You can practice on this problem. 1. A sample of men agreed to participate in a study to determine the relationship between several variables including height, weight, waste size, and percent body fat. A scatterplot with percent body fat on the y-axis and waist size (in inches) on the horizontal axis revealed a positive linear association between these variables. Computer output for the regression analysis is given below: Dependent variable is: WBE R-squared - 67.8% S - 4.713 with 250-2 - 248 degrees of freedom Variable Constant Waist Coefficient -42.734 1.70 se of coeff 2.717 0.0743 t-ratio -15.7 22.9 prob <.0001 <.0001 (a) Write the equation of the regression line (be sure to use correct notation and define your variables): (b) Explain/interpret the information provided by R-squared in the context of this problem. Be specific, (c) Calculate and interpret the correlation coefficient (r). (d) One of the men who participated in the study had waist size 35 inches and 10% body fat. Calculate the residual associated with the point for this individual.
Answers
(a) The equation of the regression line Percent Body Fat = -42.734 + 1.70 * Waist Size
(b) The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.
(c) It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.
(d) The residual associated with this point is approximately -6.766
(a) The equation of the regression line can be written as:
Percent Body Fat = -42.734 + 1.70 * Waist Size
In this equation, Percent Body Fat represents the dependent variable, Waist Size represents the independent variable, -42.734 is the intercept (constant), and 1.70 is the coefficient for the Waist Size variable.
(b) R-squared is a measure of how well the regression line fits the data. In this context, R-squared of 67.8% indicates that 67.8% of the variation in the percent body fat can be explained by the linear relationship with waist size. The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.
(c) To calculate the correlation coefficient (r), we can take the square root of the R-squared value. In this case, the correlation coefficient would be approximately √(0.678) ≈ 0.823.
Interpretation: The correlation coefficient (r) of 0.823 indicates a strong positive linear relationship between waist size and percent body fat. It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.
(d) To calculate the residual associated with the point for an individual with a waist size of 35 inches and 10% body fat, we need to substitute the waist size value into the regression equation and calculate the difference between the actual percent body fat and the predicted percent body fat.
Using the regression equation: Percent Body Fat = -42.734 + 1.70 * Waist Size
Substituting Waist Size = 35:
Percent Body Fat = -42.734 + 1.70 * 35 = -42.734 + 59.5 ≈ 16.766
The actual percent body fat for this individual is 10%. Therefore, the residual can be calculated as:
Residual = Actual Percent Body Fat - Predicted Percent Body Fat
Residual = 10 - 16.766 ≈ -6.766
The residual associated with this point is approximately -6.766. This indicates that the actual percent body fat is about 6.766 units lower than the predicted value based on the regression equation.
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Related Questions
The decimal value of 5/8
Answers
0.625
Explanation:
We know that 0.125 is equal to 1/8, so you can then multiply 0.125 by 5.
Dividing 5/8, It's Equal To 0.625
Step-by-step explanation:
5/8 = O.625
suppose each license plate has three letters followed by three digits. megan drives a car with the license plate uwu144. how many license plates differ from megan’s at exactly one position?
Answers
There are 11,390,625 license plates that differ from Megan's at exactly one position.
To do this, we will use the following formula:
Number of license plates that differ at exactly one position = Number of different options for the first position × Number of different options for the second position × Number of different options for the third position × Number of different options for the fourth position × Number of different options for the fifth position × Number of different options for the sixth position
For the first position, there are 25 different options (26 letters in the alphabet - 1 for the letter "u" that is already in Megan's license plate).
For the second position, there are 25 different options (26 letters in the alphabet - 1 for the letter "w" that is already in Megan's license plate).
For the third position, there are 25 different options (26 letters in the alphabet - 1 for the letter "u" that is already in Megan's license plate).
For the fourth position, there are 9 different options (10 digits - 1 for the digit "1" that is already in Megan's license plate).
For the fifth position, there are 9 different options (10 digits - 1 for the digit "4" that is already in Megan's license plate).
For the sixth position, there are 9 different options (10 digits - 1 for the digit "4" that is already in Megan's license plate).
So, the total number of license plates that differ from Megan's at exactly one position is:
25 × 25 × 25 × 9 × 9 × 9 = 11,390,625.
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what goes into 125 3 times
Answers
Answer:
41r6
Step-by-step explanation:
you dived 125 by 3
Answer:
Loading Answer...
Step-by-step explanation:
Loading Explanation...
a student just took two different mid-term exams. their score on the sociology test was a 92 and their score on the human sexualty test was 88. which test did they do better on.
Answers
Answer:
Step-by-step explanation:
I have two questions; One, are you the student? Two, is this a trick question because if it is it's freaking hilarious
The lines represented by the equations y = 1x – 5 and 3y + x = -15 are
O
parallel
Submit Answer
the same line
neither parallel nor perpendicular
perpendicular
Answers
Answer:
Neither parallel nor perpendicular
Step-by-step explanation:
The lines represented by the equations y = 1x – 5 and 3y + x = -15 are .....
Solve for y in 3y + x = -15.
\(3y + x = -15 \\ \frac{ - x = - x}{3y = - x - 15} \\ \\ \frac{3y = - x - 15}{3 \: \: = \: \: \: \: \: \: \: \: \: 3} \\ y = - \frac{1}{3}x - 5\)
\(y = - \frac{1}{3}x - 5 \: and \: y = 1x - 5\)
PLZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE
Answers
Answer:
D.8
Step-by-step explanation:
A cube's volume is basically the side length multiplied by itself 3 times, so if it was increased by a factor of 2, it would mean 2x2x2 which equals 8.
NEED ASAP
For a sewing project, Tanya cut isosceles triangles from a striped piece of material where the stripes are parallel. The vertex angle of the isosceles triangle is 50° and overline BC is parallel to the base.
What is the measure of BCE as shown in the diagram? Show your work and
explain your reasoning.
Answers
Answer:
∠BCE is 115°
Step-by-step explanation:
The given parameters are;
The shape Tanya cut from the striped piece = Isosceles triangles
The measure of the vertex angle of the isosceles triangle = 50°
The segment \(\overline {BC}\) is parallel to the base \(\overline {FG}\)
Therefore, we have;
∠GAF + ∠AGF + ∠AFG = 180°; Sum of the interior angles of a triangle
∴ ∠AGF + ∠AFG = 180° - ∠GAF = 180° - 50° = 130°
∠AGF = ∠AFG; Base angles of an isosceles triangle
∴ ∠AGF + ∠AFG = ∠AGF + ∠AGF = 2 × ∠AGF = 130°
∠AGF = 130°/2 = 65°
∠AGF = 65°
∠AGF ≅ ∠ACB, corresponding angles of two parallel lines, \(\overline {BC}\) and \(\overline {FG}\) cut by a transversal \(\overline {AG}\)
∠AGF = ∠ACB = 65°, definition of congruency
∠ACB + ∠BCE = 180° Sum of angles on a (straight) line
∠BCE = 180° - ∠ACB = 180° - 65° = 115°
∠BCE = 115°
solve the given differential equation dx-(1-x)2dt=0
That two suppose to be squared pls help ASAP
Answers
Answer:
You should know how to integrate both sides
Step-by-step explanation:
\(\int \: \frac{dx}{ {(1 - x)}^{2} } = \int \: dt\)
John is only allowed to work after school for 3 hours Monday to Friday and can work 7 hours on Saturday. He is not working on Sunday. How many school days and saturdays does he need to work to reach the needed amount ?
Answers
Answer:
the needed amount of what? community service?If so about 6 days of work on saturday and 3 school days. :)
Is the line x = 1 - 2t, y = 2 + 5t, z = -3t parallel to the plane 2x + y - z = 8? Give reasons for your answer.
Answers
No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.
To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.
The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).
The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).
To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:
(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4
Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.
The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.
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Steve has 12 guppies. Their population decreases by 3% each year. How many guppies will there be in one year?
Answers
Answer:
11 guppies
Step-by-step explanation:
my teacher told me the answer
Please answer I need by tonight explain a little thanks
Answers
you run a bus rental company that serves groups numbering between 20 and 80 people. if the group renting the bus has 20 people, they pay $80 per person. However, if they have 21 people, the price drops to $79 per person. For 22 people, the price is $78 per person. The price continues to dropping for each additional person in the group. Write an expression for the total amount you can charge a group of p people that rent one of you buses
Answers
The expression for the total amount you can charge a group of p people that rent one of your buses is 100 - p
How to write an expression for the total amount you can charge a group of p people that rent one of your buses?The given parameters are
20 people = $80
21 people = $79
22 people = $78
When represented on a table, we have
20 21 22.............. p
80 79 78
From the above, we have
When
People = 20 + n
Charge = 80 - n
Rewrite People = 20 + n as
p = 20 + n
Make n the subject
n = p - 20
Substitute n = p - 20 in Charge = 80 - n
Charge = 80 - p + 20
Evaluate
Charge = 100 - p
Hence, the expression for the total amount you can charge a group of p people that rent one of your buses is 100 - p
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What is the area of the triangle?
Answers
Answer:
A = 48 in²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )
Here b = 24 and h = 4 , then
A = \(\frac{1}{2}\) × 24 × 4 = 12 × 4 = 48 in²
Answer:
A = 48 in.^2
Step-by-step explanation:
Area of triangle = (Base * height) / 2
Area of triangle = (24*4)/2
Area of triangle = 48 in.^2
Mona has 3200 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area?
Answers
Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.
As given in the question,
Perimeter of the rectangular area encloses for fencing = 3200 yards
Let 'x' and 'y' be the length and width of the rectangle.
2( x + y ) = 3200
⇒ x + y = 3200/2
⇒y = 1600 - x
Area of rectangular field 'A' = xy
⇒ A = x ( 1600 - x )
⇒ A = 1600x - x²
Differentiate both the side of the equation we get,
dA/dx = 1600 - 2x
For Maximum Area dA/dx = 0
1600 -2x =0
⇒ 2x = 1600
⇒ x= 800 yards
Now, y = 1600 - 800
= 800 yards
Maximum area = (800) (800)
= 640,000 square yards
Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.
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the length of a photograph is 11.4 inches if the photo is enlarged so that its length is increased by 2.25 inches what the new length
Answers
We know
\( \\ \sf \longmapsto \: new \: length = length + increased \: length \\ \\ \sf \longmapsto \: new \: length = 11.4 + 2.25 \\ \\ \sf \longmapsto \: new \: length = 13.65in\)
7. how many different license plates are possible if state uses a. two letters followed by a four-digit integer (leading zeros are permissible and the letters and digits can be repeated)? b. three letters followed by a three-digit integer (leading zeros are permissible and the letters and digits can not be repeated)?
Answers
Number of of difference license plate are possible, when two letters followed by four digit integer is 6760000 and when three letters followed by three digit number is 17576000
Here two letters are followed by a four digit integer
There are 26 letters available
Number of possible combinations = 26 × 26
= 676 pair of numbers
In each digits of a four digit numbers 10 numbers are possible
Total number of combinations = 10 × 10 × 10 × 10
= 10000
Number of different license plate = 676 × 10000
= 6760000
Part b
Number of three letters combination = 26 × 26 × 26
= 17576
Number of three digit integer combination = 10 × 10 × 10
= 1000
Number of different licence plate = 17576 × 1000
= 17576000
Therefore, three are 6760000 combinations if it is a two letter followed by four digit integer and 17576000 combination if it is a three letters followed by three digit numbers
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1a. Write a polynomial that represents the length of the north side of the house
1b. Simplify the expression. Show all work.
2- 32. 2. Your cousin said the length of the north side of the house is 9y+2y"
a. Is he correct?
b. Explain in detail how you know if your cousin is correct or not correct?
Answers
Answer:
1a. Let’s assume that the length of the north side of the house is represented by ‘x’. Then the polynomial that represents the length of the north side of the house is x.
1b. There is no expression to simplify.
2a. Your cousin is not correct.
2b. The length of the north side of the house is represented by ‘x’ and not by ‘9y+2y’. Therefore, your cousin is not correct.
The polynomial stated by the cousin as the length of the north side of the house, 9y + 2y, simplifies to 11y. Thus, the cousin is not correct. Polynomials and simplifying expressions are part of basic algebra skills.
Explanation:Based on your cousin's statement, the polynomial representing the length of the north side of the house is 9y + 2y. To determine the correctness of this polynomial, we must first simplify the expression. By combining like terms (terms with the same variable and exponent), the expression simplifies to 11y. So, the length of the north side is represented by 11y, not 9y + 2y. Hence, your cousin's statement is not correct.
Understanding how to combine like terms, simplify expressions, and handle polynomials is an important part of basic algebra skills. Polynomials can be used to represent many real world quantities such as the length of a side of a house as in this problem. Remember that it is crucial to perform all calculations accurately to avoid errors.
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If Logan walks 7/8 mile in each 1/3 hour, how fast is he walking?
Answers
Answer:
2.625 miles per hour
Step-by-step explanation:
We Know
Logan walks 7/8 mile each 1/3 hour.
How fast is he walking?
We Take
7/8 x 3 = 21/8 = 2.625 miles per hour
So, he walks at 2.625 miles per hour.
On average, it costs $1.06 to purchase the mp3 for a particular song. On average, it takes 35 seconds to purchase that mp3. It also takes (on average) 3 min, 25 sec to find the licensing information for a particular song, and costs an average of $2.64. What's the total cost to license & purchase 500 songs? How much time will it take?
Answers
The total cost to licence and purchase 500 songs is; $1850
The time it takes to do so is; 200 minutes
Cost and TimeFrom the task content:
The total cost to licence and purchase the each song is as follows;Total cost = $1.06 + $2.64Total cost = $3.70
For 500 songs = 500 × $3.70 = $1850
The total time it takes to find the licencing information and to purchase the song is;
Total time = 35s + 3m + 25sTotal time = 4minutes
For 500 songs = 500 × 4 = 200minutes
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If m H= 68°, what is HI to the nearest tenth? Show your work.
Answers
Answer: HI = 5.3 cm
Let HI = x
GH = 2cm
m< H = 68 degrees
to find HI, we will need to apply the SOH CAH TOA RULE
HI = hypotenus
GH = adjacent
Cos 68 = adjacent / hypotenus
Cos 68 = 2 / x
Cross multiply
2 = x * cos 68
cos 68 = 0.3746
2 = x * 0.3746
Isolate x
x = 2/0.3746
x = 5.3cm
Therefore, HI is 5.3cm
a 12 inch thin‑crust cheese pizza is cut equally into eight slices. assuming a uniform distribution of sauce and toppings,
Answers
If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.
each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.
Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.
It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.
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Answer right and I will give u brainly and if u dont know dont answer
Answers
Answer:
Step-by-step explanation:
j+28.6=43
-28.6 -28.6
_________________
j=14.4
Hope this helps :>
Hello, I need some assistance with this homework question please for precalculusHW Q41
Answers
solve the expression 7-[60*(6x2)]
Answers
Answer:
7-720= -714
Step-by-step explanation:6x2=12 60x12=720 so thats the brackets then substract from seven to get the answer -714
What’s the area of this polygon answer ASAP my teacher died
Answers
Answer:
Break it into 2 sections: 18 by 3 and 6 by 20
area = 54 + 120
= 174 (answer is A.)
Step-by-step explanation:
9514 1404 393
Answer:
A. 174
Step-by-step explanation:
Use your number sense. The area can be no larger than the rectangle that is 20 high and 9 wide. That rectangle's area is ...
A = LW = (20)(9) = 180
The only answer choice smaller than 180 is ...
A. 174 . . . . . square units
__
If you want to compute it exactly, you can make note of the size of the empty space at the upper left corner. That space is 20-18 = 2 units high and 9-6 = 3 units wide. Its area is A = LW = (3)(2) = 6 square units. When that empty space is subtracted from the overall rectangle area, the result is ...
180 square units - 6 square units = 174 square units.
Whats 3x+1? for in high school its really hard to solve none of my friend cant do it
Answers
As per the zeros of the function, the value of the function 3x + 1 is x = -1/3.
Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.
Here we have given the function 3x + 1.
Now, we have to equate the function with zero, in order to solve it, then we get,
=> 3x + 1 = 0
Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,
=> 3x = -1
Now, we have to divide each side by 3, then we get the value of x as,
=> x = -1/3
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3(2c-5)
the options are
-6c-15
6c+15
6c-15
Answers
Answer:
6c-25
Step-by-step explanation:
comon man lol that's eays
Answer:
Answer would be the last one 6c-15
Step-by-step explanation:
Use distributive property!
the number outside the () times the numbers inside the ()
solve for x -2x = -4
Answers
given that:
\(-2x=-4\)Solve for x:
\(\begin{gathered} -2x=-4 \\ 2x=4 \\ x=\frac{4}{2} \\ x=2 \end{gathered}\)a bicycle had a listed price of $607.98 before tax. if the sales tax rate is 8.25% find the cost of the bicycle with sales tax included. round your answer to the nearest cent if necessary
Answers
Answer: $658.14
Step-by-step explanation: