need to take the partial derivative of the production function with respect to capital, holding labor constant at 10:
MPK = ∂q/∂k | l=10
Taking the partial derivative of the production function with respect to k, we get:
[tex]∂q/∂k = 12k^2l[/tex]
Substituting k=5 and l=10, we get:
MPK = ∂q/∂k | l=10 = [tex]12(5)^2(10) = 3000[/tex]
Therefore, the marginal product of capital is 3000 units of output when 5 units of capital and 10 units of labor are employed.
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Find the odds against hitting the ball if you have made 3 out of 19 attempts
We conclude that the odds of hitting the ball are 0.158
How to find the odds?
The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.
Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:
P = 3/19 = 0.158
We conclude that the odds of hitting the ball are 0.158
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As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.
What is the Central limit theorem?The Central limit theorem says that the normal probability distribution is used to approximate the sampling distribution of the sample proportions and sample means whenever the sample size is large.Approximation of the distribution occurs when the sample size is greater than or equal to 30 and n(1 - p) ≥ 5.Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.
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Find the roots of sin(x) which lie in [0, pi]
Answer:
Option (1)
Step-by-step explanation:
From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.
PLLLLLEASE I NEED HELP SO BADLY PLEASE ASAP PLEASE PLEASE T_T
Answer:
[tex]x^2+7x-8-\frac{3}{x-7}[/tex]
Step-by-step explanation:
I think this question is a bit hard to explain by typing, so I'll add an image down below.
I used long division for this question, and the final answer is: [tex]x^2+7x-8-\frac{3}{x-7}[/tex]
rewrite the equation to represent the resistance of resistor 2, r2, in terms of rt and r1.
The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.
In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]
We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.
To rewrite the equation, we do as follows:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]
Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
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For the complete question, refer to the attachment.
Solve for x using common denominators.
2 over the quantity 3 times the binomial x minus 1 equals x over the quantity x minus 1
Answer: 2/3
Step-by-step explanation:
The common denominator would be 3(x-1). Thus, you need to multiply the expression on the right by 3/3 to achieve a common denominator. Then you would have 3x/3(x-1).
The equation then is 2/3(x-1) = 3x/3(x-1)
You can cancel out the denominators now, and you have 2 = 3x, so x = 2/3
Answer:
A
Step-by-step explanation:
Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angles. In the figure, angle CAB measures 60°.
What is m∠ACB?
°
What is the length of segment AB?
What is the perimeter of the hexagon?
The perimeter of the hexagon is
the circumference of the circle.
The circumference of the circle is
.
The solution to the questions are:
The value of [tex]< ACB\ is\ 60\textdegree[/tex]. As a consequence, the radius of the circle is equal to the length of the segment AB.AB = BC =CA = R. As a consequence, the radius of the circle is equal to the length of the segment AB. The perimeter of the hexagon is equal to r times 6. As a result, the number 6r represents the hexagon's perimeter.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.What is the length of segment AB?1) Generally, the equation for m∠ACB is mathematically given as
CA= CB
CA = radius of the circle
Therefore,
∠CAB =
[tex]\angle CBA = 60 \textdegree[/tex]
the sum of all the angles of a triangle
the sum of all the angles of a triangle is 180°
[tex]< CAB + < CBA + < ACB = 180 \textdegree[/tex]
[tex]60\textdegree + 60\textdegree + < ACB = 180\textdegree[/tex]
[tex]120\tetxtdegree + < ACB = 180\tetxtdegree[/tex]
[tex]< ACB = 60\textdegree[/tex]
The value of [tex]< ACB\ is\ 60\textdegree[/tex].
2. What is the length of segment AB?
In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.
In a triangle with equilateral sides, each of the triangle's three sides has the same length.
AB = BC =CA = R
As a consequence, the radius of the circle is equal to the length of the segment AB.
3. What is the perimeter of the hexagon?The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.
The circumference of the hexagon is equal to 6 times a.
The circumference of the hexagon is equal to six times each side (AB)
The perimeter of the hexagon is equal to r times 6.
As a result, the number 6r represents the hexagon's perimeter.
4. The perimeter of the hexagon is 6r the circumference of the circle.
the perimeter of the hexagon = 6rthe perimeter of the circle = [tex]2 \pi[/tex][tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.
5. The circumference of the circle is 6.28r.
the perimeter of the circle = [tex]2 \pi r[/tex]
[tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a result, the diameter of the circle is a fraction of a unit bigger than.
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Answer:
1. 60 degrees
2. r
3. 6r
4. slightly less than
5. slightly greater than 6r
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
Increase 320 mangoes by 5%
Answer:
336 mangoes
Step-by-step explanation:
If 320 mangoes = 100%
Increasing them by 5% means that we will need to work out 105%
32 mangoes = 10%
3.2 mangoes = 1%
336 mangoes = 105%
Our final answer is 336 mangoes
Hope this helped and have a good day
On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). a point is at (2, 3). what is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x 2y = 4 x 2y = 8 2x y = 4 2x y = 8
The equation of the line that is parallel and passes through the point (2,3) is; x +2y =8.
What is the equation of the line that passes through (2,3)?If follows from the task content that the slope of the first line is; (-4-0)/(4-(-4)) = -1/2.
Hence, since the lines are parallel, they have the same slope and the equation of the second line is;
-1/2 = (y-3)/(x-2)
-x+2 = 2y -6
x +2y =8.
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Answer: b on edg
Step-by-step explanation:
x is directly proportional to w²
When w = 4, x = 48
y is inversely proportional to x³
When x = 2, y = 14
Find a formula for y in terms of w.
Give your answer in its simplest form.
The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³
Variationx = k × w²
w = 4, x = 48
48 = k × 4²
48 = k × 16
48 = 16k
k = 48/16
k = 3
So,
x = k × w²
x = 3 × w²
x = 3w²
y = k/x³
x = 2, y = 14
14 = k / 2³
14 × 2³ = k
14 × 8 = k
112 = k
So,
y = k/x³
y = 112/x³
y = (1/112)x³
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What is the slope of the line through parentheses two, three parentheses and parentheses -3, four parentheses?
The Slope of the line :
[tex]m=-\frac{1}{5} \approx-0.2[/tex]
What is slope?Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.
Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.
slope = (y₂ - y₁) / (x₂ - x₁)
Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.
P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
we have that:
[tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]
Fill in the blanks in the slope calculation,
[tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]
Reaction: the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]
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in 2019 there were 16 named storms, of which 8 grew into hurricanes and 5 were major. What fraction of hurricanes were major?
Which of the following sets of ordered pairs represents a function
A.{-8,14) , (-7,-12) , (-6,-10) ,( -5,-8)}
B. {(-4,-14) , (-9,-12) , (-6,-10), (-9,-8)}
C {(8,-2) , (9,-1),(10,2),(8,-10)}
D. { (-8,-6) , (-5,-3) , (-2,0),(-2,3)}
Answer: A
Step-by-step explanation:
Each value of x maps onto only one value of y.
Have a question, solve it if you can?
A carpenter cuts the corners of a rectangle to make the trapezoid shown.
An isosceles trapezoid is shown. The top left angle is (9 x) degrees and the bottom left angle is (7 x + 4) degrees.
What is the value of x?
5.375
5.5
11
13
The value of x in the trapezoid is 11.
Properties of an isosceles trapezoidThe base angles are the sameThe sum of opposite angles is 180° or supplementary.The diagonals are the same in length.Therefore, the angle 9x and 7x + 4 are supplementary.
Hence,
9x + 7x + 4 = 180
16x + 4 = 180
16x = 180 - 4
16x = 176
x = 176 / 16
x = 11
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Answer:11
Step-by-step explanation:Easy
How many roots does the polynomial….
Answer:
(a) 3
Step-by-step explanation:
The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.
RootsThe degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.
In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
The triangles are similar by SAS principle.
How to know similar triangles?Similar triangles have the same shape but may have different sizes.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are congruent.
Therefore, using SAS ratio,
6 / 8 = 8 × 3 / 32
6 / 8 = 24 / 32 = 3 / 4
Therefore, the corresponding sides are a ratio of each other.
Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal
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Which statements about the system are true? Select two options.
y = y equals StartFraction 1 over 3 EndFraction x minus 4.x – 4
3y – x = –7
Answer:
no solution
Step-by-step explanation:
y = (1/3)x - 4
3y - x = -7
put the first equation into the second
3(1/3)x - (3)4 - x = -7
x - 12 - x = -7
-12 = -7 can never be true so this is no solution
D= [xlx is a whole number}
E = {xlx is a perfect square between 1 and 9)
F = (xlx is an even number greater than or equal to 2 and less than 9]
Which of the following is D n F?
O (4, 6).
O (2, 4, 6)
O (2,4,6,8)
O (2)
Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Step-by-step explanation:
Let's first find the specific numbers that are in sets D and F.
[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.
[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.
Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.
[tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Please please help me dayson is covering a package in the shape of a rectangular prism with wrapping paper. the package is 50 centimeters by 20 centimeters by 18 centimeters. he has 1 square meter of wrapping paper. can he completely cover the package with wrapping paper? complete the explanation to show your answer. dayson has 1 m2 of wrapping paper, which is cm2. the package has a surface area of cm2. does dayson have enough paper? enter yes or no.
The package has a surface area of 4520cm². The area of the package is less than the area of the wrapping paper. So, dayson can cover the package with the wrapping paper.
According to the question,
The first step is to determine the surface area of the package.
Total surface area of a cuboid = 2 (l w + w h + l h)
where:
• l = length
• w = width
• h = height
2[(50 x 20) + (50 x 18) + (20 x 18)] = 4520cm²
The second step is to convert 1 square meter to cm
1m² = 100 cm²
100 x 100 = 10,000
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A recent survey suggests that 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus. What is the probability that a randomly chosen college student either has a job or lives on campus
[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that a randomly chosen college student either has a job or lives on campus:
Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.
So, out of 100 students, 42 students either has a job or live on campus.
43 college students have a job and 12 live on campus.
So, 43 + 42 + 12 = 85 + 54 - 42
85 + 12 = 139 - 42
97 = 97
Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
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Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole
Answer:
12.8 m.
Step-by-step explanation:
The length of the wire on the shorter pole (AC)
= √(6^2+8^2)
= √100
= 10 m.
The 2 triangles are similar so
10/16 = 8/x where x is height of taller pole.
10x = 128
x = 12.8m
A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 54.50 and a standard deviation of 9. If 67.66% of his students received grades of C or above, what is the minimum score of those students receiving a grade of at least a C
Students who receive a grade of at least a C must have a minimum score of 50.38.
Calculation of the minimum scoreWe may assume that the cut-off will be below 67.66 % because that percentage is more than 50%.
To get the value of 67.66 - 50 = 17.66, we must search in a regular normal table.
Hence, A z value of 0.458 will cause that value to occur.
Next, increase the standard deviation of 9 by 0.458.
The result is 4.122.
This indicates that the threshold for a student earning a C or higher is the mean minus 4.122.
So, the final result is 54.50-4.122 = 50.38.
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Travis jogged to his friend's house 10 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 16 mph slower than the rate when he was riding. What was his jogging rate?
Answer asap please :)))
Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:
[tex]v = \frac{10}{t + 2}[/tex]
Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:
[tex]v + 16 = \frac{10}{t}[/tex]
Then, considering the first equation and replacing in the second:
[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]
[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]
[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]
16t² + 32t - 20 = 0 -> t = 0.5.
Then his jogging rate in mph was:
[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]
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Select the correct location on the proof.
Given: TriangleXYZ with altitude h
Prove: x^2 = z^2 + y^2 - 2yz cos(X)
The first error in the proof is the fourth reason
What are mathematical proofs?Mathematical proofs are statements or collections of statements that are used to prove or disprove a statement, proof or theory
How to determine the first error in the proof?To determine the first error in the proof, we simply read through the statements and the given reason
From the table in the question, we have the following conclusions
Statement 1 is correct because the given parameter is the triangle XYZ with altitude hStatement 2 is correct because it represents the definition of cosine and sineWhen the equations in statement 2 are cross multiplied, they give the equations in statement 3 (by the multiplication operation). This means that statement 2 is correctThe reason at statement 4 is incorrect. This is so because x^ = h^2 + (y - r)^2 as used in statement 4 represents the Pythagoras theorem and not the substitution property of equalityHence, the first error in the proof is the fourth reason
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Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Finding Function Values for Elements of the Domain”Below is an example of one.
——————————————————————
Example :
For the problem below find the range for the given.
Given: b(x) = -2x + 12, find the range of b for the domain {-3, 5, 9}.
——————————————————————
2. Answer each question and write a brief step by step process on how you got the answer to each of your questions.
This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:
Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.
c(1) = 8(1) + 32 = 8 + 32 = 40
c(3) = 8(3) + 32 = 24 + 32 = 56
c(5) = 8(5) + 32 = 40 + 32 = 72
Range: {40, 56, 72}
Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, and subtracting 7.
d(-2) = -2 - 7 = -9
d(3) = 3 - 7 = -4
Range: {-9. -4}
Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.
f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5
f(11) = 7(11) + 738 = 77 + 738 = 815
Range: {748.5, 815}
Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.
g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932
g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032
g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556
Range: {-132932, -203032, -710556}
Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.
h(1) = -3(1) - 4 = -3 - 4 = -7
h(2) = -3(2) - 4 = -6 - 4 = -10
h(3) - -3(3) - 4 = -9 - 4 = -13
Range: {-13, -10, -7}
b(-3)
-2(-3)+126+1218b(5)
-2(5)+12-10+122b(9)
-2(9)+12-18+12-6Range
{-6,2,18}Rest questions
#1
k(x)=2x²-5
Find the range of k for domain {1,2,6}
#2
h(x)=9x³
Find the range of h for domain {9,0,8}
#3
o(x)=6x-7
find the range of o for domain {0,1,9}
#4
p(x)=23x²-5x
Find the range of p for domain {3,4,8}
Can someone please help us
180-180=100
2+3=5
100÷5= 20
x = 20
Answer:
[tex]5x+80=180[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
This is a straight line which is always 180°.
Here there are 3 angles adding up to the total 180°.
So the initial equation is [tex]3x+80+2x =180[/tex].
But there are coefficients that share the same variable.
So by simplifying the equation, you end up with:
[tex]5x+80=180[/tex]
The rectangle pre-image has a length of 12 and width of 6. The rectangle image has a length of 6 and width of 3.
Find the scale factor of the dilation shown in the diagram.
1/2
1/3
2
3
Answer: 1/2
Step-by-step explanation:
Scale factor = (image)/(preimage) = 6/12 = 1/2
A tub contains red, green, blue and white counters. 5% of the counters are red, with an equal number of blue and white counters. The ratio of red to green counters is 3: 7. There is 20 more green than red counters. What is the probability of picking a red or blue counter?
The probability of picking a red counter is therefore; 8/25.
What is the probability of picking a red counter?Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;
x = (2/3)× 24 = 16 red.
The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.
The total number of counters is therefore; 40/0.8 = 50 counters.
The probability of picking a red counter is therefore; 16/50 = 8/25.
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The graph shows the amount of money that Janice saves each week from her summer job. Which equation best represents the graph?
The equation which best represents the graph shows the amount of money that Janice saves each week from her summer job is option A which is y=200x.
Given a graph showing the amount of money that Janice saves each week from her summer job.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation and cubic equation.
Equation can be formed from any two points present on the graph with the help of following formula:
[tex](y-y_{1})=(y_{2} -y_{1} ) /(x_{2} -x_{1} )*(x-x_{1} )[/tex] where [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex]are the points.
So,we have to find points first which are (6,1200),(7,1400)
Put the values in the formula:
(y-1200)=(1400-1200)/(7-1)*(x-1200)
y-1200=200/1(x-6)
y-1200=200(x-6)
y-1200=200x-1200
y=200x-1200+1200
y=200x
Hence the equation shows the amount of monet that Janice saves each week from her summer job is option A which is y=200x.
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