In a call center that stays open all the time, calls arrive as a poisson process with a mean rate of 0.3 complaints per hour.(a) (5 points) after receiving a call (the 1st call), what is the probability that the 51st call arrives within 150 hours?(b) (5 points) after receiving a call, what is the probability that the next call arrives after 2 hours?(c) (5 points) the number of calls received each day is recorded for 50 consecutive days. find the probability that the sum of these 50 numbers is less than 356.

Step-by-step explanation:

hope it helps.

Answer:

6 or 5

Step-by-step explanation:

The value of x is 8.366, y is 4.582 and z is 5.477.

Using Pythagoras theorem in both Triangle as

Triangle 1:

H² = P² + B²

z²= y² + 3²

z² = y² + 9

Triangle 2:

x² = y² + 7²

x² = y² + 49

and, x² = z² - 9 + 49

x² = z² + 40.............(1)

Now, In big Triangle

x² + z² = 10²

x² + z² = 100

Now, from equation (1) we get

z² + 40 + z² = 100

2z² = 60

z² = 30

z = 5.477

and, x²= 30+40 = 70

x= 8.366

and, y²= z² - 9

y² = 21

y= 4.582

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At x=0, there is a guaranteed local maximum.

At x=5, there is a guaranteed local minimum.

At x=10, there is a potential local minimum.

At x=15, there is neither a local maximum nor a local minimum guaranteed.

At x=20, there is a potential local minimum.

At x=0, the value of f'(x) is -5. Since f'(x) is negative, it indicates that the function f(x) is decreasing in the vicinity of x=0. This suggests the presence of a local maximum at x=0.

At x=5, the value of f'(x) is 6. As f'(x) is positive, it suggests that the function f(x) is increasing near x=5. Therefore, we can infer the existence of a local minimum at x=5.

At x=10, the value of f'(x) is 3. Since f'(x) is positive, it implies that f(x) is increasing around x=10. Hence, there is a potential local minimum at x=10.

At x=15, the value of f'(x) is 0. This indicates that f(x) neither increases nor decreases significantly near x=15. Therefore, there is neither a local maximum nor a local minimum guaranteed at x=15.

At x=20, the value of f'(x) is 4. As f'(x) is positive, it suggests that f(x) is increasing near x=20. Hence, we can infer a potential local minimum at x=20.

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Complete question is:
Suppose f(x) and f′(x) are continuous but restricted to the interval 0≤x≤20, and assume the values of f'(x) are as shown.

For each value, determine whether there is a local maximum, local minimum, or nothing.

x         0          5        10       15     20

f'(x)    -5         6        3         0        4

At x=0, you guarantee _________

At x=5, you guarantee  _________-

At x=10, you guarantee ____________-

At x=15, you guarantee _____________

At x=20, you guarantee ______________

Answer:

\( \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} \times \frac{4}{1} = \frac{256}{1} = - 256\)

Step-by-step explanation:

I dont know if I'm right or not

but this is how I learned it

When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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The volume of the ice cube is 35.937 mm^3

We know that for a cube of side length L, the volume is defined as:

V = L^3

Here, we do know that each side of our ice cube measures 3.3 mm, so we have:

L = 3.3mm

Then the volume of the cube is just:

V = (3.3 mm)^3 = 35.937 mm^3

We can conclude that the volume of the ice cube is 35.937 mm^3

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The correct representation of Kirchhoff's junction rule would be:

ΣIᵢ = 0

This equation states that the sum of all currents (Iᵢ) flowing into a junction or node is equal to zero.

Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), states that the algebraic sum of currents flowing into any junction or node in an electrical circuit is equal to zero.

Among the equations you provided, none of them accurately represents Kirchhoff's junction rule. The correct representation of Kirchhoff's junction rule would be:

ΣIᵢ = 0

This equation states that the sum of all currents (Iᵢ) flowing into a junction or node is equal to zero.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{x}{48}=\cfrac{48}{64}\implies \cfrac{x}{48}=\cfrac{3}{4}\implies 4x=144\implies x=\cfrac{144}{4}\implies \boxed{x=36}\)

The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x \(p^i \times (1-p)^{(n-i)}\) ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x \(0.80^i \times (1-0.80)^{(12-i)}\)]

Using a calculator or software, we can calculate this to be approximately 0.7063.

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If a number cube is rolled 25 times and 6 appears only four times, then the experimental probability of getting 6 is 4/25.

The experimental probability of an event happening is the number of times the event occurred divided by the total number of trials. In this case, a number cube is rolled 25 times and lands on 6 four times. Here are the steps to determine the experimental probability of landing on 6:

So, the experimental probability of landing on 6 is 4/25, which means that if we roll the number cube many more times, we would expect to get a 6 approximately 4 out of every 25 rolls.

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Therefore, the inequality that has the graph shown is: y > 2x - 3.

In mathematics, an inequality is a statement that compares two values, expressions, or sets of numbers using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities can be solved using a variety of methods, depending on the complexity of the inequality and the type of variable involved. For simple linear inequalities, such as 2x + 1 < 5, the solution set can be found by isolating the variable on one side of the inequality and solving for it. The solution set for this example would be x < 2. Inequalities can also be used to represent a range of values or constraints in real-world situations, such as the maximum weight limit for an elevator or the minimum score needed to pass a test. In these cases, inequalities can help us determine if a value or expression meets the given criteria or not.

Here,

The graph shown below has a solid line passing through the points (-2, -7) and (1, -1), and the shaded region above the line. To determine which inequality has this graph, we can look at the slope of the line and the position of the shaded region.

The slope of the line can be calculated using the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line. Using the points (-2, -7) and (1, -1), we get:

slope = (-1 - (-7)) / (1 - (-2)) = 2

Therefore, the equation of the line is of the form y = 2x + b, where b is the y-intercept. We can find the value of b by plugging in one of the points on the line. For example, using the point (-2, -7), we get:

-7 = 2(-2) + b

b = -3

So the equation of the line is y = 2x - 3.

Since the shaded region is above the line, we know that y is greater than 2x - 3.

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The situation described is an experiment. An experiment involves the manipulation of variables to observe the effect on an outcome.

An experiment involves the manipulation of variables to observe the effect on an outcome. In this case, the researcher gathered data from two groups of students, where one group listened to classical music while taking a math test, while the other group did not. By assigning the students to different conditions (listening to music or not), the researcher is able to compare the effects of the independent variable (listening to classical music) on the dependent variable (student anxiety).

A sample survey involves collecting data by asking questions to a representative sample of individuals, but in this situation, there is no indication of surveying individuals.

An observational study involves observing and collecting data without actively manipulating any variables, but in this situation, the researcher manipulated the independent variable (music condition) by assigning students to different groups.

Therefore, the described situation falls under the category of an experiment.


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Answer:

Step-by-step explanation:

Using the formula for calculating speed expressed as shown;

Speed = Distance/Time

Given parameters

Distance = 280miles

Speed = 50miles/hour

Required

Time it will take t return

From the formula above, Time = Distance/ Speed

Substituting the given parameters

Time = 280/50

Time = 5.6 hours

Hence the time it will take the driver to return is 5.6hours

5. M=[T]  B  V ​  B  W ​   = [ [0, 0, 0], [1, 0, 0], [0, 1, 0] ]

6. M=[T]  B  V ​  B  W ​   = [ [0, 0, 0], [1, 1, 0], [0, -1, 1] ]

In both cases, we are given a linear transformation T from the vector space V to the vector space W.

To find the matrix representation of T with respect to the given bases B V  and B W , we need to determine how T acts on each vector in B V and express the results in terms of the basis vectors of B W .

In case 5, the linear transformation T maps a polynomial ax^2 + bx + c to cx^2 + ax + b. The basis B V = {x^2 + 1, x - 1, 1} for V=P2(R) consists of three polynomials.

We apply T to each polynomial in B V and express the results in terms of the basis vectors of B W .

The resulting matrix representation [T] B V  B W  is [ [0, 0, 0], [1, 0, 0], [0, 1, 0] ].

In case 6, the linear transformation T maps a polynomial ax^2 + bx + c to (a + b)x^2 - b + c.

The basis B V = {x^2, x, 1} for V=P2(R) consists of three polynomials.

We apply T to each polynomial in B V and express the results in terms of the basis vectors of B W .

The resulting matrix representation [T] B V  B W  is [ [0, 0, 0], [1, 1, 0], [0, -1, 1] ].

The matrix representation [T] B V  B W  provides a convenient way to compute the action of the linear transformation T by matrix-vector multiplication.

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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Answer:

13a² + 5

Step-by-step explanation:  

Not 100% but 90% sure. Work on Picture.

Answer:

y=-2/3x-7/3

Step-by-step explanation:

a parallel line has the same slope but different y intercept

so we need to solve for y=-2/3x+b

since it passes through 4,-5 we can plug it in for x and y

-5=-2/3(4)+b

-5=(-8/3)+b then add 8/3 to both sides

-5 is also -15/3

-7/3=b

so answer is y=-2/3x-7/3

Answer: x>-3

Step-by-step explanation:

−18<5x−3

Step 1: Flip the equation.

5x−3>−18

Step 2: Add 3 to both sides.

5x−3+3>−18+3

5x>−15

Step 3: Divide both sides by 5.

5x/5 > −15/5

x>−3

Answer:

x>−3

The persistent study is identified from response bias.

So, the correct answer is C.

A story reported results of a voluntary respons study stru online dating The study used online responses of 13.792 pple. Of those who responded four swe man and about free fourths had at least a bachelor's degree.

One reported finding was that 29% of men go online intending to cheat.The study has several potential sources of bias. The use of self-reported online surveys implies that people who do not have access to the internet or who are reluctant to take online surveys are excluded from the study.

This is a potential source of bias known as non-response bias. People who are more interested in online dating are more likely to participate in the survey. This is a potential source of bias known as self-selection bias.

There are several potential sources of bias in online dating studies. Response bias is one of them. Response bias happens when people are unwilling or unable to provide accurate information. In online dating research, response bias can occur when people misrepresent themselves or give false information.

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Answer:

81.64 yards

Step-by-step explanation:

The formula to find the circumference is:

Circumference = 2 · π · r

r = 13 yards

π = 3.14

C = 2 · 3.14 · 13 = 81.64 yards

So, the circumference is 81.64 yards.

Answer:

170 miles

Step-by-step explanation:

first, for 3 hours they drove 40 mph. this means you have to multiply 40 mph by the 3 hours.

40*3=120

then you have to add the extra 50 miles that they drive north because their speed changed.

120+50=170

Answer:

x = 1

Step-by-step explanation:

first you distribute :  3(x + 1) -> 3x  -2(x - 1) -> -2x + 2

next you combine like terms : 2 + 6 = 8

3x + 3 = -2x + 8

subtract 3 from both sides : 3x = -2x + 5

add 2x to both sides : 5x = 5

divide both sides by 5 and you get :  x = 1

Hope this helps :")

Answer:

Hi there!

Your answer is:

6.25% of the pizza is in each slice. Each slice represents .0625 of the pizza!

100/16= 6.25

decimal format means you divide 6.25/100

Check your work!

.0625 × 16 should equal 1 (and it does!)

6.25% × 16 should equal 100 (and it does!)

Hope this helps!

Answer:

Each slice is 0.0625

Step-by-step explanation:

Sample answer from Edmentum!

Answer:

  -8k -2

Step-by-step explanation:

You want the simplified form of -2(k+1)-6k.

The process of simplifying an algebraic expression includes ...

Parentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.

  -2(k +1) -6k

  = (-2)(k) +(-2)(1) -6k = -2k -2 -6k

Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)

  = (-2 -6)k -2 = -8k -2

The simplified expression is -8k -2.