Answer:
Step-by-step explanation:
Let n=2α⋅5β⋅m , where gcd(m,10)=1 . Then, the decimal expansion of 1n is of the form
0.a1…akak+1…ak+ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(1) ,
where k=max{α,β} and ℓ is the least positive integer for which m∣(10ℓ−1) . In other words, ℓ is the order of 10 in the multiplicative group of units modulo m . So ℓ∣ϕ(m) by Lagrange's theorem.
In particular, if gcd(n,10)=1 , then α=β=k=0 , m=n , and
1n=0.a1…aℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(2)
Therefore, we know that
117=0.a1…aℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(3)
Here ℓ is the least positive integer for which 17 divides 9…9ℓtimes , and we know that ℓ divides ϕ(17)=16 .
Successively squaring 10 modulo 17 gives
102≡−2(mod17),104≡4(mod17),108≡−1(mod17),1016≡1(mod17) .
So ℓ=16 in expansion (3) .
In fact,
a1…a16×17=1016–1.
a1…a8+a9…a16=108−1 .
The first fact has nothing to do with the denominator n being prime. The second fact has everything to do with n being prime, and was discovered by E. Midy in 1836 .
On Saturday 4 groups of people went to the restaurant at the ski resort. Each group had 5 people in it. Everyone ordered a cup of hot chocolate. Rebecca,Malaki,and Jeffery each ordered an extra cups of hot chocolate.how many many cups of chocolate did the people drink that day?
Answer:
23
Step-by-step explanation:
total number of people at the restaurant = number of groups x total number of people in the groups
4 x 5 = 20
20 people ordered hot chocolate
3 people ordered an extra cup of hot chocolate.
The total number of hot chocolate ordered = 20 + 3 = 23
what is the value of 4(a+b) when a=2 and b=7
Answer: 4x2=8
4x7=28 the full answer should be 144 since 28+8 =36 a 4x36 = 144
Step-by-step explanation:
KatyDid Clothes has a $120 million (face value) 25-year bond issue selling for 103 percent of par that carries a coupon rate of 9 percent, paid semiannually.
Answer:
8.704%
Step-by-step explanation:
The computation of the before cost of debt is as follows
Given that
Future value = $100
Present value = $103
NPER = 25 × 2 = 50
PMT = $100 × 9% ÷ 2 = $4.5
The formula is presented below:
= -RATE(NPER;PMT;PV;FV;TYPE)
After applying the above formula, the rate is 4.3518%
Yearly rate is
= 4.3518% ×2
= 8.704%
Can you help me plz? I'll mark brainilest
Solve for u.
11u = -22
Simplify your answer as much as possible. <3
u = ???
Answer:
u=-2
Step-by-step explanation:
Let's solve your equation step-by-step.
11u=−22
Step 1: Divide both sides by 11.
11u
11
=
−22
11
u=−2
Answer:
u=−2
Help me pls))))
When you show a friend your idea for an art project, he says the idea is too superficial. What can you do to fix this?
A) Strengthen and lengthen your research process.
B)Abandon the idea all together.
C)Add another topic to your original topic.
D) Ignore your friend and create the artwork anyway
HELP ME OUT GUYS ILY ALL AND I WILL GIVE BRAINLIEST
A = area of triangle + area of rectangular + half of the circle area
_________________________________
triangle area = 1/2 × base × height
triangle area = 1/2 × 3 × 5 = 15/2 = 7.50
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆
rectangular area = length × width
rectangular area = 6 × 5 = 30
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆
circle half area = 1/2 × pi × radius^2
circle half area = 1/2 × 3.14 × 3^2
circle half area = 1.57 × 9
circle half area = 14.13
_________________________________
A = 7.50 + 30 + 14.13
A = 51.63 m^2
what is 136 over 20 x 96 over 20?
Answer:
32.64
Step-by-step explanation:
136/20*96/20=32.64
A computer originally priced at $850 is on sale for 15% off. What is the sale price of the computer?
Answer:
Sale price: $722.50
Step-by-step explanation:
Subtract 15% from 100%, obtaining 85%. The computer is sold for 85% off.
Converting this 85% to a mixed decimal, we get 0.85, and then we multiply the original price ($850) by this 0.85: 0.85($850) = $722.50
if 123 and x are in proportion find the value of x
1:2=3:x
1/2=3/x
1×x=3×2
x=6
Meagan and jake both live on the same street that the librarian is on.Megan lives 3.5 blicks north of the library,and jake lives 4.5 blocks south of the library.How many blpcks apart do jake and meagan live.
Answer:
8 blocks
Step-by-step explanation:
As the north direction is upwards and the south direction is downwards the total distance between the two people 's (Megan and Jake) houses will be obtained by adding their distances from the library which is in the middle as shown in the diagram.
Hence total distance between the two houses= 3.5 + 4.5= 8 blocks
Jake and Meagan live 8 blocks apart.
Which expression could be used to evaluate the expression below?
Answer:
Step-by-step explanation:
Is there supposed to be a picture
There are 12 turtles on a log, and 9 of those turtles are green. What fraction
of the turtles are green?
Answer:
75%
Step-by-step explanation:
Take 9/12 and multiply it by 100 and you get the percentage of the turtles that are green.
What is the quotient of 1/2 divided 3
Answer:
1/6
Step-by-step explanation:
the answer is 1/10 or .1
(13x-26) (5x+8) PLEASE HELP
Answer: X= 11
Step-by-step explanation: 13x-26 and 5x+8 are Linear Pairs which are supplementary. 13x-26+5x+8 is equal to 18x-18=180. 18x=198 and then X=11
Which statement is best supported by the information in the box plots?
Answer: A
Step-by-step explanation:
Answer:
It is A
Step-by-step explanation:
The x - coordinate of A' is _____
. The y - coordinate of A' is _____
Answer:
(-3, 2)
Step-by-step explanation:
Since you are reflecting over the y-axis (the vertical axis), you are flipping the figure over to the left. As a result, you are going over to -3 and up to 2
Answer:
A' is at (-3, 2)
Step-by-step explanation:
point stays 3 units away from the x-axis and 2 units above the y-axis
Observe os pontos Z, Y, W, X e V marcados na reta numérica abaixo.
M120566H6
Desses pontos, o que melhor representa a localização do número irracional 14−−√ é o
Z.
Y.
W.
X.
V.
Y
A raiz quadrada de 14 seria 3.74165738677 ou 3.7
Arredondamos para 4 já q 7 é próximo de 10
16. Geography If a ship sailed due south from Iceland to Antarctica, it would sail
through an angle of rotation of about 140° around Earth's center. Find this measure in
radians. Then, using 3960 miles for Earth's radius, find how far the ship would travel.
Answer:
9674.28 miles
Step-by-step explanation:
From the above question, we are given:
Central angle = 140°
Radius = 3960 miles
We are to solve for the distance = Arc length
The formula for Arc length when your central angle is in radians
r × θ
θ = 140°
Converting 140° to radians
140° × π/180 = 2.443rad
Hence,
3960 × 2.443 rad
= 9674.28 miles
The ship would travel 9674.28 miles.
Alex was thinking of a number. Alex doubles it and gets an answer of 16.9. What was the original number?
Answer:
8.45
Step-by-step explanation:
Doubling a number is the same as multiplying by 2, so to go back to the original number you divide 16.9 by 2
Find the circumference of a circle with a radius of 4.4 inches. Use 3.14 for pie. Round to the nearest tenth if necessary. Please provide steps.
Answer:
2×3.14×4.4
27.62 is the answer
Below are two images with scale copies of each other. Determine the scale factor for each of the following:
ASAP HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!
Answer:
enlargement, greater than one
Step-by-step explanation:
it got bigger
11. What is the positive solution to this equation?
4x2+ 12 x= 28
Answer:
x = sqrt(37)/2 - 3/2
approximately 1.54
Step-by-step explanation:
Solve for x over the real numbers:
4 x^2 + 12 x = 28
Divide both sides by 4:
x^2 + 3 x = 7
Add 9/4 to both sides:
x^2 + 3 x + 9/4 = 37/4
Write the left hand side as a square:
(x + 3/2)^2 = 37/4
Take the square root of both sides:
x + 3/2 = sqrt(37)/2 or x + 3/2 = -sqrt(37)/2
Subtract 3/2 from both sides:
x = sqrt(37)/2 - 3/2 or x + 3/2 = -sqrt(37)/2
Subtract 3/2 from both sides:
Answer: |
| x = sqrt(37)/2 - 3/2 or x = -3/2 - sqrt(37)/2
Calculate the Mean Absolute Deviation of these data. Round answers to the nearest tenth (one decimal place).
12, 17, 20, 8, 13
Answer: 3.6
Step-by-step explanation:
It’s on the picture .
Answer:
slope 2
yint 1
equation y=2x+1
What is the missing step in this proof
Answers are: A. CAB, ACB, EDB, DEB
B. ADE, DBE, CED, EBD
C. CAD, ACE, ADE, CED
D. CAB, EDB, ACB, DEB
The missing step in the given proof is ∠DEB ≅ ∠ACE
How to prove similar triangles?From the two triangles named ΔABC and ΔDBE, we can see that in both triangles, the angles ∠ABC and ∠DBE are equal.
Now, we are told that if two parallel lines are cut by a transversal that the corresponding angles formed are congruent. Thus, we can say that ∠DEB and ∠ACE are equal.
Thus, the missing step in the given proof is ∠DEB ≅ ∠ACE.
Read more about Similar Triangles at; https://brainly.com/question/8691470
#SPJ1
What type of angle is angle G?
H
L
G
Answer:
hb
Step-by-step explanation:
Answer:
Step-by-step explanation:
Angle G is ACUTE (answer d) because it's between 0 and 90 degrees.
Will mark Brainliest. I really do not understand this at all
Answer:
basically you are writting an equation for the solution of the circle if you didnt get what i said ask a teacher
Step-by-step explanation:
There are 360 seals. Of them are 9/20 are pups. The rest are adult seals . How many pups are the beach .
Answer:
162 pups are on the beach
Step-by-step explanation:
9/20 of 360
The key word "of" tells us to multiply
Variable x = number of pups
9/20 × x/360
Cross multiply
9 × 360 = 20 × x
3,240 = 20x
Divide both sides by 20
162 = x
Check our work:
9/20 = 162/360
Cross multiply
9 × 360 = 20 × 162
3,240 = 3,240
Correct
