Answer:
its b
Step-by-step explanation:
The correlation coefficient of the set of data is 0.9957.
What is coefficient correlation? What is the general equation of a Straight line?Correlation coefficient measures the strength and direction of the relationship between two variables. Following is the formula to calculate the correlation coefficient -
[tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
r → correlation coefficient.
[tex]$x_{i}[/tex] → values of the x-variable in a sample.
[tex]$\bar{x}[/tex] → mean of the values of the x-variable.
[tex]$y_{i}[/tex] → values of the y-variable in a sample.
[tex]$\bar{y}[/tex] → mean of the values of the y-variable.
The general equation of a straight line is -
y = mx + c
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have a runner times herself to see how long it takes her to run different distances. The table shows the runner's times (in minutes) for running several distances (in miles) -
Miles -
1 2 3 4 6 8 10 12
Time -
7 16 30 35 57 75 106 132
The calculations are given below -
[X - Mₓ]
- 4.750
- 3.750
- 2.750
- 1.750
0.250
2.250
4.250
6.250
Mₓ = 5.750
[Y - My]
- 50.250
- 41.250
- 27.250
- 22.250
- 0.250
17.750
48.750
74.750
My = 57.250
[X - Mₓ]²
22.562
14.062
7.562
3.062
0.062
5.062
18.062
39.062
Sum = 109.500
[Y - My]²
2525.062
1701.562
742.562
495.062
0.062
315.062
2376.562
5587.562
Sum = 13743.500
(X - Mₓ)(Y - My)
238.688
154.688
74.938
38.938
- 0.062
39.938
207.188
467.188
Sum = 1221.500
Finding [X] - Values -
∑ = 46Mean = 5.75∑(X - Mₓ)² = SSₓ = 109.5Finding [Y] - Values -
∑ = 458Mean = 57.25∑(Y - My)² = SSy = 13743.5[X] and [Y] Combined
N = 8∑(X - Mx)(Y - My) = 1221.5R Calculation
r = ∑((X - My)(Y - Mₓ)) / √((SSₓ)(SSy))
r = 1221.5 / √((109.5)(13743.5)) = 0.9957
r = 0.9957
Therefore, the correlation coefficient of the set of data is 0.9957.
To solve more questions on correlation coefficient, visit the link below-
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I'd love some help with this, and I'll mark brainliest! :))
Answer:
He will work out for a total of 2,835 min or 47.25 hours
He will not meet his minimum workout time for the18 week period
Step-by-step explanation:
The pattern is tat he adds 15 min each week to his work out regime:
Wk1: 30min Wk11:180min
Wk2: 45 min Wk12: 195in
Wk 3: 60 min Wk 13:210min
WK4: 75min Wk 14: 225 min
Wk5 90 min Wk15: 240min
Wk6: 105 min Wk16: 255 min
Wk7; 120min Wk17: 270min
Wk8: 135min Wk 18: 285min For a total of 2,835 min and divide by
60 to get the number of hours= 47.25 hours
Wk9: 150min
Wk 10: 165 min
Please help due IN MY CLASS TODAY
Answer:
A. 3,4. E. Origin or 0,0 D. 6,-3
C. -2,-4 B. -3, 2
Step-by-step explanation:
Just go from x to y and I did this last year :p
Two bottle rockets are simultaneously launched on parallel paths, from 5 feet apart on level ground. After 0.1 second, the rockets are at the same height.
Which theorem or definition can you use to show that the rockets are still 5 feet apart 0.1 second after launch?
Help asap please it's due today :)
Answer:
The definition of parallel lines are lines that have a constant minimum distance between them at any given point along the lines, such that the lines are the same distance apart all through
Therefore, given that we have;
1) The path of the two bottle rockets are parallel,
2) The initial distance between the two rocket on level ground = 5 feet = The perpendicular (shortest) distance between the two rockets
3) The shortest distance between the rockets having the same height moving on parallel path will be constant = 5 feet
4) The height of the two rockets after 0.1 second = Constant = 5 feet
5) Therefore, by the definition of parallel lines, distance between the two rockets which are at the same height after 0.1 second will still be 5 feet
Step-by-step explanation:
please please hurry ! What is the length of side X?
Answer:
its eleven
Step-by-step explanation:
it just is....
Answer:
11
Step-by-step explanation:
They are proportional, so since side RS is 3 and MN is 6, we know that Triangle MNO is twice that size, so all of the side lengths will be twice that size. So ST being 5.5 means that the same side in Triangle MNO will be twice that amount, and 5.5 * 2 = 11.
How many terms are in this expression ?-3x + 7y - 6 *
Answer:
3 terms in the expression
It is given that the lengths of two sides of a triangle are both 7 and the length of the remaining side is an integer. Find the maximum possible and the minimum possible perimeters of the triangle.
Answer:
Have you tried |-7|?
Step-by-step explanation:
what is 6+ 4 - 2 first to answer gets brainlist
Answer:
8
Step-by-step explanation:
Answer:8
Step-by-step explanation:
what’s the answer to this question ?????????????
Answer is is 2 .........
Each interior angle of a regular polygon with 20 sides is 2° more than each interior angle of a regular polygon with n sides. Calculate the value of n. Help me please hurry any math genius:(
Answer:
400
Step-by step explanation:
The sides of the regular polygon is 20 and more than 2 so you divide the two number up to get 10 and then also you multiply all of them up together which is 400
You are standing at the edge of a cliff. You look down with an angle of depression of 20 degrees and see a a dog at the bottom that is 130 feet away from where you're standing. What is the height of the cliff? Round your answer to the nearest tenth, and round only once.
Answer:
47.3feet
Step-by-step explanation:
The set up will give a right angled triangle.
The distance of the dog away from the cliff = 130 feet = adjacent side
Angle of depression = 20°
Height of the cliff = Opposite = x
Using the SOH, CAH, TOA trigonometry identity;
According to TOA;
tan theta = opposite/adjacent
tan 20 = x/130
Cross multiply;
x = 130tan20
x = 130(0.3639)
x = 47.3 feet
Hence the height of the cliff to the nearest tenth is 47.3feet
If f(x)= x+4/x, g(x) = x-2, and h(x)= 4x-1, what is (fohog)
Answer:The answer is d (fohog)= 4x-5/4x-9
Step-by-step explanation:
Help. Examine the figure below. Determine which of the following angle measures are correct PICK up 2 answers
Answer:
RPQ = 30 and QRP = 75
Step-by-step explanation:
First we need to find "x".
Since we know that all the angles of a triangle must equal 180 and we know that angles PQR and QRP are the same (Due to the fact that two of the lengths of the triangle are the same) we can set up an equation.
x + (2x + 15) + (2x + 15) = 180
1. we can drop the parentheses (when there is a + in front of an expression in parentheses, the expression remains the same)
x + 2x + 15 + 2x + 15 = 180
2. We can collect the like terms to simplify the equation. (x and 2x and 2x combine to equal 5x) (Remember that there is a hidden 1 behind an "x" without a number next to it)
(the two 15's add together to make 30)
This leaves us with this equation
5x + 30 = 180
3. Now we suptract the constant from 180 (The constant is 30)
5x = 180 - 30
5x = 150
4. Now we devide both sides by 5
x = 30
Next we can find all of the angles
PRQ = (2x + 15)
1. PRQ = (2(30) + 15)
2. PRQ = (60 + 15)
3. PRQ = 75
RQP = (2x + 15)
1. RQP = (2(30) + 15)
2. RQP = (60 + 15)
3. RQP = 75
RPQ = x
RPQ = 30
The perimeter of the base of a square pyramid is 16 feet and it stands 20 ft tall. Calculate the volume.
Answer: [tex]1706.67 feet[/tex]
Step-by-step explanation:
Formula: Volume = [tex]\frac{1}{3} \alpha^{2}h[/tex]
a is the length of the base's edge and h is the height. Since 16 is the length we would square it as it is the length, then we would multiply it by the height which is 20 ft.
Steps: Multiply
Volume = [tex]\frac{1}{3} \alpha^{2}h[/tex]
= [tex]\frac{1}{3} * 16^{2} * 20[/tex]
= [tex]1706.67 feet[/tex]
~I hope I helped you :)~
At a pizza eating competition, Davonne at two more than twice as many slices as the runner-up. If Davonne at 11 slices, then how many slices did the runner-up eat?
Answer:the runner up ate 3.5 slices
Step-by-step explanation:
Can someone pls help me
Answer: x = 7
Step-by-step explanation:
7x+9=58
8x+2=58
These are congruent angles so they are the same value.
The mean score on a physics test was 75 points. Amy’s score was 67 points, which was 2 standard deviations below the mean. What is the variance of the data set?
Answer:
D.16
Step-by-step explanation:
took the Unit test 100%
Answer:
D
Step-by-step explanation:
Pllzzzz help it’s an exam !!!! A side of the triangle below has been extended to form an exterior angle of 125 . Find the value of x
Answer:
i think it is 105
Step-by-step explanation:
180-125=55
180-(55+25)=105
*second 180 is triangle's total interior angle
can i plz get help wit 5(6x-10y+7)
5(6x−10y+7)
Answer:
5(6x -10y +7) (use the distributive property)
30x -50y +35 (simplest form)
Step-by-step explanation:
A school district is planning a banquet to honor its teachers of the year and raise money for its scholarship foundation. The budget to hold the banquet in a hotel ballroom is at most $3,375. The venue can hold no more than 125 guests. The cost is $45 per adult but only $15 per student because the caterer offers a student discount.
What system of inequalities can represent this situation? Let x be the number of adult guests and y be the number of student guests.
Drag the tiles to the correct locations in the system. Not all tiles will be used.
Answer:
[tex]x + y = 3325 \\ i \:hope \: it \: helps[/tex]
HELPPP THIS IS TIMEDD I NEED A STEO BY STEPP
Answer:
Why do you need a step by step
Step-by-step explanation:
PLEASEEEEE HELPPPPP THIS IS ALGEBRA 1
Raise m to the 5th power, then multiply 8 by the result
Answer:
8m⁵
Step-by-step explanation:
m to the 5th power = m × m × m × m × m
= m⁵
Then multiplied by 8 = 8 × m⁵
= 8m⁵
Therefore, m to the 5th power multiplied by 8 will be represented by 8m⁵.
3 times the sum of 4 and 9:
I’m confused can anybody help me I forgot how to do it?
Answer:
39
Step-by-step explanation:
4 + 9 = 13
13 × 3 = 39
if you need more help let me know
Answer:
39 sorry if im worng
Step-by-step explanation:
3*(4+9)
Two complementary angles have a difference of 22 degrees. What are the two angles?
plz its due in 20 min
Answer:
If two angles sum is equal to 90° and makes right angle called = complementary angle...☺️✌️
Above sum solution....
one angle =x
other angle =y
According to question
x+y= 90°......(1)
x-y=22°......(2)
from one and two ....by eliminating method...
2y=68
y=68/2
y=34
put y in equation 1
x+y=90°
x+34=90°
x=90°-34
x= 56...
To verify add both
sum = 90°
Hence ..verified...
Step-by-step explanation:
hope its helps u...☺️✌️✌️
Answer:
13 degrees
Step-by-step explanation:
Select the correct answer. What is[tex]\sqrt{192}[/tex] in simplest form? A.32√3 B.3√8 C.8√3 D. 2√48
Answer:
C. 8√3
Step-by-step explanation:
Please mark me as brainlest!
Thanks!
48√2 in the simplest form of the expression √192.
Option D is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can simplify the √192 by factoring it into its prime factors:
192 = 2 × 2 × 2 × 2 × 2 × 3 × 3
Then, we can group the prime factors into pairs of two:
192 = (2 × 2) × (2 × 2) × (2 × 3) × 3
Simplifying each pair of factors under the square root gives:
[tex]\sqrt{192} = \sqrt{(2\times2)}\sqrt{(2\times2)}\sqrt{(2\times3)}\sqrt{3}\\= 4\times4\times\sqrt{6}\sqrt{3} \\= 16\sqrt{6}\sqrt{3}[/tex]
Finally, we can simplify the expression by multiplying the coefficients and combining the square roots:
[tex]16\sqrt{6}\sqrt{3} \\= 16\sqrt{18} = 16\sqrt{2\times3\times3} \\= 16\times3\sqrt{2} \\= 48\sqrt{2}[/tex]
Therefore,
48√2 in the simplest form of the expression √192.
Learn more about expressions here:
https://brainly.com/question/3118662
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On a coordinate plane, 2 lines intersect at (0, 1).
By observation, what is the solution to this system?
(–1, 0)
(1, 0)
(0, 1)
(0, –1)
Answer:
(0,1)
Step-by-step explanation:
i just did it
Answer:
(0,1) ur welcome!!
Step-by-step explanation:
Can someone help me on this? this one is confusing....
Answer:
The one you have selected is right
Step-by-step explanation:
A constant speed is a number being added or subtracted at the same right. In this case its 50 each time
50+50= 100
100+50=150
etc
The 2nd one is being multiplied by 10 and the 3rd one is adding 100 which wouldnt be right since you started out with 50.
Hope this helps (:
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? On a coordinate plane, a circle is centered around (0, 0).
Answer:
Where are the statements to choose from??
Answer:
The graph is a function of x because the line y = 5 does not intersect the graph
Step-by-step explanation:
Find the measure of each angle indicated
Answer:
D) 45 degrees
Step-by-step explanation:
145 = 100 + x
Subtract 100 from both sides
45 = x
OR
180 - 145 = 35
<FEG = 35
100 + 35 + x = 180
135 + x = 180
Subtract 135 from both sides
x = 45
Find the slope of the line that passes through A(–2, –1), B(–1, 1)
A)1/2
B)-1/2
C)-2/1
D)2/1
Integrate the following:
[tex]\displaystyle \int \frac{x^2}{x^2+x+3}\, dx[/tex]
Answer:
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx = - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Completing the SquareRearranging VariablesAlgebra II
Long DivisionCalculus
U-Substitution[Integration Trick 1] Numerator Split[Integration Trick 2] Completing the SquareIntegration Rule 1: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Rule 2: [tex]\int {f(x)+g(x)} \, dx =\int {f(x)} \, dx + \int {g(x)} \, dx[/tex]Integration 1: [tex]\int {\frac{1}{u} } \, du =ln|u| + C[/tex]Integration 2: [tex]\int {\frac{du}{u^2+a^2} } = \frac{1}{a} arctan(\frac{u}{a} )+C[/tex]Integration 3: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} +C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx[/tex]
Step 2: Simplify Function
We do long division to simplify the function inside the function.
See Attachment for Long Division Work.
Once we do long division, our function becomes [tex]1-\frac{x+3}{x^2+x+3}[/tex]
Now we rewrite our Integral: [tex]\int ({1-\frac{x+3}{x^2+x+3} }) \, dx[/tex]
Step 3: Integrate Pt. 1
Distributive Integral [Int Rule 1]: [tex]\int {1} \, dx - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Integrate 1st Integral [Int 3]: [tex]x - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Step 4: Identify Variables Pt.1
Set variables for u-substitution.
u = x² + x + 3
du = (2x + 1)dx
Step 5: Integrate Pt. 2
Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} \int {\frac{2(x+3)}{x^2+x+3} } \, dx[/tex]Distribute 2 [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+6}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+1+5}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Int Trick 1]: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{x^2+x+3} } \, dx ][/tex](2nd Int) Complete the Square: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{(x+\frac{1}{2})^2 + \frac{11}{4} } } \, dx ][/tex]Step 6: Identify Variables Pt. 2
Set variables for u-substitution for 2nd integral.
z = x + 1/2
dz = dx
a = √(11/4)
Step 7: Integrate Pt. 3
[Integrate] U-Substitution: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + \int {\frac{5}{z^2 + (\sqrt{\frac{11}{4}})^2} } \, dz ][/tex]Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 1st Integral [Int 1]: [tex]x - \frac{1}{2} [ln|u| + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 2nd Integral [Int 2]: [tex]x - \frac{1}{2} [ln|u| + 5(\frac{1}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ) ][/tex]Distribute 5 [Alg]: [tex]x - \frac{1}{2} [ln|u| + \frac{5}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ][/tex]Distribute -1/2 [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5}{2\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Rationalize [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5\sqrt{11} }{11}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Resubstitute variables [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{x+\frac{1}{2} }{\sqrt{\frac{11}{4} } } )[/tex]Simplify/Rationalize [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} )[/tex]Rewrite [Alg]: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x[/tex]Integration Constant: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]And we have our final answer! Hope this helped you on your Calculus Journey!
hope this will help you........