if f is​ continuous, the average value of the polar coordinate r over the curve r​f(​), ​, with respect to is given by the formula . use this formula to find the average value of r with respect to over the following curves ​(a​0).a. the cardioid rb. the circle rac. the circle ​,

Answer:

Jamie has 44 pairs of shoes

Step-by-step explanation:

Let

Jamie= x pairs of shoes

Suzie= 33 less than twice the amount of shoes Jamie has

2x - 33 = 55

Solve:

2x - 33 = 55

Collect like terms

2x = 55 + 33

2x = 88

Divide both sides by 2

2x / 2 = 88 / 2

x = 44

Jamie = x = 44 pairs of shoes

Therefore, Jamie has 44 pairs of shoes

Answer:

Step-by-step explanation:

There are 10 cubes all together.

You want blue and then red with replacement.

Blue

P(B then red) = 3/10 * 4/10 = 12 / 100

12/100 reduces to 3/25

The answer is A

Answer:

A?

Step-by-step explanation:

The domain of the function exists \($(-\infty, \infty)$\) range be \($[0, \infty]$\).

The components of a function are its Domain and Range. In contrast to a function's range, which is the set of all potential outputs, a function's domain is the set of all possible inputs.

All x-values, or inputs, and all y-values, or outputs, make up a function's domain and range, respectively. When viewing a graph, the domain consists of all of the graph's values from left to right. The graph's entire range, from the bottom to the top, is the range.

By listing all of the values in the column that corresponds to the input values on a mapping diagram, the domain of the function may be identified.

In general, the domain of any polynomial is \($(-\infty, \infty)$\).

The range of a positive polynomial \($y=x^a$\) where a is even is \($[0, \infty]$\).

Therefore, the domain exists \($(-\infty, \infty)$\)

Range exists \($[0, \infty]$\).

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Answer:

it's C. 5

Step-by-step explanation:

When x = 2

y = 13 - 4 * 2

= 13 - 8

= 5

Hope it will help :)❤

Answer:

Sorry about the incorrect answer

First there's some correction in your solution

and you have put value x=3 in

the correct calculation will be,

Now, answer of the (b) part is,

Given curve is,

and point P lies on C and the gradient at that point is 1.

We will take point P on curve C as

Put point P in curve C, we will get,

Now, we will differentiate

we will get,

Now, we have given that gradient at point P is 1,

corresponding these points we will get y=

So, possible co-ordinate of P is

Answer:

my fav anime is naruto :)

Step-by-step explanation:

Answer:

naruto and MHA

Step-by-step explanation:

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

60.2 is the average

Step-by-step explanation:

add all numbers together to get: 301

divide 301 by 5 because there are 5 numbers total to get: 60.2

a. The fraction of peron can it in the Garden Space is 9/40.

b. The percent of the peron can it in the Garden pace is 45%.

c. The fraction of the peron that can it in the Garden pace a a decimal is 0.45.

From the information illustrated, Café Aylanto ha a 200-peron eating capacity. If 45 peron can it in the outdoor Garden pace:l.

The fraction of peron can it in the Garden Space is:

= 45 / 200

= 9 /40

The percent of the peron can it in the Garden pace will be:

= 9/20 × 100

= 45%

The fraction of the peron that can it in the Garden pace a a decimal will be:

= 45 / 100

= 0.45

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As we have proved that if p is an odd prime, then the product 1² · 3² · ... · (p-2)² is congruent to -1 modulo p.

To prove the statement, let's consider the product P = 1² · 3² · ... · (p-2)². Our goal is to show that P ≡ -1 (mod p), which means P leaves a remainder of -1 when divided by p.

First, we note that p is an odd prime. This means that p can be expressed as p = 2k + 1, where k is an integer. We can rewrite P using this representation:

P = (1 · 1) · (3 · 3) · ... · ((2k - 1) · (2k - 1)).

Now, let's examine P more closely. We can write each factor in P as:

(2i - 1) · (2k - (2i - 1)).

Expanding this expression, we get:

(2i - 1) · (2k - 2i + 1) = 4ik - 2i + 2ki - k - 2i + 1 = 4ik - 4i + 2ki - k + 1.

We can simplify this further as:

(4ik - 4i + 2ki - k + 1) = (4ik - 4i) + (2ki - k + 1) = 4i(k - 1) + k(2i - 1) + 1.

Now, let's consider the expression (2i - 1) modulo p. Since p = 2k + 1, we can rewrite (2i - 1) as:

(2i - 1) ≡ 2i - 1 (mod p).

Substituting this back into our expression for P, we have:

P ≡ (4i(k - 1) + k(2i - 1) + 1) (mod p).

Now, let's consider the sum (4i(k - 1) + k(2i - 1)) modulo p. We can write this as:

(4i(k - 1) + k(2i - 1)) ≡ 4ik - 4i + 2ki - k ≡ -3i + k(i - 1) (mod p).

Since p = 2k + 1, we have -3i + k(i - 1) ≡ -3i + (p - 1)(i - 1) (mod p).

Expanding (p - 1)(i - 1), we get:

-3i + (p - 1)(i - 1) = -3i + pi - p - i + 1 = -4i - p + pi + 1.

Now, let's consider the expression (-4i - p + pi + 1) modulo p. We can rewrite this as:

(-4i - p + pi + 1) ≡ -4i - p (mod p).

Since -p ≡ 0 (mod p), we have -4i - p ≡ -4i (mod p).

Therefore, we have shown that:

P ≡ -4i (mod p).

Now, let's consider the range of i. We know that i takes on values from 1 to (p - 2)/2, inclusive. Since p is an odd prime, (p - 2)/2 is an integer. Therefore, we can rewrite P as:

P ≡ -4(1 + 2 + 3 + ... + [(p - 2)/2]) (mod p).

The sum 1 + 2 + 3 + ... + n can be expressed as n(n + 1)/2. Substituting this into our expression for P, we get:

P ≡ -2[(p - 2)/2] [(p - 2)/2 + 1] (mod p).

Simplifying further, we have:

P ≡ -[(p - 2)/2] [(p - 2)/2 + 1] (mod p).

Since p is an odd prime, we can rewrite p - 2 as 2k - 1. Substituting this into our expression, we get:

P ≡ -[k] [k + 1] (mod p).

Now, let's expand the product [k] [k + 1]:

[k] [k + 1] = k² + k.

Substituting this back into our expression for P, we have:

P ≡ -(k² + k) (mod p).

Now, recall that p = 2k + 1. Substituting this into our expression, we get:

P ≡ -(k² + k) ≡ -(k² + k + 1) + 1 ≡ -(k² + 2k + 1) + 1 ≡ -[(k + 1)²] + 1 (mod p).

Since p = 2k + 1, we have (k + 1)² ≡ -1 (mod p). Substituting this back into our expression, we finally have:

P ≡ -[(k + 1)²] + 1 ≡ -1 + 1 ≡ 0 ≡ -1 (mod p).

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Answer:

50.2

Step-by-step explanation:

Answer:

50.24 should be correct, (2 * pi) * r.  With pi = 3.14 and radius = 8, we get 50.24.

Answer:

\( x = 3y \)

\(7x+4y= 12 + 4x+7y\)

Step-by-step explanation:

Para resolver la pregunta, basta con definir variables adecuadas y traducir cada relación. Sea x el costo de una caja grande e y el costo de una caja pequeña. Tenemos que el costo de una caja grande es igual a 3 cajas pequeñas. Es decir, x = 3y. Luego, tenemos que

\(7x+4y= 12 + 4x+7y\)

pues al sumarle 12 al costo de 4grande y 7 pequeñas obtenemos el costo de 7 grande y cuatro pequeñas. De aquí, el sistema de ecuaciones que modela el sistema es

\( x = 3y \)

\(7x+4y= 12 + 4x+7y\)

Answer:

Step-by-step explanation:

The equation is actually y=mx+b

M is the slope

B is the Y-intercept

Y=14x+b

Answer:

y = 14x

Step-by-step explanation:

equation: y = mx

Slope(m) = 14

Since the line passes through the origin, there is no y-intercept, so the equation is in y = mx form. Since we're given the slope(m), all we have to do is rewrite the equation with the given value of m:

y = 14x

The measure of this angle in degrees is 20.52 degrees.

Step by step explanation:Given data is,1/360th of the circumference of the circle is 0.59 cm long Arc length, s = 103.25 cm We need to find the measure of the angle in degrees. Since we know that, the angle subtended by an arc at the center of the circle is 2θ, where θ is the angle subtended by the arc at any point on the circumference of the circle.And the circumference of the circle is 360θ.

Hence, we can find the length of the circumference of the circle. Circumference of the circle = 360 × 0.59Circumference of the circle = 212.4 cmNow, we can find the radius of the circle.r = s/2πr = 103.25/(2 × π) = 16.441 cmDiameter of the circle = 2 × rDiameter of the circle = 32.882 cmThe circumference of the circle = πdCircumference of the circle = π × 32.882Circumference of the circle = 103.26 cm Now, we can find the angle of the circle. Angle of the circle = 360θ103.26 = 360θθ = 103.26/360θ = 0.286 degrees So, the measure of this angle in degrees is 20.52 degrees.

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Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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Answer:

\( \sqrt{30} \)

Therefore, an expression for the height of the triangle is 8x³/3.

A triangle is a geometric shape that has three sides and three angles. It is one of the simplest polygons and is found in many different areas of mathematics and science. Triangles can be classified based on the lengths of their sides and the measures of their angles.

There are several types of triangles, including:

Equilateral triangle: A triangle with three equal sides and three equal angles of 60 degrees each.

Isosceles triangle: A triangle with two equal sides and two equal angles opposite those sides.

Scalene triangle: A triangle with no equal sides and no equal angles.

Right triangle: A triangle with one angle measuring 90 degrees, which is also the angle between the two shorter sides, called the legs. The longest side is called the hypotenuse.

Acute triangle: A triangle where all three angles are acute, or less than 90 degrees.

Obtuse triangle: A triangle with one obtuse angle, or greater than 90 degrees.

Triangles have a number of properties and formulas associated with them, such as the Pythagorean theorem, the Law of Sines, and the Law of Cosines. Understanding the properties of triangles is essential in many fields, including trigonometry, calculus, and geometry.

Here,

The formula for the area of a triangle is given by the formula:

Area = (base × height) / 2

We are given that the area of the triangle is represented by the expression 18x⁵ + 72x³, and the base of the triangle is 9x². Let h be the height of the triangle. Then we can set up an equation for the area of the triangle:18x⁵ + 72x³ = (9x² × h) / 2

We can simplify this equation by multiplying both sides by 2 and dividing by 9x²:

2(18x⁵ + 72x³) / 9x² = h

Simplifying the expression on the left-hand side gives:

2(2x³ × 9x² + 2x³ × 18) / 9x² = h

2x³(2 × 9x² + 2 × 18) / 9x² = h

2x³(36x^2) / 9x² = h

8x⁵ / 3x² = h

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The probability that the sample average amount of time taken on each day is at most 11 min is 0.5167

To solve for the probability proportion, we make use of the z statistic. The procedure to do is to calculate for the z value and using the standard probability tables, we can look up for the p value. The formula for z score is:

z =(x – μ) / (σ / √n))

where,

x = sample score = 11

μ = sample mean= 10

σ = standard deviation = 4

n = sample size

Calculating for the z and p value when n = 5:

z =(11 – 10) / (2 /√(5))

z = 0.55

Using the tables, p(5) = 0.7088

Calculating for the z and p value when n = 6:

z =(11 – 10) / (4/ √6))

z = 0.61

Using the tables, p(6) = 0.7290

If both days should be occurring, therefore the total probability that each day is at most 11 min is:

p total = p(5) * p(6)

p total = 0.7088 * 0.7290

p total = 0.5167

Hence the average amount of time taken on each day is at most 11 min.

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The sequence whose nth term is (2n+1)/(3n-1) converges to the number 2/3.

To use L'Hopital's rule, we need to take the limit of the ratio of the nth term and (n-1)th term as n approaches infinity.

Let a_n be the nth term of the sequence. lim (n->∞) a_n / a_(n-1) = lim (n->∞) (2n+1)/(3n-1) / (2n-1)/(3n-4) = lim (n->∞) [(2n+1)/(3n-1)] * [(3n-4)/(2n-1)] = lim (n->∞) [6n^2 - 5n - 4]/[6n^2 - 7n + 4]

By applying L'Hopital's rule, we can find that the limit of this ratio as n approaches infinity is 1. Thus, the sequence converges to the same limit as the ratio of consecutive terms, which is 2/3.

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Answer:

1/10

Step-by-step explanation:

I think

Answer:

Tin

Step-by-step explanation:

Density

=mass÷volume

=277÷38

=7.3 g/cm3

Hope this helps!

Answer: D. -5, 0, 0.8, 1, 1 1/2

Hope this helps!

Answer:

D. -5, 0, 0.8, 1, 1 1/2

Step-by-step explanation:

Using pythagoras theorem

Answer:

do you mean in simplest form

if so then it is 2:3

if not then 6

Step-by-step explanation:

Answer:

85.40

Step-by-step explanation: This is because if you do $70*22%, this gives $15.4. Now add this to $70 to get 80.40!  So, the total is 80.40.

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

The answer is B

Step-by-step explanation:

They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

If u and v are vectors in R^n, then:

u^T v and v^T u are related as transposes of each other. Specifically, if

u = [u_1, u_2, ..., u_n]^T

and v = [v_1, v_2, ..., v_n]^T

then:

u^T v = v^T u

= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n

So, u^T v and v^T u are scalar values that represent the dot product of u and v.

uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T

then:

uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;

u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;

...;

u_n * v_1, u_n * v_2, ..., u_n * v_n]

vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;

v_1 * u_2, v_2 * u_2, ..., v_n * u_2;

...;

v_1 * u_n, v_2 * u_n, ..., v_n * u_n]

So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

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The equation of the line in slope-intercept form is y = - 6x + 3

The two-point form of the equation of a line is used to find the equation of a straight line that passes through two given points, (x₁, y₁) and (x₂, y₂).

The formula for the two-point form is:

          (y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Here we have

A graph that passes through (0, 3) and (1, -3)

As we know the two-point form of the equation of a line is:

              (y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)  

Take (0, 3) = (x₁, y₁) and (1, -3) = (x₂, y₂)

Substituting the values from the given points, we get:

=>  (y - 3)/(x - 0) = (-3 - 3)/(1 - 0)

=>  (y - 3)/(x) = (- 6)

=>  y - 3 = - 6x

=>  y = - 6x + 3

Therefore,

The equation of the line in slope-intercept form is y = - 6x + 3

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