In a group of 900 people, 323 have blood type A 167 have blood type B, 210 have blood type o, and 200 have blood type AB. What is the probability that a person
chosen at random from this group has type A blood?
00.23
0036
0022
O 0.19

Answers

Answer 1

Answer:

0.036

Step-by-step explanation:

We can find the probability by dividing the number of people with type A blood by the total amount of people.

There are 900 people in total and 323 of them have type A blood.

323/900

= approximately 0.036

Answer 2

Answer: Choice B)  0.36

================================================

Work Shown:

323 people have blood type A

900 people are being sampled

323/900 = 0.35888888888889 approximately

This rounds to 0.36, which is the probability of picking someone with type A blood.

We don't use any other values given, so they are probably put in there as a distraction.


Related Questions

What is 20 to 7 minus 1 hour 40 mins Will award brainliest

Answers

6:40 or 6 hour 40 minutes,

if you go back(subtract) 1 hour and 40 minutes

i.e. 6hours 40 minutes- 1 hour 40 minutes

subtract minutes from minutes and hours from hours,

5:00

note that here the minutes value is not negative so it was not a problem, what If it was 6:40-1:50?

How do you figure out the answer to this sum ???20x48

Answers

Answer:

Step-by-step explanation:

20

×48

-------

160

800

---------

960

Hope this helps

plz mark as brainliest!!!!!!!

Answer:

            960

Step-by-step explanation:

20×48 =

= 20×(40+8) =

= 20×40 + 20×8 =

= 2×4×100 + 2×8×10 =

= 800 + 160 =

= 960  

Or:

20×48 = 2×48×10 = 96×10 = 960

There are two types of boxes containing mangoes. Each box of the larger type contains 4 more mangoes than the number of mangoes contained in 8 boxes of the smaller types. Each box has 100 mangoes. Find the number of mangoes contained in the smaller box.

Answers

Answer:

12 mangoes

Step-by-step explanation:

Two types of boxes contains mangoes

The larger box contain 4 mangoes than the number of mangoes that is present in 8 smaller box

Each of the box have a total of 100 mangoes

Let y represent the number of mangoes that is present in the smaller box

Therefore, the number of mangoes in the smaller box can be calculated as follows

8y + 4= 100

Collect the like terms

8y= 100-4

8y= 96

Divide both sides by the coefficient of y which is 8

8y/8= 96/8

y= 12

Hence the number of mangoes that is present in the smaller box is 12

PLEASE help me solve this question! No nonsense answers, and attach full solutions please!

Answers

Answer:

6.4 seconds

Step-by-step explanation:

Using the second equation of motion.

d= 200m/s.

a= 9.8ms^-1 . Acceleration due to gravity.

t= time.

substituting,

t=

[tex] \sqrt{2 \times \frac{200}{9.8} } [/tex]

t= 6.4 seconds

classify what type of number is 8/2

Answers

Answer:

unsimplified improper fraction

Step-by-step explanation:

8/2 could be simplified into 4 and its an improper fraction bc proper fraction form is 4/1 or just 4

Solve the equation below for y. 6x – 3y = 36 A. y = 2x − 12 B. y = 12 − 2x C. y = 12x + 6 D. y = 6 – 12x

Answers

Answer:

y=-12+2x

Step-by-step explanation:

The equation was transformed step-by-step to isolate y on one side, and we obtained y = 2x - 12 as the final solution.

Hence, the correct answer is A. y = 2x - 12.

Given is an equation 6x - 3y = 36, we need to solve for y.

To solve the equation 6x - 3y = 36 for y, we need to isolate y on one side of the equation.

Here's the step-by-step process:

Start with the given equation: 6x - 3y = 36

Get rid of the constant term (36) on the right side by subtracting 36 from both sides:

6x - 3y - 36 = 36 - 36

6x - 3y = 0

Divide both sides of the equation by -3 to isolate y:

(6x - 3y) / -3 = 0 / -3

(6x)/(-3) - (3y)/(-3) = 0

-2x + y = 0

Add 2x to both sides to isolate y:

-2x + y + 2x = 0 + 2x

y = 2x

So, the equation was transformed step-by-step to isolate y on one side, and we obtained y = 2x - 12 as the final solution.

Hence, the correct answer is A. y = 2x - 12.

Learn more about Equations click;

https://brainly.com/question/29657983

#SPJ6

Ella's pet snake is 42 inches long, and Roya's pet snake is 8 feet long. How many inches longer is Roya's snake?

Answers

Royas snake is 96 in long
96-42=54 so royas snake is 54 in longer

Answer:

54 inches

Step-by-step explanation:

First, let's convert the measurements into a common measurement.

Since inch is the smallest measurement here, let's use that.

Ella's pet snake is 42 inches long.

Roya's pet snake is 8 feet long. There are 12 inches in one foot. Therefore, 8 feet would mean 12 times 8 or 96 inches.

Therefore, Roya's snake is 96 inches long.

To find out how many inches longer is Roya's snake, subtract:

96 - 42 = 54.

Therefore, Roya's snake is 54 inches longer than Ella's.


Hey, please help solve the question.​

Answers

Answer:

75%=x-125

90%=x+250

subtract the second from the first

15%=375

100%=?

100%×375/15

100%=2500marked price is 2500

2500+250=2750

90%=2750

100%=?

cost price=3055.56

Please answer this question now

Answers

Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

Freddy the frog is climbing up a well. Every day he climbs up 3 m but some nights he falls asleep and slips back 4m at the start of the 16th day he has climbed a total of 29 m. On how many nights was he asleep?

Answers

Answer: The frog fell asleep for 4 nights.

Step-by-step explanation: First, he climbs up 3m every night. there are 16 nights before he gets to 29m. He has not climbed up for the 16th day so 15*3= 45. 45-29= 16. 16/4=4. The frog slept for 4 nights.

help pleaseeeeee!!!!!!!!!! How many unit cubes would it take to completely fill the prism with no gaps between unit cubes?

Answers

Answer:

72

Step-by-step explanation:

As you can see the top - view is a rectangle of 2 by 9 dimensions. Respectively the right - side view is a rectangle of 2 by 4 dimensions. The common dimension among both rectangles would be 2, making this rectangular prism have dimensions 2 by 4 by 9.

Therefore the rectangular prism will have a volume of 2 [tex]*[/tex] 4 [tex]*[/tex] 9

2 [tex]*[/tex] 4 [tex]*[/tex] 9 = 8( 9 ) = 72 cubic units

Solution : 72 unit cubes

What is the slope of the line below?
y=2/3 X - 3

Answers

Answer:

2/3

Step-by-step explanation:

Hey there!

Well in the equation,

y = 2/3x - 3

the slope is 2/3 because the equation shows 2/3x and wherever the x is in slope intercept that the slope.

Hope this helps :)

He’s asking which number is not supposed to be there

Answers

Answer:

65

Step-by-step explanation:

They all between 9

Answer:

the answer is 65......

The graph below represents which of the following functions?

Answers

Answer:

Option (B).

Step-by-step explanation:

From the figure attached,

There are two pieces of the function defined by the graph.

1). Curve with the domain (-∞, 2)

2). Straight line with domain (2, ∞)

1). Function that defines the curve for x < 2,

  f(x) = |4 - x²|

2). Linear function which defines the graph for x ≥ 2 [Points (2, 2), (4, 4), (6, 6) lying on the graph]

  f(x) = x

Therefore, Option (B) will be the answer.

HELP ASAP MATH QUESTION The midpoint of a line segment is located at (3, -2). If one of the endpoints is (1, 6), what is the other endpoint? Express your answer as an ordered pair.

Answers

Answer:

(5, -10)

Step-by-step explanation:

[tex]Midpoint = (3,-2)\\1st \: endpoint = (1,6)\\2nd \: endpoint = ?\\\\\\Let \: (1,6) \:be \:x_1y_1\\Let\:(3,-2)\: be\:x\:and\:y\\\\x=(x_1+x_2)/2\\y=\frac{(y_1+y_2)}{2} \\\\3 =\frac{1+x_2}{2} \\\\3\times 2 =1+x_2\\\\6 = 1+x_2\\6-1=x_2\\\\x_2 =5\\\\y=\frac{(y_1+y_2)}{2} \\-2 = \frac{6+y_2}{2}\\\\ -2 \times 2= 6+y_2\\\\-4 = 6+y_2\\\\-4-6=y_2\\\\y_2 = -10\\\\Answer = (5 ,-10)[/tex]

the angle of elevation of the top of a tower from a point 42m away from the base on level ground is 36 find the height of the tower​

Answers

Answer:

30.51 meters

Step-by-step explanation:

Given that:

The distance from the point to the base of the tower = 42 m, the angle of elevation = 36°.

According to sine rule if a,b,c are the sides of a triangle and its respective opposite angles are A, B, C. Therefore:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the height of the tower be a and the angle opposite the height be A = angle of elevation = 36°

Also let the  distance from the point to the base of the tower be b = 42 m, and the angle opposite the base of the tower be B

To find B, since the angle between the height of the tower and the base is 90°, we use:

B + 36° + 90° = 180° (sum of angles in a triangle)

B + 126 = 180

B = 180 - 126

B = 54°

Therefore using sine rule:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}\\\\\frac{a}{sin(36)}=\frac{42}{sin(54)}\\\\ a=\frac{42*sin(36)}{sin(54)}\\ \\a=30.51\ meters[/tex]

The height of the tower is 30.51 meters

find the last common denominator for these two rational expressions

Answers

Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

[tex]\frac{x^3}{x^2-2x+1}[/tex] and [tex]\frac{-3}{x^{2}-3x+2}[/tex]

Factorize the denominators of these rational expressions,

Since, [tex]x^{2}-2x+1[/tex] = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

                         = x(x - 2) -1(x - 2)

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).

A tap takes 3 hours to fill a tank. A discharge tap takes 6 hours to empty the same tank. How long will it take to fill the tank with both taps open?

Answers

Answer:

2 hours

Step-by-step explanation:

first tap= 3hours

therefore work done is = 1/3

second tap= 6hours

therefore work done = 1/6

so, 1/3+ 1/6

=2/6 + 1/6

=3/6

=1/2

=2/1 hours

=2 hours

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number.

Answers

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Four different animals live in the forest. They sleep during the daytime and hunt at night. They have similar physical characteristics but their skin colors are different as shown in the following table. Animal Skin Color A White B Brown with white spots C Dark brown D Black and white stripes Which animal is least likely to be captured by predators? Animal A Animal B Animal C Animal D

Answers

Answer:

I would gues c because brown is the hardest to see in the dark

Answer:

C dark brown

Step-by-step explanation:

please help me please ​

Answers

Answer:

14 cm

Step-by-step explanation:

Answer:

14 cm will be the answer

The function f(x)=x^2 + ax + b has a minimum at (3,9) what are the values of a and b

Answers

Answer:

Step-by-step explanation:

The function is f(x)=x^2 + ax + b

Derivate the function:

● f'(x)= 2x + a

Solve the equation f'(x)=0 to find a

The minimum is at (3,9)

Replace x with 9

● 0 = 2×3 + a

● 0 = 6 + a

● a = -6

So the value of a is -6

Hence the equation is x^2 -6x+b

We have a khown point at (3,9)

● 9 = 3^2 -6×3 +b

● 9 = 9 -18 + b

● 9 = -9 +b

● b = 18

So the equation is x^2-6x+18

Verify by graphing the function.

The vetex is (3,9) and it is a minimum so the equation is right

6=m/8 whats does m equal?

Answers

Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

El reto consiste en convertir la igualdad en verdadera, haciendo 1 movimiento y luego, otra opción, haciendo dos movimientos. (no está permitido retirar fósforos)

Answers

12

Step-by-step explanation:

9+3 =12

pls make me brainiest

Step-by-step explanation:

Un movimiento:

1 opción:

Del primer 9:

retirar el fósforo de la parte superior de tal manera que este nueve se convierte en 5 y colocarlo en la parte inferior del segundo nueve de tal manera que se convierte en 8:

5 + 3 = 8

2 opción:

en el primer nueve trasladar el fósforo vertical de la parte superior derecha a la parte inferior izquierda de tal manera que este se convierte en 6:

6 + 3 = 9

Dos movimientos:

Del primer nueve retirar el fósforo vertical superior izquierdo de tal manera que este se convierte en 3 y ese fósforo colocarlo de forma vertical en la parte inferior izquierda del 3 y recorrer de este 3 el fósforo vertical superior derecho hacia la izquierda de tal manera que se convierte en 6:

3 + 6 = 9

(x+3)(x-5)=(x+3)(x−5)=

Answers

Answer:

(x+3)(x-5)=(x+3)(x-5)

      x^2-2  = x^2-2

Step-by-step explanation:

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve your equation step-by-step.

[tex]( x + 3) ( x - 5) = ( x + 3 ) ( x - 5 ) =[/tex]

Step 1: Simplify both sides of the equation.

[tex]x^2 - 2x - 15 = x^2 - 2x - 15 - x^2\\-2x - 15 = -2x - 15[/tex]

Step 3: Add 2x to both sides.

[tex]-2x - 15 = -2x - 15\\-15 = -15[/tex]

Step 4: Add 15 to both sides.

[tex]-15 + 15 = -15 + 15 \\0 = 0[/tex]

Answer : All real numbers are solutions.

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

Answers

Answer:

The outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Step-by-step explanation:

The outcomes provided are:

(A) 0, 1, 2, 6, 7, 8

(B) 0, 1, 2, 7, 8

(C) 0, 1, 7, 8

(D) 0, 1, 2, 8

Solution:

The random variable X can be defined as the number of employees who judge their co-workers by cleanliness.

The probability of X is:

P (X) = 0.65

The number of employees selected is:

n = 8

An unusual outcome, in probability theory, has a probability of occurrence less than or equal to 0.05.

Since outcomes 0 and 1 are contained in all the options, we will check for X = 2.

Compute the value of P (X = 2) as follows:

[tex]P(X=2)={8\choose 2}(0.65)^{2}(0.35)^{8-2}[/tex]

                [tex]=28\times 0.4225\times 0.001838265625\\=0.02175\\\approx 0.022<0.05[/tex]

So X = 2 is unusual.

Similarly check for X = 6, 7 and 8.

P (X = 6) = 0.2587 > 0.05

X = 6 not unusual

P (X = 7) = 0.1373 > 0.05

X = 7 not unusual

P (X = 8) = 0.0319

X = 8 is unusual.

Thus, the outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Jerry wants to gravel an area represented by a square with side lengths of 3/4ft. What is the area he needs to fill.

Answers

Answer:

0.5625 ft^2

Step-by-step explanation:

area of square = side * side

A = s^2

A = (0.75 ft)^2 = (0.75 ft)(0.75 ft) = 0.5625 ft^2

Factor completely 3x^2 + 5x + 1. (3x + 1)(x + 1) (3x + 5)(x + 1) (3x − 5)(x + 1) Prime

Answers

Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

Answer:

[tex]\large \boxed{\sf Prime}[/tex]

Step-by-step explanation:

[tex]3x^2 + 5x + 1[/tex]

We need to find two numbers that add to 5 and multiply to get 1.

There are no real numbers.

The expression cannot be factored. The expression is prime.

7x-x ............................ .

Answers

Answer:

6x

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

Is f(x) =(x+5)2 a function, an odd function, both or neither

Answers

Answer: Neither even, nor odd

Explanation:

f(x) = (x+5)^2 = x^2+10x+25 = x^2+10x^1+25x^0

The exponents for that last expression are 2, 1, 0

The mix of even and odd exponents in the standard form means f(x) is neither even nor odd. We would need to have all exponents even to have f(x) even, or have all exponents odd to have f(x) be odd.

Other Questions
Evaluate the following expression: 2 + 1 x 2 *Please help i don't have that much time* The Soma Inn is trying to determine its break-even point. The inn has 75 rooms that are rented at $60 a night. Operating costs are as follows:Salaries $9,700 per monthUtilities 2,700 per monthDepredation 1,300 per monthMaintenance 700 per monthMaid service 8 per roomOther costs 34 per roomRequired:a. Determine the inn's break-even point in (1) number of rented rooms per month and (2) dollars.b. If the Inn plans to renting an average of 50 rooms per day (assuming a 30-day month), what is (1) the monthly margin of safety dollars and (2) the margin of safety ratio? An item was shipped from a supplier under FOB shipping point. The invoice in the amount of $2,000 included payment terms of 2/10, n/30. When the invoice was paid, a purchase discount in the amount of $40 was taken. Other details relating to the purchase of this item included the following: shipping charges of $300, storage fees of $50, and insurance premium of $100. The cost of this inventory item is *LAST QUESTION, HURRY AND PLEASE ANSWER, WILL CHOOSE BRAINLIEST FOR DETAILS AND ANSWER* How many times larger is the rectangular prism than the cube? Which type of sentence has at least one independent and one dependent clause g Refer to the Number of Motorcycles Narrative} Are these probabilities true or false? ?a. P(X > 1)=0.35 b. P(X 2)=0.85 c. P(1 X 2)=.6 d. P(0 < X < 1)=0 e. P(1 X < 3)=.6 True False Consider a small country that is closed to trade, so its net exports are equal to zero. The following equations describe the economy of this country in billions of dollars, where C is consumption, D is disposable income, I is investment, and G is government purchases: C=40+0.9DIG=80I=201. Assume that this economy initially has a fixed tax and that net taxes (taxes minus transfer payments are $100 billion. Disposable income is then (Y100), where Y is the real GDP. Aggregate output demanded is $500 billion (True/False).2. Suppose the government decides to increase spending by $10 billion without raising taxes. Because the expenditure multiplier is 10 (True/False), this will increase the economy's aggregate output demanded by $100 billion (True/False).3. Now, suppose that the government switches to an income tax, which is the type of variable tax, of 20%. Because consumers retain only 80% of each additional dollar of income, disposable income is now 0.80Y. In this case, the economy's aggregate output demanded is $500 billion (True/False).4. Given an income tax of 20%, the expenditure multiplier is approximately 3.6 (True/False). Therefore, if the government decides to increase spending by $10 billion without raising tax rates, this would increase the economy's aggregate output demanded by approximately $36 billion (True/False).5. A $10 billion increase in government purchases will have a larger effect on output under a fixed tax of $100 billion (True/False). The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected.The probability that a randomly chosen person gets an incorrect result is . simplify theta(sin theta) /2tan theta I NEED HELP ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!! [ chaye py charcha ] proverb translate it into english proverb plzz Sand Key Development Company estimates that it will generate an operating income of $7.25 million. Which financing option should Sand Key use? how many cars the baseball team needs to wash before it starts making a profit. The team spent $75 setting up the car wash, and they are charging $5 per car for a wa The first step in modeling this situation is to track how much money the baseball team will take in. Write an equation to represent the amount of money collected in dollars, y, in terms of the number of cars washed, x. Ignore the setup cost. What is the area?6 mm5 mm3 mm13 mm8 mm9 mm convert degree into Radian that is 18 degree 12' g natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that natasha is one of the leaders Solve for 'x' in both of the following problems. Show all your work/explanations on your own paper and then submit a picture of your work and answers in the dropbox below. Which multicellular clade arose first in the history of life on Earth? View Available Hint(s) Which multicellular clade arose first in the history of life on Earth? Land plants Animalia Fungi Protista Solve equation show all steps what 2x-3x+5=18 Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.