5. A Web site uses ads to route visitors to one of four landing pages. The probabilities for each landing page are equal. Consider 16 independent visitors and let the random variables W, X, Y, and Z denote the number of visitors routed to each page. Calculate the following: (a) P(W-4, X= 4, Y= 4, Z= 4) (b) P(W = 4, X= 4, Y= 4 I Z= 4) (c) P(W-6, X26, Y=4 12-2)

Answer:

ratio:3:3:2

total of ratio=3+3+2=8

total money=40

sara gets 5x 3/8=15

eiona gets 5x 3/8+15

david gets=5x 2/8=10

Step-by-step explanation:

The equation to illustrate this will be 600 + 28m m.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this situation, the owners of a recreation area are filling a small pond with water and they are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start.

The equation to illustrate this will be:

= 600 + (28 × m)

= 600 + 28m

m = number of minutes.

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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start. Write the equation to illustrate this.

Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

At the banquet in Macbeth, Lady Macbeth fulfills a traditional feminine role in several ways. Firstly, she demonstrates her hospitality and generosity by welcoming the guests and providing them with food and drink. Secondly, she shows her nurturing nature by urging Macbeth to be more hospitable and to provide the guests with more generous servings. Thirdly, she shows her graciousness and hospitality by offering the guests timely compliments. Lastly, she shows her caring and supportive nature by encouraging Macbeth to be more gracious and generous. Altogether, Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

30

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

That is a right angle

right angles are 90°

90-60 = 30

Answer:

:?

Step-by-step explanation:

:?

There are 20,000 different phone numbers possible that is 7-digits long and start with either 824 or 825.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Based on the given information, all phone numbers are 7-digits long and starts with either 824 or 825. Hence, the four last digits will be the combination of numbers from 0 to 9.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is 20,000.

= (number of phone numbers starting with 824) + (number of phone numbers starting with 825)

= (10 x 10 x 10 x 10) + (10 x 10 x 10 x 10)

= 20,000

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Answer:

y=130

Step-by-step explanation:

1) combine all like terms for the inside angles of the triangle

2) because the sum of all angles = 180 add that to the sum of all like terms

3) now you replace the x's with 23

4) now we know that (3x-19)=50

5) take 180 and subtract 50

6) 180-50=130

Main Answer: A normalized binary number typically consists of three parts:

Supporting Question and Answer:

What is a sign bit in a normalized binary number?

The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

Body of the Solution: A normalized binary number typically consists of  the following three parts:

Final Answer: A normalized binary number typically consists of three parts:

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Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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We can show that Var(K) is smaller than Var(W) using Eve's law, which is derived from Adam's law and The Rao-Blackwell theorem and allows us to construct a more optimal estimator by evaluating the conditional expected value.

According to Eve's law, Var(X) = E[Var(X|Y)] + Var[E(X|Y)]. In our context, Var(W) represents the variance of the estimator W, and the second term on the right-hand side represents Var(K), the variance of the estimator K.

By applying Rao-Blackwellization, we use the conditional expectation to construct a more optimal estimator. In this case, K is the conditional expectation of W given a sufficient statistic. Since the conditional expectation minimizes mean squared error, Var(K) is expected to be smaller than Var(W).

Therefore, based on the principles of Eve's law and the Rao-Blackwell theorem, we can conclude that Var(K) is smaller than Var(W). This demonstrates the advantage of using the Rao-Blackwellization procedure to improve the precision of estimators and obtain more optimal results.

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Answer:

x = 6

Step-by-step explanation:

If polygons are similar then the side lengths are proportional, so we can write the following equation to find the value of x:

15/6 = (5x + 10)/16 cross multiply fractions

240 = 30x + 60 subtract 60 from both sides

180 = 30x divide both sides by 30

6 = x

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Answer:

(-5,0) and (7,0)

Step-by-step explanation:

You are being asked to find "zeros", so just keep in mind that

zeros ARE roots ARE solutions ARE x-intercepts.

(there are tiny, technical differences bc math reasons, but on a simple overview, they are all the same thing!)

Set equal to zero and solve.

see image.

"ordered pairs" means write the answer like a point (x,y) We found the x when y is zero. See image.

Answer:

64 ft

Step-by-step explanation:

The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Jamie drove 61 miles Jamie's car used 4 gallons of gas.

The number of miles per gallon that Jamie's car get will be given as,

Rate = 61 / 4

Rate = 15.25 miles per gallon

The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

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Complete question :

The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation.

x 0 1 2 3 4

P(x) 3/17 5/17 6/17 2/17 1/17

Answer:

1.59 ; 1.09

Step-by-step explanation:

The Mean :

E(X) = Σx*p(x)

(0*3/17) + (1 * 5/17) + (2*6/17) + (3*2/17) + (4*1/17)

= 1.58823

= 1.59

Standard deviation = sqrt(Var(x))

Var(X) = Σx²*p(x) - E(x)²

= {(0^2*3/17) + (1^2 * 5/17) + (2^2*6/17) + (3^2*2/17) + (4^2*1/17)} - 1.59^2

= 3.7058823 - 2.5281

= 1.1777823

Standard deviation = sqrt(1.1777823)

= 1.0852567

= 1.09

Answer:

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

Step-by-step explanation:

You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².

For a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.

The total surface area of a cube with edge length s is ...

  A = 6s²

Then the edge length of the desired cube is found from ...

  4 = 6s²

  s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator

  s = √(6/9) = (√6)/3

The dimensions of the box are ...

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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Answer:

Fraction of the garden used =  \(\frac{5}{8}\)

Step-by-step explanation:

The fifth graders to plant a butterfly garden.

We are given that

Clover grows in ½ of the garden

Daisies grow in ¼ of the garden

Coneflowers grow in ⅛ of the garden

milkweed grows in ⅛ of the garden

The fifth graders notice that the butterflies land on the clover and milkweed.

We are asked to find out the fraction of the garden that the butterflies used.

Fraction of the garden used = clover + milkweed

Fraction of the garden used =  \(\frac{1}{2} + \frac{1}{8}\)

The LCM of 2 and 8 is 8

Fraction of the garden used =  \(\frac{4 +1}{8}\)

Fraction of the garden used =  \(\frac{5}{8}\)

Therefore, the butterflies used \(\frac{5}{8}\) fraction of the garden.

volume of cylinder: π * radius² * height

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

⇒ π * 4² * 4

⇒ π * 16 * 4

⇒ 64π

Thus the volume of cylinder is 64π cm³

Question :-

Answer :-

\( \rule{180pt}{4pt}\)

Diagram :-

\(\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4 \: m}}\put(9,17.5){\sf{4 \: m}}\end{picture}\)

Solution :-

As per provided information in the given question, we have been given that the Radius of a cylinder is 4 m. The height of a cylinder is 4 m. We have been asked to find the volume of a right cylinder.

To calculate the volume of a right cylinder, we will apply the formula below :-

\( \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}\)

Substitute the given values into the above formula and solve for Volume :-

\(\sf:\implies Volume_{(Cylinder)} = \pi r^2 h\)

\(\sf:\implies Volume_{(Cylinder)} = \pi \times (4 \: m)^2 \times 4 \: m \)

\(\sf:\implies Volume_{(Cylinder)} = \pi \times 16 \:m^2 \times 4 \: m \)

\(\sf:\implies Volume_{(Cylinder)} = \pi 64 \: m^3\)

\(\sf:\implies\bold{Volume_{(Cylinder)} = 64\pi \: m^3}\)

Therefore :-

\(\\\)

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Have a great day! <33

Answer:

Step-by-step explanation:

Since there are missing data, let's discuss some facts about regular polygons and their angles.

1) The sum of its Interior angles is given by:

\(S_i=180^{\circ}(n-2) \therefore \:for\: a\:pentagon\:S_i=180^{\circ}(5-2) =540^{\circ}\)

2) Since it is a regular pentagon, each interior angle is congruent:

Each interior angle:

\(Interior\:angle=\frac{540^{\circ}}{5} =108^{\circ}\)

3) If we trace an outside line, the external angle will be supplemental, i.e.

\(m\angle external= 180^{\circ}-108^{\circ} \therefore= 72^{\circ}\)

4) If we trace from each diagonal one line segment, in a regular pentagon that will form 3 triangles with one-third of 108º,i.e.,36º

As we can see, the in the picture below

Answer:

x = (-2 , 4.5)

Step-by-step explanation

Hope it helps! later!

Answer:

x=−43434309090

Step-by-step explanation:

Answer:

△DBE​  is similar to ​△ABC​ by the ​SAS Similarity Theorem​.

Step-by-step explanation:

i took the test already

Answer:

500m

Step-by-step explanation:

a rectangle has 4 sides, so 30=60 and 20=40

60x5=300

40x5=200

300+200=500

500m

reason of 500

The main reason for this is he ran AROUND the rectangle and did it 5 TIMES, doing it once would be 100m.

9 × 0 + (-80) + 8 = ?

= 0 - 80 + 8

= -80 + 8 <==> 8 - 80

= -72

~bilbul

9 × 0 + (-80) + 8

= 0 + (-80) + 8

= (-80) + 8

= -72 ✔️

:)

Answer:

maybe the amount of money by each student

Answer:

1.75+7.50h≥50

Step-by-step explanation:

The length of the wall for the ladder reach will be 3.4 meter.

What is mean by Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The foot of a ladder is 1.5 m from a vertical wall.

And, The ladder makes an angle of 68° with the horizontal.

Now,

By the figure,

The length of BC = 1.5 m

The measure of ∠ACB = 68°

So, Find the length of AC as;

cos 68° = 1.5 / AC

AC = 1.5 / 0.44

AC = 3.4 m

Therefore,

The length of the wall for the ladder reach will be 3.4 meter.

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