Answer:
129 [tex]cm^2/s[/tex]
Step-by-step explanation:
Increasing rate of length, [tex]\frac{dl}{dt}[/tex]= 9 cm/s
Increasing rate of width, [tex]\frac{dw}{dt}[/tex] = 7 cm/s
Length, l = 12 cm
Width, w = 5 cm
To find:
Rate of increase of area of rectangle at above given points.
Solution:
Formula for area of a rectangle is given as:
[tex]Area = Length \times Width[/tex]
OR
[tex]A = l \times w[/tex]
Differentiating w.r.to t:
[tex]\dfrac{d}{dt}A = \dfrac{d}{dt}(l \times w)\\\Rightarrow \dfrac{d}{dt}A = w \times \dfrac{d}{dt}l +l \times \dfrac{d}{dt}w[/tex]
Putting the values:
[tex]\Rightarrow \dfrac{dA}{dt} = 5 \times 9 + 12 \times 7\\\Rightarrow \dfrac{dA}{dt} = 45 + 84\\\Rightarrow \bold{\dfrac{dA}{dt} = 129\ cm^2/sec}[/tex]
A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5. The test rejects the null hypothesis if either 0 or 10 heads are observed.
(a) What is the significance level of the test?
(b) If, in fact, the probability of heads is 0.1, what is the power of the test?
Answer:
(a) The significance level of the test is 0.002.
(b) The power of the test is 0.3487.
Step-by-step explanation:
We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.
The test rejects the null hypothesis if either 0 or 10 heads are observed.
Let p = probability of obtaining head.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.5
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.5
(a) The significance level of the test which is represented by [tex]\alpha[/tex] is the probability of Type I error.
Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.
Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;
P(Type I error) = [tex]\alpha[/tex]
P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]
Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.
So, X ~ Binom(n = 10, p = 0.5)
P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]
[tex]\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}[/tex] = [tex]\alpha[/tex]
[tex](1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})[/tex] = [tex]\alpha[/tex]
[tex]\alpha[/tex] = 0.0019
So, the significance level of the test is 0.002.
(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.
Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.
Also, the power of the test is represented by (1 - [tex]\beta[/tex]).
So, here, X ~ Binom(n = 10, p = 0.1)
[tex]1-\beta[/tex] = P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true)
[tex]1-\beta[/tex] = [tex]\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}[/tex]
[tex]1-\beta[/tex] = [tex](1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})[/tex]
[tex]1-\beta[/tex] = 0.3487
Hence, the power of the test is 0.3487.
Solve for x and y simultaneous equations: 2x+y=10
-3x+y=-5
Step-by-step explanation:
Hey, there!
Given, equations are,
2x+y=10.............(i)
-3x+y= -5...........(ii)
From equation (i)
y=10- 2x...........(iii)
Putting the value of "y" from equation (iii) in equation (ii).
-3x+y= -5
-3x + (10-2x)= -5
-3x + 10-2x= -5
- 5x = -15
[tex]x = \frac{ - 15}{ - 5} [/tex]
Therefore, x= 3.
Now, putting the value of "x" in equation (iii).
y= 10- 2x
y= 10- 2×3
Therefore, y= 4.
Hope it helps...
Which of the following correlation values represents a perfect linear relationship between two quantitative
variables? Select all that apply.
A. 0
B. 9
c. -1
D. 1
E. .5
Answer:
C. -1
D. 1
Step-by-step explanation:
A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.
The appropriate choices are ...
C. -1
D. 1
Answer:
c=-1
d=1
Step-by-step explanation:
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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If the average fixed cost (AFC) of producing 5 bags of rice is $20.00, the average fixed cost of producing 10 bags will be
Answer:$40.00
Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00
last week a worm was 10 millimeters long. This week it is 13 millimeters long. What is the percent of increase of the worm's length from last week to this week?
Answer:
23% increase
Step-by-step explanation:
13 - 10 = 3
3/13 = 0.2307 = 23%
Hope that helped!!! k
2 1/2 cases of soda to split between 5 families
The fraction that each person gets is 1/2.
How to compute the fraction?It should be noted that 2 1/2 cases of soda to split between 5 families.
In their case, the fraction that each person will get will be:
= Total / Number of people
= 2 1/2 ÷ 5
= 2.5/5
= 0.5 or 1/2.
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2 1/2 cases of soda to split between 5 families. What fraction will each person get?
state if the triangles in each pair are similar. If so State how you know they are similar and complete the similarity statement
Answer:
fourth option
Step-by-step explanation:
∠ FTC = ∠ MTL ( vertical angles )
Since FC and ML are parallel, then
∠ FCT = ∠ TML (corresponding angles )
Thus
Δ TCF ~ Δ TML by the AA postulate
Answer:
[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]
Step-by-step explanation:
The two triangles are similar.
We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.
[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.
[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.
Therefore,
[tex]\Delta TUV \sim \Delta TML[/tex]
PLEASE HELP..............
Which of the following has no solution?
{x | x < 0} and {x I x > 0}
{x | x ≤ 0} and {x | x ≥ 0}
{x | x ≤ 0} or {x | x ≥ 0}
Answer:
{x | x < 0} and {x I x > 0} has no solution
Step-by-step explanation:
x cannot be less than zero AND more than zero at the same time, so the first inequality has no solution.
{x | x < 0} and {x I x > 0}
Answer:
A
Step-by-step explanation:
Choice A has the two options:
[tex]x<0 \text{ and } x>0[/tex]
In other words, x must be a number such that it is negative (left option) and positive (right option) at the same time.
There can't be such number (and 0 is not included in the answer choices since it is not less/more than or equal to). Thus, Choice A has no solution.
The keyword here is and. If instead of and it was or, then the choice does indeed have a solution.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 220 grams of a radioactive isotope, how much will be left after 5 half-lives?
Answer:
[tex]\boxed{6.875 \text{\: grams}}[/tex]
Step-by-step explanation:
Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by [tex]2^{x}[/tex], where x is equal to the amount of half-lives.
In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.
[tex]\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}[/tex]
Please help me!!Which of the following functions shows the linear parent function, Fx) = X,
shifted right?
5
F(x) = x
5
A. G(x) = x + 2
B. G(x) = 4x
C. G(x) = x - 9
D. G(x) = -x
Answer:
C. G(x) = x - 9
Step-by-step explanation:
You know that the transformation ...
g(x) = f(x -h) +k
causes parent function f(x) to be shifted right h units and up k units.
You're looking for a function that is shifted right, so you want something that looks like ...
g(x) = f(x -constant) = x - constant
Choice C has that form:
C. G(x) = x - 9
_____
A. the function is shifted up 2 units
B. the function is vertically expanded by a factor of 4 (no shift)
C. shifted right
D. the function is reflected over the y-axis (no shift)
Answer: C [G(x) = x-9]
Step-by-step explanation:
I got it right
Hakim is making a mosaic
from square tiles. The area he
needs to fill measures 150 mm
by 180 mm. The tiles have side
lengths of 4, 6 or 8mm and are
too small to cut. Which tiles
should Hakim use?
Step-by-step explanation:
check the tile whose side length is divisible by both 150 and180 in such a way that you don't get decimal points
150÷4=37.5 so that is impossible
150÷8=18.75 so that is also impossible
150÷6=25 180÷6=30
so the six sided tile is applicable
Find the standard form of the equation of the ellipse with the given characteristics. center: (0, 0) focus: (3, 0) vertex: (4, 0)
Answer:
[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Step-by-step explanation:
Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).
Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0
To find b we use the equation of the focus which is:
[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]
Substituting the values of a, b, h and k:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Help me please thank you
Answer: 60°
Step-by-step explanation:
apply concept: the interior angle sum of triangle is 180°
x+x+x=180
3x=180
x=60
---------------
this is also an equilateral triangle which if you know it, you will know that each angles are all 60°
Answer: x=60°
Step-by-step explanation:
We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.
3x=180 [divide both sides by 3]
x=60°
If 7time the 7th of Ap. Is equal of 11 tomes its 11th term find 18th term
0 0
,
---------------
Evaluate a + b for a = 12 and b = 6.
Answer:
Here,
a= 12
b = 6
Then,
a+b
= 12 + 6
= 18
.°. 18 is the solution
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{18}}}}[/tex]
Step-by-step explanation:
If the values of variables of algebraic expressions are given, the value of the term or expression can easily obtained by replacing the variables with numbers.
Given, a = 12 and b = 6
[tex] \sf{a + b}[/tex]
plug the values
⇒[tex] \sf{12 + 6}[/tex]
Add the numbers
⇒[tex] \sf{18}[/tex]
Hope I helped!
Best regards!!
NEED HELP NOW I have 31 stamps total. I have 4 more 1-cent stamps than 8-cent stamps and twice as many one cent stamps as 12 cent stamps. If my stamps are worth $1.78 altogether how many one cent stamps do I have?
x = number of 1-cent stamps
y = number of 8-cent stamps
z = number of 12-cent stamps
We have 31 stamps all together, so x+y+z = 31.
"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.
You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x
-------------
x+y+z = 31
x+x-8+z = 31 ... y replaced with x-8
x+x-8+0.5x = 31 ... plug in z = 0.5x
2.5x-8 = 31
2.5x = 31+8
2.5x = 39
x = 39/2.5
x = 15.6
Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).
The number of one-cent stamps is 14.
Total stamps = 31
We have three types of stamps: 1-cent stamps, 8-cent stamps, and 12-cent stamps.
The person has 4 more 1-cent stamps than 8-cent stamps.
The person has twice as many 1-cent stamps as 12-cent stamps.
We have to make equations with the given above statement.
Consider,
1-cent stamp = A
8-cent stamp = B
12-cent stamp = C
4 more 1-cent stamps than 8-cent stamps: A = 4 + B.
A = 4 + B
B = A - 4..........(1)
Twice as many 1-cent stamps as 12-cent stamps: A = 2C.
A = 2C
C = A/2...............(2)
Total number of stamps = 31
A + B + C = 31................(3)
Putting (1) and (2) in (3)
we get,
A + ( A - 4 ) + A / 2 = 31
A + A - 4 + A / 2 = 31
2A - 4 + A / 2 = 31
2A + A / 2 = 31 + 4
(4A + A) / 2 = 35
4A + A = 35 x 2
5A = 70
A = 70 / 5
A = 14
Thus the number of 1-cent stamps is 14.
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A rectangle has an area of 81 square centimeters. Which of the following would be the rectangle's length and width? (Area = equals length×times width)
Answer:
length: 9cm
width: 9cm
Step-by-step explanation:
9×9=81
Pls help me I promise I’ll mark u brainleiest if I type in the fastest answer
Answer:
1. $-50
2. $25
Step-by-step explanation:
1. If she had $150 in her bank account and bought a bike for $200, then that means she spent all of her money PLUS $50 extra then what she had. That means $200-$150=$50. Her $150 is spent and that $50 becomes negative because she paid $200 when she only had $150.
2. If she deposits $75 in her account then it will be $75+(-50). That translates to $75-$50 which is $25.
+ and - = -
+ and + = +
- and - = +
Answer:
1. $-50
2. $25
Step-by-step explanation:
1.
We know that Clare originally had $150 in her account. She then buys a bike, which means she must have taken money out of her account for this purchase.
Since she spent $200, we need to subtract 200 from 150:
150 - 200 = -50
So, her account balance is $-50.
2.
Clare earns $75 later, which means she's receiving the money and can add it back into her account. Her current balance is -50, so we add 75 to -50:
-50 + 75 = $25
Thus, her account balance is now $25.
~ an aesthetics lover
Use any estimation strategy to calculate ,51.12 times 87.906 pls help!
Answer:
the real answer is: 4493.75472
BUT for ESTIMATION STRATEGY it is: 4500
Step-by-step explanation:
These figures are similar. The area of one is given. Find the area of the other. PLZ HELP Plz ps the answer is not 12
==================================================
Explanation:
Dividing the side lengths, the scale factor is 6/3 = 2. This means the larger figure has a side length twice as long compared to its smaller counterpart.
How can we use this to figure out how the areas are connected? By simply squaring the scale factor to get 2^2 = 2*2 = 4, then we divide the larger area over 4 to get 24/4 = 6.
The longer side is 2 times longer
The larger area is 4 times larger
--------------------
Let's say we had a 3 by 3 square. It's area would be 9.
Also, let's say we had a 6 by 6 square. It's area is 36.
Notice the ratio of areas is 36/9 = 4, so the larger square is 4 times larger than the smaller. This 4 matches with what we got earlier.
----------------------
Another example:
square A is 7 by 7 with area 49
square B is 21 by 21 with area 441
ratio of areas is 441/49 = 9, which is exactly equal to 3^2, and the 3 comes from the ratio of the sides 21/7 = 3.
------------------------
So in short, you find the linear scale factor by dividing the sides. Then you square the result to get the area scale factor, which you use to find the smaller area.
linear scale factor = (new side)/(old side)
area scale factor = (linear scale factor)^2
smaller area = (larger area)/(area scale factor)
What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
What is the solution to 5x - 15 = 5(-4x - 3) ? Group of answer choices -12 6 0 -16
Answer:
x = 0Step-by-step explanation:
5x - 15 = 5(-4x - 3)
Multiply the terms in the bracket
5x - 15 = - 20x - 15
Group like terms
Send the constants to the right side of the line and those with variables to the left side
That's
5x + 20x = - 15 + 15
Simplify
25x = 0
Divide both sides by 25
We have the final answer as
x = 0Hope this helps you
Answer:
x=0
Step-by-step explanation:
5x - 15 = 5(-4x - 3)
To find the solution to this equation, we have to get x by itself on one side of the equation.
First, distribute the 5 on the right side. Multiply each term by 5.
5x - 15= (5*-4x) + (5*-3)
5x-15 = -20x + (5*-3)
5x-15= -20x -15
Next, add 20x to both sides of the equation.
(5x+20x) -15 = (-20x+20x) -15
(5+20x) -15 = -15
25x -15=-15
Next, add 15 to both sides of the equation.
25x -15 +15 = -15+15
25x= -15+15
25x=0
Finally, divide both sides of the equation by 25.
25x/25=0/25
x= 0/25
x= 0
The solution to this equation is x=0
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
Its commutative property..
Step-by-step explanation:
Commutative property says A×B=B×A
Explanation is attached below.
Which of the following expressions represents a function? (5 points) a {(1, 2), (4, −2), (8, 3), (9, −3)} b y2 = 16 − x2 c 2x2 + y2 = 5 d x = 7
Answer: Option "a" is the only expression that represents a function.
Step-by-step explanation:
A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.
So, if we have that for a given value of x.
f(x) = y and f(x) = h
where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.
Let's see the different options:
a) {(1, 2), (4, −2), (8, 3), (9, −3)}
This points are of the form (x, y)
We can see that each value of x is assigned to only one value of y, so this can represent a function.
b) y^2 = 16 − x^2
Ok, suppose that x = 0, then:
y^2 = 16 - 0 = 16
then we have that y*y = 16.
So y can take two different values:
y = 4 ---> 4*4 = 16
y = -4 ---> -4*-4 = 16.
So this is not a function.
c) 2x^2 + y^2 = 5
First, we want to isolate y in one side:
y^2 = 5 - 2*x^2
Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.
d) x = 7.
Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x+12=48,where x represents the cost of a. Ticket.how much is one ticket
Answer:
x=9; one ticket is $9
Step-by-step explanation:
4x+12=48
4x=48-12
4x=36
x=36/4
x=9
Shawna finds a study of American men that has an equation to predict weight (in pounds) from
height (in inches): y = -210 + 5.6x. Shawna's dad's height is 72 inches and he weighs 182 pounds.
What is the residual of weight and height for Shawna's dad?
a. 11.2 pounds
b. -11.2 pounds
c. 193.2 pounds
d. 809.2 pounds
Answer:
-11.2 pounds
Step-by-step explanation:
It is given that,
Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches):
y = -210 + 5.6x
Height of Shawna's dad is 72 inches
Weight is 182 pounds
We need to find the residual of weight and height for Shawna's dad.
Predicted weight of 72 inches men,
y' = -210 + 5.6(72)
y' = 193.2 pounds
So, residual is :
Y = 182 - 193.2
Y = -11.2 pounds
So, the residual of weight and height for Shawna's dad is -11.2 pounds.
Answer:
-11.2 pounds
Step-by-step explanation:
Got it right on the test.
Ernie Rolph borrowed $6700 at 4% annual simple interest. If exactly 1 year later he was able to repay the loan without penalty, how much interest would he owe? Ernie will owe $___ in interest.
Ernie will owe an interest of $268
Which equation represents the data shown in the table provided in the image?
A. y = 2x + 1
B. y = 3x — 1
C. y = 2.5x
D. y = 2.5x + 1
Please include ALL work! <3
The correct answer is A. y = 2x +1
Explanation:
An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.
First column
5 = 2 · 2 + 1
5 = 4 + 1
5 = 5
Second Column
9 = 2 · 4 + 1
9 = 8 + 1
9 = 9
Third column
13 = 6 · 2 + 1
13 = 12 + 1
13 = 13
Fourth column
17 = 8 · 2 + 1
17 = 16 + 1
17 = 17
