Can anybody help with these two problems for me please this for algebra finding slope
Answers
Answer:
Step-by-step explanation:
1. the slope is -7/2
2. the slope is 2/3
y = mx + b
m is the slope
Slope is the number before the x so
1. -7/2
2. 2/3
Related Questions
Help me please this is math
Answers
Answer:
c) none of the above
Step-by-step explanation:
this is because we should put the equation like:
1/3 - (-4/3) because the distance is 5 units and
1/3 + 4/3 = 5/3
this is because (-) × (-) = (+)
What number line correctly shows one way to find 2-6 ?
Answers
The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later
Answers
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later. Assume that the enrollment increases by the same percentage per year. a) Find the exponential function E that gives the enrollment t years after the online program's inception. b) Find E(11), and interpret the result. c) When will the program's enrollment reach 5500 students?
Let E0 be the number of students that enrolled at inception
E(t) be the number of students that enrolled at any time t
At inception i.e at t = 0, E0 = 580
The exponential function E that gives the enrollment at inception will be expressed as;
E(t) = E0e^kt (note that the exponential power is positive since number of students keep increasing yearly).
At inception:
E(0) = 580e^k(0)
E(0) = 580(1)
E(0) = 580
If after 3years, enrollment increases to 1725 students i.e at t = 3, E(t) = 1725. The equation becomes;
E(3) = P0e^kt
E(3) = 580e^3k
1725 = 580e^3k
Make k the subject of the formula:
e^3k = 1725/580
e^3k = 2.9741
Apply ln to both sides of the equation
ln(e^3k) = ln(2.9741)
3k = 1.08995
k = 1.08995/3
k = 0.3633
The exponential function E that gives the enrollment t years after the online program's inception will be expressed as;
E(t) = E0e^kt
Given E0 = 580 and k = 0.3633
E(t) = 580e^0.3633t
b) To get E(11), we will substitute t = 11 into the resulting expression in (a) above to have;
E(t) = 580e^0.3633t
E(11) = 580e^0.3633(11)
E(11) = 580e^3.9965
E(11) = 580×54.4074
E(11) = 31,556.287
E(11) ≈ 31,556 students
This means that about 31,556students enrolled 11years later.
c) To know when the program's enrollment reach 5500 students, we will set E(t) to 5500, E0 to 580 and k to 0.3633 and calculate the value of t
From the equation E(t) = 580e^0.3633t
5500 = 580e^0.3633t
e^0.3633t = 5500/580
e^0.3633t = 9.4828
Apply ln to both sides
ln(e^0.3633t) = ln(9.4828)
0.3633t = 2.2495
t = 2.2495/0.3633
t = 6.19
t ≈ 6years
This means that the program's enrollment will reach 5500 students 6 years later.
Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=vt+vt2 / 2(e) v=x2 / at3(f) a3=x2v / t5(g) x=t(h) v=5at
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
A
is dimensionally consistent
B
is not dimensionally consistent
C
is dimensionally consistent
D
is not dimensionally consistent
E
is not dimensionally consistent
F
is dimensionally consistent
G
is dimensionally consistent
H
is not dimensionally consistent
Step-by-step explanation:
From the question we are told that
The equation are
[tex]A) \ \ a^3 = \frac{x^2 v}{t^5}[/tex]
[tex]B) \ \ x = t [/tex]
[tex]C \ \ \ v = \frac{x^2}{at^3}[/tex]
[tex]D \ \ \ xa^2 = \frac{x^2v}{t^4}[/tex]
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex]
[tex]F \ \ \ x = 3vt[/tex]
[tex]G \ \ \ v = 5at[/tex]
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex]
Generally in dimension
x - length is represented as L
t - time is represented as T
m = mass is represented as M
Considering A
[tex]a^3 = (\frac{L}{T^2} )^3 = L^3\cdot T^{-6}[/tex]
and [tex]\frac{x^2v}{t^5 } = \frac{L^2 L T^{-1}}{T^5} = L^3 \cdot T^{-6}[/tex]
Hence
[tex]a^3 = \frac{x^2 v}{t^5}[/tex] is dimensionally consistent
Considering B
[tex]x = L[/tex]
and
[tex]t = T[/tex]
Hence
[tex]x = t[/tex] is not dimensionally consistent
Considering C
[tex]v = LT^{-1}[/tex]
and
[tex]\frac{x^2 }{at^3} = \frac{L^2}{LT^{-2} T^{3}} = LT^{-1}[/tex]
Hence
[tex]v = \frac{x^2}{at^3}[/tex] is dimensionally consistent
Considering D
[tex]xa^2 = L(LT^{-2})^2 = L^3T^{-4}[/tex]
and
[tex]\frac{x^2v}{t^4} = \frac{L^2(LT^{-1})}{ T^5} = L^3 T^{-5}[/tex]
Hence
[tex] xa^2 = \frac{x^2v}{t^4}[/tex] is not dimensionally consistent
Considering E
[tex]x = L[/tex]
;
[tex]vt = LT^{-1} T = L[/tex]
and
[tex]\frac{vt^2}{2} = LT^{-1}T^{2} = LT[/tex]
Hence
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex] is not dimensionally consistent
Considering F
[tex]x = L[/tex]
and
[tex]3vt = LT^{-1}T = L[/tex] Note in dimensional analysis numbers are
not considered
Hence
[tex]F \ \ \ x = 3vt[/tex] is dimensionally consistent
Considering G
[tex]v = LT^{-1}[/tex]
and
[tex]at = LT^{-2}T = LT^{-1}[/tex]
Hence
[tex]G \ \ \ v = 5at[/tex] is dimensionally consistent
Considering H
[tex]a = LT^{-2}[/tex]
,
[tex]\frac{v}{t} = \frac{LT^{-1}}{T} = LT^{-2}[/tex]
and
[tex]\frac{xv^2}{2} = L(LT^{-1})^2 = L^3T^{-2}[/tex]
Hence
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex] is not dimensionally consistent
We want to see which ones of the given expressions are dimensionally consistent. We will see that the correct options are:
a) x = 3*v*th) v = 5*a*tWhat means to be dimensionally consistent?
This means that we have the same units in the left and in the right side of the equation.
The units are:
a = [m/s^2]x = [m]v = [m/s]t = [s]Now we can analyze the expressions to see the units in each one, I will show you how to do it:
a) a = v/t + x*v^2
Replacing the units we have:
[m/s^2] = [m/s]/[s] + [m]*[m^2/s^2]
[m/s^2] = [m/s^2] + [m^3/s^2]
You can see that we have an m^3 in the right side, so these are not equivalent.
b) x = 3*v*t
Replacing the units we have:
[m] = 3*[m/s]*[s] = 3*[m]
So yes, the units are the same in both sides, so this is dimensionally consistent.
With the same procedure we can see that:
c) [m^3/s^2] = [m^3/s] not consistentd) [m] = [m] + [m*s] not consistente) [m/s] = [m^2] not consistentf) [m^3/s^6] = [m^3/s] not consistentg) [m] = [s] not consistenth) [m/s] = 5*[m/s] consistentSo the correct options are b and h.
If you want to learn more about dimensions, you can read:
https://brainly.com/question/20384972
The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Answers
Answer:
4 2/4 (NOT SIMPLIFIED)
Step-by-step explanation:
Comprising means made of (aka including). You just add 1 1/4+1 1/4+1 1/4.
=3 3/4
The 1/8 is for the front and back cover. The bookworm ate through 3 volumes so there is 6 covers. So times 1/8 by 6. I turned the 6 into a fraction by putting it over 1. So now you have 1/8×6/1=6/8. Now you are going to add the 3 3/4 to the 6/8. You are going to turn the whole fraction to an improper. You are going to multiply the whole number(3) to the denominator(4), add that to the numerator(3) , and put it over the original denominator (4)= 15/4. Now you are going to set up the problem were you add the 6/8 to the 15/4. To add fractions the denominator have to be the same. With this problem you have two options: you can either do an equation to change the 6/8 denominator equal to 4 or an equation to change the 15/4 denominator equal to 8. Either one would work fine. I'm going to show you how to set the 6/8 denominator to 4.
1. Set it up as an equation 6/8=x/4
2. Find what gets the first denominator to the second in this case dividing by 2 6/8=x/4
3. What you do to the bottom is what you have to do with the top. So to find x, you need to divide 6 by 2= 3
So now your new equation is now 3/4+15/4. Adding this should give you 18/4, but most likely you have to write it as a proper fraction. To do this you are going to divide the 18 by 4. Your remainder will become your new numerator and the 4 will still be you denominator. The number times 4 fully goes into 18 will be your new whole number.
18/4=4.5
f(x) = x - 5, translated 6 units to the right.
Answers
Answer:
[tex]g(x) = x - 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 5[/tex]
Required
Translate to the right by 6 units
When a function is translated to the right, the resulting function becomes
[tex]g(x) = f(x - h)[/tex]
Where h is the number of units moved;
Since; h = 6
[tex]g(x) = f(x - h)[/tex]
becomes
[tex]g(x) = f(x - 6)[/tex]
Solving for f(x - 6);
[tex]f(x) = x - 5[/tex]
Substitute x - 6 for x
[tex]f(x - 6) = x - 6 - 5[/tex]
[tex]f(x - 6) = x - 11[/tex]
This implies that [tex]g(x) = x - 11[/tex] is the result of the translation
G(x) = 2x^2 and h(x) = √x^2+1 .What is (goh)^-1 and is it a function?
Answers
Answer:
Step-by-step explanation:
Hello,
[tex](goh)(x)=g(h(x))=2\left( \sqrt{x^2+1}\right)^2=2(x^2+1)\\\\x=(goh)((goh)^{-1}(x))=2((goh)^{-1}(x)^2+1)\\ \\\left((goh)^{-1}(x)\right)^2=\dfrac{x}{2}-1=\dfrac{x-2}{2}\\ \\(goh)^{-1}(x)=\sqrt{\dfrac{x-2}{2}}[/tex]
And this is a function defined for x-2 [tex]\geq[/tex] 0, meaning x [tex]\geq[/tex] 2
Thanks
Find out the coordinates
Answers
c) (0,-8)
reason:
it may be easiest to visualize by putting (-3,-5) and (-6,-2) on a graph
you can see that to get from C to B you have to add 3 to the x value and subtract 3 from the y value
do the same to point B, which will give you (0,-8)
I
rep
What is the solution of 4(2y + 1) = 2(y - 13)
What is the answer
Answers
Answer:
- 5
Step-by-step explanation:
Step 1:
4 ( 2y + 1 ) = 2 ( y - 13 )
Step 2:
8y + 4 = 2y - 26
Step 3:
6y + 4 = - 26
Step 4:
6y = - 30
Answer:
y = - 5
Hope This Helps :)
WILL MARK BRAINLIEST
List all of the number sets that contain the number 15.
A. rational numbers and integers
B. rational numbers, integers, and natural numbers
C. rational numbers, integers, and whole numbers
D. rational numbers, integers, natural numbers, and whole numbers
Answers
Answer: D
Step-by-step explanation:
What is the sum of Negative 1 + (negative 3)?
Answers
Answer:
[tex]\huge\boxed{-4}[/tex]
Step-by-step explanation:
=> [tex]\sf -1 + (-3)[/tex]
According to the rule [tex]\sf + * - = -[/tex]
=> [tex]\sf -1-3[/tex]
=> -4Answer:
-4
Step-by-step explanation:
-1 + (-3)
To add two negative numbers, add their absolute values, and make the answer negative.
The absolute values of -1 and -3 are 1 and 3. We add 1 + 3 and get 4.
Then we make the answer negative.
-1 + (-3) = -4
what is the domain and range of f(x)=2x+3
Answers
Answer:
D:{x∈R}
R:{y∈R}
Step-by-step explanation:
This is just a linear function. I know this because the degree of the x-variable is 1.
Domain and range are sets of possible values the function can have - though not necessarily at the same time.
Thus, there are no restrictions to the domain and range unless context is given.
Therefore, the domain and range is:
D:{x∈R}
R:{y∈R}
Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he
records whether each plane he sees follows a north-south route or an east-west route. He also records the
day of the week that he sees each plane.
Unfortunately, Chris dropped his data in the mud and can't read all of his numbers. The absolute and
relative frequency tables below show the numbers that Chris is able to read. Can you help him figure out
the rest?
Fill in the missing values from each table.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
From the relative frequency below:
For NORTH - SOUTH:
Monday - Thursday = 115 ; has a relative frequency of 75.16%,
Hence, we can obtain the row total since it amounts to 100% thus;
75.16% of row total = 115
0.7516× row total = 115
Row total = 115 / 0.7516 = 153.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
153 - 115 = 38
FOR EAST - WEST:
Monday - Thursday = 21 ; has a relative frequency of 25.30%,
Hence, we can obtain the row total since it amounts to 100% thus;
25.30% of row total = 21
0. 253 × row total = 21
Row total = 21 / 0.253 = 83.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
83 - 21 = 62
x = (38 / 100) × 100%
x = 0.38 × 100%
x = 38.00 %
Answer:
The basic explanation:
North - South/Friday - Sunday- 38 // Row total- 153
East - West/Friday - Sunday- 62 // Row total- 83
x- 38
Solve the equation -4 = 5 -x.
Answers
X=9
So the answer is, x=9
Answer:
when x goes opposite side of equals to sign of x changes and same goes with 4 then x=5+4 then the answer will be 9
I have 4 questions
1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units,
then what is TV?
131
194
68
80
2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x?
x = 3
x = 7
x = 12.5
x = 22
3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?
4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?
Answers
You have a bin full of the letters HGUSTWQ. If four letters are drawn at random, what is the probabilty the letters drawn will spell the word GUST ( in the order they are drawn )?
Answers
Answer:
see I need help for chemistry pls anyone here helps me I must submit before 10:30
y=1/4x + 6
that passes through the point (-4, 3) in slope-intercept form.
Answers
Answer:
The answer is
[tex]y = \frac{1}{4} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line.
The equation is
y = 1/4x + 6
Comparing with the general equation above
Slope = 1/4
Since the lines are parallel their slope are also the same
That's
Slope of parallel line = 1/4
So the equation of the parallel line using point (-4 , 3) and slope 1/4 is
[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]We have the final answer as
[tex]y = \frac{1}{4} x + 4[/tex]Hope this helps you
What is the fractional equivalent of the repeating decimal 0.2 ?
Answers
Answer:
1/5
Step-by-step explanation:
I put it in a graphing calculator and converted it into a fraction
Perform the following operations and write the answers in radical form. Part A:√7+√3+√98−√18 Part B:3√5−3√11+2√121−3√90
Answers
Answer:
[tex]\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex] [tex]3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]Step-by-step explanation:
Part A ;
[tex]\sqrt{7} +\sqrt{3} +\sqrt{98} -\sqrt{18} \\\\\sqrt{98}=7\sqrt{2}\\\sqrt{18}=3\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+7\sqrt{2}-3\sqrt{2}\\\\\mathrm{Add\:similar\:elements:}\:7\sqrt{2}-3\sqrt{2}=4\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex]
Part B ;
[tex]3\sqrt{5} - 3\sqrt{11} + 2\sqrt{121} -3\sqrt{90} \\\\2\sqrt{121}=22\\3\sqrt{90}=9\sqrt{10}\\\\=3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]
Evaluate (5-3)^3+ -3^2(6-3)
Answers
Steps to solve:
(5 - 3)^3 + (-3)^2(6 - 3)
~Simplify
2^3 + (-3)^2(3)
2^3 + (-3)^6
~Solve exponents
8 + (-729)
~Subtract
-721
Best of Luck!
The product of 6 and a is 30
Answers
Answer:
30 divided by 6=5
Step-by-step explanation:
a=5
5 times 6 is the product of 30
4x – 3y = 20
2x + y = 30
Using the two equations above, solve for y.
Answers
Answer:
4x-3y+20
Step-by-step explanation:
x=6.875
y=2.5
2x+y=30
x=12.5
y=-5
The velocity of an object is given by the following function defined on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into the indicated number of subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles. v = 1/(2t + 4) (m/s) for for 0 ≤ t ≤ 88; n = 22
Answers
Answer:
The displacement of the object on this intervals is 1.33 m.
Step-by-step explanation:
Given that,
The function of velocity is
[tex]v=\dfrac{1}{2t+4}\ m/s[/tex]
For 0 ≤ t ≤8 , n = 2
We need to calculate the intervals
Using formula for intervals
For, n = 1
[tex]\Delta x=\dfrac{t_{f}-t_{i}}{n}[/tex]
[tex]\Delta x=\dfrac{8-0}{2}[/tex]
[tex]\Delta x=4[/tex]
So, The intervals are (0,4), (4,8)
We need to calculate the velocity
Using given function
[tex]v=\dfrac{1}{2t+4}[/tex]
For first interval (0,4),
Put the value into the formula
[tex]v_{0}=\dfrac{1}{2\times0+4}[/tex]
[tex]v_{0}=\dfrac{1}{4}[/tex]
For first interval (4,8),
Put the value into the formula
[tex]v_{4}=\dfrac{1}{2\times4+4}[/tex]
[tex]v_{4}=\dfrac{1}{12}[/tex]
We need to calculate the total displacement
Using formula of displacement
[tex]D=(v_{0}+v_{4})\times(\Delta x)[/tex]
Put the value into the formula
[tex]D=(\dfrac{1}{4}+\dfrac{1}{12})\times4[/tex]
[tex]D=1.33\ m[/tex]
Hence, The displacement of the object on this intervals is 1.33 m.
The displacement of the object whose velocity function is given is 1.33 m
The given parameters are:
[tex]\mathbf{v = \frac{1}{2t + 4},\ 0 \le t \le 8; n =2}[/tex]
The end point of intervals is calculated as:
[tex]\mathbf{\triangle t = \frac{b - a}{n}}[/tex]
So, we have:
[tex]\mathbf{\triangle t= \frac{8 - 0}{2}}[/tex]
[tex]\mathbf{\triangle t = \frac{8}{2}}[/tex]
[tex]\mathbf{\triangle t= 4}[/tex]
So, the intervals are (0,4) and (4,8)
Calculate the velocity at the beginning of each interval
[tex]\mathbf{v_0 = \frac{1}{2(0) + 4} = \frac 14}[/tex]
[tex]\mathbf{v_4 = \frac{1}{2(4) + 4} = \frac 1{12}}[/tex]
Calculate the displacement (S) using:
[tex]\mathbf{S = (v_0 + v_4) \times \triangle t}[/tex]
So, we have:
[tex]\mathbf{S = (1/4 + 1/12) \times 4}[/tex]
Expand
[tex]\mathbf{S = 1 + 1/3}[/tex]
Add
[tex]\mathbf{S = 1 \frac 13}[/tex]
Express as decimals to 2 decimal places
[tex]\mathbf{S = 1.33}[/tex]
Hence, the displacement is 1.33 m
Read more about displacement at:
https://brainly.com/question/17131235
Julie travels 3 times as fast as Bill. Traveling in opposite directions, they are 190 miles apart after 2.5 hours. Find their rates of travel.
Answers
Answer:
Step-by-step explanation:
Let b
Bill's rate of travel = x
Let Julie's rate of travel = 3x
The time each travels is 2.5 hours
Together they travel a distance of 190 miles
d = r*t
Bill's distance covered is r * t = 2.5x
Julie's distance travel is 2.5 * 3x = 7.5x
The total distance = Bill + Julie
2.5x + 7.5x = 190
10x = 190
x = 190/10
x = 19
Bill's distance = 2.5 * 19 = 47.5
Julie's distance = 19 * 7.5 = 142.5
Rate = distance / time
Bill's rate = 47.5 / 2.5 = 19 miles per hour.
Julie's rate = 142.5/2.5 = 57 miles per hour
Is there an easier way?
You should notice that Bill's rate is just x which is 19 miles / hour
You can also notice that Julie is going 3 times as fast or 19*3 = 57
help me asap i don't know this
Answers
Answer:
y = 3
Step-by-step explanation:
Step 1: Write equation
-2(7 - y) + 4 = -4
Step 2: Subtract 4 on both sides
-2(7 - y) = -8
Step 3: Distribute
-14 + 2y = -8
Step 4: Add 14 to both sides
2y = 6
Step 5: Divide both sides by 2
y = 3
Find the triangle of the following figure: A. 30cm2 B: 36cm2 C. 18cm2 D. 15cm2
Answers
Answer:
D. 15cm2
Step-by-step explanation:
To find the area of a triangle, you multiply the base (10cm) and height of the triangle (3cm) and divide that by 2. So 10×3=30. Then, you need to divide this by 2. Since 30 is an even number, you won't get a decimal. So 30/2=15. And dont forget your units!
please help :)) ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answers
Which of the following is an example of a translation?
a) The preimage is twice the size as the image.
b) The preimage is moved 5 spaces up.
c) The preimage is rotated 90 degrees about the origin.
d) The image is a mirror reflection of the preimage.
Answers
Answer:
Step-by-step explanation:
a)the pre image us twice the same size as the image
Martin's average score after 4 tests is 89. What score on the 5th test would bring Martin's average up to exactly 90?
Answers
Answer:
104
Step-by-step explanation:
89x4=356 90x5=450
450=356=104
Answer:
94
Step-by-step explanation:
((89x4)+94) divided by 5 = 90
The average spending at Neco's salad bar is $8.73 with a standard deviation of $3.41. The distribution follows t-distribution. The management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
Answers
Answer:
Difference between upper and lower limits is : 1,816
Step-by-step explanation:
A CI (confidence interval ) for t student distribution is:
( μ₀ - t(α/2)* s/√n ; μ₀ + t(α/2)* s/√n )
Where:
μ₀ is the mean and s the standard deviation of the dstribution
n size of the sample
CI = 90 % means α = 10 % α = 0,1 α/2 = 0,05
and degree of freedom df = n - 1 df = 40
From t student table we get:
tα/2 = 1,6839
Then:
t(α/2)* s/√n = 1,6839* 3,41/√40
t(α/2)* s/√n = 0,908
8,73 - 0,908 = 7,822
8,73 + 0,908 = 9,638
CI (90%) = ( 7,822 ; 9,638 )
Difference between upper and lower cut-offs points is:
Δ = 1,816