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
James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have
budgeted $4,000 for their reception. If the reception hall charges a $50 cleanup fee plus $35 per person, find the greatest number of people that they may invite and still stay within their budget.
Answers
Answer:
They can invite at max 112 people.
Step-by-step explanation:
4000 - 50 = 3950
3950 / 35 = 112.85 (Can't round up to 113 because then it will go over their budget), so you will get 112 people.
Jason, murray, and dana went fishing. Dana caught a red snapper. Jason caught a tuna with a weight 3 times as great as the weight of the red snapper. Murray caught a sailfish with a weight 12 times as great as the weight of the red snapper. If the combined weight of the three fish was 208 pounds, how much did the tuna weigh?
Answers
Answer:
Tuna = 39 pounds
Red Snapper 13 pounds
Sailfish = 156 pounds
Step-by-step explanation:
T = 3x
RS = x
S = 12x
3x + x + 12x = 208
16x = 208
x = 208/16
x = 13
Tuna = 3(13)=39
Red Snapper = 13
Sailfish = (12)(13) = 156
What is the value of 9 squard
Answers
I presume you mean 9 'square'
9^2= 9 X 9 = 81
Cheerio ✌️
Step-by-step explanation:
The value of 9 Square is = 9 ×9= 81
Hope it's help you
(5k-10)•-9
show work plssss
Answers
Graph the following features: Slope = 3/2 Y-intercept = 5
Answers
PLEASE ANSWER THIS
a)Convert 0.25 as fraction
b)Write ¹⁹⁄₂₀ in Decimal Form
Please Answer Ill Rate U 5/5 And Thank U
Answers
Answer:
a) 1/4
b) 0.95
Step-by-step explanation:
0.25 is 25/100, which is 1/4
19/25 is 95/100, which is 0.95
6. The cost to download a normal movie is $15.00. New released movies
cost $18.00 to download. What is the percent of increase from a normal
movie download and the new releases?
Answers
Answer:
+20% increase
Step-by-step explanation:
(V2−V1)/|V1|×100
=(18−15)|15|×100
=315×100
=0.2×100
=20%change
=+20%increase
the percent of increase from a normal movie download and the new releases are $3.00
Need helpppppppppppppppppp
Answers
Answer:
46.3
Step-by-step explanation:
Mean is the average of all values. You add all the values on the table and divide them by the amount of values (here there are 10 land animals so you would divide by 10).
[tex]\frac{70+61+50+48+45+43+40+39+35+32}{10} =\frac{463}{10} = 46.3[/tex]
the room has a rug right in the middle of a room. The rug is 3m by 4 m and it is 2 m away from all the surrounding walls. Calculate the area of the room.
Answers
Technically it should say the area of the floor of the room but whatever
Also all things done assuming "room" means "floor" and that the rug isn't suspended in midair in the middle of the 3-D room
Answer:
[tex]56~m^2[/tex]
Step-by-step explanation:
If the room is 2 meters away from the rug top and bottom, the room is an extra 4 meters bigger than the rug in width. Likewise for sideways.
WLOG let the rug have a length of 3 and a width of 4(doesn't matter which number goes where). Then, the room has dimensions of [tex](3+4)[/tex] by [tex](4+4)[/tex], which equals 7 by 8 meters.
Therefore, the area is [tex]7*8=\boxed{56~m^2}[/tex]
ILL GIVE BRANLIEST!! HELP NOW!!!
Garnet has a container with 4 1/3 cups of flour in it. She can make one dozen muffins with cups of flour. How many dozens of muffins can Garnet make with the flour she has?
A. 10 1/9
B. 1 6/7
C. 1 1/3
D. 2
Answers
She can make one dozen of muffins with 2cups of flour..
She can make muffins=
[tex]\\ \sf\longmapsto 4\dfrac{1}{3}\div 2[/tex]
[tex]\\ \sf\longmapsto 2\dfrac{1}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{3}[/tex]
But Now total dozens=
[tex]\\ \sf\longmapsto 4\dfrac{1}{3}\times \dfrac{7}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{13}{3}\times \dfrac{7}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{91}{9}[/tex]
[tex]\\ \sf\longmapsto 10\dfrac{1}{9}[/tex]
Write 41 and 4 as a mixed number
Answers
Answer:
10 and 1 fourth
Step-by-step explanation:
41 over 4 = 41/4 so you divide 41 by 4 which is 10 R1 so its 10 wholes, 1 and 4
Please show step by step. I will chose Brainlyest once it lets me. 5 s and thanks too. Please answer ASAP.
Answers
20/1 x 33/4 ( 9 1/4) = 5/1 x 33/1= 216\1
=216 (?)
Hope that helped
HELP PLEASEEE, I WILL MARK BRAINLEST!
Answers
9514 1404 393
Answer:
∠a = 133°∠b = 15°∠c = 75°∠d = 58°Step-by-step explanation:
We don't know the definitions, properties, postulates, or theorems on your list, so we'll use the following:
a right angle measures 90°a straight angle measures 180°the acute angles in a right triangle total 90°an exterior angle of a triangle is equal to the sum of the remote interior anglesthe measure of an angle is equal to the sum of the measures of its parts.__
∠a = 180° -47° = 133°; reasons 2, 5. The angles form a straight angle.
∠b = 47° -32° = 15°; reason 4
∠c = 90° - ∠b = 90° -15° = 75°; reason 3
∠d = 90° -32° = 58°; reasons 1, 5. The angles form a right angle. If you want to get picky, we know it is a right angle by reasons 1 and 2. The marked right angle and the sum of 32° and ∠d together form a straight angle.
4x^2 times what equals -5x^2
Answers
Answer:
-1.25
Step-by-step explanation:
-5/4=
-1.25
check answer
4*-1.25= -5
Please I have no clue
Question 1 A physician's “patient panel” is the list of all patients under their care. In the
US, the size of patient panels among primary care doctors is well modeled by a N(1500, 200)
distribution.
(a) If a "medium-sized” panel has anywhere from 1250 to 1750 patients, what proportion
of US primary care doctors have a patient panel that is NOT "medium-sized”?
(b) Find Q1,Q3 and the IQR of the patient panels of US primary care doctors.
Answers
Using the normal distribution, we have that:
a) The proportion of US primary care doctors have a patient panel that is NOT "medium-sized” is 0.2112.
b)
Q1 = 1365.
Q2 = 1635.
IQR = 270.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For this problem, N(1500, 200) means that [tex]\mu = 1500, \sigma = 200[/tex].
Item a:
The proportion that are medium-sized is the p-value of Z when X = 1750 subtracted by the p-value of Z when X = 1250, thus:
X = 1750:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1750 - 1500}{200}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a p-value of 0.8944.
X = 1250:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1250 - 1500}{200}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a p-value of 0.1056.
0.8944 - 0.1056 = 0.7888 are medium.
1 - 0.7888 = 0.2112.
The proportion of US primary care doctors have a patient panel that is NOT "medium-sized” is 0.2112.
Item b:
Q1 is the first quartile, which is the 25th percentile, given by X when Z has a p-value of 0.25, so X when Z = -0.675. Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1500}{200}[/tex]
[tex]X - 1500 = -0.675(200)[/tex]
[tex]X = 1365[/tex]
Thus, Q1 = 1365.
Q3 is the third quartile, which is the 75th percentile, given by X when Z has a p-value of 0.75, so X when Z = 0.675. Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1500}{200}[/tex]
[tex]X - 1500 = 0.675(200)[/tex]
[tex]X = 1635[/tex]
Thus, Q3 = 1635.
The IQR is the difference between Q3 and Q1, that is:
[tex]IQR = Q3 - Q1 = 1635 - 1365 = 270[/tex]
Then, IQR = 270.
A similar problem is given at https://brainly.com/question/15953015
Solve for x: -7 < X - 1 < 8
Answers
Answer:
4th option
Step-by-step explanation:
-7 < X - 1 < 8
Add +1 on all side
-7+1<x-1+1<8+1
-6<x<9
Answer:
D
Step-by-step explanation:
-7<x-1 and - 1<8
-7<x-1 : x>-6
x-1<8 : x<9
combine x>-6 and x<9
= -6 < x < 9
Please help me I need to pass
Answers
explanation:
if we turn the first option into an improper fraction: we get 1 3/4, so it’s not the first answer. for the second answer choice, we can convert 3/4 into the 8ths by multiplying both parts of the fraction by 2 to get 6/8. Since 7/8 is greater than 6/8, it’s not the second choice either. Knowing that 3/4 is the same as 6/8, 5/8 is less then 6/8 because 5 is less than 6. So, 5/8 is between 3/4 and 1. hope this helped!!
Answer:
5 / 8
Step-by-step explanation:
3 / 4 = 0.75
5 / 8 = 0.625
5 / 8 is between 1 and 3 / 4.
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?
Answers
Given :
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm .To find :-
how fast is the area of the rectangle increasing?Solution :-
As we know that :-
A = lbTo find the rate :-
d(A)/dt = d(lb)/dt .Differenciate :-
dA/dt = l (db/dt ) + b (dl/dt )Substitute :-
dA/dt = 6*7 + 4* 8 dA/dt = 42 + 32 cm²/s dA/dt = 74 cm²/sYou spin each spinner once. You get $50 if you spin a 2 and a vowel. You get $25 if you spin a 2 and a consonant. You get $5 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game?
$8.75
$12.50
$80
$10.25
Answers
The expected value of the game is $8.75.
----------------------
The expected value is the sum of each outcome multiplied by it's probability.A probability is the number of desired outcomes divided by the number of total outcomes.The probability of spinning a 2 and a vowel is: [tex]\frac{1}{4} \times \frac{2}{8} = \frac{2}{32}[/tex].Thus, [tex]\frac{2}{32}[/tex] probability of getting $50.The probability of spinning 2 and a consonant is: [tex]\frac{1}{4} \times \frac{6}{8} = \frac{6}{32}[/tex]Thus, [tex]\frac{6}{32}[/tex] probability of getting $25.The probability of spinning 1 and a vowel is: [tex]\frac{3}{4} \times \frac{2}{8} = \frac{6}{32}[/tex].Thus, [tex]\frac{6}{32}[/tex] probability of getting $5.
32 - (6 + 6 + 2) = 18, thus, [tex]\frac{18}{32}[/tex] probability of earning $0.
The expected value is:
[tex]E = \frac{2}{32}(50) + \frac{6}{32}(25) + \frac{6}{32}(5) + \frac{18}{32}(0)[/tex]
[tex]E = \frac{100 + 150 + 30}{32}[/tex]
[tex]E = \frac{280}{32}[/tex]
[tex]E = 8.75[/tex]
The expected value of this game is of $8.75.
A similar problem is given at https://brainly.com/question/24961584
What is one set of values for A and B that will make the equation below true? (A × 10 3 ) = 6.572
Answers
Answer:
?
Step-by-step explanation:
Someone help me pls, this is a distance time graph
Answers
Answer:
it's b
Step-by-step explanation:
just took the test
can I take a picture of my math problem
Answers
Answer:
You press the camera icon when asking a question
Step-by-step explanation:
Which statement BEST expresses a connection between gravity and friction? A. Gravity and friction work together to provide the strong, opposing force that slows a snowboarder's ride. B. Gravity and friction are connected as they are the only two factors influencing speed when snowboarding. C. Gravity and friction are opposing forces; gravity holds a snowboarder in place while friction pulls a snowboarder down. D. Gravity and friction result in successful snowboarding after the transference of gravity into energy and a lubricating water layer produced by friction.
Answers
Answer:
D
Step-by-step explanation:
I had this question on a test and D was right
it's worded the exact same way
Answer:
a.
providing a force to propel the snowboarder down a slope to gain speed
The guy above me is a fool
Step-by-step explanation:
смесь сухофруктов состоит из изюма и кураги. Изюма составляет 42% всей смеси. Сколько процентов этой смеси составляет курага?
Answers
58% должно быть вашим ответом
Answer:
58%
Step-by-step explanation:
вычтите исходный процент из 100, и вы получите еще один, и это абрикосы
Which of the following is the solution to 3|x-1|>12?
Answers
Answer:
C.
Step-by-step explanation:
3|x - 1| >= 12
|x - 1| >= 4
x - 1 <= -4 or x - 1 >= 4
x <= -3 or x >= 5
Answer: C.
3 1/4 as in improper fraction
Answers
Answer:
13/4
Step-by-step explanation:
3 lots of 4 = 12.
Add 1 from the existing numerator.
Therefore, answer is 13/4.
Hope this helps :)
The total bill was $45 and mr Spieker payed 2/6if the bill how much did mister spieker pay
Answers
Answer:
3.75 I think, not sure
Step-by-step explanation:
What is (23)(−98)(−45)(−1)
Answers
Answer:
(23)(−98)(−45)(−1)= -101430
At the close of one business day, TNT stock was trading at $40 per share. At the close of the next business day, the stock was trading at $43 per shape. Find the percent of the increase
Answers
Answer: 7.5% increase by the end of the day.
Step-by-step explanation:
new - original = #
# / original = decimal
decimal x 100 = percent.
WHAT IS 300% ON 100 ?
Answers
Answer:
300.
Step-by-step explanation:
that's the answer.
Answer:
The answer would be 300
Step-by-step explanation:
300 x 100 = 30000
30000 ÷ 100 = 300
Hope this helps!!
