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Solve the congruence equation 11x ≡ 4 (mod 31)
"
Answers
The solution to the congruence equation 11x ≡ 4 (mod 31) is x ≡ 14 (mod 31).
To solve the congruence equation 11x ≡ 4 (mod 31), we can use the method of modular inverse.
First, we need to find the modular inverse of 11 modulo 31. The modular inverse of a number a modulo m is another number b such that (a * b) ≡ 1 (mod m).
To find the modular inverse of 11 modulo 31, we can use the extended Euclidean algorithm or observe that 11 * 19 ≡ 209 ≡ 1 (mod 31). Therefore, the modular inverse of 11 modulo 31 is 19.
Now, we can multiply both sides of the congruence equation by the modular inverse of 11 modulo 31:
19 * 11x ≡ 19 * 4 (mod 31)
209x ≡ 76 (mod 31)
Simplifying further:
x ≡ 76 ≡ 14 (mod 31)
So, the solution to the congruence equation 11x ≡ 4 (mod 31) is x ≡ 14 (mod 31).
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Related Questions
Describe the shape of the distribution.
A. It is symmetric.
B. It is uniform.
C. It is bimodal.
D. It is skewed.
Answers
Question #2: Write out the steps to solving the following example:
(
3
4
)
? Explain using relevant details and supporting evidence from the video above or other reference material.
Answers
Answer:
Unknown.
Step-by-step explanation:
Need more info.
Haematuria + frequency + dysuria what is the diagnosis and investigations?
Answers
To make a diagnosis, a healthcare provider may perform a physical exam, ask about the patient's medical history, and order diagnostic tests such as a urinalysis, urine culture, blood tests, or imaging studies (e.g. ultrasound, CT scan) to determine the underlying cause of the symptoms.
Treatment will depend on the underlying cause of the symptoms, but may include antibiotics for a UTI, pain medication, or other interventions as needed. It is important to seek medical attention promptly if you experience these symptoms to ensure that you receive appropriate treatment.
What is the probability that a randomly selected datum falls within 2 standard deviations of the mean? Answer with a decimal.
Answers
The probability that a randomly selected datum falls within 2 standard deviations of the mean as required is; 0.95.
What is the probability that a datum falls within 2 standard deviations of the mean?By observation, it follows that the distribution as represented in the task content above is a normal distribution.
On this note, the empirical rule applies as follows;
For a standard normal distribution, 68% of the observations (datum) fall within 1 standard deviation of the mean; 95% of the datum lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.
On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.
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In a town there are 4352womens,5821mens and3670childrens estimate the town population by rounding of number to the nearest hundred
Answers
Answer:
13900
Step-by-step explanation:
You want an estimate of the total of 4352, 5821, and 3670 by rounding to hundreds.
EstimateThe rounded values, in hundreds, are 44, 58, 37. The sum of these is 139 hundred, or ...
13900
The town's population is estimated to be 13900.
<95141404393>
4. Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a= 8.1 in
b= 13.3 in
c= 16.2 in
ANSWERS:
1. A = 27.9°, B=54.8°, C=97.3°
2. A = 29.9°, B=54.8°, C=95.3°
3. No triangle satisfies the given conditions
4. A= 31.9°, B=52.8°, C=95.3°
Answers
Answer:
To determine the missing parts of the triangle, we can use the law of cosines, which states that for a triangle with sides of lengths a, b, and c and angles opposite those sides of A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab cos(C)
b^2 = a^2 + c^2 - 2ac cos(B)
a^2 = b^2 + c^2 - 2bc cos(A)
Using the given values of a, b, and c, we can solve for the angles A, B, and C.
a = 8.1 in
b = 13.3 in
c = 16.2 in
c^2 = a^2 + b^2 - 2ab cos(C)
cos(C) = (a^2 + b^2 - c^2) / (2ab)
cos(C) = (8.1^2 + 13.3^2 - 16.2^2) / (2 * 8.1 * 13.3)
cos(C) = 0.421
C = cos^-1(0.421)
C ≈ 97.3°
b^2 = a^2 + c^2 - 2ac cos(B)
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(B) = (8.1^2 + 16.2^2 - 13.3^2) / (2 * 8.1 * 16.2)
cos(B) = 0.268
B = cos^-1(0.268)
B ≈ 54.8°
We can find angle A by using the fact that the sum of the angles in a triangle is 180°:
A = 180° - B - C
A = 180° - 54.8° - 97.3°
A ≈ 27.9°
Therefore, the missing parts of the triangle are:
A ≈ 27.9°
B ≈ 54.8°
C ≈ 97.3°
So, the answer is option 1.
Two gym classes are participating in Field Day. One class has 24 students and the other has 27 students. The gym teachers want to divide the students in each class into the largest possible equal groups, with no students left over. If all the groups have the same number of students, how many students are in each group?
Answers
Answer:
bilmiyorum, bulamadım.
class 1 - 8 groups
class 2 - 9 groups
let me know if i’m right because i’m not 100% sure!
For what value of x is line / parallel to line m in this figure?
Answers
Answer:
132
Step-by-step explanation:
The angle with a measure of 48 degrees and the angle labeled "x" are supplementary angles. Supplementary angles add up to equal 180
This means that we can find the value of the missing angle by subtracting the measure of the known angle from 180
So x = 180 - 48
180 - 48 = 132
Hence, x = 132
Calculate the quotient below and give your answer in scientific notation.
3.8 x 10^9
400
= ?
Answers
Answer:
If your adding the 400 then it will be 3800000400
if your subtracting 400 it will be 3799999600
If your dividing 400 it will be 76000000000
If you multiplying 400 it will be 152000000000
Hope i helped
Dylan and his friends are going into a bakery. How much would it cost to buy 1 cookie and 5 brownies if each cookie costs $0.50 and each brownie costs $2.25? How much would it cost to buy 11 cookies and 55 brownies if each cookie cost \$c$c and each brownie cost \$b?$b?
Answers
Answer:
a)$ 11.75
b) $ 129.25
Step-by-step explanation:
Dylan and his friends are going into a bakery.
Each cookie costs $0.50 and each brownie costs $2.25?
a) How much would it cost to buy 1 cookie and 5 brownies
1 × $0.50 + 5 × $2.25
= $0.50 + 11.25
= $ 11.75
b) How much would it cost to buy 11 cookies and 55 brownies
11 × $0.50 + 55 × $2.25
= $5.5 + $123.75
= $ 129.25
What is the average rate of change of the exponential function g(x)=2^x-1 between x=3 and x=7?
Answers
The average rate of change over the interval x = 3 and x = 7 is 30
How to determine the average rate of changeThe average rate of change of a function, graph, table or ordered pair is simply the slope of the relation
The equation is given as
g(x) = 2ˣ - 1
The interval is given as:
x = 3 and x = 7
Start by calculating g(3) and g(7)
So, we have
g(3) = 2³ - 1 = 7
g(7) = 2⁷ - 1 = 127
So, the average rate over these intervals is calculated as:
Average rate = [g(b) - g(a)]/[b - a]
This gives
Average rate = [g(7) - g(3)]/[7 - 3]
Substitute known values
Average rate = [127 - 7]/[7 - 3]
Simplify
Average rate = 120/4
Average rate = 30
Hence, the average rate of change is 30
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A wire is first bent into the shape of a square. Each side of the square is 9cm long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 13cm, what is its width
Answers
Answer:
5 cm
Step-by-step explanation:
the perimeter of a square with sides of 9 cm is 36 cm so the rectangle must have the same perimeter
if the length of the rectangle is 13cm, its opposite side is also 13cm
add 13 + 13 to get 26
let 'n' = width of rectangle
perimeter = 26 + n + n
36 = 26 + 2n
2n = 10
n = 5
If the length of the rectangle is 13 cm then the width of the rectangle will be equal to 5 cm.
What is the perimeter?A shape's perimeter is the whole distance encircling it. It is the perimeter or length of the contour of any two-dimensional geometric body. The circumference of several figures could be compared based on the measurements.
As per the information given in the question,
Length of the side of the square = 8 cm
Then, use the formula of the perimeter of the square = 4 × side
= 4 × 9 = 36 cm
The length of the rectangle = 13 cm
Use the formula of the perimeter of the rectangle,
P = 2(l + w)
36 = 2(13 + w)
36 -26 = 2w
w = 10/2
w = 5 cm
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Which equation can be used to prove 1 + tan?(x) = sec2(x)?
cos?(x), sin?(x) =_1
sec?(x) sec (x) sec?(x)
cos?(x), sin?(x) 1
sin?(x) sin?(x) sin?(x)
cos?(x), sin?(x) =_1
tan?(x) tan(x) tan2(x)
O
cos?(X) + sin?(X) - 1
cos(x) cos(x) cos(x)
Answers
Answer: D
Step-by-step explanation:
a triangle and a quadrilateral are special cases of a
Answers
A triangle and a quadrilateral are special cases of a polygon.
A polygon is a two-dimensional geometric shape that is formed by connecting a finite number of line segments called sides. It is a closed figure with straight sides.
A triangle is a polygon with three sides, while a quadrilateral is a polygon with four sides.
In general, a polygon can have any number of sides greater than or equal to three. Triangles and quadrilaterals are specific examples of polygons with a fixed number of sides.
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Write an expression for 213 increased by d.
Answers
Write an expression for 213 increased by d: \(213+d=x\)
Avery's bottle holds 400 milliliters.
Dashawn's bottle holds 3/4 as much
How many milliliters of water do both containers hold?
Answers
Answer:
you could make this really simple by dividing 300 by 4 to see how much 1/4 of that is and then subtracting 1/4 from 300 to see how much dashawn's water bottle holds,
Step-by-step explanation:
300/4 =75 so 1/4 is equal to 75 mL
300-75=225mL
Dashawn's water bottle holds 225mL
What is the value of the question mark
Answers
Check the picture below.
The amount of rust on an old car doubles every three years. If there are 12 g of rust initially how long will it take for 96 g of rust to be formed?
Answers
Answer: 9
Step-by-step explanation:
12 doubled in 3 years = 24
24 doubled in next 3 years = 48
48 doubled in another 3 years= 96
3 years x3 is needed
Mrs. Thomas walks 3/4
of a mile every 1/3
of an hour. How far can she walk in an hour?
Answers
Answer:
dunno
Step-by-step explanation:
Answer:2.25
Step-by-step explanation:
3/4 is equal to 0.75 and 0.75*3=2.25
the outbound trip of a bus was made at 24mi/h, while the return trip was made at 30mi/h. find the one way distance fi the total running time was 4.5 hour.
Answers
With a running time of 4.5 hours and speeds of 24 mph and 30 mph, respectively, the bus covered a one-way distance of 72 miles.
With a running time of 4.5 hours and speeds of 24 mph outgoing and 30 mph inbound, the bus covered a one-way distance of 72 miles.
As the outgoing and inbound timings were equal, the computation was performed by multiplying the outbound trip's speed by the entire running time, and then dividing the result by two. Therefore, 108 miles are equal to 24 mph times 4.5 hours. The one-way distance is equal to 72 miles when you divide this result in half. When both directions' speeds are known, this calculation can be used to determine the overall distance of a round trip.
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What is the value of x in the figure?
400
709
A.
40°
B.
70°
C.
80°
D.
120°
E.
150°
Answers
Answer:
e
Step-by-step explanation:
How many factors does 72 have.
Answers
Answer:
12 factors
Since 72 is a composite number, it has more than two factors. We can use division to check whether 4, 18, and 24 are factors of 72. As they leave no remainder, they are indeed the factors of 72! 72 has a total of 12 factors: 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.
Step-by-step explanation:
Show the family of conics with the same focus
x^2/a^2+C + y^2/b^2+C = 1
is its own orthogonal family of curves.
Answers
The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.
First, we take the derivative of the equation with respect to x:
2x/a^2 = -2y/b^2 * dy/dx
Simplifying, we get:
dy/dx = -b^2*x/a^2*y
Now, we set this equal to -1/b^2:
-b^2*x/a^2*y = -1/b^2
Cross-multiplying and simplifying, we get:
x/a^2*y = 1/b^2
Finally, we can rearrange this equation to get:
y = b^2*x/a^2
This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
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2. Five pens of the same type cost the same as two notebooks of the same type. If one pen and two
notebooks cost $4.20, what is the cost of one pen?
Answers
a dinner offers a choice of wo side items from the liste with each entree. how many ways can two items be selected?
Answers
The number of ways two side items can be selected from a list depends on the number of items on the list.
For instance, if there are five side items on the list, the number of ways to choose two items from the list can be calculated as 5C2, which equals 10.
To determine the number of ways to select two side items from a list, we need to use the combination formula, nCr. In this case, n represents the number of items on the list, and r represents the number of items to be selected (in this case, 2). Using the formula, 5C2 is equal to 5! / (2! x (5-2)!) = 10. Therefore, there are 10 ways to select two side items from a list of 5.
The number of ways two side items can be selected from a list depends on the number of items on the list. To calculate this, we use the combination formula, nCr. In this case, n represents the number of items on the list, and r represents the number of items to be selected. By applying this formula, we can determine the number of ways two items can be selected from a given list.
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Seventy-Two Inc. , a developer of radiology equipment, has stock outstanding as follows: 80,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $33,000; second year, $72,000; third year, $100,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years.
Preferred stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year
Common stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year
Answers
The dividends per share on preferred stock for four years is $0.12, $0.12, $0.12, $0.12 and for common stock is $0.057, $0.152, $0.220, $0.220.
To calculate the dividends per share for each class of stock, we need to first determine the total dividends paid in each year.
For the preferred stock, the dividends are cumulative, which means any unpaid dividends from previous years must be paid before any dividends can be paid to common stockholders. Therefore, we need to calculate the total amount of unpaid dividends for each year before we can determine the amount available for common stockholders.
To calculate the unpaid dividends for the preferred stock in each year, we need to multiply the number of shares of preferred stock by the dividend rate (3%) and subtract the dividends paid in that year.
Unpaid dividends for preferred stock:
1st year: (80,000 x $20 x 0.03) - $33,000 = $9,600
2nd year: (80,000 x $20 x 0.03) - $72,000 - $9,600 = $9,600
3rd year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600
4th year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600
Now we can calculate the total dividends available for common stockholders in each year by subtracting the unpaid dividends for preferred stock from the total dividends paid in that year.
Total dividends available for common stockholders:
1st year: $33,000 - $9,600 = $23,400
2nd year: $72,000 - $9,600 = $62,400
3rd year: $100,000 - $9,600 = $90,400
4th year: $100,000 - $9,600 = $90,400
Finally, we can calculate the dividends per share for each class of stock by dividing the total dividends by the number of shares outstanding.
Dividends per share:
Preferred stock:
1st year: $9,600 / 80,000 = $0.12 per share
2nd year: $9,600 / 80,000 = $0.12 per share
3rd year: $9,600 / 80,000 = $0.12 per share
4th year: $9,600 / 80,000 = $0.12 per share
Common stock:
1st year: $23,400 / 410,000 = $0.057 per share
2nd year: $62,400 / 410,000 = $0.152 per share
3rd year: $90,400 / 410,000 = $0.220 per share
4th year: $90,400 / 410,000 = $0.220 per share
Therefore, the dividends per share on each class of stock for each of the four years are as follows:
Preferred stock (dividends per share)
1st Year: $0.12 per share
2nd Year: $0.12 per share
3rd Year: $0.12 per share
4th Year: $0.12 per share
Common stock (dividends per share)
1st Year: $0.057 per share
2nd Year: $0.152 per share
3rd Year: $0.220 per share
4th Year: $0.220 per share
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Which one of these is not a step used when constructing an inscribed equilateral triangle using technology? (5 points)
Create a circle using the center with given point tool.
Use the compass tool to create three more circles, with the same radii as the first.
Connect the point with a line through the center of the circle.
Create another circle with the same radius as the original.
Answers
Answer:
again i can not see the given point
Step-by-step explanation:
Graphically, a point is a solution to a system of two inequalities if and only if the point lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality. lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality. lies in the shaded regions of both the top and bottom inequalities. does not lie in the shaded region of the top or bottom inequalities.
Answers
Answer:
lies in the shaded regions of both the top and bottom inequalities
Step-by-step explanation:
For a point to be a solution of two inequalities, it must lie in both solution sets. It ...
lies in the shaded regions of both the top and bottom inequalities
We want to define when a point is a solution of a system of inequalities, we will see that the correct option is: "lies in the shaded regions of both the top and bottom inequalities."
Just like in a system of equations, a solution of the system is must be a solution of both equations.
Here, a solution ot the system of inequalities must be at the same time a solution of each inequality.
Remember that the solutions of the inequalities are represented by shaded regions, so the point must belong to the intersection of the two shaded regions.
So the correct option is:
"lies in the shaded regions of both the top and bottom inequalities."
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Please, Just please help me
Answers
Answer:
58
Step-by-step explanation:
The median is the middle number
There are 12 data points so we need to average the 6th and 7th numbers
57 is the 6th data point and
59 is the 7th data point
(57+59)/2 = 58
State the x- and y-intercepts for the given
function. Then graph the function
3x + 2y = 6
Answers
Answer:
x-intercepts: (2,0)
y-intercepts: (0,3)
Step-by-step explanation: