A food server records the total bill and the amount of the tip received by 5 individuals who dined alone. Here are the data: Total $4.50 $5.79 $6.25 $4.62 $6.35 Tip $0.75 $1.00 $0.75 $0.58 $1.00 (a) Is there a clear explanatory variable and response variable in this setting? If so, tell which is which. If not, explain why not. b) Make a scatterplot of these data on your work document. (c) Based on the scatterplot, describe the relationship between the total bill and tip received for these 5 customers. (d) The correlation r between the total bill and tip received is r = 0.67. Explain how this confirms the description from part (c). (e) How would r change if all the total bill amounts were reduced by 10%? tip received was measured in cents rather than dollars? (f) Suppose another customer whose total bill was $5.15 tipped $0.75. How would including this point influence r? Justify your answer without performing any calculations.
Answers
Answer:
(a) There is not a clear explanatory variable and response variable
(b) Please find attached the scatterplot created with Microsoft Excel
(c) There is some relationship between the total bill and tip received
(d) The correlation value of r = 0.67, reaffirm that there is an amount of positive correlation between the total bill and the tip received
(e) The correlation will remain positive, and will increase
(ii) The correlation will remain constant
(f) The correlation and r will increase marginally
Step-by-step explanation:
(a) The given parameters are;
Total [tex]{}[/tex] Tip
$4.50 [tex]{}[/tex] $0.75
$5.79 [tex]{}[/tex] $1.00
$6.25 [tex]{}[/tex] $0.75
$4.62 [tex]{}[/tex] $0.58
$6.35 [tex]{}[/tex] $1.00
From the given data, the relationship between the variables are not clear as the lowest and the second highest total give the same amount as tip, the second lowest receive the lowest tip and the median value of the total and the highest value give the same value of tip
Therefore, there is not a clear explanatory variable and response variable
(b) Please find attached the scatterplot
(c) Based on the scatterplot, as the total bill increases, the response the tip increases, therefore, there is some relationship between the total bill and tip received
(d) The correlation value of r = 0.67, reaffirm that there is an amount of positive correlation between the total bill and the tip received
(e) (i)Whereby the total bill were reduced by 10% each, we have, that the correlation will remain positive, and will increase
(ii) Whereby the tip received were measured in cents rather than dollars, the correlation will remain constant
(f) When the total bill of another customer whose bill is $5.15 and tipped $0.75 is added, we have three customers out of six that give an equal tip, therefore, the correlation and r will increase marginally
Creating a linear regression model of the given data, the necessary deductions required to solve the problems posed. Hence, the solutions are as follows :
A.)
The explanatory variable is not very obvious as we have similar measured or predicted value for two different data points in the data.
B.)
The scatterplot of the relationship is attached with Total being the independent and tips being the dependent variable.
C.)
The scatter plot shows a positive association or relationship between total and tips.
D.)
The Correlation Coefficient gives the strength and direction of the relationship between two variables. Hence, 0.67 is positive and shows a fairly strong association.
E.)
A reduction in total bill by 10% would still depict an increase in the tips as based on the total bill amount.
If tips was measured in cent and not dollars, then, the the value of r will remain the same, as the unit of a variable has no effect on the correlation Coefficient.
F.)
The addition of a point with total bill of 5.15 and tip amount of 0.75 will strengthen the existing relationship. Hence, the value of R will increase slightly.
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Related Questions
Manuel y Carlos encuentran un libro de matemática usado y en una de las hojas se observa la figura de un poliedro demasiado borrosa, pero se ven algunos datos sobre él que dicen: El poliedro tiene 12 aristas y la suma de su número de caras con su número de vértices es 14. Manuel afirma que se trata de un dodecaedro y Carlos dice que es un cubo. ¿Quién de ellos tiene la razón?
Answers
Answer:
Carlos tiene razón. El poliedro es un cubo.
Step-by-step explanation:
Comencemos analizando el número de caras del dodecaedro y del cubo.
El dodecaedro está conformado por 12 caras.
El cubo en cambio, está conformado por 6 caras.
En cuanto a aristas el dodecaedro tiene 30 aristas y en cambio el cubo tiene 12. Por ende, descartamos la idea de que el poliedro sea un dodecaedro.
Finalmente en cuanto a vértices, el dodecaedro tiene 20 vértices y el cubo tiene 8 vértices.
Si sumamos el número de caras y el número de vértices en el cubo obtenemos :
6 + 8 = 14
Con esto, verificamos que la figura borrosa es de un cubo y que Carlos tiene razón.
I need help with ANGLES!!!!!!!!!!
Answers
Answer: I see acute, obtuse, and right angle.
Step-by-step explanation:
The top left one is equal to 125 degrees because it’s congruent with the 125 degree angle
The bottom left one is equal to 127 because by subtracting the angle of 53 degrees from 180 we get the 2nd angle which is 127.
The top right one is equal to 110 degrees because it’s congruent with the 110 degree angle.
The bottom right one is equal to 80 degrees because by subtracting the angle of 100 degrees from 180 we get 2nd angle which is 80 degrees.
Which expression can be used to check the answer to 56 divided by (negative 14) =-4?
Answers
Answer:
-14x(-4)
Step-by-step explanation:
inverse operation i think its called
Compare the values.
4x 107 is
?
times as much as 4 x 103.
10^4
4 x 10^10
10^10
4 x 10^4
Answers
Answer:
10^4 timesStep-by-step explanation:
Compare
4*10^7 and 4*10^3Dividing
4*10^7/4*10^3 = 4/4*10^(7 - 3) = 1*10^4 = 10^4The first number is 10^4 times as much as the second number
PLLLZZ HELP ASAP! 10 PTS!!
Answers
Answer:
18.3303
Step-by-step explanation:
8x8 = 64
20x20=400
64-400= 336
√336 = 18.3303027798
or 18.3
It’s the right answer
in a survey of villages, it was found that 25% of the people have visited kaduna and 20% have visited Calabar. if 5% visited both cities, what percentage have visited neither towns
Answers
Answer:
60% have visited neither town
please answerrrr
simplify (-2)^4(-2)
Answers
Answer:
-32
Step-by-step explanation:
(-2)^4(-2)
-2x-2x-2x-2
16(-2)
-32
Violet is trying to start an Intramural Club at her school. The principal tells her she must get signatures from students to show support. Each filled sheet contains 25 signatures. By Monday, she and her friend already have 6 sheets filled with signatures. The principal tells Violet she must have 7 more sheets filled with signatures. Write an equation for the number of signatures Violet will get. If she fills all of these, how many signatures will she get in all?
Answers
Answer:
325
Step-by-step explanation:
Let s represent sheets
Let x represent number of signatures needed
s = 25 signatures
6s + 7s = x
Plug in the function
6(25) + 7(25)
= 150 + 175
= 325
x = 325
In total she will need 325 signatures
Help plzzzzzzzzzzzz help me
Answers
Answer:
wow-
Step-by-step explanation:
ngl, thats hard.
Find the slope of the line without graphing using the 2 points below.
(3 , 6) & (11, 6)
m = _______
Answers
Answer:
m = 0
Step-by-step explanation:
1. use the slope formula --> (y2-y1)/(x2-x1)
2. (6 - 6)/(11 - 3)
3. 0/8
4. m = 0
Put these into y=mx+b format SHOW YOUR WORK!!!! x-7y=7 and 6x-7y=-28
Answers
Explanation:
x - 7y = 7
-7y = -x + 7
y = (-1/-7)x + 7/-7
y = (1/7)x - 1
6x - 7y = -28
-7y = -6x - 28
y = (-6/-7)x - 28/-7
y = (6/7)x + 4
-x -x (isolate the y by subtracting x on both sides)
-7y= -x+7
— ——-
-7 -7 (Isolate the y by dividing both sides by -7)
Answer : y= 1/7x - 1
6x-7y= -28
-6x. -6x
-7y = -6x -28
—— ———-
-7. -7
Answer : y= 6/7x + 4
rationalize the denominator of 1/√3
Answers
Answer:
√3/3
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Hope this helps!! Please consider marking brainliest! Have a good one!!
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
If the radical in the denominator is a square root, then you multiply by a square root that will give you a perfect square under the radical when multiplied by the denominator. If the radical in the denominator is a cube root, then you multiply by a cube root that will give you a perfect cube under the radical when multiplied by the denominator and so forth...
Note that the phrase "perfect square" means that you can take the square root of it. Just as "perfect cube" means we can take the cube root of the number, and so forth.
Keep in mind that as long as you multiply the numerator and denominator by the exact same thing, the fractions will be equivalent.
Step 2: Make sure all radicals are simplified.
Some radicals will already be in a simplified form, but make sure you simplify the ones that are not. If you need a review on this, go to Tutorial 39: Simplifying Radical Expressions.
Step 3: Simplify the fraction if needed.
Be careful. You cannot cancel out a factor that is on the outside of a radical with one that is on the inside of the radical. In order to cancel out common factors, they have to be both inside the same radical or be both outside the radical.
[tex]\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}[/tex]
rationalize the denominator of 1/√3[tex]\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}[/tex]
[tex] \frac{1}{ \sqrt{3} } \\ \\(to \: rationalize \: the \: denominator \\ we \: have \: multiply \: \frac{1}{ \sqrt{3} } \: to \: the \:given \: fraction \: \: \: ) \\ = \frac{1}{ \sqrt{3} } \times \frac{1}{ \sqrt{3} } \\ = ( \frac{1}{ \sqrt{3} } ) {}^{2} \\ = \frac{1}{3} [/tex]
HOPE IT HELPS YOU..
Good Morning Ethansledd17!
what is 54873578x958498=?
Answers
Answer: 5.259621477e13
Step-by-step explanation: Hoped this helped!!!
Answer:
5.2596215e+13
Step-by-step explanation:
hope it helps!
Pythagoras
(Show work)
Answers
Answer:
x = 10.6
i just used the pythagorean theorem, you can copy my work.
A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 5 feet from the base of the building. How high up the wall does the ladder reach?
The ladder reaches ___ feet up the wall (round to the nearest humdredth)
Answers
Answer:
13^2-5^2=144 then u square root ur answer to get 12 ft up the wall
Step-by-step explanation:
Which of the following is a factor of f(x)=4x^3+11x^2-75x+18
Answers
Answer:
f(x)=(4x−1)(x−3)(x+6)
Step-by-step explanation:
what value of P makes the equation true
-3p+1/8= -1/4
Answers
Step-by-step explanation:
Hey there!
Given;
-3p + 1/8 = -1/4
Simplify it to get the value of"p".
[tex] - 3p + \frac{1}{8} = - \frac{1}{4} [/tex]
[tex] \frac{ - 24p + 1}{8} = \frac{ - 1}{4} [/tex]
[tex] 4(- 24p + 1) = - 1 \times 8[/tex]
[tex] - 96p + 4 = - 8[/tex]
[tex] - 96p = - 8 - 4[/tex]
[tex]p = \frac{ - 12}{ - 96} [/tex]
[tex]p = \frac{ 1}{8} [/tex]
Therefore, p = 1/8.
Check:
-3*1/8 +1/8 = -1/4
-3/8+1/8= -1/4
-1/4 = -1/4
Therefore, the value of "p" must be (1/8) to satisfy the equation.
Hope it helps...
What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
y = -1/3x + 3
y = -1/3x + 7
y = 3x – 13
y = 3x + 5
Answers
what is the answer to -2x+10=40
Answers
Answer:
-15
Step-by-step explanation:
Answer:
x=-15
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve
Question
Enter an equation in point-slope form for the line.
(2, 4) and (3, 3) are on the line.
An equation of the line in point slope form is:
Answers
Given:
(2, 4) and (3, 3) are on the line.
To find:
The equation of line in point slope form.
Solution:
If a line passes through a point [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex]
(2, 4) and (3, 3) are on the line. So, slope of the line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{3-4}{3-2}[/tex]
[tex]m=\dfrac{-1}{1}[/tex]
[tex]m=-1[/tex]
The slope of a line is -1 and it passes through (2,4). So, an equation in point slope form is
[tex]y-4=-1(x-2)[/tex]
Therefore, an equation of the line in point slope form is [tex]y-4=-1(x-2)[/tex].
A loaf of sandwich bread contains 24 slices. Which of these tables correctly shows the ratios of different numbers of loaves of bread to the numbers of total slices they contain?
Answers
Answer:
15
Step-by-step explanation: i'm not explaining why
Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each. Devin has a coupon that gives a 5% discount off of the regular price of the tickets. He will then pay a 10% purchasing fee on the discounted price of the tickets. What is Devin's total cost of the two tickets after the discount and the fee?
Answers
Given :
Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each.
Devin has a coupon that gives a 5% discount off of the regular price of the tickets. He will then pay a 10% purchasing fee on the discounted price of the tickets.
To Find :
Devin's total cost of the two tickets after the discount and the fee.
Solution :
Discount on price, D = 40×0.05 = $2 .
Price of product after discount, P = $( 40 - 2 ) = $38 .
Now, total price after adding purchasing fee is :
T = P + (P×0.10)
T = 38 + (38×0.10)
T = 38 + 3.8
T = $41.8
Therefore, Devin's total cost of the two tickets after the discount and the fee is $41.8 .
Hence, this is the required solution.
Which of the following graphs represents the equation above?
y=1/2x-2
Answers
Answer:
There’s no graphs
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the slope of the following equation? y = -x + 3
Answers
Mrs. Mireles needs to hire landscapers to maintain her yard. Company L charges $250 per month plus $30 per hour. Company S charges $200 per month plus $35 per hour. Which inequality can be used to find x, the minimum number of hours each company would have to work so that the total charges from Company L is less than the total charges from Company S?
Answers
Answer:
10 hoursStep-by-step explanation:
Step one:
given information
Company L charges
monthly charge= $250
hourly charge= $30
let the total charge be y
and the number of hours be x
y=30x+250----------1
Company S charges
monthly charge= $200
hourly charge= $35
let the total charge be y
and the number of hours be x
y=35x+200------------2
Step two:
equating 1 and 2
30x+250=35x+200
collect like terms
30x-35x=200-250
-5x=-50
x=50/5
x=10
10 hours
I just wanna know how I solve this: "Select the division equation that can be used to find the solution to the problem. 4/9 kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost? "
Answers
9514 1404 393
Answer:
$4.50
Step-by-step explanation:
To find cost per kilogram, divide the cost by the number of kilograms it corresponds to.
($2)/(4/9 kg) = (2)(9/4) $/kg = $4.50 /kg
1 kilogram costs $4.50.
can someone help me out? i’m not sure what the answers would be for these 5, thanks.
Answers
Answer:
<6 and 4 are supplementary angles. Supplementary angles add up to 180. therefore <6 and <4=180--->m<6=65---->180-65=115---> m<4-115
2. 115°
By using vertical angles theorem we see that angles opposite to each other like 5 and 8 are congruent.
Therefore m<8 = m<5
3. 122
<3 and <6 are congruent by the alternate interior angles theorem which states that interior angles that are opposite one another such as 6 and 3 are congruent.
4. 73°
<4 and <7 are supplementary since the <4 is equal to the <8 and the <8 is supplementary to 7.
180-107=73
5. 73°
Step-by-step explanation:
Write the equation of the line that passes through the points (-2,0) and (1,2).
Answers
Answer:
y = 2/3x + 1 1/3
Step-by-step explanation:
Find the slope using rise over run, (y2 - y1) / (x2 - x1)
Plug in the points:
(y2 - y1) / (x2 - x1)
(2 - 0) / (1 + 2)
2 / 3
= 2/3
Then, plug in the slope and a point into y = mx + b to solve for b:
y = mx + b
2 = 2/3(1) + b
2 = 2/3 + b
1 1/3 = b
Plug in the slope and y intercept into y = mx + b
y = 2/3x + 1 1/3 is the equation of the line
A t-shirt increased in price by
1
—
4
. After the increase it was priced at £85. What was the original price of the t-shirt? I will mark brainless!!
Answers
Step-by-step explanation:
81×1/4
=20.24
this is the answer
I need answers to the questions I didn't do
Also are the ones that I did right?
please help me with this ASAP
Answers
Question 5: 5x+20y
Yes the other ones are right