Answers
The correlation coefficient (r) is -0.96.
Given the data:
x: 0, 1, 2, 2, 3, 4, 5, 5, 6
y: 12, 9.5, 9, 8.5, 8.5, 6, 5, 5, 3.5
Step 1: Calculate the mean (average) of x and y.
Mean of x = (0 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 6) / 9 = 3
Mean of y = (12 + 9.5 + 9 + 8.5 + 8.5 + 6 + 5 + 5 + 3.5) / 9 = 7
Step 2: Calculate the deviations from the mean for x and y.
Deviation of x (dx) = x - X
Deviation of y (dy) = y - Y
x: -3, -2, -1, -1, 0, 1, 2, 2, 3
y: 5, 2.5, 2, 1.5, 1.5, -1, -2, -2, -3.5
Step 3: Calculate the product of the deviations of x and y.
(dx * dy): -15, -5, -2, -1.5, 0, -1, -4, -4, -10.5
Step 4: Calculate the sum of the products of the deviations (Σ(dx * dy)).
Σ(dx * dy) = -15 - 5 - 2 - 1.5 + 0 - 1 - 4 - 4 - 10.5 = -43
Step 5: Calculate the standard deviations of x (σx) and y (σy).
Standard deviation of x (σx) = √(Σ(dx²) / (n-1))
Standard deviation of y (σy) = √(Σ(dy²) / (n-1))
Calculating dx²:
dx^2: 9, 4, 1, 1, 0, 1, 4, 4, 9
Σ(dx²) = 33
Calculating dy²:
dy²: 25, 6.25, 4, 2.25, 2.25, 1, 4, 4, 12.25
Σ(dy²) = 61
Calculating the standard deviations:
σx = √(33 / (9-1)) = √(33 / 8) ≈ 1.84
σy = √(61 / (9-1)) = √(61 / 8) ≈ 2.70
Step 6: Calculate the correlation coefficient (r).
r = Σ(dx dy) / (√(Σ(dx²) Σ(dy²)))
r = -43 / (√(33 61))
r ≈ -43 / (√(2013))
r ≈ -43 / 44.87
r ≈ -0.96
Therefore, the correlation coefficient (r) is approximately -0.96.
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Related Questions
The function m is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
B
m(x) = -2x² +24x54
-
m(x) = -2(x - 6)² + 18
m(x) = -2(x - 3)(x-9)
Write one of the zeros.
Answers
Answer:
m(x) = -2(x - 3)(x - 9)
One of the zeros of the function is x = 3
Step-by-step explanation:
The form that most quickly reveals the zeros (or "roots") of the function is:
m(x) = -2(x - 3)(x - 9)
To find the zeros of the function, we set m(x) equal to zero:
-2(x - 3)(x - 9) = 0
From this equation, we can see that the zeros (roots) of the function occur when either (x - 3) equals zero or (x - 9) equals zero. Solving these equations gives us the zeros:
x - 3 = 0
x = 3
x - 9 = 0
x = 9
Therefore, one of the zeros of the function is x = 3.
Hope this helps!
1. Determine the three-dimensional figure that will be created using the following nets.
Answers
Answer:
triangular pyramid
Step-by-step explanation:
Answer:
triangular pyramid
cone
Step-by-step explanation:
Which graph represents the function p(x) = |x – 1|?
On a coordinate plane, an absolute value graph has a vertex at (0, 1).
On a coordinate plane, an absolute value graph has a vertex at (negative 1, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 1).
Answers
The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).
The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).
Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.
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What is the median of 8,9,10,1,6,4,7,6
Answers
Answer:
The median is 6.5
Step-by-step explanation:
To find the median, first organize the numbers from least to greatest:
1, 4, 6, 6, 7, 8, 9, 10
The median is always the number in the middle, but since there are eight numbers here, there will be two numbers in the middle: 6 and 7.
To solve for this, we have to find the average of the numbers.
Add the two numbers together and then divide by 2 (we divide by 2 because we are averaging two numbers).
(6 + 7)/2
13/2
6.5
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answers
Which of the following exam scores should lead to the better grade? Explain your answer. (4 points)
A score of X = 55 on an exam that has a mean of 60 and a standard deviation of 5.
B. A score of X = 40 on an exam that has a mean of 50 and a standard deviation of 20.
Answers
Based on the z-score calculations, score A with a score of X = 55 should lead to the better grade.(option-a)
For score A with X = 55, the z-score can be calculated as:
z = (X - mean) / SD = (55 - 60) / 5 = -1
For score B with X = 40, the z-score can be calculated as:
z = (X - mean) / SD = (40 - 50) / 20 = -0.5
The z-score represents the number of standard deviations that a score is above or below the mean. A negative z-score means that the score is below the mean.
Since a z-score of -1 is greater than a z-score of -0.5, score A with X = 55 would be the better score. This is because score A is closer to the mean (60) than score B (50), and it has a smaller standard deviation (5) than score B (20). The lower standard deviation means that scores are more tightly clustered around the mean, making it more difficult to obtain a score that is much higher or lower than the mean.(option-a)
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Dory can run 3.25 miles every hour. How long will it take her to run a race that is
16 1/4 miles long?
Answers
Answer:
it would take her 5 hours
Step-by-step explanation:
16 1/2 divided by 3.25 is 5
Brainliest plz
Write the following numeral in words.
616 845
Answers
Answer:
six hundred sixteen thousand eight hundred forty five
Step-by-step explanation:
Answer: Six hundred sixteen thousand eight hundred fourty five
!!TIP: To write numbers in letters, its spelled the same as the letters would have been said for example 66 - sixty six.
A ride in an amusement park features a swinging ship suspended from a height of 50 feet. The motion of the ship can be modeled by the graph below, where x represents the time, in seconds, since the start of the ride, and f(x) represents the angle, in radians, that the center of the ship makes with respect to the equilibrium position.
Select all the correct answers.
Answers
Answer: The first and last options are correct.
f(x) = pi/4 cos (pix/5 - pi/2)
f(x) = pi/4 sin (pix/5)
Step-by-step explanation
The graph shows that A = pi/4.
B = 10, so the period = 2pi/10 = pi/5.
sin and cos are cofunctions, so a phase shift of -pi/2 makes the two functions equal to each other.
Hope this helps :)
The correct answer is f(x) = π/4 cos (πx/5 - π/2) and f(x) = π/4 sin (πx/5).
option (A) and (D) are correct.
It is given that height of 50 feet and graph is given.
It is to find f(x).
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The graph shows that A = π/4.
B = 10, so the period = 2π/10 = π/5.
sin and cos are co-functions, so a phase shift of -π/2 makes the two functions equal to each other.
So, the option are (A) and (D).
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Jaelyn uses 3 3/4 cups of flour to make 5 batches of pancakes. How many cups of flour she need to make 1 batch?
NO ANSWERS IN UNKNOWN SITES PLEASE OR I'LL REPORT IT!!!
Answers
Answer:
3/4
Step-by-step explanation:
Divide 3 3/4 by 5. 3 3/4 as an improper fraction is 15/4. 15/4 * 1/5 (divided by 5) is 3/4. :D dont report me
Jacqueline is buying a pair of pants for $30. They are on sale for 15% off, and she has a coupon for 10% off the sale price. How much does she pay for her pants?
Answers
Answer:
$22.50
Step-by-step explanation:
To find the distance between a point X and an inaccessible point , a line segment XY is constructed. Measurements show that XY = 975m , angle XYZ=22^ 42^ prime and angle YZX=105^ 18^ prime . Find the distance between X and Z to the nearest meter.
Answers
Answer:
sorry i didn't not answer
The annual profits for a company are given in the following table, where x represents
the number of years since 2013, and y represents the profit in thousands of dollars.
Write the linear regression equation that represents this set of data, rounding all
coefficients to the nearest hundredth. Using this equation, find the projected profit
(in thousands of dollars) for 2023, rounded to the nearest thousand dollars.
Years since 2013 (x)
Profits (y)
(in thousands of dollars)
0
57
76
2
63
3
107
Answers
Della needs fabric that is 12.4 yards long. If the store sells fabric in meters, how much fabric will she need?
Answers
12.4 divided by 1.094=11.334
Hi pls help ASAP no links or you will be reported and terminated. Pls and Thx.
Answers
area- ?
Answer:
Area = [tex]x^{2} +2x+2[/tex]
Perimeter = [tex]4x+1[/tex]
Step-by-step explanation:
So the shape is made up of one [tex]x^{2}[/tex], two xs and two 1s
add that together you get [tex]x^{2} +2x+2[/tex]
Starting at the top left you have a side length of 1. Then it goes down 1 before an x. Then you have up 1 and over 1, which is 2. Going down the right side you have a 1 and an x. Then the bottom is 1, x, and 1. You go up another x and then 1 to meet back where you started.
In total that is [tex]4x+1[/tex]
A chocolate shop sells chocolates with a variety of different fillings.
hazelnut 68
caramel 8
orange 8
What is the probability that a randomly selected chocolate will have caramel filling?
Write your answer as a fraction or whole number.
Answers
Answer:
There is a [tex]\frac{2}{21}[/tex] chance of picking caramel-filled chocolate.
Step-by-step explanation:
To set this up, you need to make it a fraction. The denominator of the fraction is how many total chocolates you can pick from. You can figure this out by adding all of the chocolate choices together:
68 hazelnut + 8 caramel + 8 orange = 84 chocolates.
The numerator is defined by the number of caramel chocolates, in this case it is 8. That means the fraction will look like:
[tex]\frac{8}{84}[/tex]
Now that can be simplified down. I divided the top and bottom both by 4 to get [tex]\frac{2}{21}[/tex] and that is as far down as it can go. Therefore that is the probability you will get a caramel-filled chocolate.
Given the following information about two triangles, triangle CAT and triangle DOG:
Which postulate can be used to prove triangle CAT and triangle DOG are congruent?
SSS Postulate
SAS Postulate
SSA Postulate
ASA Postulate
AAS Postulate
Choose all that apply
Answers
Answer:
1st and 3rd im pretty sure
Step-by-step explanation:
Answer:
1 and 3
Step-by-step explanation:
Need to know angle 1, angle 2, angle 3
Answers
Answer: Step-by-step explanation:
angle 1=41°
angle 2=angle 1=41°
angle 3=180-2×41=98
5 and 6 ............?
...........................................
Answers
Answer:
5. 25
6. 4
Step-by-step explanation:
Answer:
5) 25 6) 4
Step-by-step explanation:
The absolute value is a number's distance from zero. The square root of a number is what multiples by itself to get that number. For example 4 times 4 equals 16
This test will not impact your grade.
Exam
5
Shot
1.38
Find the missing side. Round
to the nearest tenth.
S
02
17
у
SC
440
Х
x= [?]
Enter
Answers
Answer:
if i am not wrong is 119
Step-by-step explanation:
I did it like this:
I took 44 + 17= 61
And then I took 180-61= 119
The length of the arc bound by the central angle is 90 degrees is 3 pie, what is the radius?
Answers
id- 5121786233 p/w- tepQ3w
Answers
Answer:
ok
Step-by-step explanation:
3 Select the correct answer. 52 + 51 + 6 For the rational equation, 1 + 3 = 1 what is a valid value of x? ОА. B. -1 O C. 2 O D. 3 Reset Next
Answers
9514 1404 393
Answer:
B. -1
Step-by-step explanation:
[tex]\dfrac{x^2 +5x +6}{x+3}=1\qquad\text{given}\\\\\dfrac{(x+2)(x+3)}{x+3}=1\qquad\text{factor}\\\\x+2=1\qquad x\ne-3\qquad\text{cancel factors}\\\\x=-1\qquad\text{add $-2$}[/tex]
The only valid value of x is -1.
please please help me find the volume and surface area i’ll give brainliest
Answers
Answer:
Area: 272ft²
Volume = 82.6236447189ft³
Step-by-step explanation:
AREA
The area of a square pyramid is found by combining the area of the base and the area of the triangular faces:
Area of base = area of square = L² = 8² = 16ft²
Area of one triangular face = (1/2)bh = (1/2)(8)(16) = 64ft²
There are four triangular faces so the total area = 16+4(64)= 16+256= 272 ft²
VOLUME
The volume of a square pyramid = (a²)(h/3), where a is the length of the base and h is the length from the top of the pyramid to the middle of the square.
We are given a, but not h. To find h, we must imagine a right-angled triangle within the pyramid, where 16ft is the hypotenuse, h is the height and the base is half of a (since the base is a square and the distance is from the edge to the middle). We can then use pythagorus's theorem to find h:
A²=B²+C²
16²=(8/2)²+h²
256=16+h²
h=√240
h=15.4919333848ft
Knowing h, we can find the volume:
Volume = (a²)(h/3)
Volume = (8²)(15.4919333848/3)
Volume = (16)(5.16397779493)
Volume = 82.6236447189ft³
What is the value of the expression: x2 + y2 + x - y
when x = -1 and y = 3
Question 1 options:
6
8
12
16
Answers
Answer: 6
Step-by-step explanation:
x^2+y^2+x-y
Put x=-1 and y=1
(-1)^2+(3)^2+(-1)-(3)
1+9-1-3
10-4
6
Find the product of (x + 3)(x − 3).
x2 − 6x + 9
x2 + 6x + 9
x2 + 9
x2 − 9
Answers
x^2-3x+3x-9=
x^2-9
Step-by-step explanation:
[tex](x + 3)(x - 3) \\ = {x}^{2} - 3x + 3x - 9 \\ = {x}^{2} - 9[/tex]
#CMIIWWhen two 6-sided dice are rolled, there are 36 possible outcomes. Find the probability that the sum is 8
Answers
Answer:
5/36
Step-by-step explanation:
Probability is the outcome that a event will occur
Probability = Expected outcome/Total outcome
Since two sided dice are rolled, the total outcome will be expressed as;
Total outcome = 36
Since we are to find the probability that the sum is 8, the values that gives a sum of 8a re;
(2,6)(6,2), (5, 3), (3,5), (4, 4)
The expected outcome = 5
Probability = 5/36
Hence the probability that the sum is 8 is 5/36
Please please please help no link no links no links
Answers
Answer:
400
Step-by-step explanation:
V = a² * h/3
Plug in your values:
V = 10² * 12/3
Then solve:
100 * 4 = 400
will mark brianliest please help
Answers
Answer:
See below.
Step-by-step explanation:
7x^2 = 343 Divide both sides by 7
7x^2/7 = 343/7
x^2 = 49 Take the square root of both sides.
sqrt(x^2) = sqrt(49)
x = +/- 7
Answers
7- 7sqrt(49)- sqrt(49)I think the last two are kind of iffy. I'm not sure you can call them solutions, but the question probably assumes they are. If you use all four answers and get it wrong, them submit +7 and - 7.
In a middle school of 80 students, 42 girls and 38 boys. What is the probability
that if two students were randomly chosen, the first is a boy and then a girl
sequentially?
Answers
Answer:
dont have idea
Step-by-step explanation:
have not studied that topic