100 POINTS

say a cool fact about a famous mathematician

Answer:

17.7cm  (1.d.p)

Step-by-step explanation:

First do \(16^{2}\) (16 x 16) add \(7.5^{2}\) (7.5x7.5)

That gives us 312.25 cm

Then find the square root of that \(\sqrt{312.25\)

That equals 17.67059705

If you do it to one decimal place, \(x^\) is 17.7cm

Pleeease give brainliest, have a nice day.

Step-by-step explanation:

Here

\( \sf \: volume_{(Cylinder)} {\gray{\begin{cases} \sf \rightarrowtail \: \pi {r}^{2}h \\ \sf \rightarrowtail \: 3.14 \times {(2.1)}^{2} \times 6.3 \\ \sf \rightarrowtail \: 3.14 \times 4.41 \times 6.3 \\ \sf \rightarrowtail \: 87.23 \\ \sf \rightarrowtail \: 87.2 {m}^{3} \end{cases}}}\)

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

To know more about probability,

https://brainly.com/question/28005248

#SPJ11

Answer:

He did not square 40, he just multiplied by 2

Answer 41 centimeters.

Step-by-step explanation:

C²=40²+9²

C²=1600+81

C²=1681

√c²=√1681

C=41cm

Answer:

the answer is A

Step-by-step explanation:

edg

Answer:

2

Step-by-step explanation:

8/4 = 2

Answer:

2

Step-by-step explanation:

The solution to the proportion is x = 5.

solve the proportion (3x - 6)/2 = (4x - 2)/4, we can cross-multiply.

First, we multiply the numerator of the left fraction with the denominator of the right fraction:

2 * (4x - 2) = 4 * (3x - 6)

Next, we simplify both sides of the equation:

8x - 4 = 12x - 24

Now, we can rearrange the equation by subtracting 8x from both sides:

-4 = 4x - 24

To isolate the variable, we add 24 to both sides:

20 = 4x

Finally, we divide both sides by 4 to solve for x:

x = 5

Therefore, the solution to the proportion is x = 5.

Know more about denominator here:

https://brainly.com/question/32621096

#SPJ11

Answer:

-45=-2x+15

-45-15=-2x

-60=2x

x=30

Answer:

French: la somme d'un nombre inconnu et 12

Spanish: la suma de un número desconocido y 12

Latin: XII numerus ignotus est et summa

Step-by-step explanation:

If we firstly consider only the terms in x.

subtract 2x from both sides of the equation

⇒5+2x

−2x=2x−2x

+6

Observe that the x terms are eliminated and we are left with

5+0=0+6 that is 5=6 which is invalid

There is no solution to this equation.

Answer:

no solution

Step-by-step explanation:

Given

5 + 2x = 2x + 6 ( subtract 5 from both sides )

2x = 2x + 1 ( subtract 2x from both sides )

0 = 1 ← not possible

Thus indicates the equation has no solution

Area of the region enclosed by one loop of the curve is pi/288.

To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:

A = 1/2 * ∫(r^2)dθ

We can use this formula with the equation for r given:

A = 1/2 * ∫(sin^2(6θ))dθ

This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))

Thus,

A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ

This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).

Therefore, the area enclosed by one loop of the curve is

A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6

A = (1/48)(sin(2pi) + pi/6)

   = (1/48)(0 + pi/6)

   = pi/288

To know more about  area of loop of the curve refer to:

brainly.com/question/30114510

#SPJ4

Answer:

1. 5²  

2. 5⁴

3. 1/5⁶

4. 5⁰

5. 5¹⁰

Step-by-step explanation:

1. 5⁶⁺⁽⁻⁴⁾=5²

2. 5¹⁺³=5⁴

3. 5⁻³⁺⁽⁻³⁾=5⁻⁶=1/5⁶

4. 5⁽⁻⁴⁾⁺⁴⁺⁰=5⁰

5. 5⁷⁺³=5¹⁰

your answer would be the following:

1. 5²  

2. 5⁴

3. 1/5⁶

4. 5⁰

5. 5¹⁰

Right on EDGE 2021 for math

The total number of possible outcomes in this experiment is 36. To determine the total number of possible outcomes, we need to consider the range of possible values for each of the two dice.

Since a standard die has six faces numbered from 1 to 6, each die can take on any of these six values independently.

1. For the first die, there are six possible outcomes (1, 2, 3, 4, 5, and 6).

2. Similarly, for the second die, there are also six possible outcomes (1, 2, 3, 4, 5, and 6).

3. To find the total number of outcomes, we multiply the number of outcomes for each die since the outcomes are independent of each other. Using the multiplication principle, we have 6 outcomes for the first die multiplied by 6 outcomes for the second die, resulting in a total of 36 possible outcomes.

Therefore, there are 36 possible outcomes in this experiment.

It's important to note that each outcome is equally likely assuming the dice are fair, and the total number of outcomes represents the sample space of the experiment.

To learn more about possible outcomes, click here: brainly.com/question/30581717

#SPJ11

Using BODMAS we can conclude, Yes, both will give same result.

The rule used to solve mathematical expressions is known as the BODMAS rule. The order of operations for mathematical formulas requiring several operations is known as BODMAS. B. Brackets, O. Order of powers, D. Division, M. Multiplication, A. Addition, and S. Subtraction make up the acronym.

−9×(−9)−9

⇒ - 9 × 81

⇒ -729

⇒ [−9×(−9)]−9​

⇒ [81] -9

⇒ -729

To learn more about BODMAS from given link

https://brainly.com/question/16788360

#SPJ10

Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, \(B = B^{T}\)

To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:

\(AB^{T} = I^{T}\)

Using the transpose rules, we can rewrite this as:

\(B^{T} * A^{T}\) = I

Now, we can multiply both sides of this equation by A:

\(B^{T} * A^{T}\)* A = A

Since A is invertible, we can multiply both sides by A⁻¹ to get:

\(B^{T}\) = A⁻¹

Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = \(B^{T}\), which is the transpose of the matrix B.

Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.

Learn more about symmetric matrix here brainly.com/question/30711997

#SPJ4

The solution to the Loploce equation Δu = 0 in the domain [0,1]^2 with boundary conditions u(0,b) = u(1,y) = 0 and u(x,0) = sin(πx), u(x,1) = 0 can be obtained using the method of separation of variables.

The solution consists of a series of eigenfunctions, each multiplied by corresponding coefficients. To solve the Loploce equation Δu = 0, we assume a separable solution of the form u(x,y) = X(x)Y(y). Plugging this into the equation yields X''(x)Y(y) + X(x)Y''(y) = 0. Dividing by X(x)Y(y) gives X''(x)/X(x) = -Y''(y)/Y(y). Since the left-hand side depends only on x and the right-hand side depends only on y, both sides must be equal to a constant, say -λ.

Therefore, we obtain two ordinary differential equations: X''(x) + λX(x) = 0 and Y''(y) - λY(y) = 0.The solutions to these equations are given by X(x) = Asin(√λx) + Bcos(√λx) and Y(y) = Csinh(√λ(1 - y)) + Dcosh(√λ(1 - y)), where A, B, C, and D are constants to be determined.To satisfy the boundary conditions u(0,b) = u(1,y) = 0, we need X(0)Y(b) = X(1)Y(y) = 0. This implies B = 0 and Ccosh(√λ(1 - y)) = 0, which leads to C = 0.

Thus, we are left with the solutions X(x) = Asin(√λx) and Y(y) = Dcosh(√λ(1 - y)). To determine the values of A and D, we consider the remaining boundary conditions u(x,0) = sin(πx) and u(x,1) = 0. Plugging in these values and using the orthogonality properties of sine and cosine functions, we can compute the coefficients A and D using Fourier series techniques.

Learn more about eigenfunctions click here: brainly.com/question/2289152

#SPJ11

To solve the equation x + 5cos(x) = 0 to four decimal places using Newton's method with x0 = -1, 2, 4, we can follow these steps:Step 1: Find the derivative of the equation f(x) = x + 5cos(x).f'(x) = 1 - 5sin(x)Step 2: Choose an initial value for x, x0. We have x0 = -1, 2, 4.

Use Newton's method to find the root of the equation by repeatedly iterating the following formula:x1 = x0 - f(x0)/f'(x0)Step 4: Keep iterating the formula until we obtain an answer to four decimal places. Let's start with x0 = -1:Iteration 1:x1 = -1 - (-1 + 5cos(-1))/(1 - 5sin(-1)) = -0.4651Iteration 2:x2 = -0.4651 - (-0.4651 + 5cos(-0.4651))/(1 - 5sin(-0.4651)) = -0.4674Iteration 3:x3 = -0.4674 - (-0.4674 + 5cos(-0.4674))/(1 - 5sin(-0.4674)) = -0.4674 (to four decimal places).

Therefore, the root of the equation using Newton's method with  Therefore, the root of the equation using Newton's method with x0 = 4 is x = 4.7680 to four decimal places.Discussion:Newton's method is an iterative method for finding the roots of a function. It works by repeatedly refining an initial estimate of the root using the derivative of the function. In this case, we used Newton's method to find the roots of the equation x + 5cos(x) = 0 to four decimal places with x0 = -1, 2, 4.We found that the roots of the equation were -0.4674, 2.4727, and 4.7680 to four decimal places for x0 = -1, 2, 4 respectively. We also observed that the method converged to the roots in a few iterations in each case.

To know more about Newton's visit :

https://brainly.com/question/30145972

#SPJ11

Answer:

The distance between them is 277.84 m

Step-by-step explanation:

See comment for complete question.

Given

Boat A:

\(Speed = 24mph\)

\(\angle A = 340^{\circ}\)

Boat B:

\(Speed = 35mph\)

\(\angle B = 200^{\circ}\)

\(Time = 5hr\)

First, we calculate the distance traveled by both boats in 5 hours

\(Distance= Speed * Time\)

\(Boat\ A = 24mph * 5hr = 120m\)

\(Boat\ B = 35mph * 5hr = 175m\)

For more clarity, I'll make use of the attached image to represent the system.

From the attachment, we are to calculate distance C, but first we calculate the angle between them.

\(\theta = 340^{\circ} - 200^{\circ}\)

\(\theta = 140^{\circ}\)

C is then calculated using cosine law:

\(C^2 = A^2 + B^2 - 2BC\ Cos\theta\)

This gives:

\(C^2 = 120^2 + 175^2 - 2*120*175\ Cos(140^{\circ})\)

\(C^2 = 120^2 + 175^2 - 2*120*175*-0.7660\)

\(C^2 = 14400 + 30625 + 32172\)

\(C^2 = 77197\)

Take square root of both sides:

\(C = \sqrt{77197\)

\(C = 277.84\)

The distance between them is 277.84 m

Answer: x = 2

Hope this helps!

It cannot determine causation as there may be other variables or factors that could be influencing the relationship between the two variables being analyzed.

Which one of the following cannot be determined from a scatterplot is a cause and effect relationship.

A scatterplot can show the strength and direction of a relationship between two variables, whether it is a positive or negative relationship, and whether it is curvilinear.

However, it cannot determine causation as there may be other variables or factors that could be influencing the relationship between the two variables being analyzed.

To know more about variables refer here

https://brainly.com/question/17344045#

#SPJ11

Answer:

B

Step-by-step explanation:

If x is any larger than 4 it would be greater than 5, since 2*4-3=5

If x was any smaller than -1  it would be greater than 5, since 2*-1-3=|-5|=5

C hope this help you

Answer:

y=-6x+36

Step-by-step explanation:

у + 6x — 36 = 0

-add 36 to both sides

y+6x=36

-subtract 6x from both sides

y=36-6x or y=-6x+36

-This should be the correct answer

The gross profit of the Blog Inc would be $22,370.

Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that  Sales: $50,000

Returns: $4,680

Cost of goods sold: $22,950

Therefore,

Net Sales: 50,000 - 4,680

= 45,320

We can calculate the Gross Profit;

Gross Profit = (Net Sales – Cost of Goods Sold)

                      = ($45,320- $22,950)

                       = $22,370

Hence, the gross profit would be $22,370.

Learn more about the gross profit here:-

brainly.com/question/18567528

#SPJ1

Answer:

2<y<6

Step-by-step explanation:

12 < 8y-y^2

y^2 -8y +12 <0

(y-6)(y-2)<0

y < 6

y < 2

 2.       6

-       -        +

-       +.       +

+.      -         +

2<y<6

Answer:

M=2.4R

Step-by-step explanation:

Find the cost per ticket

24/10=2.4

Answer:

Chlorine, Krypton, Argon, Fluorine, Hydrogen

Step-by-step explanation:

Look at the numbers and sort them from least to greatest. It could be the opposite answer to since the larger the negative number the smaller the value.

Answer:

Hydrogen, Flourine, Argon, Krypton, Chlorine

Answer:

$422

Step-by-step explanation:

We have proved that lim xn = 2. To prove that xn^2 is always greater than or equal to 2 for n ∈ N, we can use mathematical induction.

Base case (n = 1):

x1 = 2

x1^2 = 2^2 = 4, which is greater than 2.

Inductive step:

Assume xn^2 ≥ 2 for some arbitrary value of n, and we want to show that xn+1^2 ≥ 2.

We have:

xn+1 = (1/2)(xn + xn^2)

Multiplying both sides by xn, we get:

xn * xn+1 = (1/2)(xn^2 + xn^3)

Now, let's consider the expression (xn+1)^2:

(xn+1)^2 = [(1/2)(xn + xn^2)]^2

         = (1/4)(xn^2 + 2xn * xn^2 + xn^4)

         = (1/4)(xn^4 + 2xn^3 + xn^2)

         = xn^4/4 + xn^3/2 + xn^2/4

Now, let's compare (xn+1)^2 with 2:

(xn+1)^2 - 2 = xn^4/4 + xn^3/2 + xn^2/4 - 2

            = (xn^4 + 2xn^3 + xn^2)/4 - 2

            = [(xn^2)^2 + 2xn^3 + xn^2]/4 - 2

            = xn^2[(xn^2 + 2xn + 1)/4] - 2

By using the hint (a+b)^2 = (a-b)^2 + 4ab, we can rewrite the above expression as:

(xn+1)^2 - 2 = xn^2[(xn+1)^2/4] - 2

            = (1/4)(xn+1)^2 * xn^2 - 2

Since xn^2 ≥ 2 (by the induction hypothesis), we have:

(1/4)(xn+1)^2 * xn^2 - 2 ≥ (1/4)(2)(2) - 2

                          = (1/4)(4) - 2

                          = 1 - 2

                          = -1

Therefore, we have shown that (xn+1)^2 - 2 ≥ -1, which implies that xn+1^2 ≥ 2.

Now, let's prove xn - xn+1 ≥ 0 using the fact that xn^2 ≥ 2 (which we just proved). We have:

xn - xn+1 = xn - (1/2)(xn + xn^2)

          = (1/2)(2xn - xn - xn^2)

          = (1/2)(xn - xn^2)

Since xn^2 ≥ 2, we know that xn - xn^2 ≥ 0. Therefore, xn - xn+1 ≥ 0.

Based on the fact that xn - xn+1 ≥ 0, we can conclude that the sequence {xn} is a decreasing sequence. Since xn^2 ≥ 2 for all n, the sequence is bounded below by 2. Thus, the limit of xn as n approaches infinity is 2.

Therefore, we have proved that lim xn = 2.

Learn more about arbitrary value here:

https://brainly.com/question/29479598

#SPJ11

Answer:

a^(-7)

Step-by-step explanation:

To multiply these terms, we can add the exponents of the same base, then simplify if possible.

a^−4(a^2)(a^−5) = a^( -4+2-5 ) = a^(-7)

Therefore,

a^−4(a^2)(a^−5) = a^(-7)

Answer:

If you don't agree or there's an error, let me know so I can edit.

Step-by-step explanation:

f(x) = x⁴ + 2

differentiate

f(x) = 4x³ + 0 =0

x(4x²) = 0

at x= 0 f(x) = 0 points = (0,0)

at x= 1. f(x) = 3 points = (4,3)......

The ordered pair is (4,3).

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Given:

f(x) = x⁴ + 2

Now, differentiate the above function for the small values

f(x) = 4x³ + 0 =0

x(4x²) = 0

When x= 0

f(x) = 0

So, the points = (0,0)

when x= 1

f(x) = 3

so, the points = (4,3).

Learn more about ordered pair here:

https://brainly.com/question/23922144

#SPJ2

A sailboat traveling 120m in 60s is 20.