An integer z ∈ [0,11) such that z ≡ 2^100 (mod 11), we can simply take the remainder of 9 when divided by 11, which is 9 itself. Therefore, we can say that: z ≡ 2^100 ≡ 9 (mod 11)
From exercise 11.7, we know that 2^5 ≡ 1 (mod 11). Therefore, we can write 2^100 as:
2^100 = (2^5)^20
Using the above congruence, we can reduce this to:
2^100 ≡ 1^20 ≡ 1 (mod 11)
Now, we can use the observation that 100 = 64 + 32 + 4 to write:
2^100 = 2^64 * 2^32 * 2^4
Using the fact that 2^5 ≡ 1 (mod 11), we can reduce each of these terms modulo 11 as follows:
2^64 ≡ (2^5)^12 * 2^4 ≡ 1^12 * 16 ≡ 5 (mod 11)
2^32 ≡ (2^5)^6 * 2^2 ≡ 1^6 * 4 ≡ 4 (mod 11)
2^4 ≡ 16 ≡ 5 (mod 11)
Therefore, we can substitute these congruences into the expression for 2^100 and simplify as follows:
2^100 ≡ 5 * 4 * 5 ≡ 100 ≡ 9 (mod 11)
Hence, we have found that 2^100 is congruent to 9 modulo 11. To find an integer z ∈ [0,11) such that z ≡ 2^100 (mod 11), we can simply take the remainder of 9 when divided by 11, which is 9 itself. Therefore, we can say that: z ≡ 2^100 ≡ 9 (mod 11)
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Round your answer to the nearest percent.
Answer:
Step-by-step explanation:
Givens
Number not using given app = 71
Total number of students = 219
% = ?
Solution
P(~given app) = 71 / 219
P(~given app) = 0.324
% = 0.324 * 100 = 32.4%
Answer
32.4% do not use Given App
Hi, can you help me with this math problem?
The equation of a hyperbola is shown.
[tex]\frac{(y-7)^2}{3}-\frac{(x+13)^2}{12}=1[/tex]
Determine the area of the central rectangle.
Answer:
24
Step-by-step explanation:
The semi-axis lengths are 'a' and 'b' in the equation ...
(y -k)²/a² -(x -h)²/b² = 1
AreaThe area of the central rectangle will be ...
A = LW
The axis lengths are 2a and 2b, so the area is ...
A = (2a)(2b) = 4ab
In terms of the numbers in the given equation, this is ...
A = 4√(a²b²) = 4√(3×12)
A = 4×6 = 24
The area of the central rectangle is 24 square units.
Shannon wants to make snack bags that contain an equal amount of three different types of nuts. If she has 26
almonds, 78 pecans, and 52 peanuts, what will be the most number of bags she can have?
You are flying a kite in a competition and the length of the string is 725 feet and the angle at which the kite is flying mesures 35” with the ground. How high is your kite flying?
The kite is flying 415.84 feet from the ground
How to determine the height?The given parameters are:
Length of the string, L = 725 feetAngle, x = 35 degreesLet the height be h.
So, we have the following sine function
sin(x) = h/L
Make h the subject
h = L * sin(x)
This gives
h = 725 * sin(35)
Evaluate
h = 415.84
Hence, the kite is flying 415.84 feet from the ground
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Question is in the pic.
Answer is C as all other choices are even numbers therefore make the equation non-integer.
Answer:
C)7
Step-by-step explanation:
Due to the fact that all other options are even numbers so it Wii make the equation non-integer.
f(x) is a function. O A. True 0 False 6 12 9 f(x) 3 4 7
Answer:Answer: true
Step-by-step explanation: f(x) is a function because each x value (left oval) has one y value (right oval)!
A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
The width of the box is 3 ft that can be produced using the minimum amount of material.
What are the volume and surface area of a box?Consider a box with length 'l', width 'w' and height 'h',
Volume V = l × w × h
Surface area S = 2(lw + wh + hl)
Calculation:It is given that,
Volume of the box V = 36 cubic feet and l = 2w
Using the formulae,
V = 2w × w × h = 2w²h ...(1)
S = (2w² + 2wh + 4wh) = 2w² + 6wh ... (2) (here only single lw is considered since it is open top)
From equation (1),
36 = 2w²h
⇒ w²h = 18
⇒ h =18/w²
equation (2) becomes
S = 2w² + 6w(18/w²) = 2w² + 108/w ...(3)
So, for a minimum amount of material, the width of the box is,
On differentiating the surface area w.r.t 'w'
S' = 4w - 108/w²
For a minimum amount, substituting S' = 0 we get,
0 = 4w - 108/w²
⇒ 4w = 108/w²
⇒ 4w³ = 108
⇒ w³ = 27
∴ w = 3 feet
Therefore, the width of the given box is 3 feet.
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Comparing Ratios Using Fractions
Compare 4:10 and 12:20 using fractions. Which ratio is
smaller? How do you know?
Answer:
4:10
Step-by-step explanation:
4:10 = 4/10 = 2/5
12:20 = 12/20 = 6/10 = 3/5.
So 4:10 is smaller than 12:20 because 2/5 is less than 3/5.
Answer:
4:10
Step-by-step explanation:
First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.
Joe and Sue were trying to calculate the square inches of paper needed to create a cone for the cotton candy. The radius
was 2 in and the height was 6 inches and there was a 1/2 in of overlap for the glue.
Calculations
Joe
2π√10+ √10
Sue
12π + 3
choose the correct statements below.
select one or more:
Sue was correct.
Joe was correct.
Sue used the correct height and radius and calculated the overlap by adding the area for the strip of glue.
Neither were correct.
Joe used the height and radius to calculate the slant height.
The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
How to find the square inches of paper needed.The square inches of paper needed A = surface area of cone + area of overlap
Surface area of cone
The surface area of the cone is given by A = πr[r + √(h² + r²)] where
r = radius of cone = 2 in and h = height of cone = 6 in.So, A = πr[r + √(h² + r²)]
A = π × 2 × [2 + √(6² + 2²)]
A = π × 2 × [2 + √(36 + 4)]
A = π × 2 × [2 + √40]
A = π × 2 × [2 + 2√10]
A = 2π[2 + 2√10]
A = 4π + 4π√10
The area of overlap
The area of overlap A' = wL where
w = width of overlap = 1/2 in and L = slant height of cone = √(h² + r²)So, A' = wL
A' = w[√(h² + r²)]
A' = 1/2[√(6² + 2²)]
A' = 1/2[√(36 + 4)]
A' = 1/2[√40]
A' = 1/2 × 2√10
A' = √10
So, the number of square inches of paper needed is A" = A + A'
= 4π + 8π√10 + √10
Since the number of square inches of paper needed is 4π + 4π√10 + √10
So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
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Nancy left a bin outside in her garden to collect rainwater. she notices that 1 over 2 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin. show your work. explain your answer in words.
[tex]\frac{3}{4}[/tex] gallons of water fill the bin.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Given: Nancy left a bin outside in her garden to collect rainwater.
She notices that 1 over 2 gallons of water fills 2 over 3 of the bin.
To Find: Write and solve an expression to find the amount of water that will fill the entire bin.
Let's say the amount of Water to fill the bin = W gallon
Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{2W}{3}[/tex]Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{1}{2}[/tex] gallonEquate both:
[tex]\frac{2W}{3} =\frac{1}{2}[/tex] is the expression to find the amount of water that will fill the entire bin.
[tex]\frac{2W}{3} =\frac{1}{2} \\2W=\frac{3}{2} \\W=\frac{3}{4}[/tex]
Therefore, [tex]\frac{3}{4}[/tex] gallons of water fill the bin.
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11. Write four solutions for each of the following equation: (i)7x + 2y = 9 (ii) 2x = -5y
The solutions of the equations are (0,4.5), (1, 1), (2, -2.5) & (3, -6) and (0,0), (1, -0.4), (2, -0.8) & (3, -1.2)
How to determine the solutions?Equation 1
7x + 2y = 9
Make y the subject
2y = 9- 7x
Divide by 2
y = 4.5 - 3.5x
Let x = 0, 1, 2 and 3
y = 4.5 - 3.5 * 0 = 4.5
y = 4.5 - 3.5 * 1 = 1
y = 4.5 - 3.5 * 2 = -2.5
y = 4.5 - 3.5 * 3 = -6
Hence, the solutions of the equation are (0,4.5), (1, 1), (2, -2.5) and (3, -6)
Equation 2
2x = -5y
Make y the subject
y = -0.4x
Let x = 0, 1, 2 and 3
y = -0.4 * 0 = 0
y = -0.4 * 1 = -0.4
y = -0.4 * 2 = -0.8
y = -0.4 * 3 = -1.2
Hence, the solutions of the equation are (0,0), (1, -0.4), (2, -0.8) and (3, -1.2)
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Total area=
Help asap please thank u so much
The total area of the figure shown is 320 square units.
How to get the total surface area?
We can see that we have 4 triangular faces and one square face.
The area of a square of side length S is:
A = S²
Here we can see that the side length of the square is 10 units, then the area of the base is:
a = (10)² = 100
For a triangle of base B and height H, the area is:
[tex]A = B*H/2[/tex]
Here we can see that the base measures 10 units and the height 11 units, so the area of each triangular face is:
A' = (10)*(11)/2 = 55
Then the total area is:
area = 100 + 4*55 = 320
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The graph of a sinusoidal function intersects its midline at (0,−3)and then has a maximum point at (2,-1.5). Write the formula of the function, where x is entered in radians. f(x)= Please answer fast
The sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.
How to derive a sinusoidal function
In this question we must derive a sinusoidal function based on two given points. Sinusoidal functions are periodic functions that uses trigonometric functions and have the following form:
y = A · cos (2π · x/T) + B (1)
Where:
A - AmplitudeT - Period B - Vertical midpointThe horizontal distance between the midline and the maximum point is equal to a quarter of the period. Hence,
T = 4 · (2 - 0)
T = 8
The vertical midpoint and amplitude of the sinusoidal function are now calculated:
Vertical midpoint
B = - 3
Amplitude
A = - 1.5 - (- 3)
A = 1.5
Then, the sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.
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In which diagram do angles 1 and 2 form a linear pair?
2 lines intersect and form 4 angles. Labeled clockwise from the top: blank, 2, blank, 1.
3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.
A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.
A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
Mark this and return
The diagram where angles 1 and 2 form a linear pair is D. A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
What is a linear pair?It should be noted that a linear pair simply means angles that are formed when two lines intersect each other at a single point.
In this case, when a horizontal line has 1 line extending from it. Angles 1 and 2 are formed. This depicts a linear pair
In conclusion, the correct option is D.
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.For a field trip, 6 students rode in cars and the rest filled 8 buses. How many students were in each bus if 326 students were on the trip?
Let s represent the number of students on each bus.
Equation:
Answer:
Answer:
(326-6) ÷ 8 = s
40 = s
Step-by-step explanation:
What is the solution to the equation? 2(z-4)^3/2 = 54
5
13
22
no solution
If point a (-8, 9) was rotated clockwise 180o about the origin, what would its new coordinates be?
Answer:
(8, -9)
Step-by-step explanation:
Hope this helps:)
The point (-8,9) is rotated 180° in clockwise direction about the origin, the new coordinates is (8,-9).
According to the question,
The point (-8,9) is rotated 180° in clockwise direction about the origin, the new coordinates is (8,-9).
Hence, the new coordinates is (8,-9).
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nevan typed 110 words in 2 2/4 minutes. at this rate.how many words can he
type in 4 1/4
Answer:
ther will be 240 words in 4 1/4
Answer:
187 words.
Step-by-step explanation:
His rate of typing = 110 / 2 2/4
= 110 / 2.5
= 44 words / minute.
So in 4 1/4 minutes he will type
44 * 4 1/4
= 176 + 11
= 187 words.
I was born on saturday. got marries the 10,000 day of my life. what day of the week is it?
Answer:
Tuesday
Step-by-step explanation:
Days of the week repeat every seven days, so Saturday is day (1+7n) for some integer n.
Number of weeksThe value of n that makes the day number just under 10,000 is ...
1 +7n ≤ 10000
7n ≤ 9999
n ≤ 1428 3/7
Day of the weekSo, Day 1 +1428·7 = 9997 is Saturday. Day 10,000 is 3 days later. That makes Day 10,000 a Tuesday.
__
Additional comment
1428 weeks is about 27.5 years. You got married at age 27.
Which statement is true of the graph on the
right?
The average salary doubled between year 1
and 2.
The average salary tripled between year 1
and 3.
The average salary increased by the same
amount each year.
DONE
1. The TRUE statement about the graph, which is represented here by the data table, is D. The average salary increased by some irregular amount each year.
2. The average salary per year between 2001 and 2006 is $3,600?
What is an average?An average number is the mean of a total value.
The average is computed as the total value of observations divided by the number of observations.
Data for the graph and Calculations:Year Salary
2001 $1,500
2002 2,600
2003 3,200
2004 4,100
2005 5,000
2006 5,200
Total $21,600
Average = $3,600 ($21,600/6)
Thus, the graph or the data table shows that D. The average salary increased by some irregular amount each year.
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Question Completion:1. Option D: The average salary increased by some regular amount each year.
2, What is the average salary per year between 2001 and 2006?
Answer: C-The average salary increased by the same amount each year.
NEXT ANSWER-B
Step-by-step explanation:
what is the rule for the following sequence:
-1; -4; -9; -16; -25
Answer:
It´s an exponential rule. where one of the factors is negative
Step-by-step explanation:
1 * -1 = -1
2 * -2 = -4
3 * -3 = -9
4 * -4 = -16
5 * -5 = -25
When y = -8, x = 8, what is x when y = -6?
Answer:
x = 6
Step-by-step explanation:
y = -8
x = 8
-x = -8 = y
-x = y
now, when y is -6
-x = y = -6
-x = -6
x = 6
The shape of f(x) = √ x, but shifted nine units to the left and then reflected in both the x-axis and the y-axis
Answer:
g(x) = -√(-x +9)
Step-by-step explanation:
The relevant transformations are ...
f(x -h) . . . . . shifts the graph of f(x) right h unitsf(x) +k . . . . . shifts the graph of f(x) up k units-f(x) . . . . . . . reflects the graph of f(x) over the x-axisf(-x) . . . . . . . reflects the graph of f(x) over the y-axisApplicationApplying the transformations in the specified order, we have ...
f(x) = √x
f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left
-f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis
-f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis
The shifted, reflected function is ...
g(x) = -√(-x +9)
__
Additional comment
The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.
The last time troy checked, his dog weighed 60 kilograms. troy just measured his dog again and found out that it weighs 5% less now. how much does the dog weigh now?
Answer:
57 kg
Step-by-step explanation:
5% less means it weighs 95% of what it used to weigh
95% is .95 in decimal
.95 * 60 = 57 kg
these box plots show the basketball scores for two teams.
The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.
What is a box plot ?A box plot is used to study the distribution and level of a set of scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
A box plot is symmetric when the median is at the center of the box and negatively skewed if the median is closer to the upper quartile.
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POSSIBLE OUTCOMES!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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Solve for X. Please solve this.
Answer:
32
Step-by-step explanation:
Opposite angles are congruent, so Angle BAC is 58 degrees.
Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.
Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.
Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.
Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
-Write the piecewise function for 0 to 2 miles.
f(x) = ?
The piecewise function is
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
How to determine the piecewise function?From the question, we have:
Fares = $2.00 ⇒ up to (and including) 1/2 miles
Fares = $0.70 increment ⇒ greater than 1/2 miles
Let x represent the number of miles, and f(x) the fares.
So, we have:
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
The above represents the piecewise function
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Find the perimeter and area of the figure shown in the picture.
Answer:
52 units
Step-by-step explanation:
Perimeter = sum of it sides =
15 + 8 + 6 + 17 + 6
= 52
how many 2/7 are in 150
How many 2/7 are in 150 ?
= Their are 525.
I HOPE IT HELP YOU
There are 525 number of fraction 2/7 in number 150.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator, below one is called denominator.
Given,
fraction = 2/7
Given number = 150
Number of 2/7 in 150
= 150 ÷ 2/7
= 150 × 7/2
= 1050/2
= 525
Hence, 525 is the number of fraction 2/7 in number 150.
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