Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].
Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].
Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,
[tex]3^{12} \equiv 1 \pmod{13}[/tex]
Now, observe that 2020 = 168×12 + 4, so that
[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]
and since 3⁴ = 81 = 6×13 + 3, we end up with
[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
What is the median of these figure skating ratings?
5.0 6.0 7.0 7.5 8.0 9.0 10.0
Answer:
5.0 6.0 7.0 7.5 8.0 9.0 10.0
arranging the following
5.0 , 6.0 , 7.0 , 7.5 , 8.0 , 9.0, 10.0
7.5 is the median..
Sum of 1/2*3 +1/3*4 +1/4*5 ..1/99*100
Answer:
11∗2+13∗4+15∗6+⋯+199∗100=?
=(1−12)+(13−14)+(15−16)+⋯+(199−1100)
=(1+13+15+17+⋯+199)−(12+14+16+⋯+1100)
=(1+13+15+17+⋯+199)−12(1+12+13+⋯+150)
=∑k=15012k−1−∑k=15012k
Continue further.
What is the slope of the line that passes through the points (-7, -2)(−7,−2) and (-15, -14)(−15,−14)? Write your answer in simplest form.
Answer:
please help me find em ah and I will be able to do what I can
《QUESTION 1》
The length of the side of a square is 50 cm and the breadth of a rectangle is 25 cm. If the areas of the square and the rectangle are equal, find the length of the rectangle.
《QUESTION 2》
A wire is in the shape of a rectangle with length 6 cm. It is bent to form a square whose side is 5 cm. Find the breadth of the rectangle. Also, calculate the areas of both the rectangle and the square and find which shape encloses more areas.
The length of the rectangle is 100cm.
The breadth of the rectangle is 4cm.
The square encloses more area than the rectangle.
What is the length of the rectangle?The first step is to determine the area of the square.
Area of a square = length² = 50² = 2500 cm²
Area of a rectangle = length x width
length = area / width
2500 / 25 = 100cm
What is the breadth of the rectangle?
The first step is to determine the perimeter of the square.
Perimeter = 4 x length
4 x 5 = 20cm
Perimeter of a rectangle = 2(length + width)
breadth = (perimeter / 2) - length
(20 / 2) - 6
10 - 6 = 4cm
Area of the square = 5 x 5 = 25
Area of the rectangle = 6 x 4 = 24
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A group of students at Brunel university took a test in marketing and they needed to score 50 to pass. The results showed that the final grades have a mean of 62 and a standard deviation of 8. Suppose we approximate the distribution of these grades by normal distribution. Based on this information, you are required to perform the following; a) what percetage(to 3 decimals) of the students scored more than 78? B) what percentage of the students to 3 decimal places scored under 50? And c) what percentage to 3 decimal places of the students scored between 60 and 80?
Answer:
My answer: 15.87%
Step-by-step explanation:
The Final grades follows normal distribution.
It means =70
The Given standard deviation =10
The normal random variable of a standard normal distribution is called a standard score or a z-score. In Every normal condition, random variable X will be transformed into a z score via the following equation:
z=(X)
But when X is a normal random variable, μ is the mean of X.
For That, it is X=60
Z=(60−70)/10=−1
P(X<60)=P(Z<−1)
=0.1587
Hence percent of students failed in test is 15.87%
What is the slope intercept of the line below
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option D, y = 2x - 3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The graph}[/tex]
Find: [tex]\textsf{The equation in slope intercept form}[/tex]
Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept. All we need to do now is find a second point so we can determine the slope. The line crosses at (1, -1) so we will use that as the second point. Then we just plug all of the values into the slope intercept form.
Determine the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{-1 - (-3)}{1 - 0}[/tex][tex]m = \frac{-1 + 3}{1}[/tex][tex]m = \frac{2}{1}[/tex][tex]m = 2[/tex]Plug in the values
[tex]y = mx + b[/tex][tex]y = 2x - 3[/tex]Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.
Which statement is correct when a scatterplot is constructed?
The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
Option A is the correct answer.
The independent variable is the input variable and should be represented by the x-axis.
What is Variable?A variable is a symbol and placeholder for a quantity that may change, or any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
For the Scatterplot, out of given options,
Option A is the correct option which represents The independent variable is the input variable and should be represented by the x-axis.
Thus, The independent variable is the input variable and should be represented by the x-axis.
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Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of 14 and center of dilation (0, 0).
The points are (168, 168) , (168,56) , (112,0) , (70,112)
Given a scale factor is 14 and the center of dilation (0,0)
We need to find the Points using the scale factor and polygon tool
Now to find the new points the equation is
(old points - dilation center)*scale factor + dilation center
As we know the origin is the dilation center which simplifies to
(old point)*dilation center
(12,12) * 14 = (168,168)
(12,4) * 14 = (168, 56)
(8,0)*14 = (112, 0)
(5,8) *14 = (70, 112)
Hence the new points are (168, 168) , (168,56) , (112,0) , (70,112)
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Y-6.37x=-3 which of the following function notation corresponds to the equation below
What is the mean for 14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25
Answer:
Mean: 19.366666666667
Step-by-step explanation:
Mean: Average of the Data set
If you add the numbers below and divide them by the amount of numbers there are, you will get the average of the data set.
14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25
Average= sum/count
Mean= 1162 / 60
Mean= 19.366666666667
Rounded to the nearest tenth: 19.4
Rounded to the nearest hundredth: 19.37
world problem in length (trigonometry) geometry not chemistry
Answer:
≈ 47.2 m
Step-by-step explanation:
let the height from the sea to the base of lighthouse be h₁
let the height from the sea to the top of the lighthouse be h₂
using the tangent ratio in the right triangle
tan55.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h_{1} }{610}[/tex] ( multiply both sides by 610 )
h₁ = 610 tan55.1°
tan56.5° = [tex]\frac{h_{2} }{610}[/tex] ( multiply both sides by 610 )
h₂ = 610 tan56.5°
then
height of lighthouse = h₂ - h₁
= 610 tan56.5° - 610 tan55.1°
= 610(tan56.5° - tan55.1° )
≈ 47.2 m ( to the nearest tenth )
In the past month, Ryan has had five pizzas delivered. He kept a record of how long it took to get the
pizzas: 35 minutes, 25 minutes, 15 minutes, 40 minutes, and 50 minutes.
If the sixth time he orders pizza, it takes 95 minutes, how will this affect his data?
a.) It will have little to no effect on both the mean and the median.
b.) It will have little to no effect on the mean, but it will make the median a less useful measure
of center.
c.) It will make both the mean and the median less useful measures of center.
d.) It will have little to no effect on the median, but it will make the mean a less useful measure
of center.
It will have little to no effect on the median, but it will make the mean a less useful measure of center.
How to determine the effect?The initial data elements are given as:
35, 25, 15, 40, 50
When a new data element is added, we have:
35, 25, 15, 40, 50, 95
See that 95 is far from the other data elements.
This means that 95 is an outlier of the data elements
Outliers have effects on the mean and it renders the mean useless.
However, it has little to no effect on the median
Hence, the true statement is (d)
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Answer:
Step-by-step explanation:
it will have little to no effect on the median but will make the mean a less useful measure of center.
please help me with this problem ! would appreciate it!!!
[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]
Answer: correct radical forms are:
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
Step-by-step explanation:
Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.
therefore,
radical form of given values are :
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
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Which statement describes the end behavior of the function f(x)= |x-7| -7?
A. As x approaches negative infinity, f(x) approaches negative infinity.
B. As x approaches negative infinity, f(x) approaches positive infinity.
C. As x approaches positive infinity, f(x) is no longer continuous.
D. As x approaches positive infinity, f(x) approaches negative infinity.
Answer:
A. B. C. D.
Step-by-step explanation:
because Which statement describes the end behavior of the function f(x)= |x-7| -7?
A. As x approaches negative infinity, f(x) approaches negative infinity.
B. As x approaches negative infinity, f(x) approaches positive infinity.
C. As x approaches positive infinity, f(x) is no longer continuous.
D. As x approaches positive infinity, f(x) approaches negative infinity.
A jug of drinking water contained 1 2/3 gallons. If 5/7 gallon is drinked each day, how much water was left in the jug after 2 days?
Answer:
The answer is 5/21 water left in the jug after 2 days.
Step-by-step explanation:
First convert 1 2/3 into a improper fraction. This will turn it into 5/3. After this, find a common denominator between 5/7 and 5/3. This common denominator is 21. Now, convert both fractions into a fraction with 21 as the denominator. This will transform 5/7 into 15/21, and 5/3 into 35/21. So we know from the equation that 15/21 is drank every day. So we multiply 15/21 by 2, which will make it 30/21. 35/21 will stay the same. Now we do 35/21 - 30/21, which gives you the final answer of 5/21 water left in the jug after 2 days.
Hope this helps!
What is the exact value of sin (- 105)?
Answer:
Just put it into a calculator
0.97053528353
[tex]\text{Let's find the sine of -105 degrees}\\\text{Start by typing -105 into our calculator}\\\text{and click the sin button}\\\text{It gives us an irrational number, which is the sine of -105 degrees}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The value is end less, it would take an eternity to type it here,}\\\text{ but I will round it to the nearest 100th}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{-0.97}[/tex]
Write and simplify the equation you would use to solve the problem below.
A farmer builds a rectangular pen with a perimeter of 116 feet. If the length is 5 feet more than the width, what is the width?
A.w + 5 = 116
B.4w + 10 = 116
C.2w + 5 = 116
D.2w + 10 = 116
need a hand i cant figure this one out
Answer:
4w + 10 = 116
Step-by-step explanation:
Call the width w.
The length is 5 more than that, so the length is w + 5
Perimeter is 2w + 2l
2w + 2(w+5) = 116
Distribute the 2 to the values in the parentheses.
2w + 2w + 10 = 116
Combine like terms
4w + 10 = 116
In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6965 subjects randomly selected from an online group involved with ears. There were 1302 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution
The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%
What is the claim that the return rate is less than 20% by using a statistical hypothesis method?The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:
[tex]\mathbf{H_o :p =0.2}[/tex]
[tex]\mathbf{H_i:p < 0.2}[/tex]
Given that:
Sample size (n) = 6965
Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]
The test statistics for this data can be computed as:
[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]
[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]
[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]
z = -2.73
From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.
Hence, the p-value for the test statistics can be computed as:
P-value = P(Z ≤ z)
P-value = P(Z ≤ - 2.73)
By using the Excel function =NORMDIST (-2.73)
P-value = 0.00317
P-value ≅ 0.003
Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%
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Please assist with the following questions
The answers for following questions are;
i. $244.64
ii. $ 5314.64
What is future value?Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value is important to investors and financial planners, as they use it to estimate how much an investment made today will be worth in the future.
Here, future value or amount;
A = P(1 + r)ⁿ
Where,
A = future value = ?
P = principal = $ 12,300
r = interest rate = 6%/12 = 0.06/12 = 0.005
n = number of periods = 12 X 6 years = 72
A = P(1 + r)ⁿ
= 12,300(1 + 0.06/12)⁷²
= 12300 (1 + 0.005)⁷²
= 12300 (1.005)⁷²
= 12300 (1.4384)
= 17,614.64
Each monthly payment = Total payment / number of months
= $17,614.64 / 72
= $ 244.64
Total amount of interest = Total payment - Principal payment
= 17,614.64 - 12300
= $ 5314.64
Thus, The answers for following questions are;
i. $244.64
ii. $ 5314.64
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Translate this sentence into an equation. Craig's savings decreased by 23 is .55
Answer:
x-23=.55
Step-by-step explanation:
Answer: 0.55 = x - 23
Step-by-step explanation:
let his savings = x
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. Running Play Outcomes Play 1 –3 yards Play 2 2 yards Play 3 –1 yard Play 4 –2 yards Play 5 –3 yards Play 6 1 yard What is the average change in field position per running play? –6 yards per play –1 yard per play 0 yards per play 1 yard per play Mark this and return
Answer:
Step-by-step explanation:
-3 +2 +-1 +-2 +-3 +1 = -6 yards total
-6 / 6 = -1 yard per play average
what is the average daily balance for the February 1-28 billing period in the table?
These tables of values represent continuous functions. For which function
will the y-values be the greatest for very large values of x?
y
1 7
2 21
3 63
4 189
5 567
B. x
y
17
2 207
3 407
4 607
5 807
C.xy
1 325
2 400
3 475
4 550
5625
Y
1 565
2 570
3 575
4 580
5585
What is the answer??
Answer: the answer is a
Step-by-step explanation:
This whole page i need help on
Step-by-step explanation:
1. True
2. False
3. True
5. Falsw
6.True
7.True
8.False
10.True
15. always
17. always
Help with a composition of two functions! 20 pts for a solution!
The function (fog)(x) would be (x^4 + 10x² + 27). Also, the domain of (fog)(x) is all the real numbers.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x) = x² + 2
g(x) = x² + 5
so, to take the composition of f and g (fog) replace the x in f(x) with g(x);
(fog)(x) = (x² + 5)² + 2
(fog)(x) = (x^4 + 25 + 10x² )+ 2
(fog)(x) = (x^4 + 10x² + 27)
Also, the domain of (fog)(x) is all the real numbers.
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Packs of stickers
Buy for €1.50a pack
Sell For £2.25 a pack
Media buys 5 pack's and sells them all
How Much profit does she
Make ?
Answer:
€3.75
Step-by-step explanation:
1. Formulate:
5×(2.25 - 1.5)
2. Calculate:
5×(2.25-1.5)
5× 0.75
=3.75
Answer
3.7/ €3.7
By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for sh.56 , gain is as much as percent as its cost in dollars . What is the cost price ?
The cost price of the table is $40.
What is Gain ?Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
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Charlotte practices the piano for 4 hours each week. How many minutes does she practice each week?
Answer:
4 X 60 = 240 minutes
Step-by-step explanation:
there are 60 minutes in each hour
What is 2(x+3) / 4(x+1)
Answer:
x² + 4x + 3
---------------
2
---- => fraction line
