Answer: a
Step-by-step explanation:
Every six powers of ten, the cycle repeats. In other words, a repeating decimal with a denominator of 7 can have a repeating cycle that is up to six digits long.
The repeating cycle of a repeating decimal for the rational number with a denominator of 7 can be determined by considering the factors of the denominator.
In this case, the denominator is 7, which is a prime number. The length of the repeating cycle can be determined by examining the powers of 10 modulo 7.
To find the length of the repeating cycle, we need to find the smallest positive integer "n" for which 10ⁿ - 1 is divisible by 7. In other words, we are looking for the smallest "n" such that 10ⁿ ≡ 1 (mod 7).
Let's calculate the powers of 10 modulo 7:
10¹ ≡ 3 (mod 7)
10² ≡ 2 (mod 7)
10³ ≡ 6 (mod 7)
10⁴ ≡ 4 (mod 7)
10⁵ ≡ 5 (mod 7)
10⁶ ≡ 1 (mod 7)
As you can see, the cycle repeats every 6 powers of 10. This means that the repeating cycle of a repeating decimal with a denominator of 7 can be up to six digits long.
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Part A
A sailor entered a race and made a round trip of 213.709 miles. What is 213.709 rounded to the nearest hundredth? Choose the number to complete the statement.
The estimate for the number of miles traveled is
Choose...
.
Part B
Which of the following statements explains how you should round 213.709?
A.
Since the digit in the hundreds place is less than 5, keep the digit in the hundredths place. Then drop the digits on the right.
B.
Since the digit in the hundredths place is less than 5, keep the digit in the tenths place. Then drop the digit in the hundredths and thousandths places.
C.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
D.
Since the digit in the hundredths place is less than 5, leave the digit in the hundredths place and drop all the numbers on the right.
The option C is correct.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
In the given statement is
A sailor entered a race and made a round trip of 213.709 miles. What is 213.709 rounded to the nearest hundredth?
and, Choose the number to complete the statement.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
The option C is correct.
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if f(x) = x^3, write a new function, g (x), that applies the following transformations
A reflection across the x-axis
A vertical stretch by a factor of 4
A reflection across the y-axis
A horizontal compression by a factor of 1/5
Your answer must begin with " g (x)= "
x
)
=
"
Answer:
g(x)= 0 or the factor of 0 is mine
im confused on this !
If I drove is 357.5 miles in 5 hours and 30 minutes how fast was I driving?
Answer:
65 Miles Per Hour
Step-by-step explanation:
357.5 divided by 5 1/2 equals 357 1/2 divided by 11/2, or 715/2 times 2/11 using reciprocals. Multiply and you get 1430/22 which simplifies down to 65. Therefore you were driving at 65 miles per hour
The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 730 homeless patients and no more than 1,000 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,600 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,900 per month. How many of each type of patient should it house in order to maximize profit?
Answer:
b
Step-by-step explanation:
Find the sum 6+4, 3/4, +, ( -2.5)
The required sum is 8.25
What is sum in mathematics?
A summation, also known as a sum, is the outcome of adding numbers or quantities arithmetically. A sum always has an even number of terms. There might be as few as two or as many as a hundred, thousand, or million phrases. Some sums have an unlimited number of terms.
[tex]6+4+\frac{3}{4}+(-2.5)[/tex]
[tex]= 10+\frac{3}{4} -2.5[/tex]
[tex]= \frac{40+3-10}{4}[/tex]
[tex]=\frac{33}{4}=8.25[/tex]
Hence the required sum is 8.25
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11+9k+6n
how many terms
I will mark brainliest
Answer:
The 1st one
Step-by-step explanation:
My mom is a teacher lol
look at the ordered pairs. (14,2) (12,-5) (13,0) (9,-4). is this relation a function
Answer:
Yes, it is!
Step-by-step explanation:
How to know if the ordered pairs is a function? Just look at the x values! If any of the x values repeat more than 1 time, then it is not a function. In this relation, none of the x values repeat more than 1 time, so this is a function!
Here are the ordered pairs on a graph (it passes the vertical line test):
Multiply and collect like terms (6d-1)(3d^2+2d-7)
Kurt Ross earns a 2% commission on the sale of $ 510, 00 home. What is his commission?
Answer:
1,020 if you meant 51,000
10,200 if you meant 510,000
8x = x² +4
The answer?
Answer: =4±23√
Step-by-step explanation:
Find the product. (2y - 6)2
The speed limit in Canada is 100km/hr. What is the value of this limit in mi/hr given 1mi = 1.609km?
Answer:
62.14 miles per hour
Answer: 100 km/h is equal to 62.14 mph
So, 100 km/h is equal to 62.14 miles per hour.
Answer:
62.15 mi/hr
Step-by-step explanation:
Given:
1 mile = 1.609 kmAs both speed limits are given "per hour", we only need to convert 100 km to miles. To do this, set up and solve a ratio for "miles to kilometers", where x is the number of miles to 100 km:
[tex]\implies \sf 1 : 1.609 = x : 100[/tex]
[tex]\implies \sf \dfrac{1}{1.609} = \dfrac{x}{100}[/tex]
[tex]\implies \sf \dfrac{1}{1.609} \cdot 100= x[/tex]
[tex]\implies \sf x= \dfrac{100}{1.609}[/tex]
[tex]\implies \sf x= 62.15040398...[/tex]
Therefore, 100 km/hr = 62.15 mi/hr (2 d.p.)
are used to label the quadrants.
what is solve for A K=AP/2
LITERAL EQUATION
The solution for A is given as A = 2K/P
According to the question we have been the formula to find the value of K which is given as follows:
K = AP/2
We need to find the formula to find the value of A from the given above formula. To find the formula we will solve the equation for A which is :
K = AP/2
multiplying both the sides by 2 we get,
K*2 = AP/2 *2
2K = AP
Now dividing both the sides by P we get,
2K/P = AP/P
2k/P = A
or, A = 2K/P
Hence the solution for A is given as A = 2K/P
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Hi can someone please help me with these!
Pam takes her truck in for basic service. The service agent says a few extra repairs are also needed, so Pam adds the cost of those repairs in her head, rounding to the nearest $10. The costs are as follows: Wheel alignment: $110 Transmission fluid flush: $75 Cabin air filter: $23 What is her total estimate for the repairs?
The total estimate for the repairs when Pam takes her truck in for basic service is $200.
How to illustrate the information?Based on the information given, the costs are as follows:
Wheel alignment: $110 = $100
Transmission fluid flush: $75 = $80
Cabin air filter: $23 = $20
Therefore, the total estimate for the repairs will be:
= $100 + $80 + $20
= $200
Therefore, the total estimate for the repairs when Pam takes her truck in for basic service is $200.
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2½ yards of fabric for $9.50
the ratio of red cars to blue cars in a parking lot was 5:3. If there was 40 red cars how many blue cars were there?
Answer:
24 blue cars
Step-by-step explanation:
40/5 = 8
8 x 3 = 24
For P ={10, 12, 13, 15), Q = {2, 6, 11), and R=(3, 6, 8, 11), find P U (Q n R).
Step-by-step explanation:
(Q n R) = {6, 11}
P U (Q n R) = {6, 10, 11, 12, 13, 15}
in the triangle below, z=
Answer:
Where's the triangle?
Step-by-step explanation:
Estimation Solve the equation. First estimate using the perfect square closest to 44. Then use a calculator.
g²=44
PLEASE HELP
Answer:
Step-by-step explanation:
g² = 44
[tex]\sqrt{g^{2} }[/tex]= [tex]\sqrt{44}[/tex]
g = 6.63
Good estimate: 6.5
REALLY NEED HELP ON THIS!!
Triangle MNO is formed by connecting the midpoints of the side of triangle JKL.
The measures of the interior angles of triangle JKL are shown. Find the measure of
LKNM. Figures not necessarily drawn to scale.
80°
54°
N
M
46°
K
Answer:
80*
Step-by-step explanation:
That would be the correct answer because that would be the accurate measure for the interior angle shown.
2. Error Analysis For the figure below, Adam was asked to draw all lines of reflection. His work is shown. What error did Adam make?
The vertical line is correct, but the horizontal line is not.
This is because we can reflect the left half over the vertical line to have it produce the right half, and vice versa.
Unfortunately, the top half is not the same as the bottom half. For instance, the metal part at the bottom is not found at the top. Also the top and bottom shapes don't perfectly match.
What are the ordered pairs of the solutions for this system of equations?
The ordered pairs of the solutions for this system of equations is a (-3,0) and the (3,6).
According to the statement
We have to find that the ordered pair of the solution of the equation.
So, For this purpose, we know that the
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
From the given information:
in the given graph there are the some intersecting points and the due to this graph the value of the y is 6 and the value of the x is a -3.
Then
After analyzing the graph we have to find the value of the another x and y.
We see that the parabola and the line intersect at the points -3 and the 6 of the different values.
Then the ordered pair becomes the
(-3,0) and the (3,6).
So, The ordered pairs of the solutions for this system of equations is a (-3,0) and the (3,6).
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Would you classify the number 55 as a perfect square, perfect cube, both, or neither? Explain.
Answer:
Neither because the number 55 squared is in between 7. (7*7=49) and 8. (8*8=64). When cubed, it is in between 3. (3*3*3=27) and 4. (4*4*4=64) Therefore, the number 55 cannot be perfectly squared or cubed. (You can put it in your own words)
Answer:neither
Step-by-step explanation:
because 55 is neither
K
Multiply.
(-2)(-1)(-6)
= [₂
6) = [
(-2)(-1)(-6)=
Step-by-step explanation:
I'm assuming you mean, (-2)(-1)(-6)
This will give (-2)(-1)= +2 (-)×(-) = +
(+2)×(-6) = -12
Frank camped and hiked for three days. He hiked around three of the lakes.
He estimated his hiking distance to be more than 35 miles but less than 40
miles. Which three lakes did Frank hike? explain your answer
a = 6.51
b = 8.74
c = 21.25
d = 18.68
e = 15.33
The three lakes that Frank walked were Lakes A, B, and C. This may be deduced from the distances between the lakes as well as the total distance that Frank traveled, which was more than 35 miles but less than 40 miles.
How do locate the lakes when hiking?You may determine which lakes Frank walked to by combining a total of three lakes from the set of lakes provided in the puzzle.
Assuming Frank hiked Lakes A, B, and C, the distance is;
= 6.51 + 8.74 + 21.25
= 36.5 miles
Lakes A, B, and D:
= 6.51 + 8.74 + 18.68
= 33.93 miles
Lakes A, B, and E:
= 6.51 + 8.74 + 15.33
= 30.58 miles
It can be observed that Lakes A, B, and C are the only ones that meet the requirement of having a distance of fewer than 40 miles but more than 35 miles.
The following questions should be asked next:
Lakes: a = 6.51
b = 8.74
c = 21.25
d = 18.68
e = 15.33
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Janet just graduated from college, has a job she's scheduled to begin in 3 months and has decided to treat herself to 6 weeks of travel across South America before she buckles down and starts working full-time. To do the trip, she's thinking of applying for a personal loan of $3500, and the bank she uses for her checking and savings account has offered her an interest rate of 24%. She has a goal of paying off the trip within two years. PLEASE HELP ASAP!!
3) By the time Janet pays off the loan, the total interest she would have paid is D. $941.17.
4) By the time Jane pays off the loan, the total cost of her tip is B. $4,441.17.
5) The equation to find the new balance after each month's payment is D. New balance = Previous balance - Total monthly payment.
How is the monthly payment computed?The monthly payments can be computed by first computing the total payments (future value of the loan). Then, the above figure is divided by the number of periods.
For instance, the total cost of Janet's trip is $4,441.17. The payments are made for 24 months. Dividing $4,441.17 by 24 gives $941.17.
Data and Calculations:N (# of periods) = 24 months (2 x 12)
I/Y (Interest per year) = 24%
PV (Present Value) = $3,500
FV (Future Value) = $0
Results:
PMT = $185.05
Sum of all periodic payments = $4,441.17 ($3,500 + $941.17)
Total Interest = $941.17
Thus, Janet would have spent $4,441.17 to obtain a loan of $3,500 for her trip at 24% interest with 24 months for repayment.
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