General Idea:
We need to apply the below formula to find the trend line from the given x and y values.
[tex] (1)\; mean:\; \bar{x}\;=\;\frac{\sum x_i}{n}, \; \;\bar{y}\;=\;\frac{\sum y_i}{n}\\ \\ (2) \;trend\; line: \; y=A+Bx, \;B=\frac{S_{xy}}{S_{xx}}, \;\;A=\bar{y}-B\bar{x}\\ \\ Where:\\ \\ S_{xx}=\frac{\sum x_i^2}{n}-\bar{x}^2\\ \\S_{xy}=\frac{\sum x_iy_i}{n}-\bar{x} \cdot \bar{y} [/tex]
Applying the concept:
In the graph given the trend line passes through two points (1, 8) and (7, 1).
We need to make use of the two point formula to find the equation of trend line
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Substituting the points (1, 8) and (7, 1) in the above formula to find slope we get...
[tex] m = \frac{1-8}{7-1}=\frac{-7}{6} [/tex]
The point slope form of an equation which is used to write the equation of line when we know a point and slope is given below:
[tex] y-y_1=m(x-x_1) [/tex]
Substituting the values in the above formula we get ...
[tex] y-8=\frac{-7}{6}(x-1)\\Distributing \; -7/6\; in\; the\; right\; side\; of\; the\; equation \\ \\ y-8=\frac{-7}{6}x+\frac{7}{6}\\ Adding\; 8\; on\; both\; sides\\ \\ y-8+8=\frac{-7}{6} x+\frac{7}{6} +8\\ Combining \; like \; terms\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{8 \cdot 6}{1 \cdot 6}\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{48}{6}\\ \\ y=\frac{-7}{6} x+\frac{55}{6} [/tex]
Conclusion:
The equation best represents a trend line for the scatter plot is Option B.
B. y=−7/6x+55/6
I really need help on this!! God bless you!!
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Given the function
h
(
x
)
=
x
2
−
7
x
+
7
h(x)=x
2
−7x+7, determine the average rate of change of the function over the interval
2
≤
x
≤
9
2≤x≤9.
The average rate of change of the function h(x) = x² - 7x +7 over the interval 2 ≤ x ≤ 9 is 4.
Explanation:The average rate of change for a function is determined by the difference in y values divided by the difference in x values over a specified interval. In this case, the function is h(x) = x² - 7x + 7, and the interval is 2 ≤ x ≤ 9. First, we calculate h(2) and h(9) for the y values.
h(2) = (2)² - 7(2) + 7 = 4 - 14 + 7 = -3
h(9) = (9)² - 7(9) + 7 = 81 - 63 + 7 = 25
Then, apply the formula for average rate of change which is (h(9) - h(2)) / (9 - 2).
(25 - (-3)) / (9 - 2) = 28 / 7 = 4
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Please help,I don’t get this and my friends also need your help
Can You show me how to do this?
Which word best describes the numbers 10 and –10?
Opposites
Coordinate
Absolute Value
Expression
The owner purchases 5 buckets, 10 brushes, 48 towels, and 1 case of air fresheners for the car wash. The total cost of the purchases is $144.08. Each bucket costs $2.89, each brush costs $7.91, and each towel costs $0.36.
PART B: What is the total cost, in dollars, of the case of air fresheners? Explain/justify your answer.
Which relationships hold true for the sum of the magnitudes of vectors u and v, which are perpendicular
{(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)} Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function. Select all ordered pairs that could be used to show that this claim is incorrect.
A. (–10, –10)
B. (–9, –6)
C. (–5, 1)
D. (1, 12)
E. (4, 7)
(-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given ordered pairs are {(–9, 1), (–5, 2), (0, 7), (1, 3), (6, –10)}
minus nine comma one,
minus five comma two
zero comma seven
one comma three
six comma minus ten
If Josiah claims that the ordered pair (6, –10) can be replaced with any ordered pair and the set will still represent a function.
Then we can replace with (-9, -6) (-5,1 ) (1,12) to make it incorrect. Two x values should not have same value.
Hence (-9, -6) (-5,1 ) (1,12) ordered pairs that could be used to show that this claim is incorrect.
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Which relationship describes angles 1 and 2?
Select each correct answer.
complementary angles
adjacent angles
supplementary angles
vertical angles
Which equation can be used to solve for x in the following diagram?
The equation that represents the value of [x] is -
x + 4x - 85 = 90.
What is right angle? What is equation modelling? What is a mathematical equation and expression?In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or π/2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is a geometrical image as shown.
We can write the equation as -
x + 4x - 85 = 90
Therefore, the equation that represents the value of [x] is -
x + 4x - 85 = 90.
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What is the slope of this line?
Lucy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lucy
$5.75
per pound, and type B coffee costs
$4.10
per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of
$819.55
. How many pounds of type A coffee were used?
Answer:
I think it is $204.88, but I'm not positive.
Step-by-step explanation:
819.55 divided by 4
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The graph of the function f(x)=3/x+5 is shown below.
What is the vertical asymptote of the function?
A. x = –5
B. x = –3
C. x = 3
D. x = 5
A is the answer
The vertical asymptote of the function f(x) = (3/x) + 5 is A. x = - 5
What are asymptotes?A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar contexts.
By observing the graph we can conclude that the asymptote or more specifically the vertical asymptote of the function f(x) = (3/x) + 5 is at x equals to - 5.
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A company sells cereal in two different -sized boxes.The smaller box has the dimensions of 12-inch,2-inch and 7 3/4 i.The height of the smaller box is 80% of the height of the lager box,while the other two dimensions are the same for both boxes.What is the difference in the volumes of the two boxes?
Answer: The answer is 232.5
Step-by-step explanation:First you to set up the proportion. If 80% equals to 12. You Would do 80 over hundred becuase percent is out of hundred (80/100) then you would do 12 over x or any other variable. FROM there on you would to the butter fly method. Cross multiply . ( 80 times variable, 12 times 100) now to isolate the variable you have to do inverse operation. So now do 1200 divided by 80 . And 80 divided by 80. Now you know.
X=15.
But were no done yet lol. Now do length times width times height to get the volume. 15 times 2 times 31/4 (7 3/4) . now we're done. Your welcome
This is LCM and GCF I think
I need help on #9 Brainlest rewarded
buy one 10 pack of AAA batteries for $5.49 and get one free, or buy two 4 packs for $2.98
show work^
What’s the correct answer
replacing the values for x
x = 2
2(2)^2 +3(2) +5 = 19
This figure consists of two semicircles and a rectangle.
What is the perimeter of this figure?
Use 3.14 for π.
The perimeter of the figure is 423.52 m
What is Area of Rectangle?The area of Rectangle is length times of width.
From the figure the length of rectangle is 105m and width is 68m.
Perimeter of rectangle=2(length+width)
First the rectangle part with the length is 105m,
2(105)=210m
For the semicircle part, the circumference of the circle is 2πr
The circumference of the semicircle is 1/2(2πr)=πr
Diameter of semicircle=68
Radius is 34
circumference of the semicircle is 34(3.14)=106.76
As there are two semicircles=2(106.76)=213.52
The total perimeter of this figure is 213.52+210=423.52m
Hence, the perimeter of this figure is 423.52 m
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In a certain card game, for every 44 blue cards, there are 33 yellow cards. There are a total of 84 blue and yellow cards in the game.
How many blue cards are in the game
Sarah is making flower bouquets that she will put in 10 vases. She will put 15 roses and some lilies in each vase.
Which expressions represent the total number of flowers Sarah will put in all the vases?
Choose all answers that are correct.
a. 10 *(15+f) b. 10+15+f c. (10*15)+(10*f) d. 10*(15*f)
Wilma bought a skateboard for 20% off. The normal price was 120.90. How much did Wilma pay for the skateboard, not including tax?
1) $96.72
2) $97.82
3) $98.92
4) $99.02
Hey please please please please please help have a Struggling with this all day
If SinA = 2/3, find the value of 2 secA/1+ tan2A
NEED HELP ASAP need help with number 2
a varies directly as b and inversely as the square of c. If a = 197 when b = 5 and c = 5, find a if b = 3 and c = 3
Final answer:
The value of 'a' is found to be approximately 328.33 when b = 3 and c = 3, using the constant of proportionality obtained from the given values a = 197 when b = 5 and c = 5.
Explanation:
When a quantity varies directly as another quantity and inversely as the square of a third quantity, we can express this relationship with the following equation:
a = k x (b / c2)
where k is the constant of proportionality. Given that a = 197 when b = 5 and c = 5, we can solve for k:
197 = k x (5 / 52)
197 = k x (5 / 25)
197 = k / 5
k = 197 x 5
k = 985
Now we can use this value for k to find a when b = 3 and c = 3:
a = 985 x (3 / 32)
a = 985 x (3 / 9)
a = 985 x (1/3)
a = 328.333...
Hence, the value of a, when b = 3 and c = 3, is approximately 328.33.
A bag contains 20 marbles: 12 red, 4 blue, 3 yellow, and 1 green. Arielle takes out 2 marbles. What is the probability that they are both blue?
Total number of marbles in the bag =20
Number of blue marbles =4
Now we just want two blue marbles out of four.
Probability of taking out first marble which is blue =4/20
Now after we took out one blue marble , number of blue marbles left are 3.
Probability of taking out second marble which is blue =3/20
Total probability = 4/20 *3/20 = 12/400
So probability of taking out two blue marbles is 0.03 or 12/400.
What answers factor the expression 24y + 88x