Nihal, Rosie and Isaac sold books at a car boot sale.
The ratio of the numbers of books that they each sold is 3:5:1
Rosie sold 32 more books than Isaac.
How many books did Nihal, Rosie and Isaac sell in total?

1. The points on the elliptic curve E: y^2 ≡ x^3 - 2 (mod 7) are:

(3, 4), (3, -4), (5, 4), (5, -4), (6, 4), (6, -4)

For the points on the elliptic curve E: y^2 ≡ x^3 - 2 (mod 7), we can substitute different values of x into the equation and check if they satisfy the congruence.

For x = 0, we have:

y^2 ≡ 0^3 - 2 ≡ -2 ≡ 5 (mod 7)

The congruence is not satisfied.

For x = 1, we have:

y^2 ≡ 1^3 - 2 ≡ -1 ≡ 6 (mod 7)

The congruence is not satisfied.

For x = 2, we have:

y^2 ≡ 2^3 - 2 ≡ 8 - 2 ≡ 6 (mod 7)

The congruence is not satisfied.

For x = 3, we have:

y^2 ≡ 3^3 - 2 ≡ 27 - 2 ≡ 25 ≡ 4 (mod 7)

The congruence is satisfied.

For x = 4, we have:

y^2 ≡ 4^3 - 2 ≡ 64 - 2 ≡ 62 ≡ 6 (mod 7)

The congruence is not satisfied.

For x = 5, we have:

y^2 ≡ 5^3 - 2 ≡ 125 - 2 ≡ 123 ≡ 4 (mod 7)

The congruence is satisfied.

For x = 6, we have:

y^2 ≡ 6^3 - 2 ≡ 216 - 2 ≡ 214 ≡ 4 (mod 7)

The congruence is satisfied.

Therefore, the points on the elliptic curve E: y^2 ≡ x^3 - 2 (mod 7) are:

(3, 4), (3, -4), (5, 4), (5, -4), (6, 4), (6, -4)

2. Now, let's find the sum of (3, 2) and (5, 5) on the curve.

Using the addition formula for elliptic curves, we have:

s = (y2 - y1) / (x2 - x1) ≡ (5 - 2) / (5 - 3) ≡ 3 / 2 ≡ 5 (mod 7)

x3 = s^2 - x1 - x2 ≡ 5^2 - 3 - 5 ≡ 25 - 3 - 5 ≡ 17 ≡ 3 (mod 7)

y3 = s(x1 - x3) - y1 ≡ 5(3 - 3) - 2 ≡ -2 (mod 7)

Therefore, the sum of (3, 2) and (5, 5) on the curve is (3, -2) or equivalently (3, 5) (since -2 ≡ 5 (mod 7)).

3. To determine 2(5, 5), we can find the sum of (5, 5) with itself:

2(5, 5) = (5, 5) + (5, 5)

Using the same addition formula as before, we have:

s = (y2 - y1) / (x2 - x1) ≡ (5 - 5) / (5 - 5) (The points are the same, so we take the slope as the limit) ≡ 0 (mod 7)

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Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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The table is not provided in the question. However, we can use some general probability principles to solve this problem.

We are given two events:

A: The outcome is a divisor of 2.

B: The outcome is prime.

We want to find the conditional probability of A given B, denoted by P(A | B).

The formula for conditional probability is:

P(A | B) = P(A and B) / P(B)

We need to find the probability of the intersection of A and B, i.e., P(A and B), and the probability of event B, i.e., P(B).

Since 2 is the only even prime number, we know that A is equivalent to the event "the outcome is 2". Therefore, we have:

P(A) = P(the outcome is 2)

We also know that the outcome is either prime or composite, and that the prime numbers less than 10 are 2, 3, 5, and 7. Therefore, we have:

P(B) = P(the outcome is 2, 3, 5, or 7)

To find P(A and B), we note that A and B are mutually exclusive events. Therefore, if the outcome is prime, it cannot be a divisor of 2. Thus, we have:

P(A and B) = P(the outcome is 2 and the outcome is prime) = 0

Using the above equations and applying the formula for conditional probability, we get:

P(A | B) = P(A and B) / P(B) = 0 / P(B) = 0

Therefore, the conditional probability of A given B is 0. This means that if the outcome is prime, the probability that it is a divisor of 2 is 0.

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The degree of rotation that transforms triangle ABC into A'B'C' is 15.07°.

To determine the degree of rotation, you need to find the angle between any two sides of one of the triangles and the corresponding two sides of the second triangle.

Let the original triangle be ABC and the image triangle be A'B'C'. In order to find the degree of rotation, we will take one side from the original triangle and compare it with the corresponding side of the image triangle. If there is a difference in angle, that is our degree of rotation.

We will repeat this for the other two sides. If the degree of rotation is the same for all sides, we have a rotation transformation.

Angle ABC = \(tan^-1[(-2 - 0) / (1 - 2)] + tan^-1[(5 - 0) / (-3 - 2)] + tan^-1[(0 - 5) / (2 - 1)]\)

Angle A'B'C' = \(tan^-1[(1 - 2) / (2 - 0)] + tan^-1[(-3 - 2) / (-5 - 0)] + tan^-1[(2 - 1) / (0 - 2)]\)

Now, calculating the angles we get:

Angle ABC = -68.20° + 143.13° - 90° = -15.07°

Angle A'B'C' = -45° + 141.93° - 63.43° = 33.50°

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Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

Answer:

The correct graph is graph B.

Answer:

c

Step-by-step explanation:

2+3x-18

Answer: the last one

Step-by-step explanation:

==========================================================

Explanation:

The main cluster of values is somewhere between 650 and 799, as this is where the highest bars are located. The median is somewhere in this region. The mean however is smaller than the median because the outliers to the left that pull on the mean. The outliers pull the mean toward them. Having small outliers will make the mean smaller than it should be. The median is not affected by outliers. Therefore, the median is the best measure of center in this case.

Side note: we consider this distribution to be "skewed to the left" or "negatively skewed" since the left tail is longer than the right tail.

Answer:

3 raise to -7 ÷3 raise to -10 × 3 raise to -5

3 raise to -7-(-10)×3 raise to -5

3 raise to 3×3 raise to -5

3 raise to 3+-5

3 raise to -2

1/3²

1/9

hope it helps you!

The function \(f(x)=(logn)2+2n+4n+logn+50 belongs to the Θ(n)\) complexity category, in accordance with the big theta notation.

Let's get started with the solution to the given problem.

The given function is:

\(f(x) = (logn)2 + 2n + 4n + logn + 50\)

The term 4n grows much more quickly than logn and 2n.

So, as n approaches infinity, 4n dominates these two terms, and we may ignore them.

Thus, the expression f(x) becomes:

\(f(x) ≈ (logn)2 + 4n + 50\)

Next, we can apply the big theta notation by ignoring all of the lower-order terms, because they are negligible.

Since 4n and (logn)2 both grow at the same rate as n approaches infinity,

we may treat them as equal in the big theta notation.

Therefore, the function f(x) belongs to the Θ(n) complexity category as given in the question,

which is a correct option.

Alternative way of solving:

Given function:

\(f(x) = (logn)2 + 2n + 4n + logn + 50\)

Hence, we can find the upper and lower bounds of the given function:

\(f(x) = (logn)2 + 2n + 4n + logn + 50<= 4n(logn)2 (\)\(using the upper bound of the function)\)

\(f(x) = (logn)2 + 2n + 4n + logn + 50>= (logn)2 (using the lower bound of the function)\)

So, we can say that the given function belongs to Θ(n) category,

which is also one of the options mentioned in the given problem.

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The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

Step-by-step explanation:

4/9 = 32 / x

Let x be any marble that is not red and the red ones.

Cross Multiply

4x = 9*32

4x = 288             Divide by 4

x   = 288/4

x = 72

So the whole bag contains 72 marbles.

Answer:

16

Step-by-step explanation:

father's age=46

half of father's age=46/2=23

Xiao's age=15

so when Xiao is half of her father age =23-15=8

then add 8 to his sister's age

so 8+8=16

hope its was helpful<3<3

plz rate the answer

Answer:

His sister will be 16 year old

Step-by-step explanation:

46/2 = 23

15-8=7

23-7=16

Answer:

x= 65 z= 38 y= 77

Step-by-step explanation:

x=65° (opposite angles are equal)

z= 180°-[71+71 (bc the other side is also equal to 71)]

z= 180°-142°=38°

y= 180 - [sum of angle x (65°) and angle z (38°)]

y= 180 - 103= 77°

to make sure ur answer is correct the sum of angle x, y and z MUST = 180

lets check:

65° + 38° + 77° = 180°

:)

The z-score that has 69.8% of the distribution's area to its right is approximately 0.47.

To find the z-score that corresponds to a given percentage of the distribution's area, we need to look up the z-score in the standard normal distribution table or use statistical software. In this case, we are interested in finding the z-score that has 69.8% of the distribution's area to its right.

When we refer to the right side of the distribution, we are considering the area under the curve from the z-score to positive infinity. Since the total area under the normal distribution curve is 1, the area to the right of a specific z-score corresponds to the remaining percentage.

By looking up the value of 69.8% in the standard normal distribution table or using statistical software, we can find that the z-score is approximately 0.47. This means that approximately 69.8% of the distribution's area lies to the right of the z-score of 0.47.

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Answer:

it is true

Step-by-step explanation:

Answer:

0.2584

Step-by-step explanation:

First off 10 to the 5th power is 10 x 5 = 50, so 12.92 / 50 is 0.2584.

let x as the total sales

26 250 = 14 250 + 0.06x

26 250 - 14 250 = 14 250 - 14 250 + 0.06x  (subtract 14 250 both sides)

12 000 = 0.06x

x = 200 000

26 250 = 14 250 + 0.06(200 000)

26 250 = 14 250 + 12 000

26 250 = 26 250

Therefore, Peter have total sales of RS 200 000.

Step-by-step explanation:

The man's rowing speed in still water is 8 miles per hour.

Let's assume the speed of the man in still water is represented by "x" miles per hour. Since the man is rowing downstream, his effective speed is increased by the speed of the current (2 miles per hour), resulting in a speed of (x + 2) miles per hour.

The distance traveled downstream is 30 miles, and the time taken to travel this distance can be calculated using the formula:

time = distance / speed

So, the time taken downstream is 30 / (x + 2) hours.

When the man turns around and rows upstream, his effective speed is reduced by the speed of the current (2 miles per hour), resulting in a speed of (x - 2) miles per hour.

The distance traveled upstream is also 30 miles, and the time taken to travel this distance can be calculated in the same way:

time = distance / speed

So, the time taken upstream is 30 / (x - 2) hours.

According to the problem, the total trip took 8 hours, so we can write the equation:

time downstream + time upstream = total time

30 / (x + 2) + 30 / (x - 2) = 8

To solve this equation and find the value of "x," we can multiply both sides of the equation by (x + 2)(x - 2) to eliminate the denominators:

30(x - 2) + 30(x + 2) = 8(x + 2)(x - 2)

Simplifying the equation:

\(30x - 60 + 30x + 60 = 8(x^2 - 4)\)

Combining like terms:

\(60x = 8x^2 - 32\)

Rearranging the equation:

\(8x^2 - 60x - 32 = 0\)

Now, we can solve this quadratic equation. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± \(\sqrt{(b^2 - 4ac)}\)) / (2a)

For this equation, a = 8, b = -60, and c = -32. Plugging these values into the quadratic formula:

x = (-(-60) ± \(\sqrt{(-60)^2 - 4 * 8 * -32)}\)) / (2 * 8)

x = (60 ± \(\sqrt{(3600 + 1024)}\)) / 16

x = (60 ± \(\sqrt{4624}\)) / 16

x = (60 ± 68) / 16

Simplifying further:

x = (60 + 68) / 16 or x = (60 - 68) / 16

x = 128 / 16 or x = -8 / 16

x = 8 or x = -0.5

The negative value, x = -0.5, doesn't make sense in the context of rowing speed, so the man's rowing speed in still water is 8 miles per hour.

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Answer:

2.28871.0005^14

Step-by-step explanation:

Answer:

i got 8067661468.26  

Step-by-step explanation:

The equation \(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0 is true

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

Using digits 0 to 9, no more than once each.

we want to place them in such a way that the division will be zero.

As we know that a quotient is equal to zero iff the numerator is equal to zero and the denominator other than zero.

So if we put some numbers on the numerator in such a way by adding them gives 0.

So, 5 - 3 - 2 = 0

Use all the other numbers in the denominator.

\(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0

which is true.

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Answer:

Line A is the right answer.

Answer:

a is right linear means straight line

Step-by-step explanation:

Answer:

X=6

Step-by-step explanation:

As you know x then you can use tan to do

\( \tan( \binom{5}{6} ) = o \\ \)

Then you will get the answer of 39°48'

Answer:

x=17.

Step-by-step explanation:

If you need me to explain this to you just comment .

hope this helps

Answer:

X=51÷3=17

Step-by-step explanation:

51÷3=

17

/(alternate angles)X=17

alternate angles

are always

eaqual

I hope this helps you

please mark me as brainliest

Answer:

60 degrees

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Its a fifth degree function so it will have 5 roots.

One of the 3 roots is complex ( imaginary):-  4 + i so there must be another root value 4 - i because these roots always occur as conjugate pairs.

The fifth root must be real because you cant have just one imaginary root.

Sum of two opposite angles in a Cyclic Quadiratral is 180°

\(\\ \sf\longmapsto 110+<CDE=180\)

\(\\ \sf\longmapsto <CDE=180-110\)

\(\\ \sf\longmapsto <CDE=70°\)

Answer:

let <CDE be x:

\({ \tt{110 \degree + x = 180\degree}} \\ \\ { \tt{x = 180 \degree - 110 \degree}} \\ \\ { \tt{x = 70 \degree}}\)