Answer:Given that y represents the cost, and x represents the number of classes, to complete the statements, the table is given for Gymnastics while the equation, y = 18x + 20 is given for Ice-skating program.
Since the table already shows the cost for each specific number of classes for Gymnastics, find that of Ice-skating program for 1, 2, 3, and 4 classes.
For 1 class, substitute x = 1 into y = 18x + 20:
y = 18(1) + 20
y = $38
For 2 class, substitute x = 2 into y = 18x + 20:
y = 18(2) + 20
y = $56
For 3 class, substitute x = 3 into y = 18x + 20:
y = 18(3) + 20
y = $74
For 4 class, substitute x = 4 into the equation y = 18x + 20:
y = 18(4) + 20
y = $92
From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.
Ice-skating is less expensive when the classes is 3 or 4.
Step-by-step explanation:
From the given function, When the number of classes is 1 the football is less expensive.
When the number of classes is 1, the basketball is less expensive.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Four main categories can be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
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Scientists estimate that less than
one-billionth of the Sun's total energy
output each day reaches Earth. What do
you think happens to the rest?
The vast majority of the Sun's energy radiates out into space and does not reach Earth.
Why does so little of the Sun's energy reach Earth?
The reason is that space is vast, and the Sun's energy radiates out in all directions, spreading out over enormous distances. By the time it reaches Earth, it has become highly diluted, with only a tiny fraction of the original energy remaining.
Factors that reduce the amount of the Sun's energy reaching Earth-
The Sun's energy is produced through nuclear fusion in its core, where hydrogen atoms are fused together to form helium, releasing vast amounts of energy in the process. This energy then radiates outwards from the core, passing through various layers of the Sun's atmosphere before eventually reaching the surface and being emitted into space.
As the Sun's energy travels through space, it encounters various obstacles, such as interstellar dust and gas, as well as the solar wind, which is a stream of charged particles that constantly flows out from the Sun. These obstacles can scatter and absorb some of the Sun's energy, further reducing the amount that reaches Earth.
Only a small fraction of the Sun's energy is intercepted by Earth, where it is absorbed by the atmosphere, oceans, and land. The energy that is absorbed by Earth drives the planet's weather and climate systems, powering phenomena such as wind, rain, and the water cycle. The rest of the Sun's energy continues to radiate out into space, where it can influence the temperature and behavior of other planets and celestial objects.
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Use the functisn value to find the indicoted trigancmetric value in the specified quodrant. Futietion value quadrant. Trigonomstric Value
cosich (C)= 3
2
coc(O)
chic(a)
The indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).
To find the indicated trigonometric value in the specified quadrant using the function value, we need to use the relationships between the different trigonometric functions. The given function value is cosich (C) = 3 in quadrant 2.
First, we can use the relationship between cosine and secant to find the value of secant. The relationship is:
sec(O) = 1/cos(O)
Since cosich (C) = 3, we can substitute this value into the equation and solve for sec(O):
sec(O) = 1/3
Next, we can use the relationship between cosine and sine to find the value of sine. The relationship is:
sin^2(O) + cos^2(O) = 1
Substituting the value of cosich (C) = 3 into the equation, we get:
sin^2(O) + 3^2 = 1
Solving for sin^2(O), we get:
sin^2(O) = 1 - 9 = -8
Taking the square root of both sides, we get:
sin(O) = sqrt(-8)
Since we are in quadrant 2, the value of sine will be positive. Therefore, the value of sin(O) is sqrt(-8).
Finally, we can use the relationship between sine and cosecant to find the value of cosecant. The relationship is:
csc(O) = 1/sin(O)
Substituting the value of sin(O) = sqrt(-8) into the equation, we get:
csc(O) = 1/sqrt(-8)
Therefore, the value of csc(O) is 1/sqrt(-8).
In conclusion, the indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).
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3.
The box-and-whisker plot shown below represents
600 scores on a district geometry test.
Therefore , the solution of the given problem of plotting data comes out to be 75 represents the top quartile (Q3) outside the whiskers are also depicted on the plot as individual points.
Describe a data plotting.The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.
Here,
The following details are displayed by the box-and-whisker plot:
The cutoff is somewhere around 35.
=> Around 55 constitutes the bottom quartile (Q1).
=> At around 65, the median (Q2) is.
=> Around 75 represents the top quartile (Q3).
The top number is somewhere around 95.
The whiskers stretch to the minimum and maximum scores, while the box represents the middle 50% of the scores (between Q1 and Q3).
A few outliers that lay outside the whiskers are also depicted on the plot as individual points.
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i need help please this makes no sense
Answer:
Step-by-step explanation:
open the icon
16. Arden surveyed the 6th grade to see what there favorite colors were.
If 48
students chose yellow, how many students
were surveyed in all?"
How
students chose blue?
many
red?
How many chose purple, green& other?
Ifx >= 0 , which function, f(x) models the total monthly cost based on the number of songs a subscriber downloads?
The function that models the total monthly cost, based on the data in the table is; f(x) = 1.25·x + 30
What is a function?A function is a rule, definition or law that specifies an output based on the input provided , such that each input is mapped to exactly one output
The function that models the monthly cost can be found as follows;
Number of songs downloaded [tex]{}[/tex] Monthly cost
0 [tex]{}[/tex] 30.00
1[tex]{}[/tex] 31.25
2[tex]{}[/tex] 32.50
3[tex]{}[/tex] 33.75
4 [tex]{}[/tex] 35.00
The required value of x is; x ≥ 0
The function, f(x) can be found by analyzing the data provided in the table as follows;
The first difference of the data in the Monthly cost column is; 35 - 33.75 = 33.75 - 32.5 = 32.5 - 31.25 = 31.25 - 30.00 = 1.25 = Constant
The (first) difference in the values in the Number of Songs Downloaded column is 1 (constant), therefore, the function is a linear function with a slope of 1.25
The value of the function which is the Monthly cost When the Number of Songs Downloaded is 0 is 30, therefore, the y-intercept is; c = 30
The function f(x) is therefore; f(x) = 1.25·x - 30
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What is the value of x?
Answer:
12
Step-by-step explanation:
Which choice is equivalent to the expression
4 (1/2x - 3y)
Answer:
2x-12y
Step-by-step explanation:
This is equivalent to the original fraction--4(1/2x - 3y)
If we were to solve 4(1/2x - 3y), we'd get: 2x-12y.
Meaning, 2x-12y is equivalent to 4(1/2x - 3y).
Trevor plotted 12 points on a coordinate plane.
Point Location
Z
(4,8)
(4,8)
(6,-2)
Y
X
W
V
U
SA
T
S
nise
R
e
P
O
(6,2)
(3,9)
(3,-5)
(-3,6)
(1,6)
(5,0)
(-1,0)
(0,9)
Which set(s) of points has (have) a distance of 4 units between them?
Select ALL that apply.
Point Z and Point Y
Point X and Point W
Point V and Point U
Point T and Point S
Point R and Point Q
Point P and Point O
The sets of points that have a distance of 4 units between them are:
Point X and Point W
Point T and Point S
How to find the distance between two points?To find the distance between two points, we use the distance formula:
distance = √ (x₂ – x₁)² + (y₂ – y₁) ²
We can calculate the distances between each pair of points and check if any of them are equal to 4.
The distances between the following pairs of points are 4 units:
Point X (3,9) and Point W (5,0): distance = √((5 - 3)² + (0 - 9)²) = √52 = 4.12
Point T (5,0) and Point S (-1,0): distance = √((-1 - 5)² + (0 - 0)²) = √36 = 6
Point T (5,0) and Point S (-3,0): distance = √((-3 - 5)² + (0 - 0)²) = √64 = 8
Point R (1,6) and Point Q (-1,2): distance = √((-1 - 1)² + (2 - 6)²) = √20 = 4.47
Point P (-1,0) and Point O (0,9): distance = √((0 - (-1))² + (9 - 0)²) = √82 = 9.06
Therefore, the only sets of points that have a distance of exactly 4 units between them are Point X and Point W, and Point T and Point S.
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Given that the lines with arrows in figure 10. 29 are parallel , determine the sum of the angles a+b+c+d+e without measuring the angles. Explain your reasoning
The parallel line pairs, AB and BC ; CE and AD are present in the above figure. The sum of the angles a+b+c+d+e without measuring the angles is equals to the 180°.
We have the lines, AB and BC with arrows in above figure are parallel and we determine the sum of the angles a + b + c + d + e, without measuring the angles. Both of lines, AB and BC intersects each other at point B. Similarly, AD and CE lines also intersect. Properties of parallel lines are
Corresponding angles are equal.Vertically opposite angles are equal.Alternate interior angles are equal.Alternate exterior angles are equal.Measure of angle, ECD = d
Measure of angle, CED = c
Measure of angle, ADE = b
Measure of angle, DAE = e
Measure of angle CBA = a ( corresponding angles)
Now, measure of angle ACE, ∠ACE= ∠CED = c ( alternating angles)
Similarly, ∠CAE = ∠CDE = e (alternating angles)
Now, measure of angle ACB = measure of angle BCE + measure of angle ACE
= c + d
Measure of angle CAB = measure of angle CAD + measure of angle DAB
= e + b
Sum of interior angles of a triangle is equals to the 180°. So, ∠ACB + ∠ABC + ∠BAC = 180°
=> c + d + e + b + a = 180°
Hence, required sum of angles is 180°.
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Complete question:
Given that the lines with arrows in above figure are parallel , determine the sum of the angles a+b+c+d+e without measuring the angles. Explain your reasoning
To determine the number of squirrels in a conservation area, a researcher catches and marks squirrels. Then the researcher releases them. Later squirrels are caught and it is found that of them are tagged. About how many squirrels are in the conservation area?
Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.
Unitary method: what is it?To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:
There were n1 squirrels in the first group.
Second sample's fox count is equal to n2.
Second sample's total number of labelled squirrels is m2.
The following provides the Lincoln-Petersen index:
=> n1 * n2 / m2
Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.
=> n1 * n2 / m2 = 100 * 200 / 20 = 1000
Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.
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What is equivalent to 14-6 A. 14 + 6 B. 14+(-6) C. -14 + 6 D. -14+(-6)
Answer:
B. 14 +(-6)
Step-by-step explanation:
Adding the term negative 6 to 14 is equivalent to subtracting 6 from 14
Answer:
Step-by-step explanation:
ifdk
Describe the graph of y = 1/2x-10 -3 compared to the graph of y=1/x
The graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.
What is a graph ?
Graph can be defined as visual representation of data using ordered pairs.
The graphs of y = 1/2x - 10 - 3 and y = 1/x have different shapes and behaviors.
The graph of y = 1/2x - 10 - 3 is a linear function with a slope of 1/2 and a y-intercept of -13. This means that the graph will have a constant slope of 1/2, and will be downward sloping from left to right. As x increases, y decreases at a steady rate.
On the other hand, the graph of y = 1/x is a non-linear function that is a hyperbola. This means that the graph will be curved and will have two branches, one in the first quadrant and the other in the third quadrant. The graph will approach the x and y-axes but will never touch them. The curve will be symmetric about the line y = x, which means that for every point (x, y) on the graph, there will be a corresponding point (y, x) on the graph.
Therefore, the graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.
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vide as indicated. Simplify the answer. (x^(2)+11x+28)/(x^(2)+4x-21)-:(x^(2)+2x-8)/(6x-18)
To solve this problem, we need to first find the common denominator of the two fractions and then subtract the numerators. The common denominator is (x^(2)+4x-21)*(6x-18).
So, we can rewrite the problem as:
[(x^(2)+11x+28)*(6x-18) - (x^(2)+2x-8)*(x^(2)+4x-21)]/[(x^(2)+4x-21)*(6x-18)]
Next, we need to simplify the numerators by distributing and combining like terms:
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+4x^(3)-21x^(2)+2x^(3)+8x^(2)-16x-8x^(2)-32x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+6x^(3)-21x^(2)+8x^(2)-48x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - x^(4)-6x^(3)+21x^(2)-8x^(2)+48x-168]/[(x^(2)+4x-21)*(6x-18)]
Next, we can combine like terms in the numerator:
[-x^(4)+12x^(2)-30x-336]/[(x^(2)+4x-21)*(6x-18)]
Finally, we can simplify the denominator by factoring:
[-x^(4)+12x^(2)-30x-336]/[(x+7)(x-3)*(6x-18)]
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Sean planted seeds in 0.2 square yards of his garden in 1.5 hours. How long will it take Sean to plant seeds in 0.5 square yards of the garden?
3 hours
3 hours
3.5 hours
3.5 hours
3.75 hours
3.75 hours
30 hours
It will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.
What is multiplication ?Multiplication is a basic arithmetic operation that involves combining two or more numbers to get a product. It is often represented using the multiplication symbol "*", and the numbers involved are referred to as factors. The result of a multiplication operation is called the product.
According to given information :We can start by using the ratio of square yards to time as a proportion:
0.2 sq yd / 1.5 hrs = 0.5 sq yd / x hrs
Cross-multiplying, we get:
0.2 sq yd * x hrs = 1.5 hrs * 0.5 sq yd
Simplifying, we get:
x = (1.5 hrs * 0.5 sq yd) / 0.2 sq yd
x = 3.75 hrs
Therefore, it will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.
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What are the coordinates of R′ for the dilation centered at P with scale factor 0.5?
Type answer as a decimal where needed.
The coordinates of R′ for the dilation centered at P with scale factor 0.5 are R' (-1, -0.5).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 0.5 centered at the point P (-3, -3) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate R, we have;
Coordinate R = (1, 2) → (0.5(1 - (-3)) + (-3), 0.5(2 - (-3)) + (-3))
Coordinate R = (1, 2) → (0.5(1 + 3) - 3, 0.5(2 + 3) - 3)
Coordinate R = (1, 2) → (0.5(4) - 3, 0.5(5) - 3)
Coordinate R' = (1, 2) → (-1, -0.5)
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simplify 4p+5+4p
choose 1 answer
*8(a+5)
*13a
*5
*8a+5
*20a
Answer:
4p + 5 + 4p
Adding similar terms => 8p + 5Answer:
8p+5
Step-by-step explanation:
4p+4p+5
8p+5
...............
A cone has a volume of 2863.68 cubic meters and a height of 19 meters. What is its radius?
r ≈ 12 meters is your answer :)
Anyway, it is from this formula: V=πr^ 2 h/ 3
it is actually ≈ 11.99696m
Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. )
tan2(x) = sec(x) − 1
The solution to the equation tan²(x) = sec(x) − 1 in the interval [0, 2π) is x = 0
Consider equation tan²(x) = sec(x) − 1
We know that tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x)
so the equation becomes,
[tex]\frac{sin^2(x)}{cos^2(x)}-\frac{1}{cos(x)}+1=0[/tex]
sin²(x) - cos(x) + cos²(x) = 0
We know that the trignometric identity sin²(x) + cos²(x) = 1
(1 - cos²(x)) - cos(x) + cos²(x) = 0
1 - cos²(x) - cos(x) + cos²(x) = 0
1 - cos(x) = 0
cos(x) = 1
We know that for x = 0 and 2π, the value of cos(x) is 1
In the interval [0, 2π), the solution for equation would be x = 0
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The complete question is:
Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) tan²(x) = sec(x) − 1
Logan invested $3,800 in an account paying an interest rate of 5½ % compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6¹/8%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.
What is Compound Interest?Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Here, A = Amount,
P = Principal Amount
r = Rate of interest
n = Number of times interest is charged in a year
t = number of years
Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),
the number of times the interest is charged in a year (n=4),
and the final amount is $660,
therefore, number of years will be equal to,
[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]
[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]
[tex]1.6923 = (1.01375)^{4*t}[/tex]
[tex]log_{1.01375}1.6923 = 4t[/tex]
[tex]4t = 38.5234[/tex]
[tex]t = 9.63[/tex]
Hence, number of years it will take for $390 to become $660 is 9.63 years.
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olve the compound inequality. 4u+5>13 and 2u+6>=16 raph the solution on the number line. there is no solution, click on "No solut
we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.
To solve the compound inequality, we need to isolate the variable on one side of the inequality.
For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8
Then, we can divide both sides by 4 to get:
u > 2
For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10
Then, we can divide both sides by 2 to get:
u >= 5
Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.
On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.
The solution to the compound inequality is u >= 5.
Here is the graph of the solution on the number line:
0 1 2 3 4 5 6 7 8 9 10
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A large container of breath mints has a mass of 50 g. A small container has a mass of 32 g. What is the percent decrease from the mass of the large container to the mass of the small container?
Answer:
The percent decrease is 36%.
Step-by-step explanation:
4500 dollars is placed in an account with an annual interest rate of 7%. To the nearest tenth of a year, how long will it take for the account value to reach 10800 dollars?
It will take 13 years for the account value to reach $10,800.
How long will it take to grow to $10,800?Compound interest means addition of interest to the principal sum of a loan or deposit which means interest on principal plus interest.
We will use the formula for compound interest [tex]A = P(1 + r/n)^{nt}[/tex]
Given that
A = Final account value ($10,800)
P = Principal amount ($4,500)
r = Annual interest rate (7% or 0.07)
n = 1
t = ?
$10,800 = $4,500(1 + 0.07/1)^(1*t)
Dividing by $4,500:
2.4 = (1.07)^t
Taking the logarithm of sides:
log(2.4) = log((1.07)^t)
Using logarithmic identity log(a^b) = b*log(a):
log(2.4) = t*log(1.07)
Dividing by log(1.07):
t = log(2.4) / log(1.07)
t = 12.9394949072
t = 13.
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Please answer number 10. Please answer both parts. Show work. Thank you
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.
The dimensions of the triangular prism are (2x + 2), (x + 5), and (3x - 2). Then the volume is given as,
V = (1/2) · (2x + 2) · (x + 5) · (3x - 2)
V = (x + 1) · (x + 5) · (3x - 2)
V = (x² + 6x + 5) · (3x - 2)
V = 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, then the volume is given as,
V = (1/2) · [0.50 × (2x + 2)] · (x + 5) · (3x - 2)
V = (1/2) · (x + 1) · (x + 5) · (3x - 2)
V = (1/2) · (x² + 6x + 5) · (3x - 2)
V = (1/2) · (3x³ + 16x² + 3x - 10)
V = 1.5x³ + 8x² + 1.5x - 5
The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.
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What is the equation of the line of best fit for the above data? Round the slope
and y-intercept to the nearest hundredth. Interpret the slope and y-intercept.
We can conclude that the equation of the line of best fit is -
ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -
intercept is 1077.04596.
What is line of best fit?A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.Given is a table as shown in the image.
{X - M(x)}-6.6
-5.6
-3.6
-1.6
-0.6
0.4
2.4
3.4
5.4
6.4
{Y - M(y)}-4887.5
-3887.5
-2587.5
-1287.5
-637.5
962.5
1762.5
2312.5
3737.5
4512.5
{X - M(x)}²43.56
31.36
12.96
2.56
0.36
0.16
5.76
11.56
29.16
40.96
{SS} : 178.4
{X - M(x)}{Y - M(y)}32257.5
21770
9315
2060
382.5
385
4230
7862.5
20182.5
28880
{SP} : 127325
Sum of {X} = 66
Sum of {Y} = 57875
Mean {X} = 6.6
Mean {Y} = 5787.5
Sum of squares {SSₓ} = 178.4
Sum of products {SP} = 127325
Regression Equation -
ŷ = bX + a
b = SP/SSₓ = 127325/178.4 = 713.70516
a = MY - bMₓ = 5787.5 - (713.71*6.6) = 1077.04596
ŷ = 713.70516X + 1077.04596
Slope -
{m} = 713.70516
{y} - intercept = 1077.04596
Therefore, we can conclude that the equation of the line of best fit is -
ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -
intercept is 1077.04596.
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The table shows the distance a runner has traveled y, in miles, x minutes after the start of a race. What is the runner's average rate of change, in miles per minute, from 60 to 120 minutes?
Time (min) Distance (miles)
0 0
30 3. 48
60 6. 42
90 9. 18
120 12. 0
The runner's average rate of change from 60 to 120 minutes is 0.093 miles per minute based on the given information.
Given that,
In the table, it shows the distance a runner has traveled.
The time (in minutes) and distance (in miles) values are as follows:
0 minutes: 0 miles
30 minutes: 3.48 miles
60 minutes: 6.42 miles
90 minutes: 9.18 miles
120 minutes: 12.0 miles
To find the runner's average rate of change from 60 to 120 minutes,
Use the formula:
The average rate of change = (Change in the distance) / (Change in time)
From the table,
At 60 minutes:
The runner has traveled 6.42 miles,
And at 120 minutes:
The runner has traveled 12.0 miles.
So, the change in distance is 12.0 miles - 6.42 miles = 5.58 miles.
The change in time is 120 minutes - 60 minutes = 60 minutes.
Now, we can calculate the average rate of change:
The average rate of change = 5.58 miles / 60 minutes
The average rate of change = 0.093 miles per minute.
Hence,
The runner's average rate of change from 60 to 120 minutes is 0.093 miles per minute.
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what type of transformation has occurred from f(x) to g(x) on the graph
a)cant be determined
b)rotation
c) reflection
d) vertical translation
The solution is, it represents a vertical translation, and value is (d) k = 8.
What is transformation?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
here, we have,
Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.
When looking at the graph we can discard 2 of the options, these are rotation (as they are parallel, it is impossible to find a rotation axis) and reflection. We can observe that it occur a translation. To know what kind of translation happened, let's look at the y intercept of both lines.
For f(x) the y intercept is 0 and for g(x) the y intercept is -4, it means it occured a vertical translation down 4 units.
so, we have,
The value k in the equation ...
g(x) = f(x) +k
represents a vertical translation by k units.
The vertex coordinates for f(x) and g(x) are ...
f(x): vertex = (-3, -3)
g(x): vertex = (-3, 5)
This means ...
f(-3) = -3
g(-3) = 5 = f(-3) +k = -3 +8
⇒ k = 8
Hence, The solution is, it represents a vertical translation, and value is (d) k = 8.
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
The triangles are similar thus option A. Yes, SSS
What are similar triangles?When the corresponding properties of two or more triangles have common relations, then the triangles are said to be similar. Thus the similarity property can be expressed as either Side-Side-Side, Side-Angle-Side, Side-Angle-Angle, Angle-Side-Side etc.
Though two or more triangles are said to be similar but not congruent.
Considering the properties of the triangles ABX and YZX, it can be concluded that the triangles are similar by Side-Side-Side similarity property. Therefore the appropriate option is A. Yes, SSS.
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Find y(t) of the following equation.
y’’ + 3y’ - 4y = 2 , y(0) = 0, y’(0) = 0
The given equation is a second order differential equation, which can be solved using the method of undetermined coefficients. The homogenous solution of the equation is:
yh = c1e2t + c2e-t
By applying the initial conditions, we get: c1 = 0, c2 = 0.
Therefore, the homogenous solution is: yh = 0.
The particular solution of the equation is:
yp = At2 + Bt + C
Substituting yp and its derivatives in the given equation and equating the coefficients of each term on both sides, we get:
A = 1/2, B = 0, C = 0
Therefore, the particular solution is: yp = 1/2t2
Thus, the solution of the given equation is:
y(t) = yh + yp = 1/2t2
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What is the area of the arrow shaped polygon in square units
The area of the arrow shaped polygon in square units is: 80 square units
How to find the area of the Polygon?For triangle BCD:
b = Base = 4 - 2 = 2 units
h = Height = 4 units
Area = [tex]\frac{1}{2}[/tex]bh
Area = [tex]\frac{1}{2}[/tex] × 2 × 4
Area = 8 square units
For triangle DEF
b = Base = 2 - (-1) = 3 units
h = Height = 4 units
Area = [tex]\frac{1}{2}[/tex] × 3 × 4
Area = 6 square units
For trapezoid ABFG:
a = 4 - (-1) = 5.5 units
b = 4 - (-8) = 12 units
h = 8 units
Area = [tex]\frac{1}{2}[/tex](a + b)h
Area = [tex]\frac{1}{2}[/tex](5.5 + 12)8
Area = 70 square units
Total area = 8 + 6 + 70
Total Area = 84 square units
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