1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oxana [17]
1 year ago
12

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

Mathematics
2 answers:
FromTheMoon [43]1 year ago
8 0

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

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}

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

x = \dfrac7{11}

Multiply the numerator and denominator by 9,

x = \dfrac{63}{99}

It follows that

x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots

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.

Svetlanka [38]1 year ago
5 0

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

You might be interested in
Which is better 9.95 for 30oz of coffee or 3.50 for 12oz of coffee
MaRussiya [10]

Answer:

9.95 for 30oz

Step-by-step explanation:

30/9.95 = 3.02

12/3.5 = 3.43

7 0
2 years ago
The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean
Elden [556K]

Answer:

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

Step-by-step explanation:

Data given and notation  

\bar X=3.8 represent the sample mean

s=0.5 represent the sample standard deviation for the sample  

n=15 sample size  

\mu_o =4 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:  

Null hypothesis:\mu \geq 68  

Alternative hypothesis:\mu < 4  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

3 0
3 years ago
In a right triangle, one leg is 20 cm and the hypotenuse is 30 cm. To the nearest hundredth of a cm, find the length of the miss
max2010maxim [7]

Answer:

Step-by-step explanation:

Use Pythagoras’ theorem

square of hypotenuse = sum of squares of two other sides

let the missing side be d

30^2 = 20^2 + d^2

600 = 400 + d^2

d^2 = 200

d = square root of 200

d = 14.142 cm

3 0
3 years ago
Read 2 more answers
Ryan needs $100 for a new bike. He already has $28 and will make $12 per day working for his grandfather. Write an inequality to
bezimeni [28]

Answer:

100 ≥ 12x + 28

Step-by-step explanation:

He needs $100 for the new bike but already has the $28 so you also have to add 12x because thats what you need to find. X represents the amount of days he has to work.

3 0
3 years ago
If ΔRED ≅ ΔTAN, then which of the following statements is not true? RE ≅ TA ∠E ≅ ∠A RD≅ TA ∠D ≅ ∠N
Assoli18 [71]

Answer:

RD≅ TA

Step-by-step explanation:

RD≅ TA is not true statement as they are not corresponding sides.

4 0
3 years ago
Other questions:
  • The shed is filled with sawdust whose density (kg/m3) at any point is proportional to the distance of that point from the floor.
    8·1 answer
  • What is the value of f(4) if f(x) = 2x?<br> A. 2<br> B. 6<br> C. 8<br> D. 10
    11·1 answer
  • 5/4 gallons of water fill 5/6 of a bucket how many gallons of water fill the entire bucket
    15·1 answer
  • Bruce weighs 12 pounds less than three times what Dylan weighs. Write an expression for Bruce's weight in terms of Dylan's weigh
    9·1 answer
  • Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least
    11·1 answer
  • Solve the following equation for a. Be sure to take into account whether a letter is
    10·1 answer
  • The coefficients of a, b, and c in the following quadratic equation are a = 4, b = 4, and c = -1:
    13·1 answer
  • Find the missing side
    8·1 answer
  • Which is equivalent to 2 (t - 4) + 1?
    12·2 answers
  • Roots of Quadratics 50 PTS!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!