Steve, an entrepreneur, decides to open a flower shop and looks for an appropriate location for his shop. He wants to use the center-of-gravity method for the purpose. He researches the zip codes in his area and finds the following information: Identify a true statement about the best center of gravity for the possible shop location.
A) The x-axis and the y-axis are less than 5.0.
B) The x-axis is less than 7.0 and the y-axis is more than 7.0.
C) The x-axis is more than 7.0 and the y-axis is less than 7.0.
D) The x-axis and the y-axis are more than 7.0.

Answer:

For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]

And the average is calculated with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]

After calculate the average they got:

[tex] \bar X= 35031[/tex]

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data

Step-by-step explanation:

For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]

And the average is calculated with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]

After calculate the average they got:

[tex] \bar X= 35031[/tex]

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data

Answer: 24,000 tickets

Step-by-step explanation: The idea is just to round up the original ticket sold to the nearest thousand. That is 23,847 tickets to the nearest thousand is 24,000 since the next number after 3 is 8 which is greater or equal to five so you take it as 1 and add it to 3 making the total number of tickets sold as 24,000.

Answer:

36,995,475

Step-by-step explanation:

In the year 2050, a country's elderly population is predicted to be 8,176,000

This is 22.1% of the tota population

If x=total population in the year 2050

and 22.1% of x = 8,176,000

Then:

22.1% of x = 8,176,000

[tex]\frac{22.1}{100}x= 8176000[/tex]

On Cross multiplication

22,1x = 817,600,000

x=[tex]\frac{817600000}{22.1}[/tex] =36995475.11

We jettison fractional values because we are dealing with population.

Therefore, In the year 2050, the total population of the country will be 36,995,475

According to the chain rule, if we have a function:

[tex]f(x)=k(g(x))[/tex]

The derivative at a point [tex]a[/tex] will be:

[tex]f'(a)=k'(g(a))g'(a)[/tex]

We know that:

[tex]f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}[/tex]

Answer:

289/4

Step-by-step explanation:

x² + 17x + 12 = 0

x² + 17x = -12

Take half of the second coefficient, square it, then add the result to both sides.

(17/2)² = 289/4

x² + 17x + 289/4 = -12 + 289/4

(x + 17/2)² = 241/4

The answer is 289/4.

By using quadratic equation formula a[tex]x^{2}[/tex] + bx + c = 0, we get:

⇒ [tex]x^{2}[/tex] + 17x + 12 = 0

⇒ [tex]x^{2}[/tex] + 17x = -12

Take half of the second coefficient, square it, then add the result to both sides.

⇒ (17/2)² = 289/4

⇒ [tex]x^{2}[/tex] + 17x + 289/4 = -12 + 289/4

⇒ (x + 17/2)² = 241/4

Quadratic equations are second-degree algebraic expressions and are of the form a[tex]x^{2}[/tex] + bx + c = 0.

Learn more about quadratic equations here: brainly.com/question/8649555

#SPJ2

Answer:

A Mudslinger tire weighs 20.71 pounds and a Roadripper tire weighs 19.52 pounds

Step-by-step explanation:

Let the weight of a Mudslinger tire=m

Let the weight of a Roadripper tire=r

4 Mudslinger tires and 6 Roadripper tires weigh 200 pounds

4m+6r=200.....(i)

7 Mudslinger tires and 2 Roadripper tires weigh 184 pounds

7m+2r=184....(ii)

To find the values of m and r, we solve the two derived equations simultaneously.

4m+6r=200.....(i)

7m+2r=184....(ii)

Multiply (ii) by 3 to get (iii)

21m+6r=552....(iii)

4m+6r=200.....(i)

SUbtract (i) from (iii)

17m=352

m=352/17=20.71 pounds

Substitute m=20.71 in (i)

4(20.71)+6r=200

6r=200-82.84=117.16

r=117.16/6=19.52 pounds

Answer:

(0.353, -48)

Step-by-step explanation:

dy/dx = 9x² + 28x - 11 = 0

Using the quadratic formula:

x = -3.46 and 0.353

d²y/dx² = 18x + 28

Minima when d²y/dx² is positive

x = 0.35284 or (-14+sqrt(295))/9

y = 3x³ + 14x² - 11x - 46

y = -48.00651351

The relative minimum of a function is (1/2, -65/4), derive the function, set it to zero, solve for x, and find the corresponding y-value.

To find the relative minimum of the function y = 3x^3 + 14x^2 - 11x - 46, we need to first take the derivative of the function, set it equal to zero, and then solve for the critical point.

This will give us the x-coordinate of the minimum. Next, plug this x-value back into the original function to find the corresponding y-coordinate.

The relative minimum of the function y = 3x^3 + 14x^2 - 11x - 46 is at the point (1/2, -65/4).

It would be 3 hours. This is 3 hours because the problem says that daniel takes 9 hours to clean and office building and mark takes 6 hours so if you subtract 9hours from 6 hours it would be 3 hours total. Now this can be 2 answers it can also be 15 hours if you were to add 9 hours to 6 hours.

Answer: it will take 3.6 hours

Step-by-step explanation:

If it takes Daniel 9 hours to clean an office building, it means that the rate at which he cleans the office building per hour is 1/9

If it takes Mark 6 hours to clean the office building, it means that the rate at which Mark cleans the office building per hour is 1/6

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/9 + 1/6 = (6 + 9)/54 = 15/54

Assuming it takes t hours for both of them to clean the office working together, the working rate per hour would be 1/t. Therefore,

15/54 = 1/t

t = 54/15 = 3.6 hours

Answer:

(-1, 19) and (3, -81)

Step-by-step explanation:

f(x) = 2x³ − 6x² − 27x

f'(x) = 6x² − 12x − 27

-9 = 6x² − 12x − 27

0 = 6x² − 12x − 18

0 = x² − 2x − 3

0 = (x + 1) (x − 3)

x = -1 or 3

f(-1) = 19

f(3) = -81

The points are (-1, 19) and (3, -81).

The student made a mistake in setting their proportion, which resulted in the wrong calculation. The correct proportion should have been 4/6 = x/24, where x is the number of oranges needed. Solving this proportion gives us 16 oranges needed for 24 fluid ounces of juice.

The error in the student's work lies in the improper establishment of the proportion. The initial ratio provided was 4 oranges to 6 fluid ounces.

The proportion, therefore, should have been StartFraction 4 over 6 EndFraction = StartFraction x over 24 EndFraction, where 'x' is the number of oranges required for 24 ounces of juice. The student incorrectly used '24' as the numerator rather than the denominator, causing an error in calculation.

To correct this, we can cross-multiply to get 4 * 24 = 6 * x, leading to x = 16 oranges. Therefore, 16 oranges are needed for 24 fluid ounces of juice, which is the correct solution.

https://brainly.com/question/31776433

#SPJ3

Sample response: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in the proportion as the first ratio

Step-by-step explanation:

Answer:

A = (5+4) divided by 1/2 x 11 (h) = 49.5 in

Answer:38 inches

Step-by-step explanation:A=1/2 (base 1 + base 2) x height = area

Base 1 = 11 in

Base 2 = 8 in

Height = 4 inches

Area if trapezoid = 1/2 x 11 + 8 x 4 =!19 sum of bases

19x4(H) = 76

76/2=38 inches

Area of trapezoid = 38 inches

Answer: the horizontal distance between the tower and the fire is 732.89 feet

Step-by-step explanation:

Considering the situation, a right angle triangle is formed. The height of the fire watch tower represents the opposite side of the right angle triangle.

The horizontal distance, h between the tower and the fire represents the adjacent side of the right angle triangle.

If the angle of depression to the fire that is 7°, the angle of elevation from of the tower watcher from the fire is also 7° because they are alternate angles.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan 7 = 90/h

h = 90/tan7 = 90/0.1228

h = 732.89 feet

The requried, Dominic pays an average interest rate of approximately 9.115% on the total $26,000 he owes.

To find the average interest rate Dominic pays on the total $26,000 he owes, we can use a weighted average approach based on the interest rates and amounts of each loan.

Given:

College loan amount: $15,000

College loan interest rate: 7%

Car loan amount: $11,000

Car loan interest rate: 12%

Let's calculate the weighted average interest rate:

Calculate the total interest paid for each loan:

Interest paid on the college loan = 0.07 * $15,000

Interest paid on the car loan = 0.12 * $11,000

Calculate the total interest paid for both loans:

Total interest = Interest on college loan + Interest on car loan

Calculate the weighted average interest rate based on the total interest paid and the total amount owed:

Weighted average interest rate = (Total interest / Total amount owed) * 100

Let's do the calculations:

Interest on college loan: 0.07 * $15,000 = $1,050

Interest on car loan: 0.12 * $11,000 = $1,320

Total interest: $1,050 + $1,320 = $2,370

Total amount owed: $15,000 + $11,000 = $26,000

Weighted average interest rate: ($2,370 / $26,000) * 100 ≈ 9.115%

So, Dominic pays an average interest rate of approximately 9.115% on the total $26,000 he owes.

Learn more about interest rates here:

https://brainly.com/question/28338253

#SPJ12

Dominic pays a total interest of $2,370 on his college and car loans, which sums up to $26,000. Therefore, the average interest rate he pays on the total loan amount is calculated to be 9.12%.

Dominic's interest for his college loan is calculated by multiplying the total loan amount of $15,000 by 7% which equals $1,050. The interest on his car loan is calculated by multiplying $11,000 by 12%, equalling $1,320. His total interest paid for both loans is $1,050 + $1,320 = $2,370. To find the average interest rate that Dominic pays on the total amount of $26,000, you would divide his total interest paid ($2,370) by the total loan amount ($26,000) and then multiply by 100%. That's $2,370 / $26,000 * 100% = 9.12%. Therefore, on average Dominic is paying an interest rate of 9.12% on his total owed amount.

https://brainly.com/question/33721479

#SPJ3

In this exercise, we know some facts:

The problem tells us nothing about the number of minutes Elena read more than Lin. However, let's say Elena read one-third more than the number of minutes Lin read. Therefore:

For Lin:

[tex]Number \ of \ minutes \ Lin \ read=x[/tex]

For Elena:

[tex]Number \ of \ minutes \ Elena \ read=x+\frac{1}{3}x \\ \\ Number \ of \ minutes \ Elena \ read=\frac{3x+x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ \\ By \ using \ decimals: \\ \\ Number \ of \ minutes \ Elena \ read \approx 1.33x[/tex]

Final answer:

The expression for the number of minutes Elena read is x + 1.

Explanation:

To write an expression for the number of minutes Elena read, we can use the variable x to represent the number of minutes Lin read. Since Elena read for more than Lin, we can use the expression x + 1 to represent the number of minutes Elena read. This expression indicates that Elena read for one minute more than Lin.

Answer:

(A)62.8 square feet

Step-by-step explanation:

Height of the barrels = 5 feet

Radius of the barrels= 2 feet

[tex]\pi[/tex]=3.14

The barrel is in the shape of a cylinder and the area of the label the company needs is that of the round sides(curved surface area) of the cylinder.

Curved Surface Area of a Cylinder=[tex]2\pi rh[/tex]

=2X3.14X2X5

=62.8 square feet

The company need 62.8 square feet of label.

Final answer:

The y-intercept of the line y = 11x + 6 is (0, 6), and the x-intercept is (-6/11, 0). To find these, you set x to 0 to find the y-intercept and set y to 0 to solve for the x-intercept.

Explanation:

To determine the intercepts of the line given by the equation y = 11x + 6, we need to find where the line crosses the x-axis and the y-axis. The y-intercept is found when x = 0; substituting x = 0 into the equation gives us y = 6. Therefore, the y-intercept is at the point (0, 6). To find the x-intercept, we set y = 0 and solve for x; setting y = 0 in our equation results in 0 = 11x + 6. Solving for x gives us x = -6/11. The x-intercept is at the point (-6/11, 0).

Answer:

The length of the remaining piece of thread is  [tex]\frac{1}{16}.[/tex]

Step-by-step explanation:

Given:

A tailor cuts a piece of thread One-half of an inch long from a piece Nine-sixteenths of an inch long.

Now, to find the length of the remaining piece of thread.

Total thread  = [tex]\frac{9}{16} \ inch.[/tex]

Tailor cuts a piece of thread = [tex]\frac{1}{2}\ inch.[/tex]  

Now, to get the length of the remaining piece of thread by subtracting tailor cuts a piece of thread from the total thread:

[tex]\frac{9}{16} -\frac{1}{2} \\\\=\frac{9-8}{16} \\\\=\frac{1}{16}[/tex]

Therefore, the length of the remaining piece of thread is  [tex]\frac{1}{16}.[/tex]

Answer lovely

Step-by-step explanation:

Answer:

a c

Step-by-step explanation:

Final answer:

All three calculated numbers are positive, and therefore, the product of any two of them will also be positive. Option B is correct, which states that at least two numbers must be positive, making the resulting product nonnegative.

Explanation:

The statement that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001, and 244493 - 58192 + 71777 is nonnegative relies on the principles of arithmetic involving the addition and multiplication of numbers with different signs. Calculating the given numbers:

651000 - 82001 + 3177 = 573176 (positive)

791212 - 92399 + 22001 = 710814 (positive)

244493 - 58192 + 71777 = 255078 (positive)

All three numbers are positive, so the product of any two would also be positive, according to the multiplication rules that state the product of two positive numbers is always positive.

Therefore, the correct answer to the statement is:

B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative.

transformation: Translating then diilating

first you go from A to C

then you shrink it down to size n

Answer: The statement is true (see Step-by-step explanation).

Step-by-step explanation:

The slope of the tangent line for all point of the curve is determine by derive the expression abovementioned in the statement:

[tex]y' = 12 \cdot x^{2} + 7[/tex]

The previous expression represents a parabola, whose output will be positive for all [tex]x[/tex] due to the symmetry of [tex]x^{2}[/tex] and the positive coefficients of the polynomial. If the function is evaluated at [tex]x = 0[/tex], where the minimum occurs, it is evident that the smallest value is [tex]y' = 7[/tex] . Therefore, the inexistence of any tangent line with slope 2 associated with that curve is true.

Answer:

  BG = 3; GE = 6

Step-by-step explanation:

The centroid of a triangle divides the median into two parts in the ratio 1 : 2. That is, the short segment is 1/3 the length of the median, and the long segment is 2/3 the length of the median.

  BG = 1/3·BE = 9/3 = 3

  GE = 2/3·BE = 2/3·9 = 18/3 = 6

Answer:

They are equivalent

Step-by-step explanation:

Priya rewrites the expression 8y - 24 as 8(y - 3).

Han rewrites 8y - 24 as 2(4y - 12)

The two expressions are equivalent. This is reached by taking note of the fact that if the factorized form is expanded, they both give the same result.

In Priya's Version,

8(y - 3)=(8 X y)-(8 X 3)=8y-24

Likewise In Han's Version

2(4y - 12)=(2 X 4y) - (2 X 12) =8y-24

We can see from the bolded that our results are the same. Priya's Version is a fully factorized form while Han's Version can still be factorized further to get Priya's version.

i.e. 2(4y - 12)=2 X 4(y-3)=8(y-3)

Both Priya's expression (8(y - 3)) and Han's expression (2(4y - 12)) are equivalent to the original expression 8y - 24. By distributing the multiplicative factors, both expressions simplify to the original expression, proving their equivalence.

Yes, both Priya's and Han's expressions are equivalent to 8y - 24. To confirm that Priya's and Han's expressions represent the same value as the original expression, we can simplify their expressions through the distributive property, which states that multiplying a sum by a number gives us the same result as multiplying each addend by the number separately and then adding the products.

For Priya's expression, 8(y - 3), we distribute the 8:

Thus, Priya's expression simplifies to 8y - 24, which is the original expression.

For Han's expression, 2(4y - 12), we also distribute:

So, Han's expression simplifies to 8y - 24, which is again the original expression.

Therefore, we can conclude that both methods provide equivalent expressions to 8y - 24, showcasing that math provides multiple paths to reach the same answer.

The arc length of AB is 8 m (app.)

Explanation:

Given that the radius of the circle is 8 m.

The central angle is 60°

We need to determine the arc length of AB

The arc length of AB can be determined using the formula,

[tex]arc \ length=\frac{central \ angle}{360^{\circ}} \times circumference[/tex]

Substituting central angle = 60° and circumference = 2πr in the above formula, we get,

[tex]arc \ length=\frac{60^{\circ}}{360^{\circ}} \times 2 \pi(8)[/tex]

Simplifying the terms, we get,

[tex]arc \ length=\frac{8 \pi }{3}[/tex]

Dividing, we get,

[tex]arc \ length=8.37758041[/tex]

[tex]arc \ length=8(app.)[/tex]

Hence, the arc length is approximately equal to 8.

Therefore, the arc length of AB is 8 m

Just got the test and answered 67...was absolutely sure it is correct answer...Most likely the answer is 9 ....Since to get every next sum is +9.. Well, at least 67 is a wrong answer..:(

The seventh partial sum is 280

Option D is the correct answer.

It is a sequence where the difference between each consecutive term is the same.

We have,

The sequence has a common difference of 9, so it is an arithmetic sequence.

The first term is 13.

To find the seventh partial sum, we need to add up the first seven terms of the sequence:

= 13 + 22 + 31 + 40 + 49 + 58 + 67

= 280

Therefore,

The seventh partial sum is 280

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ3

Answer: the cost of each pencil is $0.5

the cost of each eraser is $0.15

Step-by-step explanation:

Let x represent the cost of one pencil.

Let y represent the cost of one eraser.

Becky spent $1.45 for 2 pencils and 3 erasers. This means that

2x + 3y = 1.45- - - - - - - - - -1

Luke spent $2.65 for 5 pencils and 1 eraser. This means that

5x + y = 2.65- - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 3, it becomes

2x + 3y = 1.45

15x + 3y = 7.95

Subtracting, it becomes

- 13x = - 6.5

x = - 6.5/- 13

x = 0.5

Substituting x = 0.5 into equation 2, it becomes

5 × 0.5 + y = 2.65

2.5 + y = 2.65

y = 2.65 - 2.5

y = 0.15

The cost of one eraser is [tex]\(\$0.15\).[/tex]

Let's denote the cost of one pencil as p dollars and the cost of one eraser as e dollars.

According to the given information:

1. Becky spent $1.45 for 2 pencils and 3 erasers, so her total cost can be expressed as:

[tex]\[ 2p + 3e = 1.45 \][/tex]

2. Luke spent $2.65 for 5 pencils and 1 eraser, so his total cost can be expressed as:

[tex]\[ 5p + 1e = 2.65 \][/tex]

We can now solve this system of equations to find the cost of one eraser (e ).

From equation 1, we can express p in terms of e :

[tex]\[ 2p = 1.45 - 3e \]\[ p = \frac{1.45 - 3e}{2} \][/tex]

Substitute this expression for p  into equation 2:

[tex]\[ 5\left(\frac{1.45 - 3e}{2}\right) + e = 2.65 \][/tex]

Multiply both sides by 2 to eliminate the fraction:

[tex]\[ 5(1.45 - 3e) + 2e = 5.3 \]\[ 7.25 - 15e + 2e = 5.3 \][/tex]

Combine like terms:

[tex]\[ 7.25 - 13e = 5.3 \][/tex]

Subtract 7.25 from both sides:

[tex]\[ -13e = 5.3 - 7.25 \]\[ -13e = -1.95 \][/tex]

Divide both sides by -13:

[tex]\[ e = \frac{-1.95}{-13} \]\[ e = 0.15 \][/tex]

Therefore, the cost of one eraser is [tex]\(\$0.15\).[/tex]

Answer:

5 cups

Step-by-step explanation:

2 1/4 + 2 3/4= 5 cups of flour

Answer:

The answer is 5

Step-by-step explanation:

A trick you can use here is by understanding what the fraction is indicating, the number 4 indicates a full cup reached and the first 1/4 is 1 part out of 4 parts to be reached. the second fraction is 3 out of 4 and if you add the one on the other fraction then you get 3+1==4 which majes a full cup

and once you ad the other 4 cups you get 5

the measure of the angle outlined on the sign is 50∘.

To find the measure of the angle outlined on the sign, we simply multiply the number of one-degree angles by the measure of one degree.

Given that the angle turns through 50 one-degree angles, we can calculate the measure of the angle as follows:

Measure of the angle = Number of one-degree angles × Measure of one degree

Measure of the angle=50 * 1

Measure of the angle=50

So, the measure of the angle outlined on the sign is 50∘.

The probable question maybe:

David waits by the crosswalk sign on his way to school. The angle outlined on the sign turns through 50 one-degree angles. What is the measure of the angle outlined on the crosswalk sign?

Answer: there is nothing shown below

Step-by-step explanation:

Answer:

The solution (x, y) = (-5, 3)

Step-by-step explanation:

-x - 8 = -y .... (1)

9y - 12 + 3x = 0 .... (2)

from equation (1)

-x = - y + 8 ... (3)

multiply equation (3) by -1

x = y - 8 ..... (4)

substituting equation (4) in equation (2)

9y - 12 + 3 ( y - 8) = 0

9y - 12 + 3y - 24 = 0

12y - 36 = 0

12y = 36

y = 36 /12

y = 3

Substitute y = 3 in equation (4)

x = y - 8

x = 3 - 8

x = -5

Answer:

20 mangoes.

Step-by-step explanation:

Given:

Total  number of mangoes, a trader bought = [tex]x[/tex]

A trader bought at the rate of 4 mangoes for 10 naira.

Five of the mangoes were bad.

He sold the remaining at the rate of 5 mangoes for 20 naira.

He made a gain of 10 naira

Question asked:

Total  number of mangoes, a trader bought = [tex]x[/tex] = ?

Solution:

Unitary method

Cost price of  4 mangoes =  10 naira.

Cost price of  1 mango = [tex]\frac{10}{4}[/tex]

Cost price of [tex]x[/tex] mango = [tex]\frac{10}{4}\times x= \frac{5}{2} x[/tex]

As 5 of the mangoes were bad and he sold the remaining mangoes, then Total number of mangoes sold =  [tex]x-5[/tex]

Sale price of 5 mangoes = 20 naira

Sale price of 1 mango = [tex]\frac{20}{5}[/tex]

Sale price [tex]x-5[/tex] of mango = [tex]\frac{20}{5}\times(x-5)=4(x-5)=4x-20[/tex]

Now, as we know,

[tex]Gain = Sale price - cost price[/tex]

[tex]10 = 4x-20 -\frac{5}{2} x\\ 10=4x-\frac{5}{2} x-20\\10=\frac{8x-5x}{2} -20[/tex]

[tex]10 =\frac{3x}{2} -20[/tex]

Adding both sides by 20

[tex]30=\frac{3x}{2}[/tex]

Multiplying both sides by 2

[tex]60 = 3x[/tex]

Dividing both sides by 3

[tex]x=20[/tex]

Therefore, total number of mangoes, a trader bought is 20.