When 7/11 is written as a decimal, what is the sum of the first 20 digits after the decimal point? Pls Help

Answers

Answer 1

There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then

[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]

It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let

[tex]x = \dfrac7{11}[/tex]

Multiply the numerator and denominator by 9,

[tex]x = \dfrac{63}{99}[/tex]

It follows that

[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]

The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.

Answer 2

Answer:

90

Step-by-step explanation:

Using long division, we find that  Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90


Related Questions

Eric throws a biased coin 10 times. He gets 3 tails. Sue throw the same coin 50 times. She gets 20 tails. Aadi is going to throw the coin once.

1. Which one of the following statements is, correct about the probability of Aadi getting Tails?
A. Sue's estimate is best because she throws it 50 times.
B. Sue's estimate is best because she gets more Tails.
C. Sue's estimate is best because she throws it more times than Eric

2. Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write out your fraction in the form a/b.

Answers

Sue's estimate is best because she throws it more times than Eric. Regarding the probability of Aadi obtaining tails, Statement C is accurate.

What is probability?

The chances of an event occurring are defined by probability. Probability has several uses in games, and in business to create probability-based forecasts.

Ten biased coin throws are made by Eric. He is dealt 3 tails. Sue tosses a coin 50 times. I give her 20 tails.

Aadi will only toss the coin once. Regarding the probability of Aadi obtaining tails.

Sue's estimate is best because she throws it more times than Eric.

Hence option C is correct.

2)

An estimate for the likelihood that Aadi will receive tails using the findings of Eric and Sue. 3/20 will be the fraction of the form a/b.

The probability of the Aadi getting tails;

P(Aadi) = 3 / 360 = 1/120

P(Sue) = 20/50×36 = 1/90

Hence the fraction in the form of a/b willl be 4/3.

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At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equations represents p, the number of seashells that Pierre collected. O 3p+p-52 52+p-3p At the beach , Nardia collected triple the number of seashells that Pierre did . Together , they collected 52 seashells . Which equations represents p , the number of seashells that Pierre collected . O 3p + p - 52 52 + p - 3p​

Answers

Answer:

If Nardia is N and Pierre is P an equation that would represent this problem is 52-3n=p

Complete the steps 4/9 divided by 1/2

Answers

Answer: 0.88 (the 8 recurs)

Step-by-step explanation:

[tex]\frac{4}{9}[/tex]÷[tex]\frac{1}{2}[/tex]

[tex]\frac{4}{9}[/tex]×[tex]\frac{2}{1}[/tex]  (Then the the fraction should reciprocal so the values should shift to          the opposite side were 2 goes up and 1 goes down and the sign turns to the multiplication sign)

then u should multiply the two fractions which gives 8/9

next you should divide 8 by 9 which gives 0.88(the number eight is recurring which means that the number 8 keeps repeating no matter how many times you try to divide)

A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
(Answer is not 10 cents) Tried it

Answers

the answer is 5 cents because if the bat is a dollar more, then it the bat would be $1.05, and 0.05 + 1.05 = $1.10

you could also use the equation x + (x + 1) = 1.10 where x is the cost if the ball and x + 1 is the cost of the bat. x + x + 1 is the same as 2x + 1 = 1.10, and when solved x = 0.05.

options for 1 or two are not available but i got c= radical 125

Answers

Answer:

[tex]c=4 \sqrt{2}[/tex]

Step-by-step explanation:

Pythagoras Theorem

    [tex]a^2+b^2=c^2[/tex]

where:

a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangle

Given values:

a = 4b = 4

Substitute the given values into Pythagoras Theorem formula and solve for c:

[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies 4^2+4^2 & =c^2\\16+16 & =c^2\\32 & =c^2\\ \sqrt{c^2}& =\sqrt{32}\\ c & =\sqrt{16 \cdot 2}\\& = \sqrt{16}\sqrt{2}\\& =4\sqrt{2}\end{aligned}[/tex]

Therefore, the measure of the third side of the given right triangle is [tex]4 \sqrt{2}[/tex]

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In MODE, (second line), fix the number of decimal places to be 2. Then the slope and the y-intercept values of the LinReg line will round to the nearest hundredth. Find the LinReg line of best fit for the National Health Expenditures data. Then predict national health expenditures for 2010. (Hint: You may have to expand the calculator window to include the year 2010 on your screen.)

Answers

The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.

What is the equation of a line passing through two points?

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

In MODE, (second line), fix the number of decimal places to be 2.

Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.

(x₁, y₁) → (1997, 1093)

(x₂, y₂) → (2002, 1553)

Then we have

y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)

y – 1093 = [460  / 5] (x – 1997)

y – 1093 = 92 (x – 1997)

           y = 92x – 182631

If x = 2010, then the value of y will be

y = 92 × 2010 – 182631

y = 184920 – 192631

y = 2289

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help i am struggling

Answers

Choice D. Add exponents of the 7’s on top, and subtract from bottom exponents to get 7^4. Then same idea it would be 2^-4 so 1/ 2^4. But since multiplying by 7^4 it would go on top, getting 7^4 / 2^4, which is choice D.

Answer: it's D

Step-by-step explanation:

NEED HELP ASAP 1 HOUR LEFT

Answers

Using the vertex of a quadratic function, it is found that:

a) The revenue is maximized with 336 units.

b) The maximum revenue is of $56,448.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.

The demand function is given by:

p(x) = 336 - 0.5x.

Hence, the revenue function is:

R(x) = xp(x)

R(x) = -0.5x² + 336x.

Which has coefficients a = -0.5, b = 336.

Hence, the value of x that maximizes the revenue, and the maximum revenue, are given, respectively, as follows:

[tex]x_v = -\frac{336}{2(-0.5)} = 336[/tex][tex]y_v = -\frac{336^2 - 4(-0.5)(0)}{4(-0.5)} = 56448[/tex]

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In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?

Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.

s = Θ · r
r = Θ · s
s = Θ + r
r = Θ + s

Answers

The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

How to determine the arc length?

The attached image completes the question

The given parameters are:

Angle = ΘRadius = r

Since, the angle is in radians.

The arc length is calculated as:

Arc length = Angle * Radius

So, we have:

s = Θ * r

Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

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In a stadium, 1,000 tickets were sold. Children’s tickets cost $2.50 each and adults’ tickets cost $5.00 each. The revenue collected for the game was $4,000. How many children’s tickets were sold? How many adults’ tickets were sold?

Answers

Answer:

400 children tickets and 600 adult tickets.

Step-by-step explanation:

children tickets in total cost=400x2.50

                                             =1000

adult tickets in total cost=600x5.00

                                             =3000

total cost is 4000

Please Help!!!! This Sucks

Answers

Answer:

Step-by-step explanation:

Derive tan(A+B)+tan(A+B)- tan(A+B)+tan(A+B).​

Answers

Step-by-step explanation:

the answer will be zero 0


Which is equivalent to 80^1/4x

Answers

Answer:

x=20

Step-by-step explanation:

80^1/4x

or,80/4=x

or,20=x

•°•x=20

ans

a hyperbola centered at the origin has vertices PLEASE HELP QUICK

Answers

The equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0) is  [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

Given, that a hyperbola centred at the origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0)

What is hyperbola?

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The formula for a hyperbola centred at the origin is [tex]\frac{x^2}{a^2} -\frac{y^2}{b^2 } =1[/tex]

The vertices are located at (±a, 0), so we have that the value of a is [tex]\sqrt{61}[/tex].

The foci are located at (±c, 0), where [tex]c^2 = a^2 + b^2[/tex].

So if we have that [tex]c = \sqrt{98}[/tex], we can find the value of b:

[tex]98 = 61 + b^2[/tex]

⇒ [tex]b^2 = 37[/tex]

⇒ [tex]b = \sqrt{37}[/tex]

So, the formula for this hyperbola is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

Therefore, the equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0) is  [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

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If a varies directly as the square of b, and a = 4 when b = 3, find a when b = 2

Answers

Answer:

a = 46. Look down to find out more↓:

Step-by-step explanation:

a = kb²

4 = k(3)²

4 = k9

k = 4/9

a = 4/9(9²)

a = 4/9 (81)

a = 324/9

a = 36

please help me
i'll mark u as brainiest if u get it right

Answers

Answer: a) 46 minutes
               
b) 10:47

The basic knowledge for this is that 60 minutes = 1 hour

a) Question a asks for how long it took from a 10:34 bus from Mosley to reach Bamford. From the table you can see that the 10:34 bus reaches Bamford at 11:20. All you have to do is count from 10:34 to 11:20.
10:34 will become 11:00 at 10:60 right? Clock's generally don't show 10:60 but goes directly to 11:00 after 1 minute is passed at 10:59. So from 10:34 to 11:00, it takes 26 minutes. Remember the bus reaches at 11:20 so from 11:00 to 11:20, it takes 20 minutes. Now add them up:
26 minutes + 20 minutes = 46 minutes

Here you go! Total 46 minutes from Mosley to Bamford.

b) From question b, we can see that Trina did not ride the first bus or by any chance missed it because the bus left at 10:14 and she is at the station at 10:15. Now think it from your perspective! You missed the first bus and you are in a big rush. So to reach your destination as early as possible, you will obviously take the next earliest bus. The next bus is at 10:24 (Belton). So if we take the 10:24 bus in Belton, it reaches at 10:47 in Garton.


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Solve for x: 4(x + 2) = 3(x-2)

Answers

The answerrr is 18 for thisvprblme

Priya wants to sketch a graph of the polynomial f defined by f(x)=x^3+5x^2+2x-8. She knows f(1)=0, so she suspects that (x-1) could be a factor of x^3+5x^2+2x-8 and writes (x^3+5x^2+2x-8) = (x-1) (?x^2+?x+?) and draws a diagram.

1. Finish Priya's diagram
2. Write f(x) as the product of (x-1) and another factor.
3. Write f(x) as the product of three linear factors.
4. Make a sketch of y=f(x).

Answers

Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.

Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;

18 = 2 x 9

18 = 2 x 3 x 3

18 = 3 x 6

In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.

2. Now, to write f(x) as the product of (x-1) and another factor.

x³+5x²+2x-8 = (x-1)(x²-6x+8).

3. Now, to write f(x) as the product of three linear factors.

x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)

4. Look at the sketch below.

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Determine if the following scenarios are mutually exclusive or overlapping. Explain your reasoning.
1. You are taking a multiple choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.
2.You survey students in your school about what grade they are. Event A is the person is a senior. Event B is the person is a junior.

Answers

An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin.

What is an event in probability?

An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin. This experiment results in the coin landing 'heads' or 'tails.' These are the events that are associated with the experiment.

Scenario 1: You are taking a multiple-choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.

The two of the given events will overlap since there is a possibility that the correct answer is option D.

Scenario2: You survey students in your school about what grade they are in. Event A is the person is a senior. Event B is the person who is a junior.

The two of the given events are mutually exclusive events since a person can not be a senior and a junior at the same time.

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Two students are registered for the same class and attend independently of each other, student a 90% of the time and student b 70% of the time. the teacher remembers that on a given day at least one of them is in class. what is the probability that student a was in class that day

Answers

The probability of student A is 15/44

Given student A is 70% of time and student B is 60% of time

We need to find the probability of student A

Using formula of conditional probability is P(X/Y) = P(X and Y) / P(Y)

Here X = A and Y = A or B

Therefore,

P(A/A or B) = P(A and (A OR B) / P (A or B)

Now, There is none complement for at least 1

We know that Student A attends 70 % of time

So , his absence is 30% of the time .

Hence the probability of absence is 0.3

Now Considering B in the similar way

We get,

Probability of the absence is 0.4

They are both absent (0.3)(0.4)= 0.12

Here we can say that 12 % of time both are absent

So one or another present on that time is 88%

The probability of present of the time is 0.88

Now calculating the probability,

P(A/A or B) = P(A and (A OR B) / P (A or B)

= 0.3/0.88

= 30/88

= 15/44

Hence the Probability Of A is 15/44

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The histogram to the right represents the weights​ (in pounds) of members of a certain​ high-school math team.
How many team members are included in the​ histogram?

Answers

Answer:

The basic way to calculate the number of members is finding the area under the curve. The total members are 20

Step-by-step explanation:

The given graph shows that how many team members have a particular weight.

The first rectangle shows that 5 team members have a weight of 115kg.

The second rectangle shows that 3 team members have a weight of 115kg.

The third rectangle shows that 2 team members have a weight of 115kg.

The forth rectangle shows that 0 team members have a weight of 115kg.

The fifth rectangle shows that 3 team members have a weight of 115kg.

The sixth rectangle shows that 4 team members have a weight of 115kg.

The seventh rectangle shows that 3 team members have a weight of 115kg.

So, the total team members are = 5 + 3 + 2 + 0 + 3 + 4 + 3 = 20

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what is the answer??? so confused

Answers

Answer:

3  1/2

Step-by-step explanation:

Put '3' where 'y' is and compute :

[12 -3(3) ] / 2   + 3 [ (2(3)-4 )/3) =

   3/2              +   2  

    =   3  1/2

If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?

Answers

Answer:

26

Step-by-step explanation:

Define the variables:

2n = first even number2n + 2 = consecutive even number

Given information:

2 times the sum of two consecutive even numbers is greater than 94

Create an inequality from the defined variables and the given information:

⇒ 2(2n + 2n + 2) > 94

Solve the inequality:

⇒ 2(4n + 2) > 94

⇒ 8n + 4 > 94

⇒ 8n > 90

⇒ n > 11.25

Therefore:

2n > 22.52n + 2 > 24.5

As 2n and 2n+2 are even numbers:

smaller number (2n) ≥ 24larger number (2n + 2) ≥ 26

Therefore, the smallest possible value of the larger number is 26.

wonder woman made a reglangular fence around her invisable airplane so it would not get hurt by her dog. her fence was 4ft long, 2 ft wide, and 3 ft high. how much material did she use t make her fence

Answers

Answer:

36 ft^2

Step-by-step explanation:

Perimeter = 4 + 4 + 2 +2 = 12 feet

  12 feet x 3 feet high = 36 ft^2

If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml?

Answers

7.7278 g/ml is the most accurate density of the substance.

What is density?

It is define as the quantity per unit volume, unit area, or unit length.

i.e. the mass of a substance per unit volume.

Mathematically,

[tex]\rho =\frac{m}{v}[/tex]       ----- equation  (1)

Where,

p is the density

m is the mass

v is the volume

According to the question,

Mass = 27.82 grams  

Volume = 3.6 ml

By substituting the Value of m and v in equation 1.

[tex]\rho =\frac{27.82}{3.6}[/tex]

[tex]\rho = 7.7277777 g/ml[/tex]

Therefore,

The most accurate density of the substance in g/ml is  7.7277777 g/ml.

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3. Solve the following system of equations. 2v 3w = 16 2u + w = 4 v/6 - u/6 = 1​

Answers

Answer:

this is what i got


If c = 7, then the value of b is...

Answers

Answer:

3.5

Step-by-step explanation:

The triangle shown is a 30-60-90 special right triangle. All right triangles that have a 30-degree angle will be, but if needed you can use the equation: 180 - (90 + 30) = x, to find the missing angle.

Special Right Triangles

Special right triangles are useful because they allow us to easily find missing sides without having to use sin, cos, or tan. All special right triangles have formulas that can be used to find missing sides.

Formulas

30-60-90 triangles have 3 sides: the hypotenuse (c), the short leg (b), and the long leg (a).

The formulas are as follows:

c = 2bb = 0.5ca = b[tex]\sqrt{3}[/tex]

Solving for b

We are already given c, so the easiest way to find b is to use the formula b = 0.5c. Just plugin the c-value.

b = 0.5(7)

Once simplified the final answer is

b = 3.5

What are the solutions, if any, of the equation x2−25=−7?

Answers

Answer:

[tex]x=\pm3\sqrt{2}[/tex]

Step-by-step explanation:

1) Add 25 to both sides.

[tex]x^2 = -7 + 25[/tex]

2) Simplify -7 + 25 to 15.

[tex]x^2=18[/tex]

3) Take the square root of both sides.

[tex]x=\pm18[/tex]

4) Simplify [tex]\sqrt{18}[/tex] to [tex]3\sqrt{2}[/tex].

[tex]x=\pm3\sqrt{2}[/tex]

Which is a sum of cubes?

a3 + 18
a6 + 9
a9 + 16
a12 + 8

Answers

Answer:

a^12+8

Step-by-step explanation:

let's check all the expressions

1. a^3+18

here 18 is not a perfect cube.

2. a^6+9

here 9 is not a perfect cube.

3. a^9+16

here 16 is not a perfect cube.

4. a^16+8

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

(a^4)^3+2^3

Thus,  is a sum of cubes.

a^12+8

albert worked for 8 hours and earned $24. how much does albert earn for 24 hours

Answers

Answer:

$72

Step-by-step explanation:

Other Questions
If you click a hyperlink, your browser will: you plan to use a slingshot to launch a ball that has a mass of 0.025kg Which exchange of dialogue is formatted correctly? A. Dominic squinted suspiciously. "Why are you here?" he asked. "I don't need a reason," Jill said, walking past him. B. Dominic squinted suspiciously. "Why are you here?" he asked. "I don't need a reason," Jill said, walking past him. C. "Dominic squinted suspiciously. Why are you here? he asked. I don't need a reason, Jill said, walking past him." D. "Dominic squinted suspiciously. Why are you here? he asked." "I don't need a reason, Jill said, walking past him." Select all the correct answers.Read the third paragraph from the passage. A common misunderstanding among Americans is about the amount of money NASA receives from the U.S. government. NASA's budget has accounted for 0.5 percent of the total U.S. federal budget. That amounts to roughly $10 of an annual personal income tax going toward the best space program in the world. NASA accounts for 40 times less than what the federal government spends on the Department of Defense. Unfortunately, programs such as Project Constellation, which promised to return American astronauts to the moon, and ExoMars, which was designed to look for evidence of life on Mars and eventually land humans on Mars, have been put on hold due to budget cuts.The author uses this paragraph to develop which two claims?All the nations should come together in order to help NASA raise the necessary funds.Project Constellation and ExoMars have been deferred due to a shortage of funds.Collaboration with Russia to build the International Space Station resulted in the depletion of funds.The majority of the federal budget should be spent on NASA, as its work is more important than the Department of Defense.The U.S. Department of Defense is the strongest in the world, as it uses the funds that should actually be used by NASA.The amount of money spent on NASA is much less than the amount of money spent on the Department of Defense. Which of the following statements is true?Readers can use a word's orthography to help them determine its meaning.Prefixes and suffixes can change the meaning and part of speech of a word.The denotation of a word is different from its connotation.The subject and the verb of a sentence must agree in number.All of the choices are correct. What is the degree of the monomial?8xyz4 need help figuring out the answers What is the status in DAX Studio after you add a patient's name to a note?REMOVEDACTIVEIn ProgressAvailable Read the following sentence: Because he had such a logical mind, Bernie usually had autilitarian solution that was reasonable and worked for every problem. Use context clues to determine which of the following words would best replace the word utilitarian.practicalfoolishAll of the choices are correct.clearGunaware tick the correct answerI have been waiting 4'On clock What impact does the church have on a visitor? If c = 16, solve for b Find the area.help pls Narrowing of the coronary arteries caused by a buildup of fatty deposits is called: a farmer uses 1/6 of his land to plant pineapples, 5/9 to plant durians and the remaining 48.5 acres to plant vegetables. calculate the area of land used to plant pineapples and durians what were the Major geologic process of the precambrian and Paleozoic eras in the horn of Africa? Which is the United States largest transfer payment program?A.welfareB.MedicareC.food stampsD.Social Security Identify the structure below: A , B, and C The involvement of the United States in the ______ and ______ resulted in _______ . your message, you will describe your typical daily routine and responsibilities as well as another teenager or child in your house. (brother, sister, cousin, niece, etc.). Describe at least two activities you do in your daily routine using reflexive verbs and at least two activities that the other person does. You will also include at least two chores you do and at least two chores the other person does and how often you do them.