PLEASE HELP! Use a graphing calculator to find an equation of the line of best fit for the data in the table. Round the slope and y-intercept to the nearest tenth. Then Identify and interpret the correlation coefficient.
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
The equation of the line of best fit is y=
To the nearest thousandth, the correlation coefficient is r=
Answers
Answer:
ŷ = -0.895X + 13.600
Slope = -0.9
Intercept = 13.6
r = - 0.964
Step-by-step explanation:
Given the data:
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
Inputting the data given into the online regression calculator :
The equation of line of best fit :
ŷ = -0.895X + 13.600
Slope = - 0.9(to the nearest tenth)
Intercept = 13.6 (to the nearest tenth)
The correlation Coefficient 'r' of the data supplied is - 0.9643, which implies that a strong negative correlation exists between the dependent and independent variables.
r = - 0.964 (to the nearest thousandth)
Inputting the data into the STAT then Fit Data function of the HP 50g
Graphing Calculator.
The equation of the line of best fit is; y ≈ 13.6 - 0.9·xThe correlation coefficient is r ≈ -0.964The meaning of the strong negative correlation is that the x-values
of the data is decreasing, while the corresponding y-values of the data
increasing.
Reasons:
The least squares regression line equation is the best fit line for the data
The formula for the least squares regression line is [tex]\hat Y = b \cdot X + a[/tex]
Where;
[tex]b = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right )\left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b \cdot \sum X}{n}[/tex]
n = The sample size
Inputting the given data into the function Fit Data on a graphing calculator,
by editing ∑DAT.
The left column, represent the x-values, and right column represent the y-
values as follows;
[tex]\begin{array}{|c|cc|} \mathbf{Column \ 1}&&\mathbf{Column \ 2}\\10.1&&4.3\\9.8&&4.8\\9.7&&5.3\\9.4&&5.2\\8.9&&5.6\\8.7&&5.8\\8.4&&6.1\\8.1&&6.3\end{array}\right][/tex]
After inputting the data as above, press enter.
Move the pointer to the Model options line, select choose to choose the
Linear Fit model by selecting OK.
Select OK again for the calculator to do the calculations.
The least squares regression line equation given by the calculator is
presented as follows;
y = 13.5998272884 - 0.894645941278·x
The slope and the y-intercept rounded to the nearest tenth gives;
y = 13.6 - 0.9·xThe slope = -0.9The y-intercept = 13.6Correlation coefficient:
The correlation coefficient is given from the data using the following
formula;
[tex]r = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right ) \cdot \left (\sum Y \right )}{\sqrt{n \cdot \sum X^{2} - \left (\sum X \right )^{2}\times n \cdot \sum Y^{2} - \left (\sum Y \right )^{2}}}[/tex]
From the graphing calculator, we have the correlation coefficient, given as
follows;
Correlation: (-0.964276229529)
Therefore, to the nearest thousandth;
The correlation coefficient, r ≈ -0.964The high negative value of the correlation coefficient indicates a strong
and near perfect relationship between the variables, x, and y, such that we
have;
A decrease in the value of x leads to a proportional increase in the value of y.Learn more here:
https://brainly.com/question/24848242
Related Questions
Choose the best estimate for the weight of a strawberry A 1 ounce B 8 ounces
Answers
Answer:1 ounce
Step-by-step explanation:
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answers
Answer:
B
Step-by-step explanation:
Recall that [tex](g \circ f)(x)=g(f(x))[/tex]. In other words, we need to find [tex]f(x)[/tex] first and then put that value into [tex]g(x)[/tex].
We need to find [tex](g \circ f)(4) =g(f(4))[/tex]
[tex]f(x)=4x-2\\[/tex]
[tex]f(4)=4(4)-2=14[/tex]
[tex](g \circ f)(4) =g(f(4))=g(14)[/tex]
[tex]g(x)=-6x^2-8x-8[/tex]
[tex]g(14)=-6(14)^2-8(14)-8[/tex]
[tex]g(14) = (g \circ f) (4) =-1296[/tex]
*Brainliest* What is the domain of the function shown in thr table?
Answers
Answer:
Domain is { 3,5,7,9}
Step-by-step explanation:
The domain is the input values
Domain is { 3,5,7,9}
Answer:
Domain - {3, 5, 7, 9} (B)
Step-by-step explanation:
Domain - imput values, X values
Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and y represents the total cost. The total cost for 35 brochures is $41.45. The total cost for 65 brochures is $55.55. Step 1: Write the ordered pairs (35, 41.45) and (65, 55.55). Step 2: Find the slope. M = StartFraction 55.55 minus 41.45 Over 65 minus 35 EndFraction = 0.47 Step 3: Find the y-intercept to write the equation in slope intercept form. Y minus 55.55 = 0.47 (x minus 35). Y minus 55.55 = 0.47 x minus 16.45. Y = 0.47 x + 39.1. Which explains the error that Lila made? Lila made in error in Step 1 by reversing the ordered pairs. Lila made an error in Step 2 by not using the slope formula. Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair. Lila made an error in Step 3 when she did not use the distributive property correctly when multiplying.
Answers
Answer:
The answer is C. Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.
Hope this helps!
Stay safe at home :)
(those of you doing edge hang in there!)
The y intercept of the problem is equal to 25+14.1/30*x.
What is total cost?The total cost is the sum of the fixed cost and the variable cost to make a product.
How to find y-intercept?x is showing no. of bruchers
y is showing total cost.
Total cost for 35 bruchers=41.45
Total cost for 65 bruchers=55.55
The points are (35,41.45), (65,55.55)
The y intercept can be calculated as :
y-41.45=(55.55-41.45/65-35)*(x-35)
30y-14.1x=750
y=25+14.1/30*30
Hence the value of y intercept is 25+14.1/30*30.
Learn more about intercept at https://brainly.com/question/26233
#SPJ2
Ravi lost 80 dollars from his pocket.
Write a signed number to represent this change.
Answers
Answer:
x - 80
Step-by-step explanation:
Ravi had x dollars in all.
x - 80
At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?
Answers
Answer:
x = -2
Step-by-step explanation:
The root will touch the axis and bounce off when the exponent is even. In that case, that means (x + 2)² is the binomial that will bounce. Therefore, the root which bounces and touches the x-axis is x = -2.
I need this answered quickly. What is the value of d to the nearest hundredth?
Answers
Answer:
6.48
Step-by-step explanation:
you have to use the sin rule
Answer:
6.48
Step-by-step explanation:
Given the coordinates for the function below which of the following are coordinates for its inverse
Answers
0.0396 x 10 to the power of 9
Answers
Answer:
Brainliest!
Step-by-step explanation:
0.0396 x 10^9
10^9 = 1,000,000,000
0.0396 x 1,000,000,000 = 39,600,000
Answer:
39600000
Step-by-step explanation:
1) 10^9 = 1000000000
2) 0.0396*1000000000 = 39600000
Let p and q be real numbers such that the roots of
x^2 + px + q = 0 are real. Prove that the roots of
x^2 + px + q + (x + a)(2x + p) = 0 are real, for any real number a.
Answers
Answer:
Step-by-step explanation:
Known fact: all roots of quadratic equation [tex]ax^2 + bx + c = 0[/tex] are real if and only if
discriminant [tex]D = b^2 - 4ac \geq 0.[/tex]
We know that all roots of [tex]x^2 + px + q = 0[/tex] are real. We can derive from this condition that
[tex]p^2 - 4q \geq 0[/tex]. (<----------- HERE)
Let's do some simplification of second equation:
[tex]x^2 + px +q + (x + a)(2x + p) = 3x^2 + x(2p + 2a) + ap + q.[/tex]
So we want according to Known fact prove that discriminant of equation
[tex]3x^2 + x(2p + 2a) + ap + q = 0[/tex] is greater or equal zero.
[tex]D = (2p + 2a)^2 - 4\cdot 3 (ap + q) = 4(p^2 + a^2 + 2ap - 3ap - 3q) = 4(a^2 - ap + p^2 - 3q)[/tex].
To prove that [tex]D \geq 0[/tex], we can view D as polynomial of a:
[tex]D(a) = 4a^2 - a(4p) + 4(p^2 - 3q)[/tex].
Known fact #2: if quadratic polynomial have positive greatest coefficient and it's discriminant [tex]\leq 0[/tex] then polynomial always positive.
So remains to prove that
[tex](4p)^2 - 4\cdot 4\cdot 4(p^2 - 3q) \leq 0[/tex]
lets divide both side by [tex]4^2[/tex]:
[tex]p^2 - 4(p^2 - 3q) \leq 0[/tex]
[tex]-3p^2 + 12q \leq 0[/tex]
divide by 3
[tex]-p^2 + 4q \leq 0[/tex]
transfer terms to the other side:
[tex]0 \leq p^2 - 4q[/tex]
But we know that from "(<----------- HERE)"!!!
So Q.E.D.
PLZ HELP! WILL MAKE A BRAINLIST
Which types of dilation are the given scale factors?
Answers
Answer:
see explanation
Step-by-step explanation:
For a given scale factor k
If k > 1 then expansion
If k < - 1 then expansion in the opposite direction
If 0 < k < 1 or - 1 < k < 0 then contraction
k = - 2 ← expansion in opposite direction
k = 1.5 ← expansion
k = [tex]\frac{1}{4}[/tex] ← contraction
k = - [tex]\frac{6}{7}[/tex] ← contraction
type < = to mean <
or > = to mean .
Jake began the day with 6 dollars in his wallet. Then he withdrew some
money from the bank and added that to what was already in his wallet. After
doing that, he had 31 dollars in his wallet.
Answers
Answer:
He added $25 to the contents of his wallet.
Step-by-step explanation:
Here's what's happening, symbolically:
$6 + m = $31, or m = $25. Jake added $25 (represented by m) to the contents of his wallet.
What value of x is in the solution set of 3(x – 4) > 5x + 2?
Answers
Answer:
-10
Step-by-step explanation:
expand: 3x-12>5x+2
subtract 3x and subtract 2 to both sides
-14>2x
which is just
2x<-14
so x<-7.
the only value is -10. :D
Answer:
-10
Step-by-step explanation:
3(x – 4) > 5x + 2
Distribute
3x -12 > 5x+2
Subtract 3x from each side
3x-12-3x > 5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12 -2 > 2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
X must be less than -7
-10 is less than -7
1. Martha pays 20 dollars for materials to make earrings. She makes 10 earrings and sells 7 for
5 dollars and 3 for 2 dollars. Write a numerical expression to represent this situation and then
find Martha's profit?
Answers
Answer:
Numerical expression to represent this situation : 41 = 20 + P
Martha's profit is $21
Step-by-step explanation:
Total cost price for earrings for Martha = total money invested in material to make earrings = $20
No. of ear rings made = 10
No. of earrings sold for $5= 7
Total Price for these 7 earrings= $5*7 = $35
No. of earrings sold for $2= 3
Total Price for these 3 earrings= $2*3 = $6
Total price for all of the ten earrings = $35+$6 = $41
We know that
selling price = cost price + profit
Total price for all of the ten earrings = Total cost price for 10 earrings + total profit made on those 10 earrings
let total profit be P
41 = 20 + P
Thus,
P = 41-20 = 21
numerical expression to represent this situation : 41 = 20 + P
Thus, Martha's profit is $21
Kevin's bank offered him a 4.5% interest rate for his mortgage. If he purchases 3 points, what will be his new rate?
Answers
Answer:
The new rate would be 3.75%
Step-by-step explanation:
Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.
A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)
New interest rate=4.5%-0.75%=3.75%
Answer: mine was: 4.125%
Step-by-step explanation:
What single decimal multiplier would you use to increase by 4% followed by a 3% increase
Answers
Answer:
1.0712
Step-by-step explanation:
if you increase by 4%, it means you will have a new total of 104%. In decimals it is 1.04 (divide your percentage by 100) after that you do the same with the 3% increase. you'll have a new total of 103%. In decimals 1.03. If you want to know what single multiplier you can use, you need to multiply the both decimals. So you get 1.04 x 1.03 = 1.0712
hope this will help you, have a nice day!
Consider the reduction of the rectangle. A larger rectangle has a length of 18 inches and width of 8 inches. A smaller rectangle has a length of x inches and width of 3 inches. Write a proportion and then solve to find the missing measure of the reduced rectangle. What two ratios can be used in the proportion? What is the value of the missing measure?
Answers
Answer:
18/8 = x/3
x = 6.75 inches (length)
Step-by-step explanation:
Hi, to answer this question we have to write 2 ratios using the information given:
A larger rectangle has a length of 18 inches and width of 8 inches.
Inches /width = 18/8
So, for a rectangle that has a length of x inches and width of 3 inches the ratio is :
x/3
Solving for x:
18/8 = x/3
18/8 (3) =x
6.75 in= x
Feel free to ask for more if needed or if you did not understand something.
Use the table to identify the values of pand q that should be used to factor x2
- 3x - 10 as (x + p)(x + 9).
Answers
Answer:
A
p = -5 and q = 2 or p = 2 and q = -5
Step-by-step explanation:
Technically, you don't need the table to help you out here. If you solely just factor out x²-3x-10, you would get (x-5)(x+2). So one variable would always have to be -5 and the other variable would always have to be 2.
The equation a=1/2(b^1+b^2)h can be determined the area, a, of a trapezoid with height, h, and base lengths, b^1 and b^2 Which are equivalent equations?
Answers
The complete question is as follows.
The equation a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex] can be used to determine the area , a, of a trapezoid with height , h, and base lengths, [tex]b_1[/tex] and [tex]b_2[/tex]. Which are equivalent equations?
(a) [tex]\frac{2a}{h} - b_2 = b_1[/tex]
(b) [tex]\frac{a}{2h} - b_2 = b_1[/tex]
(c) [tex]\frac{2a - b_2}{h}[/tex] = [tex]b_1[/tex]
(d) [tex]\frac{2a}{b_1 + b_2} = h[/tex]
(e) [tex]\frac{a}{2(b_1 + b_2)}[/tex] = h
Answer: (a) [tex]\frac{2a}{h} - b_2 = b_1[/tex]; (d) [tex]\frac{2a}{b_1 + b_2} = h[/tex];
Step-by-step explanation: To determine [tex]b_1[/tex]:
a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]
2a = ([tex]b_1 + b_2[/tex])h
[tex]\frac{2a}{h} = b_1 + b_2[/tex]
[tex]\frac{2a}{h} - b_2 = b_1[/tex]
To determine h:
a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]
2a = [tex](b_1 + b_2)h[/tex]
[tex]\frac{2a}{(b_1 + b_2)}[/tex] = h
To determine [tex]b_2[/tex]
a = [tex]\frac{1}{2}(b_1 + b_2 )h[/tex]
2a = [tex](b_1 + b_2)h[/tex]
[tex]\frac{2a}{h} = (b_1 + b_2)[/tex]
[tex]\frac{2a}{h} - b_1 = b_2[/tex]
Checking the alternatives, you have that [tex]\frac{2a}{h} - b_2 = b_1[/tex] and [tex]\frac{2a}{(b_1 + b_2)}[/tex] = h, so alternatives A and D are correct.
please help Multiply -4w(w+2)
Answers
Answer:
-4w² - 8w
Step-by-step explanation:
All you need to do is distribute -4w. That means to multiply -4w to w and 2 separately. When you multiply -4w to w, you will get -4w² and when you multiply -4w to 2, you will get -8w.
the -4w becomes squared and you multiply -4 and 2
At the beach, 11% of people have white towels and 53% have blue towels. If
the rest have red, what percentage of the people at the beach have red
towels?
Answer here
SUBMIT
ASAP help plz
Answers
Answer:
36 percent.
Step-by-step explanation:
We have been given that 11 percent of people of the peach have white towels, and 53 percent have blue towels.
With this information, we can find the remaining percentage of people that have red towels.
Recall that the total percentage is always 100 percent.
lets make r for the percentage of people that have red towels.
You can solve it by changing it to fraction, decimal, or just keep it at percent.
I will show you all of the possible ways.
Percent:
11 percent plus 53 percent plus r =100 percent
combine the like terms, or add 11 plus 53 to simplify the equation.
You have 64 percent plus r =100 percent Our goal is to isolate r, so subtract both sides by 64 percent.
100-64 is 36 percent.
r=36 percent of people who have red towels.
With fractions.
Write it as 11/100 plus 53/100 plus r/100= 100/100.
Combine the fractions.
64/100 plus r/100=100/100.
Subtract both sides by 64/100.
You are left with r=36/100, 9/25, or 36 percent.
With decimals.
11 percent as a decimal is 0.11. Just move the decimal spot 2 times. In 11, since you can write it as 11.0, you move it to the right twice.
53 percent is 0.53.
r is r.
100 percent is 1.
0.11 plus 0.53 plus r=100
Combine or add 0.53 and 0.11. That is 0.64.
Subtract both sides by 0.64.
You get r to be 0.36 or 36 percent.
I hope this helps, and I hope you have a good day!
Answer:
36%[tex]percentage \: of \: people \: who\: have \: white \\ towels = 11 \\ percentage \: of \: people \: who \: have \: blue \: \\ towels = 53 \\ percentage \: of \: people \: who \: have \: \\ white \: and \: blue \: towel \\ = 11 + 53 \\ = 64 \\ percentage \: of \: people \: who \: have \ \: red \\ towels = 100 - 64 \\ \: \: \: \: \: \: \: \: \: \: \: = 36[/tex]
hope this helps ..
Good luck on your assignment
A saleperson receives a base salary of $37,000 in commission of 8% of the total sales of the year if the sales person sells $265,000 of merchandise what is his total salary for the year
Answers
Answer:
Sale-person's total salary for the year is $ 82,050
Step-by-step explanation:
Base salary of salesperson = $37,000
commission percentage of salesperson = 17% of sales
sales made in a year = $265,000
commission for salesperson in $ = 17% of sales
commission for salesperson in $ = 17 / 100 * $265,000 = $45,050
Thus, total commission for the given year salesperson is $45,050
Total salary for year = Base salary + total commission for the given year
Total salary for year = $37,000 + $45,050 = $ 82,050 (Answer)
The radius of a semicircle is 5 feet. What is the semicircle's diameter?
Answers
Answer:
The diameter of the semicircle is 10 feet.
Step-by-step explanation:
This is because d=r2 or diameter=radius*2
Answer:
Step-by-step explanation:
[tex]Diameter= 2* Radius\\D = 2* 5\\D= 10[/tex]
Looking at twentieth century mathematicians 1900 to 1999, what is the surname of the Iranian-born mathematician who won the highest honour in mathematics, the Fields Medal?
Answers
Answer: Maryam Mirzakhani
Step-by-step explanation:
the area of a square field is 50625 meter square find its perimeter
Answers
Answer:
900
Step-by-step explanation:
A=S^2
50265=SxS
S=√50265
S=225
P=Sx4
P=225x4
P=900
Can someone please help me I’m stuck
Answers
Answer:
6
Step-by-step explanation:
Since the two triangles are similar, their ratios of sides must be constant. Therefore:
[tex]\dfrac{9}{3}=\dfrac{x}{2} \\\\x=2\cdot 3=6[/tex]
Hope this helps!
a triangle has it side as r is 53 degree which is hypotenuse t opposite which is 14 s is adjacent find r and s
Answers
Answer:
sin(53°) = t/r
= 14/r
r = 14/sin(53°)
r = 17.53
tan(53°) = t/s
= 14/s
s = 14/tan(53°)
s = 10.55
If f(x) = 1 - x and g(x) = 1-X, which is the rule of function (f-g)(x)?
Answers
Answer:
0
Step-by-step explanation:
f(x) = 1 - x
g(x) = 1-X
f(x) - g(x) = 1-x - (1-x)
Distribute
=1-x-1 +x
Combine like terms
0
The answers to this question
Answers
Answer:
See explanation
Step-by-step explanation:
The discriminant is [tex]{b^{2}-4ac }[/tex]
1. 9² - 4(1)(20) = 81 - 80 = 1 so there are 2 solutions
2. (-9)² - 4(3)(-13) = 81 + 156 = 237, so there are 2 solutions
3. The first answer is correct
4. The third answer is correct
What is the following product? square root of 10 times square root of 10
Answers
Answer: 10
Step-by-step explanation:
√10 x √10
When a square root of an expression is multiplied by itself, the result is that expression...
10