The accompanying data on x= head circumference z score (a comparison score with peers of the same age - a positive score suggests a larger size than for peers) at age of 6 to 14 months and y =volume of cerebral grey matter (in ml) at age 2 to 5 years were read from a graph in an article.
A) what is the value of the correlation coefficient? (Give the answer to two decimal places.) r=
B)Find the equation of the least- squares lines. (Give the answer to two decimal places.)
C) Predict the volume of cerebral grey matter for a child whose head circumference z score at age 12 months was 1.9. (Give the answer to two decimal places.)
Answers
Answer:
[tex]r=0.77[/tex], [tex]\hat{y}=770.50+39.37x[/tex] and volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.9 is [tex]\hat {y}=920.10[/tex]
Step-by-step explanation:
We attached a table below,
[tex](a)[/tex] We attached a table below,
Therefore ,
correlation coefficient [tex]r=\frac{\frac{1}{18}(21766.7)-(\frac{27.25}{18} )(\frac{13890}{18} ) }{\sqrt{\frac{1}{18} (59.8435)-(\frac{27.25}{18} )^2}\sqrt{\frac{1}{18}(10767400)-(\frac{13890}{18} )^2 } }[/tex]
[tex]=\frac{41.04}{53.19}[/tex]
[tex]=0.77[/tex]
[tex](b)[/tex] We calculate the least squares equation.
[tex]b_1=r(\frac{\sigma_y}{\sigma_x} )\\ =(0.77)(\frac{\sqrt{\frac{1}{18} (10767400)-(\frac{13890}{18} )^2} }{\sqrt{\frac{1}{18}(59.8435)-(\frac{27.25}{18} )^2 } } )\\ =0.77(\frac{52.15}{1.02} )\\ =0.77(51.13)\\ =39.37[/tex]
Now , calculate intercept coefficient.
[tex]b_0=\bar{y}-r\bar{x}\\[/tex]
[tex]=(\frac{\sum{y}}{n} )-0.77(\frac{\sum{x}}{n} )\\=(\frac{13890}{18} )-0.77(\frac{27.25}{18} )\\=771.67-1.17\\=770.50[/tex]
Therefore, the regression equation is, [tex]\hat{y}=770.50+39.37x[/tex]
[tex](c)[/tex] Find the volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.8
[tex]\hat{y}=770.50+39.37x[/tex]
[tex]=770.50+39.37(1.9)\\=770.50+74.80\\=920.10[/tex]
Related Questions
Find the equation of the line shown.
Can someone help me please
Answers
Answer:
y= -2x + 9
Step-by-step explanation:
I got 2x because you use rise over run. As you can see in the image, the slope goes up two and to the left one ( 2x). It's plus 9 because that where it intersects the 9 on the y-intercept. The slope is negative because the line is going down from left to right ( always read it from left to right).
I hope this helps. I'm not that great at explaining so....:)
Answer:
2x+y-9=0
Step-by-step explanation:
let's take two co ordinates
(X1,y1)=(4,1)
(X2,y2)=(3,3)
Equation using two point :
(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
plug in the values,(y-1)/(3-1)=(x-4)/(3-4)
(y-1)/2=(x-4)/-1
-1*(y-1)=(x-4)*2
-y+1=2x-8
0=2x+y-9
2x+y-9=0
Simplify the expression: 2(2 + g) =
Answers
Answer:
4 + 2g
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
2(2 + g)
Step 2: Expand
Distribute 2: 2(2) + 2(g)Multiply: 4 + 2gexplanation: you have to use the distributive property to get rid of the 2 that is outside the parentheses. to do so, you would multiply the 2 to what is inside the parentheses and that would give you 4+2g.
A line passes through the points (-1, 4) and (3, 6). A second line passes through the points (-1, 8) and (3, 2). At what point do the two lines intersect?
Answers
Answer:
its 6
Step-by-step explanation:
6
I GIVE BRAINLIEST
Point A is located in which quadrant?
Answers
Answer:
II
Step-by-step explanation:
Quadrant I is +x + y
Quadrant II is -x + y
Quadrant III is -x - y
Quadrant IV is +x -y
EASY MATH!!! LOTS OF POINTS!!! WILL MARK BRAINLIEST!!!
The speed of a boat in still water is 25 mph. The boat is traveling on a river with a current flowing south at 10 mph. At what angle upstream should the boat head to travel due west?
A. 21.80°
B. 23.58°
C. 66.42°
D. 68.20°
Answers
Answer:
23.58
Step-by-step explanation:
The rectangle below has an area of 30k3 + 6k2.
The width of the rectangle is equal to the greatest common
monomial factor of 30k3 and 6k2.
What is the length and width of the rectangle?
Answers
9514 1404 393
Answer:
length: (5k +1)width: 6k^2Step-by-step explanation:
The GCF of the two terms is the second term: 6k^2. When that is factored out, you have ...
area = (6k^2)(5k +1)
According to the problem statement, this is interpreted as ...
width: 6k^2
length: 5k+1
Please answer this correctly without making mistakes
Answers
Answer:
63 gallons
Step-by-step explanation:
3 gallons = 4x 3 = 12 quarts
12+2 = 14
14 x 18 = 252 quarts
252 / 4 = 63 gallons
Question #7
Revisit
The average age of three people, A, B and C is 32 years. If 2 more people, D and E are
included, the five people's average age becomes 34 years. What is D and E's average age?
Answers
Answer:
ytviykgti
Step-by-step explanation:
At the grocery store, Mr. Arnett allowed
Answers
7
Write a 6-digit numeral
that has
7 in the hundredths place,
5 in the thousands place,
4 in the hundreds place,
and o in all other places.
7a. Write the number.
7b. Write in word form.
7c. Write in expanded form.
7d. Write as a fraction.
Answers
Step-by-step explanation:
Let's use the number Zero as a placeholder.
7 in the hundredths place,
0.07
5 in the thousands place,
5000.07
4 in the hundreds place,
5400.07
7a. Write the number.
5400.07
7b. Write in word form.
Five thousand four hundred and seven hundredth
7c. Write in expanded form.
5000 + 400 + 0.07
7d. Write as a fraction.
540007 / 100
The equation below expresses the approximate
height h, in meters, of a ball t seconds after it is
launched vertically upward from the ground.
h(t) = –16t2 + 25t. At how many different times will the ball be 7 ft. High?
Answers
Answer:
The ball will be the 7 ft high at 2 different times.
Step-by-step explanation:
The height in meters of the ball is given by the following equation:
[tex]h(t) = -16t^2 + 25t[/tex]
7 feet high
The height, by the equation, is given in meters, so we have to work in meters. Since each feet has 0,3048 meters, 7 feet have have 2.1336 meters. So, we have to solve the following equation
[tex]2,1336 = -16t^2 + 25t[/tex]
[tex]16t^2 - 25t + 2,1336 = 0[/tex]
At how many different times will the ball be 7 ft. High?
We have to find the number of solutions for the equation above.
It is given according to the value of [tex]\Delta = b^2 - 4ac[/tex]. If it is positive, there are two solutions, zero one solution and negative no solutions.
In this equation [tex]a = 16, b = -25, c = 2.1336[/tex]. So
[tex]\Delta = b^2 - 4ac = (-25)^2 - 4*16*2.1336 = 488[/tex]
Since the coefficient is positive, the ball will be the 7 ft high at 2 different times.
look at the geometry question and solve for X.
Answers
Answer:
The value of x = 24.4 units.
Step-by-step explanation:
Given
a = 14b = 20c = xFor a right-angled triangle with sides a and b, the hypotenuse c is defined as
[tex]c=\sqrt{a^2+b^2}[/tex]
substituting c = x, a = 14 and b = 20
[tex]c=\sqrt{14^2+20^2}[/tex]
[tex]c=2\sqrt{149}[/tex]
[tex]c = 24.4[/tex] units
Therefore, the value of x = 24.4 units.
Are carnivores consumers
Answers
Answer:
Yes, herbivores, carnivores, and omnivores are consumers.
Hope this helps :)
Answer:
yes it is yes here's your answer for the emanation use search hope it works
what multiples to -64 and adds to -12
Answers
Answer:
Sum :- -76 Product :- 768
Step-by-step explanation:
x is 4 more than two - thrice of y
Answers
Answer: x = 2/3y + 4
Hope it helped u,
pls mark as the brainliest
^v^
The acceleration, in meters per second per second, of a race car is modeled by A(t)=t^3−15/2t^2+12t+10, where t is measured in seconds. What is the car’s maximum acceleration on the time interval 0≤t≤6 ?
Answers
Answer:
The maximum acceleration over that interval is [tex]A(6) = 28[/tex].
Step-by-step explanation:
The acceleration of this car is modelled as a function of the variable [tex]t[/tex].
Notice that the interval of interest [tex]0 \le t \le 6[/tex] is closed on both ends. In other words, this interval includes both endpoints: [tex]t = 0[/tex] and [tex]t= 6[/tex]. Over this interval, the value of [tex]A(t)[/tex] might be maximized when [tex]t[/tex] is at the following:
One of the two endpoints of this interval, where [tex]t = 0[/tex] or [tex]t = 6[/tex].A local maximum of [tex]A(t)[/tex], where [tex]A^\prime(t) = 0[/tex] (first derivative of [tex]A(t)\![/tex] is zero) and [tex]A^{\prime\prime}(t) <0[/tex] (second derivative of [tex]\! A(t)[/tex] is smaller than zero.)Start by calculating the value of [tex]A(t)[/tex] at the two endpoints:
[tex]A(0) = 10[/tex].[tex]A(6) = 28[/tex].Apply the power rule to find the first and second derivatives of [tex]A(t)[/tex]:
[tex]\begin{aligned} A^{\prime}(t) &= 3\, t^{2} - 15\, t + 12 \\ &= 3\, (t - 1) \, (t + 4)\end{aligned}[/tex].
[tex]\displaystyle A^{\prime\prime}(t) = 6\, t - 15[/tex].
Notice that both [tex]t = 1[/tex] and [tex]t = 4[/tex] are first derivatives of [tex]A^{\prime}(t)[/tex] over the interval [tex]0 \le t \le 6[/tex].
However, among these two zeros, only [tex]t = 1\![/tex] ensures that the second derivative [tex]A^{\prime\prime}(t)[/tex] is smaller than zero (that is: [tex]A^{\prime\prime}(1) < 0[/tex].) If the second derivative [tex]A^{\prime\prime}(t)\![/tex] is non-negative, that zero of [tex]A^{\prime}(t)[/tex] would either be an inflection point (if[tex]A^{\prime\prime}(t) = 0[/tex]) or a local minimum (if [tex]A^{\prime\prime}(t) > 0[/tex].)
Therefore [tex]\! t = 1[/tex] would be the only local maximum over the interval [tex]0 \le t \le 6\![/tex].
Calculate the value of [tex]A(t)[/tex] at this local maximum:
[tex]A(1) = 15.5[/tex].Compare these three possible maximum values of [tex]A(t)[/tex] over the interval [tex]0 \le t \le 6[/tex]. Apparently, [tex]t = 6[/tex] would maximize the value of [tex]A(t)\![/tex]. That is: [tex]A(6) = 28[/tex] gives the maximum value of [tex]\! A(t)[/tex] over the interval [tex]0 \le t \le 6\![/tex].
However, note that the maximum over this interval exists because [tex]t = 6\![/tex] is indeed part of the [tex]0 \le t \le 6[/tex] interval. For example, the same [tex]A(t)[/tex] would have no maximum over the interval [tex]0 \le t < 6[/tex] (which does not include [tex]t = 6[/tex].)
Estimate the sum or difference for 5/6 + 7 6/7.
Answers
Answer:
8 29/42
Step-by-step explanation:
5/6 + 7 6/7 = 35/42 + 7 36/42 = 7 71/42 = 8 29/42
Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) x1 2x2 8x3
Answers
Answer:
Infinitely solution exists,
Required solution is, [tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
Step-by-step explanation:
We have the given equations:
[tex]x_1+2x_2+8x_3=8[/tex]
[tex]x_1+x_2+4x_3=4[/tex]
Here, the augmented matrix is :
[tex]\left[\begin{matrix}1&2&8&8\\1&1&4&4\end{matrix}\right][/tex]
Now, find the echelon form of the augmented matrix.
[tex]=\left[\begin{matrix}1&2&8&8\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_2-R_1}[/tex]
[tex]=\left[\begin{matrix}1&0&0&0\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_1+2R_2}[/tex]
Therefore, [tex]x_1=0[/tex]
[tex]-x_2-4x_3=-4[/tex]
[tex]\Rightarrow x_2=4(1-x_3)[/tex]
Let [tex]x_3=t[/tex], then the required solution is
[tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
Can the sides of a triangle have lengths 1, 5, and 5?
Yes or no?
Answers
Answer:
Yes it can have the lengths 1, 5 and 5
Solve for x x-5=-7
X=-2
X=-5
X=-1
X=-3
Answers
Answer:
X=-2
Step-by-step explanation:
x-5=-7
x-5+5=-7+5
X=-2
There are 65 children in the sixth grade.There are 5 more boys than girls.
a.how many girls are in the class
b.what is the ratio of boys to girls.
c.If 5 more girls joined the class what is the ratio of boys to girls now?
HURRY
Answers
Michael made 19 out of 30 free-throws this basketball season. Larry's free throw average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-throw shooter
Answers
Answer: Charles
Step-by-step explanation:
Michael made 19 out of 30 free-throws. This gives 19/30 = 0.63
Larry's free throw average was 0.745.
Charles' was 0.81.
John made 47 out of 86 free-throws. This gives 47/86 = 0.55
The best free-throw shooter was Charles
Answer:
Charles
Step-by-step explanation:
The best free-throw shooter was Charles
What is the output of the equations y=2x + 8 if the input is -2?
Answers
Answer:
y=4
Step-by-step explanation:
Step-by-step explanation: Input is the same as the x term.
If the input is -2, we substitute a -2 in for x.
So we have y = 2(-2) + 8 or y = -4 + 8 which is 4.
So the output or the y term is 4.
Help out pls need help on this question
Answers
Answer:
[tex]\huge\boxed{\sf Option \ 4}[/tex]
Step-by-step explanation:
y = The total cost
x = The number of movie tickets.
So, The equation that represents the function is:
y = 10.25 x
This shows that the total cost is equal to the cost of 1 ticket multiplied by the no. of tickets.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807median of 57,75,40,34,45,60,45,44\
Answers
Answer:
the median is 45
Step-by-step explanation:
The computation of the median is as follows:
First arrange in a sequential order
34, 50, 44, 45, 45, 60, 57, 75
Now as we can see that there are 8 numbers
= n ÷ 2
= 8 ÷ 2
= 4 number
= 45
Hence, the median is 45
The same is relevant and considered too
If you traveled 2,500 meters over the weekend, how many kilometers is that?
Answers
Answer:
25 kilometers
Step-by-step explanation:
Help ASAP!!! What’s the value of x
Answers
Answer:
x=8
Step-by-step explanation:
∠B=∠A
Base Angle Thm/ Def. of Iso.
72=9x
x=8
What is the slope of this line?
- 2/3
2/3
1/3
- 1/3
Answers
Answer:
2/3
Step-by-step explanation:
slope =(y1-y2)/(x1-x2)
slope=(1-(-1))/(6-3)
slope =2/3
What is the value of the expression 4+(-2)
-3+3
Answers
Answer:
The answer is 2
Step-by-step explanation:
Addition is considered first before subtraction
So 4+(-2) and -3+3 are considered separately and later their results are added
(2+0=2)
the maximum slope for a hand propelled wheelchair ramp should be a 1 inch rise to every 12 inches of blank. What is the maximum ramp angle recommended to the nearest degree?
Answers
9514 1404 393
Answer:
5°
Step-by-step explanation:
The angle for 12 inches of ramp length and the angle for 12 inches of run are very similar. Both are near 4.8°, so are 5° when rounded.
If we say 12 inches of run, then the tangent relation applies.
Tan = Opposite/Adjacent
tan(α) = (1 in)/(12 in)
α = arctan(1/12) ≈ 4.764°
The maximum angle is about 5°.