Answers
The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.
What is linear regression?Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.
Note that the regression equation is usually given as:
ŷ = bX + a; where
y = dependent variable
b = Slope/coefficient
X = Independent Variable
a = Constant/ Intercept.
Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.
From the graphing calculation, we have:
The sum of X = 21
The sum of Y = 33.39
Mean X = 3
Mean Y = 4.77
Sum of squares (SSₓ) = 28
Sum of products (SP) = 22.96
Recall that the regression equation is given as:
ŷ = bX + a;
Where;
b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]
Hence,
b = 22.96/28
= 0.82
a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31
hence,
ŷ = 0.82X + 2.31.
Lets find Y if x = 10
y = 0.82 (10) + 2.31 [plugging in the value]
= 8.2 +2.31
= 10.51
Let's find X where Y = 10
10 = 0.82X + 2.31. [Plugging in the value]
collect like terms over the equation sign
10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X
X = 9.37804878049
X [tex]\approx[/tex] 9.38
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Related Questions
How to solve Y=2x-1 2x+y=3 in solving systems using substitution
Answers
Answer:
x = 1, y = 1
Step-by-step explanation:
This Question involves the concept of Solving Simulteanous Equations.
Simulteanous EquationsSimulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.
Example:
2x + 4y = 67
3x + 9y = 90
ApplicationWe are given the 2 equations:
y = 2x - 1 (Equation 1)
2x + y = 3 (Equation 2)
We are asked to use the Substitution Method.
We first substitute Equation 1 to Equation 2 to find the value of x.
2x + (2x - 1) = 3
2x + 2x - 1 = 3
4x - 1 = 3
4x = 3 + 1
4x = 4
x = 4 ÷ 4 = 1
Now we can substitute x into Equation 1 to find the value of y.
y = 2(1) - 1
y = 2 - 1 = 1
Are the following Parallel, Perpendicular, or neither: y = 2x - 5 and -x + 2y = -5
Answers
two lines are parallel if their slope is equal
equation of line is
y=mx+c
where m=slope
for y=2x-5
m=2
for -x+2y=-5
2y=-5+x
y=-5/2+x/2
m=1/2
lines are nor parallel becuase m (slope) is not equal
now we will test for perpendicularity
perpendicular lines have slopes that are reciprocal of each other
first line , m=2
second line, m=1/2
2 and 1/2 are reciprocals
therefore, the lines are perpendicular
the gmat scores of all examinees who took that test this year produced a distribution that is approximately normal with a mean of 410 and a standard deviation of 33. the probability that the score of a randomly selected examinee is less than 370, rounded to three decimal places, is:
Answers
The probability that the score of a randomly selected examinee is less than 370 is 0.113
Mean of the gmat score = 410
Standard deviation of the deviation = 33
The randomly selected examinee be X ,
Thus X = 370
So , we need to find the probability that the score of a randomly selected examinee is less than 370 i.e.
P(X < 370)
Now , let us the z-score with normal distribution formula
Z = (X - μ) / σ
Z = (370 - 410) / 33
Z = -40 / 33
Z = -1.21
Thus P(X < 370) = P(Z < -1.21)
From the z - table , we can get that
P(Z < -1.21) = 0.11314
By rounding off to three decimals ,
P(Z < -1.21) = 0.113
Therefore , the probability of Z< -1.21 is 0.113
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please help thank you
Answers
78x100/6.5= 1200
Since it’s a percent you cross multiply 100 but that’s the simple equation to do it.
In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
Answers
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?
Answers
With the width and length being held constant, the height of the box decreases at rate 5 cm/s
Let:
l = length
w = wide
h = height
Then, the volume of the box is given by:
V = l . w. h
The length and the width are assumed to be constant. Hence, the derivative with respect to time is:
dV/dt = l . w dh/dt
Parameters given:
dV/dt = - 541 cm³/dt
l = 9 cm
w = 12 cm
Plug these parameters into the formula:
-541 = 12 . 9 . dh/dt
dh/dt = 5 cm/s
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The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each. Managers Fatima and Jorge need to figure out how many boxes they can ship out of the factory each day.
Answers
As per the concept of division, they sold 271 cookies boxes per day and there are 6 cookies are remained.
Division:
Division means splitting of a large group into smaller groups such that every group will have an equal number of items.
There are four parts of the division, which are dividend, divisor, quotient, and remainder.
Given,
The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each.
Here we need to find the number of boxes sold per day.
Through the given question we know that,
Number of cookies per day = 3,258
Number of cookies in one box = 12
So, the dividend is 3,258 and the divisor is 12.
So, the number of boxes per day is illustrated using the following diagram.
Based on these, there are 271 boxes are sold per day with 6 remaining cookies.
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gary gets an average of 15 text messages during his 8 hour work day. in order to find the probability that gary will get exactly 3 text messages in a 2 hour portion of his work day using the poisson distribution, what is the time interval of interest?
Answers
The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours
Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.
Let x be the Poisson random Variable Such that X ~Poisson (15).
We need to find P(x≤3) in 2 hours.
Thus, the time interval of interest is 2 hours.
What is probability ?
Probability is the likelihood of an event occurring. It can range from an impossible event to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely happen. The median is 0.5 or half and these events are equally likely. A good example of half probability is tossing a coin. It gets straight heads or tails.
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Traci planted a tree in her backyard.She made this graph to show the tree growth over 5 years. 100 POINTS IF YOU HELP!!!!
Answers
A. The slope of the function = 1.5.
a = 15; b = 3; c = 3; d = 1.5
B. y-intercept (b) = 7.5
C. The equation of the function is: y = 1.5x + 7.5.
The height in 10 years is approximately 17.5 feet.
How to Write the Equation of a Linear Function?The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.
Part A:
Using the two points on the graph, we can find the slope of the function as shown below:
The two points are (3, 12) and (5, 15):
Slope of the function = (15 - 12)/(5 - 3)
= 3/2
Slope (m) = 1.5.
Thus, the values that represents each letters would be:
a = 15; b = 3; c = 3; d = 1.5
Part B: The y-intercept of the function
The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.
Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:
12 = 1.5(3) + b
12 = 4.5 + b
12 - 4.5 = b
7.5 = b
b = 7.5
y-intercept (b) = 7.5
Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:
y = 1.5x + 7.5.
Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.
To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:
y = 1.5(10) + 7.5
y = 10 + 7.5
y = 17.5 feet
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9th grade math HHhH HHhH
Answers
Answer:y=-x+3
Step-by-step explanation:
The area of a rectangle is 60 cm². The length is 11 cm more than the width. Find the width
Answers
Answer:
5
Step-by-step explanation:
let width be x
and because length is 11 times more than the width, therefore length equals to 11x
hence the equation equals to
area = length x width
60 = 11x + x
60 = 12x
x = 60/12
therefore, the width of the rectangle is 5
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
Answers
Answer:
c. ∠MPN
Step-by-step explanation:
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, ∠MPN is supplementary to ∠NPI.
a standard poker deck of cards contains 52 cards, of which four are kings. suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. find the probability that the first card is a king and the second card is not a king. (round your answer to four decimal places.)
Answers
The probability that the first card is a king and the second card is not a king is 0.0045
Suppose two cards are drawn sequentially so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. To find the probability that the first card is a king and the second card is not a king.
In the first case let's find the probability of drawing a king from the deck of cards,
A = ( 4/52 )
In the second case the probability of drawing a card that is not a king from the deck is,
B = ( 3/51 )
At last, to get the final probability to draw that the first card is a king and the second card is not a king we need to multiply the above two cases as,
A x B = ( 4/52 ) ( 3/51 )
= 1/221
= 0.0045
The probability that the first card is a king and the second card is not a king is 0.0045
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Sigma notation for 22, 28, 34, 40, 46
Answers
The sigma notation for the sequence 22, 28, 34, 40, 46 is as follows:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
How to represent a notation in sigma notation?A sequence is represented in sigma notation according to the following rule:
[tex]\sum_{n = 0}^{n = N-1} a + bn[/tex]
In which the parameters are described as follows:
N is the number of terms in the sequence.a is the first term of the sequence.b is the common difference between the terms of the sequence.In the context of this problem, the sequence is:
22, 28, 34, 40, 46.
Hence the values of these parameters are given as follows:
N = 5, as there are 5 terms in the sequence.a = 22, which is the first term of the sequence.b = 6, as the difference between each term of the sequence is.Hence the sigma notation of the sequence is given by:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
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PLEASE HELP IF YOU KNOW AP STATS OR HAVE TAKEN THIS QUIZ!! THANK U
The data set for the average height of men at a ballgame compared to their shoe size is represented by the table.
Table with two columns titled men's shoe size (U. S. ) and height (inches). Data values 7 and 64, 10 and 69, 12 and 72, 8 and 67, 9. 5 and 69, 10 and 70, 11. 5 and 75, 12. 5 and 73, 13. 5 and 71, 10 and 68.
Part A: What is the equation of the least-squares regression line? (3 points)
Part B: Carlos wears a size 9 and is 71 inches tall. What is the residual for Carlos's data? Show your work. (4 points)
Part C: Interpret the meaning of the residual from part B. (3 points)
Answers
An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.
By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:
y = 0.25x + 66.6
Interpret the meaning of the residual from part B is given below.
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12. Find the value of x.
+f
(7x+4) +(10x-11)=180 mid segment
Answers
The value of x is 11.
What is an equation?
Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.
We are given an equation (7x+4)+(10x-11)=180
We open brackets and simplify the equation by adding similar values we get
17x-7=180
17x=187
on dividing both sides by 17 we get
x=11
Hence the value of x is 11
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X^2+8x-35=0 which number would be added to complete the square
Answers
Answer:
x =(8-√204)/2=4-√ 51 = -3.141
x =(8+√204)/2=4+√ 51 = 11.141
Step-by-step explanation:
Factoring x2-8x-35
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -35
Step-1 : Multiply the coefficient of the first term by the constant 1 • -35 = -35
Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is -8 .
-35 + 1 = -34
-7 + 5 = -2
-5 + 7 = 2
-1 + 35 = 34
HELP ASAP PLSSSPLSPSLPSLPLSS
Given f(x) = 3x − 4 and g(x) = f(2x), which table represents g(x)?
Answers
The values of g(x) at x = 1, 2 and 3 are 2, 8 and 14 respectively.
Which table contains the values of g(x)?
Since f(x) = 3x - 4 and g(x) = f(2x)
so, in f(x) = 3x - 4, we can replace x with 2x:
g(x) = f(2x) = 3(2x) - 4 = 6x - 4
when x = 1:
g(x) = 6(1) - 4
= 6 - 4 = 2
when x = 2:
g(x) = 6(2) - 4
= 12 - 4 = 8
when x = 3:
g(x) = 6(3) - 4
= 18 - 4 = 14
Therefore, when x = 1, 2 and 3, their corresponding values of g(x) are 2, 8 and 14. So 4th table contains the values of g(x).
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Answer: D
Step-by-step explanation: I Chose D and got it right for my quiz.
The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
Answers
Use the ratios to determine the number that you should multiply by.
See details:
462 people get on an empty train at a station. At the first stop, 234 more people get on the train, and 95 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train. How many people get off the train at the final destination?
Answers
Answer:
wow your so goood
Step-by-step explanation:
Apologies if anything is incorrect.
If y= 4 1/4 when x= 3/4, find y when x= 4 1/2
Answers
when y = 17/4, x= 3/4
then assume y varies directly as x
then y =kx
k = y/x
k= 17/4× 4/3
k= 17/3
when x= 3/4, y = 27/34
What is variation?A variation is a relation between a set of values of one component and a set of values of other component.
Direct variation is a type of variation in which two variables go line in line with their values
y= kx where k is the proportionality constant
k = 17/3 when y = 17/4 and x= 3/4
using thesame value of k in the expression k=y/x
and x = 3/4, then
y= 27/34
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Last night, the two dinner specials at Rhianna's favorite restaurant were salmon filet and steak. The restaurant served 52 specials in all, 25% of which were salmon filets. How many salmon filets did the restaurant serve?
Answers
There were 13 salmon fillets that the restaurant served.
How do we calculate how many salmon fillets the restaurant served?The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.
We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.
52 × 25% =
52 × 25/100 =
(52 × 25)/100 =
1,300/100 = 13
There were indeed thirteen salmon fillets served by the restaurant.
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3f(5) x f(2)
Anyone understand this question?
Answers
Answer:
I do!
Decimal Form: f=−0.¯6,5
Step-by-step explanation:
If any individual factor on the left side of the equation is equal to 0 the entire expression will be equal to
0.3f+2=0f−5=0
Set
3f+2 equal to 0 and solve for f.
more steps...
f=−23
Set
f−5 equal to 0 and solve for f.
more steps...
f=5
The final solution is all the values that make
(3f+2)(f−5)=0
true.
f=−23,5
The result can be shown in multiple forms.
Exact Form :f=−23,5
HOPE IT HELPS :)
PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table?
Answers
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24
15yards to 18 yard increase or decrease
Answers
Answer:
Increase
Step-by-step explanation:
You start at 15 yards then proceed to MOVE UP(Increase) 3 more yards getting you to 18.
Answer:
increase
Step-by-step explanation:
because your going 3 more yards on a number line you would travel right
Given two terms from a geometric sequence, identify the first term and the common ratio: a10 = 1 and a12=1/25
Answers
Given:
a denotes first term and r denotes the common ratio.
[tex]a_{10}=1\colon a_{12}=\frac{1}{25}[/tex][tex]a_n=ar^{n-1}[/tex][tex]a_{10}=ar^{10-1}[/tex][tex]1=ar^9\ldots.\text{ (1) }[/tex][tex]a_{12}=ar^{12-1}[/tex][tex]\frac{1}{25}=ar^{11}\ldots.(2)[/tex]Divide the equation (2) by (1)
[tex]\frac{\frac{1}{25}}{1}=\frac{ar^{11}}{ar^9}[/tex][tex]\frac{1}{25}=r^2[/tex][tex]r=\pm\frac{1}{5}[/tex][tex]\text{If r=}\frac{1}{5}[/tex][tex]1=a(\frac{1}{5})^9[/tex][tex]a=1953125[/tex][tex]\text{If r=-}\frac{1}{5}[/tex][tex]1=a(-\frac{1}{5})^9[/tex][tex]a=-1953125[/tex][tex]a=-1953125\text{ ; r = -}\frac{1}{5}[/tex][tex]a=1953125\text{ ; r = }\frac{1}{5}[/tex]Judy is 12 years old and is 8 years old mukta is 16 years old which of the following ratios best expresses the relationship between the ages 4 ratio 3 ratio to 2 ratio 3 ratio 4:3 ratio 2 ratio 4:3 ratio 4 ratio 2 ratio 4 ratio 3
Answers
Age of Judy = 12 yrs old
Age of x = 8 yrs old
Age of Mukta= 16 yrs old
Ratio between the 3 ages = 12 : 8 : 16
Since all the three numbers are divisible by 4
Therefore the ratio comes out to be 3 : 2 : 4 or 3 ratio 2 ratio 4
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Answer:
= 12 : 8 : 16
all the three numbers are divisible by 4
the ratio is 3 : 2 : 4
Which sequence shows the numbers in order from least to greatest?
A. |-8.23| < 8 1/5 < 8.3
B. 8 1/5 > 8.3 > |-8.23|
C. 8 1/5 < |-8.23| < 8.3
D. 8.3 < |-8.23| < 8 1/5
Answers
The sequence that shows the numbers in order from least to greatest is A. |-8.23| < 8 1/5 < 8.3
How to illustrate the information?It's important to note that arranging numbers from the least to the greatest simply means ascending order.
In this case, it's vital to note that the negative value is the smallest. Then 8 1/5 is 8.2. This conea after. The greatest number is 8.3 since it's the biggest.
In conclusion, the correct option is A.
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how many 1/5 inch pieces can be cut from a piece of ribbon 7/20 of an inch long.
Answers
1) Gathering the data
1/5 inch
7/20 inches long
2) Let's them divide, 7/20 by 1/5 inches
When divide fractions, we multiply the reciprocal of the second fraction
and if possible we can simplify
If Fx) = x-5 and G(x) = x2 , what is G(F(x))?
Answers
Explanation:
Given the functions
f(x) = x-5
G(x) = x^2
We are to find the composite function G(f(x))
