Answers
(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers n.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when a = 2.
Related Questions
TIMED HURRY!! For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: y = x squared + 7 x Table A a b c up or down y-intercept 1 7 0 up (0,0) Table B a b c up or down y-intercept 7 1 0 up (0,0) Table C a b c up or down y-intercept 7 1 0 down (0,0) Table D a b c up or down y-intercept 1 7 0 down (0,0) a. Table A c. Table C b. Table B d. Table D
Answers
Answer:
the answer is c
Step-by-step explanation:
We can see that Table A best illustrates the values for the equation.
The answer is (a) Table A.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The given equation is y = x² + 7x.
We can determine the values of a, b, and c by comparing the equation to the standard form of a quadratic equation,
which is y = ax² + bx + c.
In this case,
a = 1, b = 7, and c = 0.
To determine the direction in which the parabola opens, we can look at the coefficient of the x² term, which is a.
Since a is positive, the parabola opens upwards.
The y-intercept is the point where the parabola intersects the y-axis.
To find it, we can set x = 0 in the equation:
y = 0² + 7(0) = 0
So the y-intercept is (0,0).
Thus,
We can see that Table A best illustrates the values for the equation.
The answer is (a) Table A.
Learn more about equations here:
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For which of the following sample sizes is the sample median most likely to be above $250,000?
A. n = 10
B. n = 50
C n = 100
D. n = 1000
E Impossible to determine without more information
Answers
Answer:
A. n=10
Step-by-step explanation:
your welcome
Answer:
n=100
Step-by-step explanation:
In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be above $250,000? That was the exact question I had on the quiz. I'm not sure why it is n=100, but I got it correct.
PLSSSS HALLPP!!! DUE TODAY!!! PLS AND THANK YOU!!
Find the Compound Interest
Principal: 100
Interest Rate: 0.4%
Time: 1 year
Answers
Answer:
$100.4
Step-by-step explanation:
Compound Interest Formula:
A = P[tex]([/tex]1 + [tex]\frac{r}{100}[/tex][tex])^{t}[/tex]
=> A = 100 x ( 1 + [tex]\frac{0.4}{100}[/tex])^1 = 100.4 (If they asked ... interest rate ... per year, if not then depends - most likely to be days and therefore you will need to change 1 year = 365 days and you will also need to change 1 in the formula above to 365, then you will get the right ans)
What is the value of S3 for
20/9
20/3
65/9
65/3
Answers
Answer:
65/9
Step-by-step explanation:
Substitute 3 for the infinity sign above the sigma and solve with a calculator. Correct edge2021
QUESTION 5
One card is selected from a standard deck of playing cards. Find the probability it is an ace or a 9.
Give the answer as a fraction
SHOW ALL WORK!
WILL GIVE U BRAINIEST
Answers
Answer: 2/13
Step-by-step explanation:
4 aces, 4 nines in a deck of 52 cards
so 8/52 chance of getting one of them reduce to 2/13
10. Beth has a wooden box. The inside of the box is 5 inches wide, 8.25
inches long, and 4.5 inches tall.
Answers
Answer:
185.625in^2
Step-by-step explanation:
This is volume right?
5*8.25*4.5=
find the value of x
help pleaee
Answers
Answer:
x = 180 - 57 - 79 = 44°
Is the first answer correct and what's the next answer? Thanks
Answers
Answer:
First answer is correct and the answer for the second question is a = 30
Please help Due in 3 Min!
Answers
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below.
A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.
Which interval contains the median water bill?
$150–$175
$175–$200
$200–$225
$225–$250
Answers
The interval which contains the median water bill is $200 - $225
The tabulated data :
Class interval ____ Frequency ___ Cummulative frequency
100 to 125, ________ 1 ___________ 1
125 to 150, 2 ______ 2 ___________3
150 to 175, 5 _______5 ___________8
175 to 200, 10 ______10 __________18
200 to 225, 13 _____13 __________ 31
225 to 250, _______ 8 __________40
The median class = Cummulative frequency / 2
The median class = 40 / 2
The class interval which contains the 20th frequency.
This is the 200 - 225 class
The interval which contains the median water bill is $200 - $225
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Mr. & Mrs. Dargen spent $46.25 on a meal, about how much should they
leave for a 18% tip?
Answers
Answer:
$8.32
Step-by-step explanation:
I found one percent of 46.25 ( which was 0.4625) by dividing it by 100 then i multiplied that number by 18 in order to get how much the 18% tip would be. From that I got 8.325 but since this is in a currency the answer would be 8.32
thats just how I do it there's other ways
4. A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter.
How high is the cylinder?
O A. 8 mm
OB. 14 mm
O C. 16 mm
O D. 18 mm
Answers
Answer: The answer is A, 8 mm.
Step-by-step explanation:
Simplify.Solution may include surds
√3x²y².√2x
Answers
√6x^3y^2
Step-by-step explanation:
A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 6 or 10, you win $4. If the sum is 5, 9, or 12, you win $1. If the sum is any other value (2, 3, 4, 7, 8, or 11), you lose $2. Let X be a random variable that corresponds to your net winnings in dollars. What is the expected value of X
Answers
Answer:
The expected value of X is $0.0833.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are [tex]6^2 = 36[/tex] desired outcomes.
Desired outcomes:
Sum 5: (1,4), (2,3), (3,2), (4,1).
Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)
Sum of 9: (3,6), (4,5), (5,4), (6,3)
Sum of 10: (4,6), (5,5), (6,4)
Sum of 12: (6,6)
Probabilities:
5 + 3 = 8 outcomes in which the sum is 6 or 10, that is, 8/36 probability of winning $4.
4 + 4 + 1 = 9 outcomes in which the 5, 9, or 12, that is, 9/36 probability of winning $1.
36 - (8 + 9) = 36 - 17 = 19 remaining outcomes, that is, 19/36 probability of losing $2.
What is the expected value of X?
Multiplication of each outcome by its probability. So
[tex]E(X) = \frac{8}{36}*4 + \frac{9}{36}*1 - \frac{19}{36}*2 = \frac{8*4 + 9*1 - 19*2}{36} = \frac{32 + 9 - 38}{36} = \frac{3}{36} = 0.0833[/tex]
The expected value of X is $0.0833.
Find the length of AC using Pythagorean Theorem.
Answers
Answer:
23
Step-by-step explanation:
Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT.
Answers
Answer:
A,B,D
Step-by-step explanation:
FSA Mathematics Practice Test Questions
Session 1
2.
What fraction is represented by point A on the number line shown?
Answers
Brainliest would be nice
Find the average of 62 ℓ, 28 ℓ, 45 ℓ and 33 ℓ.
Answers
Answer:
the average is 168
Step-by-step explanation:
Hurrry dont be bots A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles A marble is drawn from the bag at
random. How many possible outcomes are there?
BI
03
O 5
06
O 14
Answers
Answer:
14
Step-by-step explanation:
im so sorry that the other people's comments are making you feel uncomfortable :(
there are 14 marbles in total since:
5 marbles+3 marbles+6 marbles = 14 marbles
each marble has one chance of being pulled out, therefore, there are 14 different outcomes.
Help! Will give Brainliest
Answers
Answer:
B
..................... ....
A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair.
Answers
Answer:
Step-by-step explanation:
If this class contains these types of hair color THEN the class will have
3/10 kids with black hair
1/10 kids have red hair
2/5 kids have brown hair
1/5 kids have blonde hair
_________________________
In total the class has 20 kids
It is found that the total number of students in the class is 20.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and also 2 with red hair.
If this class contains these types of hair colors of the students, then the class will have;
3/10 kids with black hair
1/10 kids have red hair
2/5 kids have brown hair
1/5 of kids have blonde hair
Total = 6 + 8 + 4 + 2 = 20
In total, the class has 20 students.
To learn more about the unitary method, please visit the link given below;
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The complete question is;
A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. What is the total number of students in the classes?
Find the accumulated value of an investment of $14,000 at 10% compounded semiannually for 11 year
Answers
Given:
Principal = $14000
Rate of interest = 10% compounded semiannually.
Time = 11 years.
To find:
The accumulated value of the given investment.
Solution:
Formula for amount or accumulated value after compound interest is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is the principal values, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.
Compounded semiannually means interest compounded 2 times in an years.
Putting [tex]P=14000,r=0.10,n=2,t=11[/tex] in the above formula, we get
[tex]A=14000\left(1+\dfrac{0.10}{2}\right)^{2(11)}[/tex]
[tex]A=14000\left(1+0.05\right)^{22}[/tex]
[tex]A=14000\left(1.05\right)^{22}[/tex]
[tex]A\approx 40953.65[/tex]
Therefore, the accumulated value of the given investment is $40953.65.
Answer:
A = $41,867.06
A = P + I where
P (principal) = $14,000.00
I (interest) = $27,867.06
Step-by-step explanation:
Given: Investment = $14,000 Annual Rate: 10% compounded semiannually = 11 year
To find: The accumulated value of an investment
Formula: [tex]A = P(1 + \frac{r}{n}) ^n^t[/tex]
Solution: First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 14,000.00(1 + 0.1/12)(12)(11)
A = 14,000.00(1 + 0.008333333)(132)
A = $41,867.06
Henceforth:
The total amount accrued, principal plus interest, with compound interest on a principal of $14,000.00 at a rate of 10% per year compounded 12 times per year over 11 years is $41,867.06.
Your car uses 15 1/2 gallons of gasoline on a 310 mile trip
Answers
Explanation:
divide 310 miles by 15 gallons of gas
310/15=20.6
When an object moves on a circular path, the centripetal force varies directly as the square of the velocity and inversely as the radius of the curve. If the force is 640 lb for a velocity of 20 mi/h and radius of 5 m, find the radius for a velocity of 30 mi/h and a force of 1800 lb.
Answers
Answer: I think it's 40
Step-by-step explanation:
I don't know, I just need points. If you take the 640 and divide it by the nearest angular velocity, then square it, then divide by the radius, you get Bolivia
HIGH POINTS)Please help! (20 points)
Answers
Answer:
What the other person said
Step-by-step explanation:
Help I would love to give you a thanks
Answers
Answer:
Formula
Step-by-step explanation:
Answer:
formula because it gives you the number and tells you what to do.
1.Charlie buys two circular pizzas.
The first pizza has a 12- The second pizza has a
inch diameter
14-inch diameter.
How much greater, in square inches, is the area of the second pizza than the first pizza?
Round your answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
ANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIEST
Answers
Answer:
-3/2
Step-by-step explanation:
the constant of variation is commonly known as k .
y/x= k
so -3/2 is your answer
Answer:
it is a
Step-by-step explanation:
Rectangle ABCD has vertices A(–6, –2), B(–3, –2),
C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1),
C’(–7, –3), and D’(–10, –3).
Which rule was used to translate the image?
Answers
Answer:
The rule is ( x - 4, y + 3)
Step-by-step explanation:
James recorded the distance he ran each day:
Monday - 2.05 miles
Tuesday - 1.8 miles
Wednesday - 1.45 miles
Thursday - 0.923 miles
Friday - 2.55 miles
What is the difference between his longest distance and shortest distance?
Answers
Answer:
1.627 miles
Step-by-step explanation:
Longest distance: 2.55 miles
Shortest distance: 0.923 miles
difference: 2.55 miles - 0.923 miles = 1.627 miles