the poisson random variable x is the number of occurrences of an event over an interval of ten minutes. it can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in ten minutes is 5.1. what is the probability that there are 8 occurrences in ten minutes?

Answer: $192.18

Step-by-step explanation:  531.49+240.42+281.67=1053.58

1053.58 - 275.66 = 777.92 - 48.29 = 729.63 - 107.64 = 621.99 - 429.81 = 192.18

Answer:

D

Step-by-step explanation:

It is the law of cos

C^2= A^2+B^2-2*A*B*cosL where L is the angle between A and B

so C = 32^2 + 35^2 - 2(32)(35)cos120°

Answer:

  x - 6

Step-by-step explanation:

You want the algebraic equivalent of "x decreased by 6."

If a quantity is decreased by 6, it means 6 has been taken away. You might have seen this as "__ take away 6." It means 6 has been subtracted.

We represent the subtraction of 6 using a minus sign.

  x - 6

__

Additional comment

Other math symbols are associated with different wording:

Answer:

y = -4/5x + 5

Step-by-step explanation:

In order to solve for y, we need to isolate the variable. First, let's subtract 4x on each side. After doing said step, we should now have this equation:

5y = -4x + 25

Next, we need to divide 5 on each side, giving us this new equation:

y = -4/5x + 5

There you go! Let me know if I did anything wrong ^-^

Using the Midpoint Rule the value of the integral \(\int\limits^\frac{\pi }{2} _0 {cos^{5}x } \, dx\)  is approximately 0.4904.( Rounding to four decimal places).

To approximate the integral \(\int\ {cos^{5}x } \, dx\) dx in the interval [0,\(\pi\)/2] using the Midpoint Rule with n = 4, we divide the interval [0, π/2] into four subintervals of equal width.

The width of each subinterval is Δx = (π/2 - 0) / 4 = π/8.

Next, we evaluate the function cos⁵(x) at the midpoint of each subinterval and multiply it by the width Δx.

Using the Midpoint Rule formula, the approximation of the integral is given by:

\(\int\limits^\frac{\pi }{2} _0 {cos^{5}x } \, dx\) ≈ Δx * [f(x_1) + f(x_2) + f(x_3) + f(x_4)]

where x₁, x₂, x₃, and x₄ are the midpoints of the subintervals.

Substituting the values:

\(\int\limits^\frac{\pi }{2} _0 {cos^{5}x } \, dx\) ≈ (π/8) * [cos⁵(π/16) + cos⁵(3π/16) + cos⁵(5π/16) + cos⁵(7π/16)]

Evaluating each term and performing the calculation:

∫[0,π/2] cos⁵(x) dx ≈ (π/8) * [0.9973 + 0.8910 + 0.5431 + 0.1081] ≈ 0.4904

Rounding to four decimal places, the approximation of the integral is approximately 0.4904.

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The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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The variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

The step for the simplification are-

Finally, on a broad note:

(2n)! - (2(ⁿC₁)(2n - 1)! - 2²(ⁿC₂)(2n - 1)! + .....2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

On further simplifying;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

Thus, the variety of arrangements we can make for the 2n people to stand in a line such that nobody is next to their spouse;

(2n)! - ∑ⁿₓ₋₁ 2ˣ(-1)ˣ(ⁿCₓ)(2n - x)!

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Answer:

( 3,-5)

Step-by-step explanation:

To find the midpoint add the two end point coordinates and divide by two

Let G be ( x,y)

The midpoint of GH is (2,2)

( x+1) /2 = 2

Multiply by 2

x+1 = 4

Subtract 1

x+1-1 = 4-1

x=3

( y+9) /2 = 2

Multiply by 2

y+9 = 4

Subtract 9

y+9-9 = 4-9

y = -5

The coordinates of G is ( 3,-5)

Answer:

(3,-5)

Step-by-step explanation:

and please follow me and brainlist answer

The required answer is  the antiderivative of s(x) is: 4x^2 + 4x

Given that s(x) = -1x + 8 + 9x - 4, we want to find the antiderivative of s(x) without including the constant C.
Antiderivatives are also called general integrals, and sometimes integrals. The latter term is generic, and refers not only to indefinite integrals but also to definite integrals. If the word integral is used without additional specification, the reader is supposed to deduce from the context whether it refers to a definite or indefinite integral. Define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.
First, simplify s(x):
s(x) = -1x + 9x + 8 - 4
s(x) = 8x + 4
A antiderivative is a function reverses, they are taken the form of a function is an arbitrary constant. By second fundamental theorem of calculus , the antiderivative is related to the definite integral . Definite integral of a new function over a band interval.
Now, find the antiderivative of s(x):
Antiderivative of 8x + 4 = (8/2)x^2 + 4x
The natural logarithm function, if a positive real variable. This is a  inverse function. Logarithm is useful for solving equations. Decayed constant or unknown time in problems.  
So, the antiderivative of s(x) is:
4x^2 + 4x

where the function is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

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The equation that represents the equal distribution of ' d ' dumplings among Eli and Ana is -

x = nd/2.

Unitary method is used to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given is a situation in which Eli and Ana are having dinner. They both have same number of dumplings to eat and each dumpling container contains 'd' dumplings.

Let's assume that there are 'n' containers of dumplings and both Eli and Ana got 'x' number of dumplings. Now -

In 1 container we have - 'd' dumplings

In 'n' containers, we will have -  n × d   dumplings.

Both Ana and Eli got same number of dumplings = x.

Therefore -

x + x = n × d

2x = nd

x = nd/2

Therefore, the equation that represents the situation is -

x = nd/2

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Answer:

59cm^2

Step-by-step explanation:

first you can do 8x9 to get 72 then you can subtract 4x2 from 72 to get 64 and lastly you have to subtract 4 from 9 to get the area of the small rectangle on the left so you get 5 and then you have to get the width which is 4+3 from the top and subtract that from 8 on the bottom which is 1 so now you have 5x1 which is 5 and subtract that from 64 to get 59cm^2

hope this helps

Patrick’s August finance charge will be $0.6717 more if it is calculated using the previous balance method.

Previous balance method: Interest charges are based on the amount owed at the beginning of the previous month's billing cycle.

Adjusted balance method: Based on finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments have been posted.

The total amount on which interest will be applied using the previous balance method is;

\(= 1,466.22+28.48+40.00+31.76\\\\ = 1566.46\)

So, interest levied on this is;

\(= 1566.46 \times 15.40 \times \dfrac{30}{360} \times \dfrac{1}{100}\\\\=20.10\)

Now, the total amount on which interest will be applied using the adjusted balance method is;

\(= 1566.46-150.00-115.75\\\\=1300.71\)

So, interest levied on this is;

\(= 1300.71 \times 15.40 \times \dfrac{30}{360} \times \dfrac{1}{100}\\\\=16.69\)

The difference between charges by previous balance method and adjusted balance method is;

= 20.10 - 16.69 = 3.41

Hence, Patrick’s August finance charge will be $0.6717 more if it is calculated using the previous balance method.

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Answer:

1/24 + 1/24 = 1/12

Step-by-step explanation:

1/24 + 1/24 = 1/12 I think it’s this.

I don’t have any options though so I just thought of that.

The equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

In this question we have been given a point (6, 3) and slope m = 2

We need to find an equation of line passing through (6, 3) with slope m = 2

Using formula of the point-slope form:

(y - y1) = m(x - x1)

(y - 3) = 2(x - 6)

y - 3 = 2x - 12

y = 2x - 12 + 3

y = 2x - 9

This is slope-intercept form of equation of line.

slope = 2

y-intercept = -9

Therefore, the equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

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Answer:

See below

Step-by-step explanation:

Attachment 1 : (a) Remember that it mentions x is the years since 1900. That would mean that the table is a bit different. To create this " new table " simply subtract 1900 from the years provided, and substitute.

To create this equation we will need a regression calculator. The equation will be as follows.

y = 0.125873x - 7.11916 ( note that you can double check this equation be substituting points from the table in the attachment )

(b) 2025 - 1900 = 126 years,

y = 0.125873(125) - 7.11916 = $ 8.614965

Minimum Wage : $ 8.614965

Attachment 2 : The rest of the problems can be solved similarly...

(a) Quadratic Regression Equation : - 0.49311x² + 23.2798x + 996.029

(b) - 0.49311(20)² + 23.2798(20) + 996.029 = 1264.381 mg/cm³

Attachment 3 : (a) Exponential Regression : 9.08292(1.09965)ˣ

(b) 9.08292(1.09965)⁶⁰ = \(2713.27743\dots\) ( About 2713 recommendations )

In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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Answer:

\(y= \frac{1}{5}x + 1\)  

Step-by-step explanation:

Given points (0,1) and (5,2):

Let (x1, y1) =  (0,1)  

(x2, y2) = (5,2)

Use the follwing slope formula to calculate the slope of the line:

\(m = \frac{y2 - y1}{x2 - x1}\)

Plug in the values for (x1, y1) and (x2, y2):

\(m = \frac{y2 - y1}{x2 - x1} = \frac{2 - 1}{5 - 0} = \frac{1}{5}\)

Therefore, the slope of the line is \(\frac{1}{5}\) .

Next, we must determine the y-intercept, which is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is the value of y when x = 0.

Therefore, using the slope-intercept form, y = mx + b, and one of the points, (5, 2):

Let y = 2,  x = 5, and m = \(\frac{1}{5}\)

y = mx + b

2 = \(\frac{1}{5}(5)\) + b

2 =  1 + b

Subtract 1 from both sides of the equation:

2 - 1 =  1  + b - 1

b = 1

The y-intercept of the line is (0, 1), or b = 1.

Therefore, the equation of the line is:

\(y= \frac{1}{5}x + 1\)  

Answer:Let PQRS to be the rhombus where PQ=12cm and RS = 16cm

step 1:let,PQ and RS intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

STEP 2:Since POQ is a right angled triangle, by pythagoras theoram.

STEP 3:After applying formula , PQ =10cm .length of each side of rhombus is 10cm.

Step-by-step explanation:

Answer:

10cm

Step-by-step explanation:

As you can see in the first image is a rhombus with its diagonals 12cm and 16cm

You can see that the diagonals divide the rhombus into four right triangles and that the hypotenuse of each triangle is one side of the rhombus.

In the second image I picked out one triangle from the rhombus and slashed the length of the diagonals of the rhombus in half to get the sides of the triangle.

Now all you have to do is use the Pythagorean theorem to find the hypotenuse of the triangle which will give you the length of side of rhombus

6² + 8² = hypotenuse²

36 + 64 = h²

100 = h²

h = √100

h = 10

All the side of the rhombus are equal so all the sides of the rhombus are 10cm

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\(\large \bold {ANSWER}\)

\(\large \bold {SOLUTION}\)

The first thing we must do is convert kilometers to meters. We will do this by multiplying by 1,000, since 1 km corresponds to 1,000 meters.

Now that we've done that, let's divide the values by 3,600, because an hour is 60 minutes, and each minute is 60 seconds, so 60*60 is 3,600.

\(\frac{80.0\not0\not0}{3.6\not0\not0}=22.22\)

\(\frac{120.0\not0\not0}{3.6\not0\not0}=33.33\)

Hence, 80 km/h = 22.22 m/s, 120 km/h = 33.33 m/s

Answer:

what is the equation ? lmk

Answer:

\(57,600cm {}^{2} \)

Solving steps:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

=> 40 cm\( {}^{2} \) × 30cm\( {}^{2} \) × 48 cm\( {}^{2} \)

multiply all the numbers

=> 57,600cm\( {}^{2} \)

Hi hi hi hi

Answer:

\(57,600cm {}^{2} \)

Solving steps:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

=> 40 cm × 30cm × 48 cm

multiply all the numbers

=> 57,600cm\( {}^{2} \)

Answer:

this has to do with trial and error

since N=21÷3-3

so 21÷3-3=4

therefore N=4

substitute for N

2×4=8

8×3=24

therefore 24÷3=2×4

Given:

There are given that the 4 m from A and 2 m from CD.

Explanation:

To draw

The correct option is The surface area will decrease by 672 sq. ft.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular parallelepiped or a rectangular cuboid.

The surface area of a rectangular prism can be calculated using the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism.

Given that the original rectangular prism has l = 33 ft, b = 14 ft, and h = 15 ft, we can calculate its surface area as:

SA = 2lw + 2lh + 2wh

= 2(33)(14) + 2(33)(15) + 2(14)(15)

= 924 + 990 + 420

= 2,334 sq ft

Now, if we halve the width (b), we get a new width of b/2 = 14/2 = 7 ft. The new surface area can be calculated using the same formula as:

SA = 2lw + 2lh + 2wh

= 2(33)(7) + 2(33)(15) + 2(7)(15)

= 462 + 990 + 210

= 1,662 sq ft

The decrease in surface area can be calculated as:

2,334 - 1,662 = 672 sq ft

Therefore, the correct option is:

The surface area will decrease by 672 sq. ft.

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Answer:

algebraic expression for 180 degree clockwise rotation about the origin (x,y) → (-y, x) algebraic expression for 270 degree clockwise rotation about the origin equals a 270 degree counterclockwise rotation 90 degree clockwise rotation equals a 90 degree counterclockwise rotation

Step-by-step explanation:

hope this helps

have an awesome day -TJ

Answer:

Step-by-step explanation:

Four times a certain number “a”:

Ten more than thrice the number:

The statement is: