Let $x=(0.\overline{6})\cdot (0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answers
The sum of the first 15 digits after the decimal point when writing out the value of $x$ is 32.
To find the sum of the first 15 digits after the decimal point when writing out the value of $x=(0.\overline{6})\cdot (0.\overline{60})$, we can first determine the value of $x$ and then extract the desired digits.
Let's calculate the value of $x$:
$x = (0.\overline{6})\cdot (0.\overline{60})$
To simplify this expression, we can consider $0.\overline{6}$ as $0.\overline{6} = \frac{6}{9} = \frac{2}{3}$, and $0.\overline{60}$ as $0.\overline{60} = \frac{60}{99} = \frac{20}{33}$.
Now, we can substitute these values into the equation:
$x = \left(\frac{2}{3}\right) \cdot \left(\frac{20}{33}\right)$
$x = \frac{40}{99}$
The value of $x$ is $\frac{40}{99}$.
To determine the sum of the first 15 digits after the decimal point, we need to convert $\frac{40}{99}$ into a decimal and extract the desired digits.
When we divide 40 by 99, the result is approximately 0.404040...
The decimal representation of $\frac{40}{99}$ repeats the block 40 infinitely. Therefore, the first 15 digits after the decimal point will be 404040404040404.
Now, let's calculate the sum of these digits:
4 + 0 + 4 + 0 + 4 + 0 + 4 + 0 + 4 + 0 + 4 + 0 + 4 + 0 + 4 = 32
The sum of the first 15 digits after the decimal point when writing out the value of $x$ is 32.
Learn more about decimal point here
https://brainly.com/question/26090574
#SPJ11
Related Questions
How much would it cost to buy a sheet of 5 m by 2 m which cost E90 to a 4 m by 75 cm
Answers
It costs £33.3 to buy a sheet of 5 m by 2 m
Here, the cost of 4 m by 75 m paper is £90
Let us assume that A represents the area of the paper of dimension 4 m by 75 m
Using the formula for the area of rectangle,
A = 4 × 75
A = 300 m²
The cost for the paper of unit area would be,
c = 300/90
c = £3.33 per unit square
The area of the paper with dimension 5 m by 2 m is:
A₂ = 5 × 2
A₂ = 10 m²
So using unitary method, the cost for this sheet would be,
C₂ = 3.33 × A₂
C₂ = 3.33 × 10
C₂ = £33.3
Therefore, the required cost = £33.3
Learn more about the unitary method here:
https://brainly.com/question/28276953
#SPJ4
Which of the following are assumptions underlying the simple linear regression model y = Bo B1x e? Check all that apply The variance of the error term e varies for differing values of x. The error term is a random variable with an expected value of zero. The error term is normally distributed. The error term E follows a chi-square distribution.
Answers
The error term is a random variable with an expected value of zero.2. The error term is normally distributed
The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.
The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.
Learn more about random variable
https://brainly.com/question/30789758
#SPJ11
1. a) Starting with the second order rate law [] / = −[]
2 derive the integrated rate law in the form below: [] = []0 /
1+ []0 (10 Marks)
b) Explain how
Answers
a) To derive the integrated rate law from the second order rate law, we start with the differential rate equation:
\[ \frac{d[A]}{dt} = -k[A]^2 \]
where \([A]\) represents the concentration of the reactant A and \(k\) is the rate constant.
To integrate this equation, we separate the variables and integrate both sides:
\[ \int \frac{d[A]}{[A]^2} = -\int k dt \]
This gives us:
\[ -\frac{1}{[A]} = -kt + C \]
where \(C\) is the integration constant. We can rearrange this equation to isolate \([A]\):
\[ [A] = \frac{1}{kt + C} \]
To determine the value of the integration constant \(C\), we use the initial condition \([A] = [A]_0\) at \(t = 0\). Substituting these values into the equation, we get:
\[ [A]_0 = \frac{1}{C} \]
Solving for \(C\), we find:
\[ C = \frac{1}{[A]_0} \]
Substituting this value back into the equation, we obtain the integrated rate law:
\[ [A] = \frac{1}{kt + \frac{1}{[A]_0}} \]
b) The integrated rate law describes the relationship between the concentration of a reactant and time in a chemical reaction. It provides a mathematical expression that allows us to determine the concentration of the reactant at any given time, given the initial concentration and rate constant.
In the derived integrated rate law, we observe that the concentration of the reactant \([A]\) decreases with time (\(t\)). As time progresses, the denominator \(kt + \frac{1}{[A]_0}\) increases, leading to a decrease in the concentration. This is consistent with the second order rate law, where the rate of the reaction is directly proportional to the square of the reactant concentration.
The integrated rate law also highlights the inverse relationship between the concentration of the reactant and time. As the denominator increases, the concentration decreases. This relationship is important in understanding the kinetics of a chemical reaction and can be used to determine reaction orders and rate constants through experimental data analysis.
By deriving the integrated rate law, we can gain insights into the behavior of chemical reactions and make predictions about the concentration of reactants at different time points. This information is valuable in various fields, including chemical engineering, pharmaceuticals, and environmental science, as it allows for the optimization and control of chemical processes.
To know more about rate, refer here:
https://brainly.com/question/25565101
#SPJ11
Solve system of equations by the substitution method.
Chris has $3.85 in dimes and quarters. There are 25 coins in all. How many of each type of coin does he have?
Answers
Solving a system of equations we can see that he has 9 quarters and 16 dimes.
How to solve the system of equations?Let's define the variables:
x = number of dimes
y = number of quarters.
There are 25 coins, so:
x + y = 25
The value is $3.85, so:
x*0.10 + y*0.25 = 3.85
So the system of equations is:
x + y = 25
x*0.10 + y*0.25 = 3.85
We can isolate x on the first equation to get:
x = 25 - y
Replacing that in the other one we get:
(25 -y)*0.10 + y*0.25 = 3.85
2.5 + y*0.15 = 3.85
y = (3.85 - 2.5)/0.15
y = 9
Then the other 16 coins are dimes.
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
In ΔABC, BD is perpendicular to AC as shown in the figure.
Which equations are true?
Answers
Answer:
2nd, 3rd, and 6th option are correct
Step-by-step explanation:
using a²+b²=c² those are the obly that meet the criteria (im pretty sure)
In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.
What is a right angle triangle?
A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.
Given that,
ABC is a right angle triangle.
And BD is perpendicular to AC.
To show the equations which are true,
Use Pythagorean theorem,
(Hypotenuse)² = (base)² + (height)²
In triangle ABC,
AC² = AB² + BC²
In triangle ABD,
(AB)² = AD² + BD²
And in triangle BCD,
BC² = CD² + BD²
Therefore, option (2), (3) and (6) are correct.
To know more about Triangle on :
https://brainly.com/question/2773823
#SPJ2
I WILL GIVE BRAINLIEST I NEED HELP NOW!!! I PROMISEThe table shows the relationship “Kevin read 35 pages per hour.”
Hours (h)
Pages (p)
1
35
2
70
3
105
4
140
5
175
Which statements are correct? Check all that apply.
The variable h is the independent variable.
The variable p is the independent variable.
The number of pages read increases as the amount of time decreases.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
The variable h is the dependent variable.
The more pages that are read, the less time it takes.
Answers
Answer:
The correct answers are:
The variable p is the independent variable.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
Step-by-step explanation: Hope this helps :)))
These two statements are correct and applicable
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
What is a variable?"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."
What is a dependent variable?"A dependent variable is the variable that changes as a result of the independent variable manipulation."
What is a linear graph?"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"
We have,
Kelvin read 35 pages per hour
According to the question,
Number of hours increasing, number of pages also increasing
∵ The table data shows linear graph
We can clearly say that from a line graph definition,
These two are correct and applicable to Kelvin's situation
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
Learn more about Line graph and variable here
https://brainly.com/question/20106471
https://brainly.com/question/20291071
#SPJ2
Algebra, Solve for x
Answers
Answer:
-6
Step-by-step explanation:
3-6x=-11*3
-6x=33-3
-6x=30
x= 30/6
x=-6
PLEASE HELP ME! MY HOME WORK IS DUE IN AN HOUR!!!
The right triangle below has legs of length a=10 and b=7. The hypotenuse has length c. (look at the image)
Part 1: compute the total combined area of the four triangles.
Part 2: Compute the area of the large (outer) square.
Part 3: Using your answers from parts 1 and 2, find the area of the small inner square.
Part 4: We are given the side lengths a=10 and b=7. Compute a²+b².
Part 5: use , or = to complete the statement below.
Answers
Part 1
The area of one triangle is \((1/2)(7)(10)=35\). Multiplying this by 4 yields \(\boxed{140}\).
Part 2
\((10+7)^2=\boxed{289}\)
Part 3
\(289-140=\boxed{149}\)
Part 4
\(10^2+7^2=\boxed{149}\)
Part 5
The statement is missing.
Which statistical measurement informs a CTRS about how well the assessment results compare to what is being measured?A.Equivalent-forms reliabilityB.Criterion-related validityC.Test-retest reliabilityD.Construct validity
Answers
The statistical measurement that informs a CTRS about how well the assessment results compare to what is being measured is Construct validity.
Construct validity assesses how well the assessment measures the intended construct or trait, and compares the results to other tests or measures of the same construct to determine how accurate and reliable the assessment is.
To know more about statistical measurement visit:
https://brainly.com/question/31036349
#SPJ11
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year
Work out the value of her investment after 4 years. Give your answer to the nearest penny. GUYS PLLS SAVE MEEE
Answers
The formula for this is:
Initial amount x multiplier^years
So that is £8000 x 1.028^4 = £8934.33938
That is £8934.34
_____________ are created by imaginary lines that intersect the body into parts.
Answers
Answer:
Step-by-step explanation:
Anatomical planes are created by imaginary lines that intersect the body into parts
In the equation shown, what is the value of n?
9^7/9^n=9^2
PLEASE HELP
Answers
Answer:
n=5
Step-by-step explanation:
All of the bases are 9 so you can set the exponents equal to each other.
Exponents in a fraction mean subtraction so 7-n = 2
-n=-5
n=5
Plsssss answerrr
Directions if l || m solve for x and y
Answers
Answer:
x = 11
y = 3
Step-by-step explanation:
Okay so we know that l is parallel to m. We also know that (9x + 25) and (13x - 19) are the same because they are corresponding angles. So to find x just set them equal to each other and solve.
(9x + 25) = (13x - 19)
-9 -9
---------------------
25 = 4x - 19
+19 +19
-----------------
44 = 4x divide both sides by 4 and x equals 11
Now, we know that a straight line equals 180º so we just plug x into the first equation, and set both equations to equal 180. It should look like
(13 x 11 - 19) + (17y + 5) = 180
13 x 11 = 143
(143 - 19) + (17y + 5) = 180
143 - 19 = 124 + 5 = 129
129 + 17y = 180
-129 -129
17y = 51
Divide by 17 from both sides and y = 3
Answer:
x = 11 and y = 3
Step-by-step explanation:
(13x - 19) and (9x + 25) are corresponding angles and congruent, thus
13x - 19 = 9x + 25 ( subtract 9x from both sides )
4x - 19 = 25 ( add 19 to both sides )
4x = 44 ( divide both sides by 4 )
x = 11
Then
13x - 19 = 13(11) - 19 = 143 - 19 = 124
(17y + 5) and (13x - 19) are adjacent angles and are supplementary, thus
17y + 5 + 124 = 180, that is
17y + 129 = 180 ( subtract 129 from both sides )
17y = 51 ( divide both sides by 17 )
y = 3
WILL GIVE BRAINLIEST + 100 PTS
The mean of four positive integers is 5. The median of the four integers is 6.
What is the mean of the largest and smallest of the integers?
Answers
Answer:
4
Step-by-step explanation:
(b + c)/2 = 6
b + c = 12
(a + b + c + d)/4 = 5
(a + 12 + d) = 20
a + d = 8
Hence,
the sum of the largest and smallest is 8. The mean has to be 8/2 = 4.
Hope this helps and be sure to mark this as brainliest! :)
We know that the median of the four integers is 6, which means that b and c must both be 6.
We also know that the mean of the four integers is 5, so:
(a + b + c + d) / 4 = 5
Substituting in b and c, we get:
(a + 6 + 6 + d) / 4 = 5
(a + d + 12) / 4 = 5
a + d + 12 = 20
a + d = 8
So the sum of the largest and smallest integers is a + d, which we know is 8.
To find their mean, we divide by 2:
(a + d) / 2 = 8/2 = 4
Therefore, the mean of the largest and smallest of the integers is 4.
plz help im bad at this type of math
Answers
2x + 28 = 24 + x
2x - x = 24 - 28
x = -4
DF = x + 14
= (-4) + 14
= 10
Find the value of BD.
Answers
if you divide 18 by the number of line marks you have between A-D than u get 6. so do 27 divided by 6 & get 4.5 - and then count the line marks between B-D which is 4 and multiple 4x4.5=18 :)
it takes a river 4.5 hours downriver to get from port a to port b. The return journey takes 6.3 hours. The river flows at 40 minutes per minute. What is the distance between the two ports
Answers
Answer:
Step-by-step explanation:
you gotta multiply the mins which is 40 by 60 which is 2, 400 meters per hour
What is the solution to 3x + 30+ I= 10 + 2 + 5x + 2? O 6 018 9/2
Answers
Answer:
x=8.5
Step-by-step explanation:
3x+31=14+5x
17=2x
x=8.5
choose an appropriate procedure. for each of the following, indicate whether you would use a hypothesis test or a confidence interval. then state hypotheses if you would use a hypothesis test, or indicate the parameter(s) using correct notation if you would use a confidence interval. you do not need to carry out any procedures or define the parameters.
Answers
It involves setting up null and alternative hypotheses and testing the evidence against the null hypothesis.
When would you choose to use a hypothesis test instead of a confidence interval?To determine whether to use a hypothesis test or a confidence interval, we need to consider the goal of the analysis. A hypothesis test is appropriate when we want to make a conclusion about a population based on sample data.
It involves setting up null and alternative hypotheses and testing the evidence against the null hypothesis. On the other hand, a confidence interval is used to estimate an unknown parameter of a population.
It provides a range of plausible values for the parameter with a specified level of confidence. Thus, if we are interested in making a conclusion or testing a claim about a population, we would use a hypothesis test.
If our objective is to estimate an unknown parameter, we would employ a confidence interval and state the parameter using the correct notation.
Learn more about hypothesis
brainly.com/question/19263925
#SPJ11
First consider 100% what is the 100% of 40
Answers
Answer:
Step-by-step explanation:
100% means all of 40.
So 100% of 40 is 40
Answer:
40
Step-by-step explanation:
Of means Multiply.
Multiply.
100% * 40 = 40
~I hope I helped you! :)~
Find the missing value.
Hint: Use the number line to find the missing value.
—9+
--
—3
主
-15
-10
-5
0
5
10
15
Answers
Answer:
-9 + 6 = -3
Step-by-step explanation:
The Number Line
The original number -9 is located as the red dot in the number line as shown in the figure below.
To move to the number -3 (as a blue dot) we must jump right 6 numbers. Thus, this is the number that must be filling the box.
-9 + 6 = -3
9t + 21t - 8
It needs to be factored
Answers
I think this is the answer 2(15t−4)
But I don’t think I did it right
Algebra 1
1.1 Evaluating Expressions
Evaluate each using the values given.
1) z−5+ x; use x = 1, and z = -3
Answers
Evaluating Expressions-
z−5+ x= -7
x = 1, and z = -3
z−5+ x=-3 + (-5) + 1
= -3-5+1=-7
to assess an algebraic expression way to find the price of the expression while the variable is changed by using a given range.
to evaluating expression, we replacement the given range for the variable within the expression and then simplify the expression the use of the order of operations
What does “Evaluating Expressions” suggest?
Simplification of expressions can be performed with the help of operations’ order. It consists of changing the variable to discover the expression’s fee. The given number is substituted to evaluate expressions. After this, one needs to simplify it primarily based at the order of the operations
To learn more about Evaluating Expressions visit , https://brainly.com/question/25197597
#SPJ9
Instructions: Interpret the function given in the context ofthe real-world situation described to answer the question.Nichole bought a new car. The depreciation equation isgiven by f(x) = 27,000(.86), where a representsthe number of years since the purchase of the car, andf(x) represents the value of the car. By what percentdoes Nichole's car depreciate each year?%
Answers
The depreciation equation is given by
\(f(x)=27000(0.86^x)\)where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have
\(\text{ initial value = f\lparen0\rparen=27000}\)After one year, the car value corresponds to x=1, that is,
\(\text{ after 1 year = f\lparen1\rparen=27000\lparen0.86}\rparen^1\text{=27000}\times0.86=\text{23220}\)Now, let's find the depreciation percentage by means of a rule of three:
\(\begin{gathered} 2700\text{ ----- 100 \%} \\ 23220\text{ ------- x} \end{gathered}\)so we have
\(x=\frac{23220\times100}{27000}=86\text{ \%}\)So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year
Will spent $15 for 12 pounds of granola. What is his unit rate in dollars per pound?
Answers
Answer:
1.25
Step-by-step explanation:
to find the unit rate you have to find out how much one pound will be so you divide 15 by 12 and you get 1.25
Please Help 50 POINTS!!
Answers
Answer:
D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)
Step-by-step explanation:
hope this helps
Answer: D has the largest perimeter
Step-by-step explanation:
The top numbers of fractions describe the vertex and the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.
A.
P = 2(11) + 2(3)
P = 22+6
P=28
B.
P = 2(4) + 2(9)
p = 8 +18
P = 26
C.
P = 2(5) + 2(9)
P = 10 +18
P = 28
D.
P = 2(8) + 2(7)
P = 16 +14
P = 30
A backpack that normally sells for $39 is on sale for $25. Find the
percent of change.
Answers
Answer: To find the discount, simply multiply the original selling price by the %discount:
ie: 39 x 33/100= $12.87
So, the discount is $12.87.
Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:
ie: 39- 12. 87= 26.13
So, the sale price is $26.13
the sum of two numbers is 495. the one digit of one thte numbers is you cross off the zero the resulting number will eqal the other number what are the numbers
Answers
The two numbers whose sum is 495 and follows the required conditions are 450 and 45.
Let the two numbers be "AB0" and "AB," where A and B are digits, and 0 represents a zero.
The sum of the two numbers is equal to 495.
The last digit of one of the numbers is zero, which means the first number is a multiple of 10, so we can rewrite it as 10x.
If you cross off the zero from the first number, you get the second number, so the second number is AB.
Now, let's substitute the values into the equation:
10x + x = 495
Now, add the like terms, and we get,
11x = 495
Divide both sides by 11, and we get,
x = 495/11
x = 45
And, 45 times 10 is 450.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ12
The complete question:
The sum of the two numbers is equal to 495.
The last digit of one of them is zero.
If you cross the zero off the first number you will get the second.
What are the numbers?
Complete the proof that angle XYZ is congruent to angle WXY.
Answers
Answer:
Step-by-step explanation:
They are the same angle in the obtuse triangle and same points but mixed up proof: you can highlight the lines and make points for the letters w x and y hope this helps :)
*97 POINTS*
Use the numerals representing cardinalities in the Venn diagram, shown on the right, to give the cardinality of the set
A' ∩ B' ∩ C. '
n(A' ∩ B' ∩ C')= ___________
Answers
Answer:
19
Step-by-step explanation:
A' represents everything out A
B' represents everything out B
C' represents everything out C
So only the outside is left hope this helps