2, -3, -8, -13, -18,

Given:

The shaded sector above covers \(\dfrac{1}{3}\) of the circle.

Radius of the circle = 3 cm

To find:

The area of the sector in terms of π.

Solution:

The area of a circle is

\(A=\pi r^2\)

Substituting \(r=3\), we get

\(A=\pi (3)^2\)

\(A=9\pi\)

It is given that the shaded sector above covers \(\dfrac{1}{3}\) of the circle.

The area of shaded sector \(=\dfrac{1}{3}A\)

                                             \(=\dfrac{1}{3}(9\pi)\)

                                             \(=3\pi\)

Therefore, the area of shaded sector is 3π sq. cm.

d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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The bacteria increases 90% the formula adds the percentage, as a decimal to the 1.

The answer would be 0.90

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The answer is C in Edge. Just took the assigment. Hope this helps! :)

The values of the elements of the matrix will ψ(t)⟩=e−iE1t/ℏ|2⟩

Let's say the block matrix is used to represent the 2n by 2n matrix A.

Displaystyle A="begin" "bmatrix" "a&b" "c&d" "end"

where n-by-n matrices a, b, c, and d. The requirement that b and c be symmetric and that a + dT = 0 are similar to the requirement that A be Hamiltonian. The fact that A is of the form A = JS with S symmetric is another equivalent requirement.

Two Hamiltonian matrices can be added together (as can any linear combination), and their commutator is also Hamiltonian. The space of all Hamiltonian matrices is hence a Lie algebra, indicated by the symbol sp (2n). Sp(2n) has a dimension of 2n2 + n.

H^=E0(|1⟩⟨1|+|3⟩⟨3|)+E1|2⟩⟨2|+A(|1⟩⟨3|+|3⟩⟨1|)H^=E0(|1⟩⟨1|+|3⟩⟨3|)+E1|2⟩⟨2|+A(|1⟩⟨3|+|3⟩⟨1|)

It is then straightforward to see that :

• |2⟩|2⟩ is an eigen state with eigen value E1E1 as you have already noticed. Hence if the initial state is |2⟩|2⟩ then

|ψ(t)⟩=e−iE1t/ℏ|2⟩

• (|1⟩+|3⟩)(|1⟩+|3⟩) and (|1⟩−|3⟩)(|1⟩−|3⟩) are eigen states with respective eigen values of E0+AE0+A and E0−AE0−A. Hence if the initial state is |3⟩=12[(|1⟩+|3⟩)−(|1⟩−|3⟩)]|3⟩=12[(|1⟩+|3⟩)−(|1⟩−|3⟩)], then

|ψ(t)⟩=12[e−i(E0+A)t/ℏ(|1⟩+|3⟩)−e−i(E0−A)t/ℏ(|1⟩−|3⟩)]

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incomplete question: complete question is

Let

⎡⎣⎢E00A0E10A0E0⎤⎦⎥[E00A0E10A0E0]

be the matrix representation of the Hamiltonian for a three-state system with basis states |1>,|2>and |3>|1>,|2>and |3>.

a. If the state of the system at time tt = 00 is |ψ(0)>=|2>|ψ(0)>=|2> what is |ψ(t)>|ψ(t)>?

b. If the state of the system at time tt = 00 is |ψ(0)>=|3>|ψ(0)>=|3> what is |ψ(t)>|ψ(t)>?

Answer:

10n=10n

Step-by-step explanation:

n-10+9n-3=10n-13

n+9n

10n-10-3=10n-13

-10-3

10n-13=10n-13

    +13        +13

10n=10n

Answer: 9500000

Step-by-step explanation: 95 × 100000 = 9500000

*Multiply the value by 100000*

Answer:

x = 8.98782862707

Step-by-step explanation:

Base on the given we can infer that we are solving for x:

Given equation:

1000x+27x+5.5=9236

Combine similar terms

1027x + 5.5 = 9236

Subtract both side by 5.5

1027x + 5.5 = 9236

             -5.5      -5.5

-------------------------------------

1027x = 9230.5

Now divide both sides by 1027x

9230.5 / 1027

x = 8.98782862707

[RevyBreeze]

since she didn't have any money in there when she first started, and she puts it in every month, the correct answer is

y = 230x

hope this helps!!

A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).

We have given that,

Sample mean of peoples who like drama , x₁-bar = 190

Sample mean of peoples who like comedy,x₂-bar = 150

Sample size for darama sample, n₁ = 17

Sample size for comedy sample, n₂ = 14

Standard deviations, s₁ = 60

Standard deviations, s₂ = 30

Confidence level = 0.95 or 95%

Using Z-table , Z-score for 95% confidence level is 1.96..

We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.

It is given by following Confidence interval formula,

x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))

= 190 - 150 ± 1.96(√(60²/17 + 30²/14))

= 40 ± 1.96(√3600/17 + 900/14))

= 40 ± 32.56

= (7.44, 72.56)

Hence, the required 95% confidence interval is

(7.44, 72.56) .

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Complete question:

A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a

95%

confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places

The price elasticity of demand for x is -1.25.

Price elasticity of demand (PED) is a measure of how responsive quantity demanded is to changes in price. It is calculated as follows:

```

PED = (% change in quantity demanded)/(% change in price)

```

In this case, the price of x increases by 12% and the quantity demanded decreases by 15%. Therefore, the PED is -1.25.

A PED of -1.25 means that the quantity demanded is relatively inelastic. This means that a change in price will have a relatively small effect on quantity demanded.

The demand for x is a normal good. This means that as the price of x increases, the quantity of value demanded of x will decrease.

The demand for x is relatively inelastic. This is because the PED is -1.25, which is less than -1. A PED of -1 or less indicates that the demand is inelastic.

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Answer and Step-by-step explanation:

The correct answer choice would be to grind the solvent into smaller pieces.

When the solid is in smaller pieces, it would take less time for the dissolver to dissolve the smaller bits, since the pieces are smaller and take up less volume for the dissolver to go through.

With a bigger solid, the dissolver would just chip away at the solid before eventually dissolving the solid, although this could take some time.

#teamtrees #PAW (Plant And Water)

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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f(x) is an exponential function with an initial value of 33,966.17 and a decay rate of 0.310, which matches the trend of the data.

We can plot the data points and look for a pattern to see if an exponential or linear function better fits the provided data.

The provided data point can first be plotted as a scatter plot.

(1, 16890.32) (2, 14259.09) (3, 12001.57) (4, 10051.16)

To find the specific exponential function that would fit this data, we can use the formula for exponential decay:

f(x) = a * \(e^(-bx)\)

where f(x) is the value of the investment at time x, a is the initial value of the investment, and b is the decay rate.

Using the given data, we can plug in the values for f(x) and x to solve for a and b. Here is the calculation:

16,890.32 = a * \(e^(-b1)\)

14,259.09 = a * \(e^(-b2)\)

12,001.57 = a * \(e^(-b3)\)

10,051.16 = a * \(e^(-b4)\)

Dividing the second equation by the first, and the third equation by the second, and so on, we can get rid of the constant a:

14,259.09/16,890.32 = \(e^(-b)\)

12,001.57/14,259.09 = \(e^(-b)\)

10,051.16/12,001.57 = \(e^(-b)\)

Taking the natural logarithm of both sides, we get:

ln(14,259.09/16,890.32) = -b

ln(12,001.57/14,259.09) = -b

ln(10,051.16/12,001.57) = -b

Simplifying these equations, we get:

b ≈ 0.310

a ≈ 33,966.17

So the exponential function that best models this data is:

f(x) = 33,966.17 * \(e^(-0.310x)\)

This function has an initial value of 33,966.17 and a decay rate of 0.310, which matches the trend of the given data.

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Complete question:

The value of a certain investment over time is given in the table below. Answer the questions below to explain what kind of function would better model the data, linear or exponential.

Number of Years Since Investment Made,

x          1                  2               3              4

Value of Investment ($),

f(x)   16,890.32  14,259.09   12,001.57   10,051.16

the function would better model the data because as x increases, the y values change. The of this function is approximate.

The area of the given  isosceles triangle is 480 square units.

Isosceles triangle:

An isosceles triangle is a triangle with two sides of equal length. Let's do a little activity to understand this better. Take a square piece of paper and fold it in half. Draw a line from the folded top corner to the bottom edge (see image below). Open the sheet and you will see a triangle. Mark the triangle vertices as O, D, C. Then measure OD and OC. Repeat this activity at different scales and observe patterns. We can see that OD and OC are always the same. A triangle with two equal sides is called an isosceles triangle.

Given,

base (b) = 20 units and

height (h) = 120 units.

The formula to calculate the area is 1/2 × b × h square units.

By substituting the values, we get

⇒ Area = 1/2 × 20 × 120

            = 480 unit Squares

Therefore, the area of the given  isosceles triangle is 96 square units.

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We have shown that:  lim (n → ∞) ∑[(x²+1)Δx] = 14/3  and we have calculated the definite integral of f(x) over the interval [0, 2].

A definite integral is a mathematical concept that represents the area under the curve of a function between two specific points on the x-axis.

It is denoted by ∫f(x)dx, where f(x) is the function being integrated, and dx represents an infinitely small change in x

This problem requires us to recognize the limit as a Riemann sum for a function and calculate the definite integral of the function.

Given: Ax=2, xᵢ= iAx = 2i, n → ∞, f(x) = x² + 1.

First, we can express the Riemann sum as:

∑[f(xᵢ)Δx] = ∑(2i)² + 1 = 4∑(i²) + 2n

Next, we can recognize the limit as the definite integral of f(x) over the interval [a, b]:

lim (n → ∞) ∑[f(xᵢ)Δx] = ∫[a, b] f(x) dx = ∫[0, 2] (x² + 1) dx = [x³/3 + x] [0, 2] = 8/3 + 2 = 14/3

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for 7 pints

answer 14 cups

Answer:

find it out

Step-by-step explanation:

Answer:

BCD=100

hope it helps

Step-by-step explanation:

Brainliest please

The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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Answer:

438976

Step-by-step explanation:

76^3

Answer:

Because a 2 or a 4 was rolled 3 out of 12 times in the experiment, t so the fraction would be 3/12 (or 3 over 12).

Simplified: 1/4 (or 1 over 4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we subtract 7 from both sides, we get -2 on the right.  This is not possible, since absolute values are always 0 or greater.

The probability that a randomly selected month's number of order is more than 150 is 0.13%

Given, shawn finds that the monthly number of take-out orders at a restaurant is normally distributed with mean 132 and standard deviation 6.

⇒ mean = 132

⇒ standard deviation = 6

Analysis:

Set the monthly number of take out order as x.

From the question, we know:

P(x > 150) = P(x-132/ > 150-132/6)

= P(x=132/6 > 3)

= 1 - P(x-132/6 ≤ 3)

≈ 1 - 0.9987 {standard normal distribution table}

≈ 0.0013

= 0.13%

Hence we get the probability as 0.13%.

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Answer:

-4

Step-by-step explanation:

1. \(f(1) = (1-2)(1+3)\)

2. \(f(1) = -1(1+3)\)

3. \(f(1) = (-1)(4)\)

4. \(f(1) = -4\)

Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

The diversification merits strong consideration at single-business companies when:

1. It confronts strong bargaining power from both suppliers and customers.

2. Managers conclude the company has more resource weaknesses and competitive deficiencies than it has resource strengths and competitive assets.

3. It has achieved global leadership in its present industry and needs new market challenges to conquer.

4. Industry conditions take a turn for the worse and are expected to be long-lasting.

5. It encounters strong competition from rival companies and/or is currently losing money.

6. A "cash hog" type of business generates negative cash flows from internal operations and thus requires cash infusions from its corporate parent to report a profit.

7. It generates cash flows that are too small to fully fund its operations and growth, requiring periodic cash infusions by the corporate parent to provide additional working capital and finance new capital investment.

8. It is a business that is losing money and requires cash infusions from its corporate parent to continue operations.

9. It is a business that faces a liquidity crisis due to declining sales revenues and profits.

10. It is a business that has substantially more current liabilities than current assets.

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Answer:

5x+2y+14

Step-by-step explanation:

3x+2x+2y+8+6

5x+2y+14