Since 2⁵ = 32, and
2⁵ ≡ 32 ≡ 10 (mod 22),
we have
2⁵¹ ≡ 2 • 2⁵⁰ ≡ 2 • (2⁵)¹⁰ ≡ 2 • 10¹⁰ (mod 22)
Now consider 10¹⁰ (mod 22):
10 = 2 • 5
10¹⁰ ≡ 2¹⁰ • 5¹⁰ ≡ (2⁵)² • 5¹⁰ ≡ 10² • 5¹⁰ ≡ 2² • 5¹² (mod 22)
so that
2⁵¹ ≡ 2³ • 5¹² (mod 22)
Now consider 5¹² (mod 22):
5 and 22 are coprime, and ɸ(22) = 10 (where ɸ(n) is the Euler totient function). By Euler's theorem,
5¹² ≡ 5² • 5¹⁰ ≡ 5² • 1 ≡ 25 ≡ 3 (mod 22)
and so
2⁵¹ ≡ 2³ • 3 ≡ 24 ≡ 2 (mod 22)
Another, more tedious method: Start with smaller powers of 2 and look for a pattern.
2 ≡ 2 (mod 22)
2² ≡ 4 (mod 22)
2³ ≡ 8 (mod 22)
2⁴ ≡ 16 (mod 22)
2⁵ ≡ 32 ≡ 10 (mod 22)
2⁶ ≡ 2 • 32 ≡ 2 • 10 ≡ 20 (mod 22)
2⁷ ≡ 2 • 20 ≡ 40 ≡ 18 (mod 22)
2⁸ ≡ 2 • 18 ≡ 36 ≡ 14 (mod 22)
2⁹ ≡ 2 • 14 ≡ 28 ≡ 6 (mod 22)
2¹⁰ ≡ 2 • 6 ≡ 12 (mod 22)
2¹¹ ≡ 2 • 12 ≡ 24 ≡ 2 (mod 22)
2¹² ≡ 2 • 2 ≡ 4 (mod 22)
and so on, with a cyclic pattern of length 10. That is, [tex]2^{10k+1}\equiv2\pmod{22}[/tex] for any integer k ≥ 0. So 2⁵¹ ≡ 2 (mod 22).
I NEED HELP!! The amount of food a dog should eat daily is based on its weight. The picture shows the ratio of weight to cups of food.
A photo of a dog is shown. The caption shows that the dog is fifty pounds and the food dish contains two cups.
Question 1
Part A
What is the ratio of cups of dog food to the dog’s weight in pounds? Use a fraction or a colon to write the ratio
Answer:
100 llbs
Step-by-step explanation: i think
Is (8,2). (7,2). (6,3) a function?
0.000032 ÷ (8 × 10-3)
4x10^-3
Answer:
Step-by-step explanation:
=0.000002x10−3
symbolab the calculator will help you with the steps and answer
Find the equation of the linear function represented by the table below in slope intercept form.
Answer:
Y=1x-7
Step-by-step explanation:
First use two points to find the slope. I used the first 2. The formula is (y1-y2)/(x1-x2). So (6-8)/(1-3)= -2/-2 = 1. Then you plug in a point and the slope for the equation y1-y2=m(x1-x2). I am using the first point and m is the slope which is 1. Y-6 = 1(x-1)
y-6 = 1x -1 then get y by itself
y=1x-7
ne of best on this seriet
thing
are the triangles congruent. if they are state how they are congruent.
Answer:
Step-by-step explanation:
Yes, the triangles are congruent.
SSS
Answer:
When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
Mr. Roberts had $9,512 in savings. He saved another $488. He then used all his money to buy 500 books. He sold the books for $35 each. How much did Mr. Roberts earn from selling each book? a. Mr. Roberts earned $ from selling each book. b. Travis got $20 as the answer or the amount Mr. Roberts earned from selling each book. Is his answer correct? yes no c. Tell why Travis is or is not correct.
Answer:
a. Profit from each book = $15
b. No, Travis was wrong.
c. Travis isn't correct because Mr. Roberts made $15 from the sales of each book.
Step-by-step explanation:
Given the following data;
Number of books bought = 500
Selling price = $35
Robert savings (cost price) = $9,512 + $488
Robert savings (cost price) = $10,000
Purchasing price = $10,000/500 = $20
Revenues from book sold = 500 * 35 = $17,500
Total profit = Revenues - Cost price
Total profit = $17,500 - $10,000
Total profit = $7,500
To find the amount earned from each book;
[tex] Profit \; from \; each \; book = \frac {Total \;profit}{Numbers \; of \; book} [/tex]
Substituting into the equation, we have;
[tex] Profit \; from \; each \; book = \frac {7500}{500} [/tex]
Profit from each book = $15
Therefore, Mr. Roberts earned $15 from selling each book.
Check:
Selling price = purchasing price + profit = $20 + $15 = $35
Roberto is 3 years older than Carolyn. In 7 years the sum of their ages will be 81. How old is Roberto now?
Answer: 35
the age of Roberto is x (x > 3)(x ∈ N)
because Roberto is 3 years older than Carolyn => the age of Carolyn is x - 3
in 7 years, the age of Roberto is x + 7; the age of Carolyn is x - 3 + 7 = x + 4
because In 7 years the sum of their ages will be 81 =>
x + 7 + x + 4 = 81
⇔ 2x + 11 = 81
⇔ 2x = 70
⇔ x = 70/2 = 35
=> the age of Roberto is 35
Step-by-step explanation:
In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest
tenth.
a= 7.7 ft, b= 16 ft
9514 1404 393
Answer:
c = 17.8, A = 25.7°, B = 64.3°
Step-by-step explanation:
Side c can be found from the Pythagorean theorem:
c = √(a² +b²)
c = √(7.7² +16²) = √315.29
c ≈ 17.8 . . . feet
__
The tangent relation is ...
Tan = Opposite/Adjacent
tan(A) = a/b = 7.7/16
A = arctan(7.7/16)
A ≈ 25.7°
B = 90° -25.7°
B = 64.3°
Suppose you observe a star orbiting the galactic center at a speed of 1300 km/skm/s in a circular orbit with a radius of 18 light-days. Calculate the mass of the object that the star is orbiting.
Answer: 1.1818^37 kg
Step-by-step explanation:
Given that:
Orbit speed = 1300 km/s
Radius (r) = 18 light days
Mass of object the star is orbiting :
Using the relation :
M = rv² / G
Where ; r = Radius in m ; v = velocity in m/s
G = 6.67 * 10^-11 = gravitational constant
18 light days in meters = 4.662 * 10^14 m
v = 1300km/s to m/s
v = (1300 * 1000)m /s = 1300000 m/s = 1.3 * 10^6 m/s
Hence ;
M = (4.662 * 10^14 * (1.3 * 10^6)^2 / (2/3) * 10^-10
M = (4.662 * 10^14) * (1.69 * 10^12) / (2/3) *10^-10
M = (7.87878 * 10^26) / 6.67 * 10^-11
= 1.1818^37 kg
When adding 35.64 to a certain number, the sum is 38.24, as seen below. What number should go in the box to complete the addition problem?
The decimal 35.64 is added to an unknown whole number and 6 tenths to equal 38.24.
(5 points)
2
3
13
14
Answer:
it would be 2
Step-by-step explanation:
5he answer is two so you subtract and then add and then multiply to get your answer 6ou divide it by pie
Answer:
i checked his answer it was right good job
Step-by-step explanation:
Sharleen is considering joining for either 3 months, 8 months, or 12 months. Will the costs for the
two clubs ever be the same? Is one a better deal? Write a summary of the costs for each club and give
Sharleen advice on which one she should choose. Include a graph with your explanation.
Answer:
More explanation please
Step-by-step explanation:
Can you add how much money is in the problem for each of the 2 clubs for 3, 8 and 12 months? Then people will help you I think
The expressions to represent the costs of each club is $10 + ($15 * m)
Let's begin by writing expressions for the costs of each club:
Multiplayer Madness:
Joining Fee: $50 (one-time payment)
Monthly Fee: $0 (since it's not mentioned, we assume there's no additional monthly fee)
The total cost for Sharleen to join Multiplayer Madness would be the joining fee only, which is $50.
Games Galore:
Joining Fee: $10 (one-time payment)
Monthly Fee: $15 (recurring monthly charge)
The total cost for Sharleen to join Games Galore would be the joining fee plus the cumulative monthly fees over time. Let's represent the total cost of Games Galore as a function of the number of months (m) Sharleen stays in the club:
Total Cost of Games Galore = Joining Fee + (Monthly Fee * Number of Months)
Total Cost of Games Galore = $10 + ($15 * m)
To know more about expression here
https://brainly.com/question/14083225
#SPJ2
Complete Question:
Your friend Sharleen is thinking about joining an online gaming club. She's trying to decide between Multiplayer Madness and Games Galore. Her brother insists that Multiplayer Madness is a better deal. Multiplayer Madness charges a joining fee of $50. It's a bit more expensive than Games Galore, a club that charges a $10 joining fee. But, Games Galore charges a fee of $15 a month. That's $5 more each month than the fee charged at Multiplayer Madness! Checklist Did You... Write expressions to represent the costs of each club?
There are 40 students in the class. If 10% are absent on Friday, what is the number of students present in the class?
Answer:
36
Step-by-step explanation:
if 10% are absent the other 90% are present
40 students represent 100%
? students represent 90%
?=40*90/100=36 students
In tilton school there are
3)
Ross wants to know what interest rate he needs to make his $800 grow to
$1000 in 4 years.
Answer:
Why?:
The interest formula is A = P(1+r/m)^mt
A is the Amount, P is principal (initial investment), R is rate, M is times per year (not used) and T is time.
So if we want 1000 = 800(1+r)^4, we need to find R. In this case, R is about 5 percent. (I'm not super confident, so see if you have other answers)
Which inequality is true?
Answer:
[tex]\frac{3}{4}[/tex] > [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Answer: 2. Is true
Step-by-step explanation: (second option is true)
The rams football team Lost 18 yards on three consecutive plays they lost the same number of yards on each plate how many yards did they lose on the second play
total yards lost = 18
no. of matches = 3
given,
they lost the same number of yards on each play
yards lost on each match = 18/3 = 6
yards lost on second match = 6
Answer:
Step-by-step explanatio
A.6 yards
how many tiles did tim walk around?
PLEASE HELP ME 50 POINTS!!!
Explain how to simplify this expression:
(8a + 8) + (5a – 6).
8a+8+5a−6
=8a+8+5a+−6
Combine Like Terms=8a+8+5a+−6
=(8a+5a)+(8+−6)
=13a+2
=> (8a + 8) + (5a – 6)
=> (8a + 5a) + (8 – 6) [Combine like terms]
=> (13a + 2)
Would someone mind helping me? I really need this answer but I'm so confused. I would appreciate any help :) and if you get the answer right, ill give you brainliest.
Answer:
A. the slope is -2
the y-intercept is (0,1)
Step-by-step explanation:
If y=mx+b, m is the slope and b is the y-intercept.
If we replace the variables with y=-2x+1, we can see -2 is the slope and the y-intercept is (0,1).
HELP! WILL GIVE BRANLIEST!!
Answer:
About 46 pples
Step-by-step explanation:
evaluate 9.5v + 8.9w when v=6 and w=7
Answer:119.3
Step-by-step explanation:
9.5*6=57
8.9*7=62.3
57+62.3=119.3
A caterer charges $275 for 15 people and $425 for 25 people. The cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this situation. *
Answer:
The equation of the given situation is y = 15x + 50
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
m is the slope b is the y-interceptThe rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the line∵ A caterer charges $275 for 15 people
∵ A caterer charges $425 for 25 people
∵ x represents the number of people
∵ y represents the cost
∴ (x1, y1) = (15, 275)
∴ (x2, y2) = (25, 425)
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{425-275}{25-15}=\frac{150}{10}[/tex]
∴ m = 15
→ Substitute it in the form of the equation above
∴ y = 15x + b
→ To find b substitute x by 15 and y by 275
∵ 275 = 15(15) + b
∴ 275 = 225 + b
→ Subtract 225 from both sides
∴ 275 - 225 = 225 - 225 + b
∴ 50 = b
→ Substitute it in the equation
∴ y = 15x + 50
∴ The equation of the given situation is y = 15x + 50
Please help with the question in the attachment. Do not give an improper answer or you will be reported.
9514 1404 393
Answer:
2876 books
Step-by-step explanation:
If we let y1 and y2 represent the costs from method 1 and method 2, then we have, for x books published, ...
y1 = 12841 +24.25x
y2 = 48072 +12x
These costs will be equal when ...
y1 = y2
12841 +24.25x = 48072 +12x
12.25x = 35231 . . . . . . . . . . . . . subtract 12841+12x
x = 2876 . . . . . . . . . . divide by 12.25
The costs will be the same for production of 2876 books.
At the store, 10 ounces of candy cost $3.20. How many ounces can you get for $1?
Answer:
3.125 ounces
Step-by-step explanation:
10/3.20=3.125
Plzz, Helpppp!!!!!!!
Solve for x in the equation X^2-12x+36 = 90.
Answer:
Steno lo sebroo disculpa pero lo hice por los puntos gracias
Please I need help badly I also have stuff on my account
Answer:
B) y = 1/5x + 12/5
Step-by-step explanation:
2 = 1/5(-2) + b
2 = -0.4 + b
2.4 = b
2.4 = 12/5
Which point represents 3.9?
Answer:
What do you mean there is not a graph...do you have a picture?
Step-by-step explanation:
Answer: B
Step-by-step explanation:
A = 3.8
B = 3.9
C = 4.0
D = 4.2
You take 4.5 - 3,6 = 0.9, so each big line should be .3.
)Kelly read 30 pages of her 300-page book in 6 hours. At this rate, how long will it take her to read the entire book? 60 hours 5 hours 6 hours 30 hours
Answer:
What would you want the answer in?
Step-by-step explanation:
Answer:
60 hours
Step-by-step explanation:
That is really slow reading