The table contains data on the mileage displayed on a bicycle odometer as it relates to the number of days since the bicycle was purchased. Using the Scatter Plot tool, find the value of the correlation coefficient for this data set.
0.8
1.0
0.3
0.1
Answers
Answer:
Hence, the correlation coefficient is:
r=1.0
Step-by-step explanation:
We know that the correlation coefficient ''r'' is calculated by the formula:
[tex]r=\dfrac{\sum{XY}}{\sqrt{\sum{X^2}\sum{Y^2}}}--------------(1)[/tex]
Let x denote the data point (Number of days since purchase)
Let y denote the data point (Mileage Displayed on odometer)
x y X=x-x' Y=y-y' XY X² Y²
15 67 -20 -95 1900 400 9025
25 122 -10 -40 400 100 1600
35 164 0 2 0 0 4
45 210 10 48 480 100 2304
55 247 20 85 1700 400 7225
x' be the mean of the data of the x-values.
[tex]x'=\dfrac{15+25+35+45+55}{5}\\\\\\x'=\dfrac{175}{5}\\\\\\x'=35[/tex]
Also let y' denote the mean of the y-values.
[tex]y'=\dfrac{67+122+164+210+247}{5}\\\\\\y'=\dfrac{810}{5}\\\\\\y'=162[/tex]
Now we have:
∑ XY=4480
∑ X²=1000
∑ Y²=20158
Hence, we put all the values in the formula (1) to obtain:
r=0.997 which is close to 1.0
Also from the scatter plot we could observe that the relationship is linear and also strong positive relationship.
Hence, the correlation coefficient is 1.0
Related Questions
A baseball that usually cost $65 is on sale for $55.25. what is the percent off?
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What is the length of the hypotenuse of a right triangle with leg lengths of 8 inches and 15 inches?
A. 13 inches
B. 17 inches
C. 21 inches
D.25 inches
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Answer:
B.17 INCHESStep-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
just helping the other guy get brainliest.
Find the inverse of f(x)=2x^2+5
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12 liters is about how many quarts
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Larry Klaus withdrew $310.80 simple interest from an account after 4 years. If he invested $1,110.00, how much was his rate of interest?
7%
6%
4%
5%
Answers
Answer:
7% is the answer (hope this helps) or do you need explanations?
Step-by-step explanation:
What is the side length of a cube with a volume of 4913 m3? m
Answers
m = ∛4913
m = 17
So, your final answer is 17
Hope this helps!
The recursive formula An+1 = 2∙An number of people with a virus in a school each week. If there are 96 people infected with the virus after 3 weeks, how many people will be infected after 6 weeks? What is the explicit formula?
Answers
768.
Factor the expression.
t^2 - 14t + 49
Answers
which is a factored form of 216p^3 + 125q^3?
Answers
you have: [tex] 216p^{3} + 125p^{3} [/tex]
Simplify it by factoring out [tex] p^{3} [/tex]-->>
[tex] p^{3} (341)[/tex]
Or, just add it-->>
[tex] 341p^{3} [/tex]
Thus, your answer.
The factored form of [tex]\( 216p^3 + 125q^3 \) is \( (6p + 5q)(36p^2 - 30pq + 25q^2) \).[/tex]
To find the factored form of the expression [tex]\(216p^3 + 125q^3\)[/tex], we can use the sum of cubes formula:
[tex]\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \][/tex]
Where a = 6p and b = 5q.
Substituting these values into the formula, we get:
[tex]\[ 216p^3 + 125q^3 = (6p)^3 + (5q)^3 \][/tex]
[tex]\[ = (6p + 5q)((6p)^2 - (6p)(5q) + (5q)^2) \][/tex]
[tex]\[ = (6p + 5q)(36p^2 - 30pq + 25q^2) \][/tex]
Therefore, the factored form of [tex]\( 216p^3 + 125q^3 \) is \( (6p + 5q)(36p^2 - 30pq + 25q^2) \).[/tex]
Complete question:
What is the factored form of 216p³+125q³?
Does it matter if you add azero when you divide a dcimal.
Answers
Answer:
no it does not matter
Step-by-step explanation:
How many years will it take for 2000 to double at a simple interest rate of 8%? explain how you found your answer
Answers
A (Future) = 2000(2) = 4000
P (Principal) = 2000
R (Rate) = 8% =.08
T (Time) = Unknown
Create the equation:
4000 = 2000(1+.08t)
Distribute the 2000:
4000 = 2000 + 2000(.08t)
Multiply the 2000(.08t):
4000 = 2000 + 160t
Subtract the 2000 from both sides:
2000 = 160t
Divide by 160:
12.5
Answer:
It will take 12.5 years (12 years and 6 months) to double the 2000 to double.
Rachel and Sierra are selling boxes of fruit as a fundraiser. Rachel has sold 9/10 boxes of fruit and Sierra has sold 2 has sold 5/8 of her boxes.which girl has sold a greater fraction of her boxes of fruit?Draw a model and Explain
Answers
If the principal is $350 and the interest rate is 3 percent, what is the simple interest earned in one year? simple interest = P × r × t Select one of the options below as your answer: A. $10.50 B. $30.25 C. $105
Answers
Answer:
The option A. $10.50 is correct
Step-by-step explanation:
Principal = $350
Rate = 3%
⇒ Rate = 0.03
Time = 1 year
Now, Simple Interest is given by the formula : Principal × Rate × Time
Therefore, Simple Interest = 350 × 0.03 × 1
⇒ Simple Interest = $10.50
Hence, The option A. $10.50 is correct
5 lollipops and 12 toffees have a mass of 61 grams and 10 lollipops and 13 toffees have a mass of 89 grams . Calculate the mass of one lollipop and one toffee
Answers
b - mass of yhe toffee
5a + 12b = 61
10a + 13b = 89
10a = 89 - 13b
a = 8.9 - 1.3b
5*(8.9 - 1.3b) + 12b = 61
44.5 - 6.5b + 12b = 61
5.5b = 16.5
b = 3
a = 8.9 - 1.3*3 = 5
a = 5
b = 3
Lollipop has a mass 5g and toffee 3g
Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answers
Answer:
B
Step-by-step explanation:
What is the answer to 0.1 * n = 89.9 ?
Answers
n = 89.9/0.1 = 899
How? Let's solve your equation step by step.
0.1n=89.9
Step 1: divide both sides by 0.1.
0.1n = 89.9
0.1 0.1
so 89.9/0.1 we get
n=899
The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.
Estimate the value of T′(8). Give units in your answer.
What is the meaning of T′(8)?
t 0 2 4 6 8 10 12 14
T 73 73 70 68 73 80 86 89
Answers
We need to estimate the value of T'(8) and then we need to give the meaning of this value. Since we have a table and not an expression of a function our goal is to find the Average Rate of Change between two points.
For a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is the slope of the line through the two points. So:
[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} =\frac{Change \ in \ y}{Change \ in \ x}=m_{sec}[/tex]
1. Estimated value of T′(8).
T'(8) means the derivative of the function T(t) when t = 8 hours. So, we can estimate this value using the average rate of change:
[tex]ARC=\frac{T(8)-T(6)}{8-6} =\frac{73-68}{8-6}=\frac{5}{2} \ degrees \ per \ hours[/tex]
2. The meaning of T′(8)
This means the average temperature after midnight in Phoenix on March 15, from t = 6 to t = 8 hours, that is, for each hour the temperature rises 5/2 degrees on the Fahrenheit scale. The points have been plotted in the Figure bellow.
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
We can estimate the rate of change of the temperature, in degrees Celsius per hour, by calculating the average of two consecutive secant lines, whose expression is presented below:
[tex]T'(t) \approx \frac{1}{2}\cdot \left[\frac{T(t+\Delta t)-T(t)}{\Delta t} + \frac{T(t)-T(t-\Delta t)}{\Delta t} \right][/tex] (1)
If we know that [tex]\Delta t = 2[/tex], [tex]T(6) = 68[/tex], [tex]T(8) = 73[/tex] and [tex]T(10) = 80[/tex], then the estimated value of the rate of change of the temperature is:
[tex]T'(8) = \frac{1}{2}\cdot \left[\frac{80-73}{2}+\frac{73-68}{2} \right][/tex]
[tex]T'(8) \approx 3\,\frac{^{\circ}C}{h}[/tex]
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
We kindly invite to check this question on rates of change: https://brainly.com/question/18904995
jack has no more than $24 to spend on DVD's for a party. Each DVD rents for $4. Find the maximum number of DVD's jack can rent for his party. answer must be written on a number line
Answers
$24/$4 = 6
Jack can rent a maximum of 6 DVD's
Answer:
Jack can rent a maximum of 6 DVD's
Step-by-step explanation:
15x+1= y solve for x ...?
Answers
15x + 1=y subtract 1 from both sides
15x=y-1 divide both sides by 15
x=(y-1)/15
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.
What is the missing step of her solution?
Add 10.4 to both sides.
Add negative 10.4 to both sides.
Multiply both sides of the equation by 10.4.
Divide both sides of the equation by 10.4.
Mark this and return
Answers
Answer: Last Option is correct.
Step-by-step explanation:
Since we have given that
[tex]2.3 + 8(1.3x-4.75) = 629.9[/tex]
We need to solve the above equation,
[tex]2.3 + 8(1.3x-4.75) = 629.9\\\\2.3+10.4x-38=629.9\\\\-35.7+10.4x=629.9\\\\10.4x=629.9+35.7\\\\10.4x=665.6\\\\\text{ Dividing 10.4 on both sides}\\\\x=\frac{665.6}{10.4}\\\\x=64[/tex]
Hence, Divide both sides of the equation by 10.4.
Therefore, Last Option is correct.
Answer:
D
Step-by-step explanation:
The slope of a line is -, and the y-intercept is . What is the equation of the line written in general form?
A) 10x + 3y - 1 = 0
B)x + 3y + 10 = 0
C) x + 3y - 10 = 0
Answers
C) x + 3y - 10 = 0
Hope it helped : )
URGENT! PLEASE HELP MATH!
Which shows the conversion of 0.427 kg to pounds?
There are 2.2 pounds in 1 kilogram.
A.
0.427 kg × 2.2 lb/kg = 9.39 lb
B.
0.427 kg × 2.2 lb/kg = 0.939 lb
C.
0.427 kg + 2.2 lb/kg = 2.627 lb
D.
0.427 kg ÷ 2.2 lb/kg = 0.194 lb
Answers
conversion factor is
2.2lb/1kg
since they are equal, that equals 1
0.472kg times (2.2lb/1kg)=0.9349 lb
answer is B
Remember, the numerator of a fraction is whatever is on top. The denominator is on the bottom!
Explanation aside let's use it in a problem!
[tex] \frac{0.427kg}{1} * \frac{?}{?} [/tex]
We want the denominator to have kg, so let's put the kg unit next to the ? in the denominator.
[tex] \frac{0.427kg}{1}* \frac{?}{?kg} [/tex]
Now, glance back at your conversion rate and look at what the over unit is. In this case it is pounds (lb). So put that next to the ? in the numerator.
[tex] \frac{0.427kg}{1}* \frac{?lb}{?kg} [/tex]
The ? are to be filled in with the conversion rate. Meaning 2.2lb per 1kg. So wherever there is the unit for lb, you put 2.2 in. Same thing for the kg unit.
[tex] \frac{0.427kg}{1}* \frac{2.2lb}{1kg} [/tex]
Multiply across. (Multiply the numerator by the numerator, and denominator by denominator!)
The problem can be rewritten as this:
0.427kg * 2.2lb
The final answer to this problem is:
0.427kg*2.2lb = 0.939
AKA: B
The ordered pair below is a solution to which equation? (2, 12) A. y = 6x B. y=1/2x C. y = 2x D. y=1/6x
Answers
14 inches of snow fell in 4 hours how much snow fell each hour
Answers
14 inches / 4 hours
14/4 = 3.5
3.5 inches of snow fell every hour.
In order to purchase a home, a family borrows $159,000 at 6.5% for 30 years. Use the table to find their monthly payment. Round the answer to the nearest cent.
a.
$954.00 c.
$1,186.14
b.
$1,006.47 d.
$1,276.36
Answers
Answer:
B
Step-by-step explanation:
Determine the volume of the right circular cone generated by rotating the line y = 1/3x about the y-axis between y = 0 and y = 3.
A) V = 81pi cu.units
B) V = 84pi cu.units
C) V = 82pi cu.units
D) V = 85pi cu.units
E) V = 83pi cu.units
Answers
Below is the solution:
Rotating around the y-axis; solve for x. y = x/3
x = 3y
Find x^2
x^2 = 9y^2
Integrating it using the limits of 0 and 3, remember to add the pi and integrate 9y^2.
The answer is 81pi cubic units which is A.
In this exercise we want to calculate the volume of a circular cone in this way we have that the rotation will be given by:
Letter A
First let's write the rotation in favor of the X, this will be equal to:
[tex]y = x/3\\x = 3y[/tex]
So substituting this value in the function we find that:
[tex]x^2 =(3y)^2= 9y^2\\\int\limits^3_0 {9y^2} \, dx =81 \pi[/tex]
See more about volume at brainly.com/question/1578538
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated. find p(b/not
a.
Answers
If f(x) = 3x + 10x and g(x) = 4x – 2, find (f + g)(x).
A. 17x – 2
B. 3x – 6x + 2
C. 3x + 14x – 2
D. 3x + 6x + 2
Answers
= 17x - 2
answer is A. 17x – 2
Answer:c
Step-by-step explanation:
being timed help
What is the common ratio for the geometric sequence?
43,4,12,36,...
Answers
see what number the previous term must be multiplied by to get the next term
4 *something = 12, 12*something=36
common ratio is 3
In which quadrant is point (4,5) located