A bank offers two different investment options.
Option 1 pays compound interest of 3.6% compounded monthly, meaning that each month the balance increases by 112 of 3.6% of the previous month's balance.
Option 2 pays simple interest of 6% per year, meaning that each year the balance increases by 6% of the initial deposit.
Which type of function can be used to model each option?
The function that can be used to represent option 1 is an exponential function.
The function that can be used to represent option 2 is a linear function.
Linear functions
A linear function is a function that has a single variable raised to the power of 1. Linear functions are usually in the form x + 10.
Option 2 expressed as a linear function is b x 0.06 x 1
Where b represents the amount of money deposited.
Exponential functionsAn exponential function is usually in this form: y = \(a^{x}\).Option 1 expressed as an exponential function is p(1.036)^y
Where:
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Evaluate:
\( {8}^{ - \frac{2}{3} } \)
with steps please
\(8^{-\tfrac 23}\\\\\\=\left(8^{\tfrac 13 }\ \right)^{-2}\\\\\\=\left[\left(2^3\right)^{\tfrac 13} \right]^{-2}\\\\\\=\left(2^{\tfrac 33} \right)^{-2}\\\\\\=2^{-2}\\\\=\dfrac 1{2^2}\\\\\\=\dfrac 14\)
\( {8}^{ - \frac{2}{3} } \\ = {2}^{3 \times - \frac{2}{3} } \\ = {2}^{ - 2} \\ = \frac{1}{2^{ 2}} \\ = \frac{1}{4} \)
Hope you could get an idea from here.
Doubt clarification - use comment section.
Solve for x. Options are 6,3,5,4.
The value of x as required to be determined in the given task content is; 3.
What is the value of x in the given diagram?It follows from the task content that the value of x is required to be determined in the given task content.
By observation; the triangles formed by the parallel lines and the common vertex they share are similar triangles.
On this note, the ratio of their corresponding sides are equal and hence; we have that;
15 / (15 + x) = 10 / (10 + 2)
(15 × 12) = 10 (15 + x)
180 - 150 = 10x
30 = 10x
x = 3.
Consequently, it follows that the value of x as required is; 3.
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A tablet and a digital camcorder are both on sale for 30% off. The regular price of the tablet is $185. The regular price of the camcorder is $140.
Answer:
355
Step-by-step explanation:
185+140= 325
325+20= 355
Answer:
30/185×100=
Step-by-step explanation:
30/140×100=
Complete the missing value in the solution to the equation: 3y+2x=x+4 ( ,2/3)
PLS HELP I BEG WILL GIVE BRAINEIST
Answer:
here ya go
Step-by-step explanation:
example x=7 is a root then ( -7 ) is a factor
Root implies factor of polynomial equation.
How to determine a factor if a root is given?If x=7 is a root of a polynomial equation, it means that when x=7 is substituted into the equation, the value of the equation becomes 0. This implies that (x-7) is a factor of the polynomial equation using the factor theorem.
This is because if we divide the polynomial by (x-7), the remainder will be 0, confirming that (x-7) is a factor of the polynomial. Similarly, if any value of x makes the polynomial equation equal to 0, that value is considered a root of the equation and the corresponding linear factor will be (x - the root value).
Therefore, finding the roots of a polynomial equation is an important step in factoring it completely into linear factors.
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Who likes math?AAAAAAAAA
Answer:is this a literal question?
Step-by-step explanation:
if so than it depends on the subject for me
a researcher is interested comparing quality of sleep between people who work overnight shifts and people who work day shifts. a sample of 50 day shift workers and 50 night shift workers are asked to complete a quality of sleep measure, which the researcher will treat as an interval scale measure. the researcher will compare the mean levels of each group to see if there is a statistically significant difference between the groups. which analysis would be acceptable to use?
The correct analysis would be 3 option
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.
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Guys, again, you only have 100 points for you to answer my math word problem questions from my math homework package from The Hung Vuong Learning Centre Incorporated but please help me with 2 of the math word problem questions from my math homework package from The Hung Vuong Learning Centre Incorporated like immediately as soon as possible, please pay attention carefully in order to understand what I'm asking on The Brainly. :(
Like I really said, "Question #61. There's a cylinder and a cone that have the same radius. But the cone is half as tall as the cylinder. Can you explain how does the volume of the cylinder compares to the volume of the cone?
Question #62. A cylinder has a radius of 15 centimetres and a height of 30 centimetres. There's a sphere with a radius of 15 centimetres will be placed inside the cylinder. What is the volume of the part of the cylinder that remains? Please explain your own answer.
Plus, I need to get my math homework package from The Hung Vuong Learning Centre Incorporated as soon as possible, so please answer it faster without wasting your time, and also please don't post a very fake useless answer because it's a bad habit to do that, so anyways, good luck on answering 2 of the math word problem questions and I will check the answers to see if it’s appropriate. :)"
I hope you understand guys what I asked on The Brainly 2 hours ago. :)
#61
Radius he r and height be h
r1=r2=r2h1=h2\(\\ \tt\longmapsto \dfrac{v1}{v2}=\dfrac{\dfrac{1}{3}\pi r^2h}{\pi r^22h}\)
Cancel πr^2\(\\ \tt\longmapsto \dfrac{v1}{v2}=\dfrac{1/3}{2}\)
\(\\ \tt\longmapsto v1:v2=1:6\)
Cylinder has 6times more volume
#62
For cylinder
r=15cmh=30cm\(\\ \tt\longmapsto V=\pi r^2h=\pi 15^2(30)=225(30)\pi=6750\pi cm^3\)
For sphere
r=15cm\(\\ \tt\longmapsto V=\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\pi 15^3=\dfrac{13500\pi }{3}=4500\pi cm^3\)
Volume left=6750-4500=2250cm^3Answer:
#61
Radius he r and height be h
r1=r2=r
2h1=h2
Cancel πr^2
Cylinder has 6times more volume
#62
For cylinder
r=15cm
h=30cm
For sphere
r=15cm
Volume left=6750-4500=2250cm^3
Step-by-step explanation:
What is 5.1x10^-2 in standard form
Answer:
0.051
Step-by-step explanation:
Because the 10 is to the power of -2, you would move the decimal twice to the left to get 0.051.
Hope this helps!!
Match the graph
with its inequality.
6.677
a. y<-3
b. x > 2
C. 5x+10y > 0
d. y < x
e. 2y – x < 6
f. 6x + 3y >9
g. 3y - 4x > 12
h. y < -2x – 4.
i. 8x – 6y < 10
j. 3x – 1 zy
-10
The characteristics of the given graph that can be used to find the
inequality are the y-intercept and the shaded region of the inequality.
Correct response:
The inequality of the given graph is \(\underline{j. \hspace{0.3 cm} 3 \cdot x - 1 \geq y}\)Method used to find the inequality of the graphGiven:
From the given diagram, we have that the inequality is a linear inequality,
therefore, the inequality can be expressed as y ≤ m·x + c.
Where:
m = The slope
c = The y-intercept
From the graph, the y-intercept of the graph of the inequality is at the point (0, -1)
Therefore;
At x = 0, y = -1The shaded region which is to the right of the line with a positive slope
(the straight line increasing from left to right) indicates that the value of y is
less than the equation of the line of the inequality.
The solid line in the graph indicates that the inequality relationship is less
than or equal to (≤).
The inequality that has -1 as the y-intercept and a shaded region to the right of the solid line from among the given options is option j. 3·x - 1 ≥ y
The above inequality can be written as follows;
y ≤ 3·x - 1
Therefore;
The inequality of the graph is \(\underline{j. \hspace{0.3 cm} 3 \cdot x - 1 \geq y}\)Learn more about inequalities here:
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Find the slope of the line containing the points (4,8) and (4,6) then find the slope of a line parallel to this line and the slope of the line perpendicular to this line.
To calculate the slope between 2 points we use the following equation:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Replacing the points:
\(\begin{gathered} m=\frac{8-6}{4-4} \\ m=\frac{2}{0} \\ m\to\infty \end{gathered}\)In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.
For the perpendicular case, the slope is equal to:
\(\begin{gathered} m_{\perp}=\frac{1}{m} \\ m_{\perp}=\frac{1}{\frac{2}{0}} \\ m_{\perp}=\frac{0}{2} \\ m_{\perp}=0 \end{gathered}\)For the perpendicular case, the slope is zero and would equal one parallel to the X axis.
Answer:
not definednot definedzeroStep-by-step explanation:
The question is asking us to find the slope.
First, we will find the slope of the line that passes through (4,8) and (4,6).
We'll use the slope formula:
\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)
Plug in the data :
\(\bf{m=\dfrac{6-8}{4-4}}\)
\(\bf{m=\dfrac{-2}{0}}\)
\(\bf{m=not\:de fined}\)
If a line's slope is not defined, then it's a vertical line:
\(\rule{1}{350}\)
------
Now, what is the slope of a line that's parallel to the one above? Well, since parallel lines have equal slopes, that one will have an undefined slope too.
As for perpendicular lines, they have slopes that are negative reciprocals of each other. We got that the slope is -2/0. The negative reciprocal of that is 0/2, which simplifies to 0.
Alternatively, you could look at it this way: a horizontal line (a line with zero slope) is perpendicular to a vertical line. So the slope of that line is m = 0.
\(\rule{350}{1}\)
A recipe for cake calls for a ratio of 1 cup of sugar for every 2 cups of flour. If Janelle wants
to use this recipe to bake three cakes, how many cups of sugar and how many cups of flour
would she use in total?
Answer:
3 cups of sugar and 6 cups of sugar
PLZ MARK BRAINLIEST!!!
Step-by-step explanation:
Three cups of sugar and six cups of flour are required to bake the cake, if for cake calls for a ratio of 1 cup of sugar for every 2 cups of flour.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given data:
A recipe for cake calls for a ratio of 1 cup of sugar for every 2 cups of flour.
Calculate the ratio for 1 cake
1 cup of sugar / 2 cups of flour
Calculate the sugar and flour for 3 cake
1 cup of sugar / 2 cups of flour × 3
3 cups of sugar / 6 cups of flour
Therefore, 3 cups of sugar and 6 cups of flour are required to bake the cake if for cake calls for a ratio of 1 cup of sugar for every 2 cups of flour.
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if necessary, how can a student determine the change in angular momentum δlδl of the cylinder from t=0t=0 to t=t0t=t0?
To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:
ΔL = I * Δω
where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.
To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:
Δω = ωt0 - ω0
Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.
The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:
I = (1/2) * m * r^2
where m is the mass of the cylinder and r is the radius of the cylinder.
By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.
It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.
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A gym subscription runs several promotions. Customers can choose from the following offers.
Option A: 25% off an annual subscription of $308. 00
Option B: pay $29 per month
How much will a customer save by purchasing the annual subscription over paying per month?
a
$348
b
$231
c
$79
d
$117
A customer will save $117 by purchasing the annual subscription over paying per month. So the (d) $117 is the right answer.
To determine how much a customer will save by purchasing the annual subscription over paying per month, follow these steps:
Calculate the discounted annual subscription cost:
Option A: 25% off an annual subscription of $308.00
Discount = 25% of $308 = 0.25 * $308 = $77
Discounted Annual Subscription = $308 - $77 = $231
Calculate the total cost of the monthly subscription for one year:
Option B: Pay $29 per month
Total Monthly Subscription Cost = $29 * 12 months = $348
Calculate the savings:
Savings = Total Monthly Subscription Cost - Discounted Annual Subscription
Savings = $348 - $231 = $117
So, a customer will save $117 by purchasing the annual subscription over paying per month. Your answer is d. $117.
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Shelly ran 20 minutes and burned 130 calories.
Part A: Which equations can be used to find the average number of calories, c, burned per minute?
Answer: you can divide 130c/20 minutes to find the average per minute
Step-by-step explanation:
A man bought a computer on hire purchase by making a down payment of$1500 and twelve monthly payments of $250 each. calculate the total hire purchase price
Answer:
$4500
Step-by-step explanation:
Given parameters:
Down payment = $1500
Monthly payment for twelve months =$250
Unknown;
Total hire purchase price = ?
Solution:
To find the total hire purchase price;
Total hire purchase price = Down payment + 12($250)
Total hire purchase price = $1500 + $3000
Total hire purchase price = $4500
You are given a set of data with a mean of 50 and standard deviation of 8. Using the normal curve, give an example of an outlier and explain why.
Answer:
Anything less than 26, and greater than 74.
Step-by-step explanation:
In normal distribution, the outlier is more than e ≈ 2.72 standard deviations above quartile 3, and e standard deviations below quartile 1. These quartiles are divisions that make up what is known as the innerquartile range(IQR). Which defines the variability of a data set given by IQR = Q3-Q1.
Given that the mean of this data is 50, and the standard deviation is 8.
Our outliers are anything less than 26, and anything greater than 74. Since outliers are anything outside the mean plus and minus the standard deviation times 3
\( outliers :/ = :/ mean :/ \pm \)
if u had 76 lessons to do before summer and its march 5th how many would u need to do per week before June?
Answer:
Step-by-step explanation:
From March 5th to May 31st, that is 88 days.
So, you need to do 76 lessons in 88 days = 12.6 weeks.
You need to do 76 : 12.6 = 6.03174603.... (round to 6) lessons per week.
Consider the following solid s. The base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares. Set up an integral that can be used to determine the volume V of the solid.
The volume of the described solid is V = 16r³/3
A solid line S should be drawn between z = a and z = b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A(x).
Volume of S = limₙ→∞ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^a_b {A(x)} \, dx\)
The equation of circle x² + y² = r² where r is the radius of the circle.
Equation of upper semicircle yu= √(r²-x²) and
Equation of lower semicircle yl = -√(r²-x²)
Area of cross-section A(x) = (yu² - yl²)
Substitute yu and yl values
A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²) (1)
The limit for volume v varies from -r to r
Thus Volume v = \(\int\limits^{r}_{-r} {A(x)} \, dx\)
Substitute A(x) from (1)
V = \(\int\limits^{r}_{-r} {4(r^{2}-x^2 )} \, dx\)
V = 4[r²x - x³/3 ]
V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3
The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3
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A circular bike race track 5 meters wide has a inside diameter of 20 meters. What is the area of the track rounded to the nearest sauare meter?
The area of the track is approximately 706.5 square meters.
To find the diameter of the outside of the track, we add twice the width of the track to the inside diameter:
Outside diameter = Inside diameter + 2 × width
Outside diameter = 20 + 2 × 5
Outside diameter = 30 meters
Now that we know the outside diameter, we can find the area of the track. The area of a circle is given by the formula:
Area = π × (diameter/2)²
where π (pi) is a mathematical constant approximately equal to 3.14.
In our case, the diameter of the outside of the track is 30 meters, so the radius is 15 meters. We can now substitute these values into the formula for the area:
Area = π × (30/2)²
Area = π × 15²
Area ≈ 706.5 square meters.
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Need help asap pleaseeeeee
Ayaan deposited $746 into a tax-free savings account. He earns 2.15% interest. How much money will he have in his account after 6 months?
The amount that Ayaan will have in his tax-free savings account after 6 months of depositing $746 at 2.15% interest is $754.02.
What is the future value?The future value refers to the present value plus the interest.
The future value for this savings account can be computed using the simple interest system since there is no compounding of interest.
The initial deposit (present value) = $746
Interest rate = 2.15%
Savings period = 6 months
Future value = $754.02 ($746 + ($746 x 2.15% x 6/12)
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Help me plz this is to much
9514 1404 393
Answer:
1 triangle: 2 m²2 triangles: 4 m²large rectangle: 32 m²small rectangle: 3 m²total area: 39 m²cost of tile: $487.50Step-by-step explanation:
You will run across many examples of poorly edited curriculum materials. This is one of them. We presume that every instance of "inches" should be an instance of "meters". The difference between in and m is not always obvious in a diagram, and m apparently got misinterpreted here.
__
The area of a triangle is given by the formula ...
A = 1/2bh
where b is the base and h is the height perpendicular to the base.
The triangles in this figure have a base of 4 m, and a height of 1 m. Using this formula, we find the area of 1 triangle to be ...
A = 1/2(4 m)(1 m) = 2 square meters . . . . area of 1 triangle
__
The triangles are the same size, so the area of both together is ...
2(2 m²) = 4 square meters . . . . area of both triangles together
__
The large rectangle is 8 m long and 4 m high. Its area is given by the formula ...
A = LW
where the length is L and the width is W. Using this formula, we find the area of the large rectangle to be ...
A = (8 m)(4 m) = 32 m² . . . . area of large rectangle
__
The small rectangle has a length of 3 m and a width of 1 m. Its area is ...
A = (3 m)(1 m) = 3 m² . . . . area of small rectangle
__
The total area is the sum of the areas of the pieces:
total area = 2 triangles + large rectangle + small rectangle
total area = 4 m² + 32 m² + 3 m² = 39 square meters
_____
At $12.50 per square meter, the cost of covering the patio is ...
($12.50/m²)(39 m²) = $487.50 . . . . cost of tile
I need help with this Mathematics question my answer was 1 I not for sure
In the given figure, for Angle X and Angle Y to be equal, line AB and CD should be parallel.
Therefore, the answer is CHOICE 2 : The lines are parallel.
Kiara peeled 2 oranges every 4 hours. At that rate, how many would she peel in 12 hours?
please put an explanation, thank you!
the numerator of a certain fraction is 6 less the denomintate, if the fraction is equal to 3/4 what is the denominator od this fraction
if the fraction is equal to 3/4 what is the denominator od this fraction, the denominator of the fraction is 24.
To find the denominator of the fraction, let's assume it is represented by the variable "x". The numerator of the fraction is then "x - 6". We are given that this fraction is equal to 3/4. So, we can write the equation:
(x - 6) / x = 3/4
To solve for "x", we can cross-multiply:
4(x - 6) = 3x
Expanding the left side of the equation:
4x - 24 = 3x
Subtracting 3x from both sides:
x - 24 = 0
Adding 24 to both sides:
x = 24
Therefore, the denominator of the fraction is 24.
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Problem of Tartaglia (1500-1577): among all positive numbers a, b whose sum is 8, find those for which the product of the two numbers and their difference is largest. (Enter your answers as a comma-separated list.)
a, b = _____
Let x = a - b and express abx in terms of x alone.
As per the information provided, a = 4√3/3 + 4, b = 4 - 4√3/3 the answer can be calculated with optimization method. it will be as follows:
Sum of a and b is 8, we get
a+b=8
b=8−a
Now, let x=a−b
Then we get,
\(x=a−(8−a) \\ x=2a−8 \\ x+8=2 \\ 1 \div 2x+4=a
\)
we use this to answer to solve for b
\(b=8−a \\ =8−(1 \div 2x+4) \\ =4−1 \div 2x
\)
Now we use the product of two numbers and its difference. This can be expressed as:
\(a⋅b⋅x=(1 \div 2x+4)(4−1 \div 2x) \\ x=2 {x}^{2} − \frac{1}{4} {x}^{3} +16x−2x^{2} \\ =−14x^{3} +16x
\)
Thus, this expression that we need to maximize. Take the derivative, set it equal to zero, and solve for x
\(−3 \div 4x ^{2} +16=0 \\ 16 =3 \div 4 x ^{2} \\ 643=x \\ 28√3 \div 3=x\)
Now for us to check that this is a maximum, we have to note that the second derivative is
\(−3 \div 2x
\\ At \\
x=8√3 \div 3
\)
the second derivative is −4√3. Since this number is negative, the point is a maximum.
Now we must find the values of a and b for this x. We have to use the relationship
\(a=1 \div 2x+4\)
\(a=1 \div 2 \times 8√3 \div 3+4 \\ =4√3 \div 3+4\)
now we use the relationship b=8−a
\(b=8−(4√3 \div 3+4) \\ =4−4√3 \div 3\)
The first step in determining a function's maximum or minimum value is differentiating it. Then, set this derivative to zero and conduct the computation.
x. This will reveal the location of a function's maximum or minimum, but it won't reveal which.
Take the second derivative to get more details. A local maximum occurs when both the first and second derivatives are negative. You have a local minimum when both the first derivative and the second derivative are zero.
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Can someone please help me ASAP?? It’s due today!! I will give brainliest If It’s correct.
The correct option that indicates how Christa sliced the rectangular pyramid is the second option.
Christa sliced the pyramid perpendicular to its base through two edges.
What is a rectangular pyramid?A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.
The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.
The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid
The correct option is therefore the second option;
Christa sliced the pyramid perpendicular to its base through two edges
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The scatter plot below shows nine points from a data set. 12.0 10.8 9.6 8.4 7.2 6.0 4.8 3.6 2.4 1.2 ● 0 1 2 3 4 5 6 7 8 9 10
A 4,4,5,5,6,6
b 4,10,4,11,4,12
C8,9,8,10,8,11
D10,10,10,11,10,12
Answer:
Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.
Step-by-step explanation:
The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.
Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.
Now let's examine the given answer choices:
A. .4,4,5,5,6,6
B. .4,10,4,11,4,12
C. 8,9,8,10,8,11
D. 10,10,10,11,10,12
Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.
Therefore, based on the given scatter plot, the set of numbers that matches the points is C.
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