ime left 1 The number of calls coming in to an office follows a Poisson distribution with mean 5 calls per hour. What is the probability that there will be exactly 7 calls within the next hour ? Question 6 Answer saved Marked out of 1.00 P Flag question O a. 0.090 O b. 0.104 Oc. 0.123 O d. 0.071 The number of calls coming in to an office follows a Poisson distribution with mean 5 calls per hour. What is the probability that there will be exactly 7 calls within the next three hours? Question 5 Answer saved Marked out of 1.00 P Flag question O a. 0.090 O b. 0.104 O c. 0.010 O d. 0.071

Answer: To find the surface area of a cylinder, we need to add the areas of the top and bottom circles to the lateral surface area (the curved surface that connects the circles).

1.) Given that the diameter (d) of the cylinder is 10m and the height (h) is 8m.

First, let's find the radius of the cylinder (r):

r = d/2 = 10m/2 = 5m

Then, we can find the surface area of the cylinder:

The area of each circle is given by A = πr^2

A(top and bottom circles) = 2π(5m)^2 = 2π(25m^2) = 50πm^2

The lateral surface area is given by A = 2πrh

A(lateral) = 2π(5m)(8m) = 80πm^2

The total surface area is the sum of the areas of the top and bottom circles and the lateral surface area:

A(total) = A(top and bottom circles) + A(lateral)

A(total) = 50πm^2 + 80πm^2

A(total) = 130πm^2

Therefore, the surface area of the cylinder is 130π square meters (or approximately 408.4 square meters if you round to one decimal place).

Ms. Hernandez began her math class by saying: I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14 then, the 5th number is 18. The correct answer is option E.

Since there are five numbers and the middle is the center esteem when the numbers are organized in arrange, the center esteem must be one of the given values: 8, 14, 14, or 16.

The cruel of five numbers is the whole of the numbers isolated by 5. On the off chance that the cruel break even with the middle, at that point the whole of the five numbers must rise to five times the middle.

The whole of the primary four numbers is:

14 + 8 + 16 + 14 = 52

So, the fifth number must be:

5 × 14 - 52 = 18

Hence, the reply is E. 18.

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The missing length in the attached right triangle is 8.7

The missing length of a triangle can be calculated using any of the basic trigonometry function

To illustrate this, I will use the attached right triangle where the missing length is x

The value of x in the right triangle can be calculated using the following sine ratio

sin(75) = x/9

Cross multiply the equation

So, we have

x = 9 * sin(75)

Evaluate the products

x = 8.7

Hence, the value of missing length in the attached right triangle is 8.7

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The probability of X being equal to 4 is 0.1755.

The probability of X being less than 4 is 0.60687.  

The probability of X being greater than or equal to 4 is 0.39313.

The probability of X being between 4 and 6 (inclusive) is 0.49719.

The first thing we need to do is to identify the parameters of the Poisson process. In this case, we are given that the mean is u=5.

(a) P(4):

P(X=4) = (e^(-u) * u^x) / x!

= (e^(-5) * 5^4) / 4!

= 0.1755


(b) P(X<4):

P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

= (e^(-5) * 5^0) / 0! + (e^(-5) * 5^1) / 1! + (e^(-5) * 5^2) / 2! + (e^(-5) * 5^3) / 3!

= 0.12465 + 0.20593 + 0.17547 + 0.10082

= 0.60687



(c) P(X>=4):

P(X>=4) = 1 - P(X<4)

= 1 - 0.60687

= 0.39313



(d) P(4<=X<=6):

P(4<=X<=6) = P(X=4) + P(X=5) + P(X=6)

= (e^(-5) * 5^4) / 4! + (e^(-5) * 5^5) / 5! + (e^(-5) * 5^6) / 6!

= 0.1755 + 0.17547 + 0.14622

= 0.49719

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A valid argument is a logical argument in which the conclusion follows necessarily from the premises.

In the context of establishing the truth of a theorem, a valid argument serves as a proof that shows the theorem is true, given certain assumptions.

The statements used in a proof can include axioms, which are statements we assume to be true, as well as previously proven theorems.

Axioms provide the foundation for building the argument, while proven theorems allow us to apply already established knowledge to strengthen our proof.

By using a combination of axioms and proven theorems, we can create a valid argument that effectively establishes the truth of a theorem.

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This expression gives us the probability of observing 0 to 9 jobs arriving at the processor per minute with an average arrival rate of 20 jobs per minute.

Given that jobs arrive at a processor according to a Poisson distribution with an average arrival rate λ (per minute), we can calculate the probability of observing a specific number of jobs arriving in a given time interval using the Poisson probability formula:

P(X = k) = (e^(-λ) * λ^k) / k!

In your expression, we have the following terms: (201) (1 + 20λ + (20λ)^2 / 2! + (20λ)^3 / 3! + ... + (20λ)^9 / 9!). This expression is actually the expansion of the Poisson probability formula for k=0 to k=9, with a specific arrival rate λ = 20.

To calculate the probability, we can rewrite the expression as:

P(X ≤ 9) = e^(-20) * (1 + 20 + 20^2 / 2! + 20^3 / 3! + ... + 20^9 / 9!)

This expression gives us the probability of observing 0 to 9 jobs arriving at the processor per minute with an average arrival rate of 20 jobs per minute.

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Answer: I can’t read the words

Step-by-step explanation:

Based on the data provided, we can calculate the slope and y-intercept of the line that fits the data points.

First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). We can use the first two data points for this calculation:

m = (27 - 32) / (10 - 5) = (-5) / 5 = -1

Now, let's find the y-intercept (b) using the formula: y = mx + b. We can use the first data point (5, 32) and the slope we found:

32 = -1 * 5 + b
32 = -5 + b
b = 37

Therefore, the correct slope is -1, and the y-intercept is 37.

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The solution of the given equation; tan 23 = 22 / x for the variable x as required is; 52.07.

It follows from the task content that the value of x in the given equation is to be determined.

Since the given equation is; tan (23) = 22 / x;

By multiplying both sides by; x / tan (23); we have that;

x = 22 / tan (23)

x = 22 / 0.4225

x = 52.07.

Ultimately, the solution of the equation for x is; 52.07.

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Answer:

Step-by-step explanation:

o.10

Answer: The answer is A -48 dollars

Step-by-step explanation: you times 16 by 3 which make 48 and since its debt you take away so thats negative 48

Note that the system of graphs has two y-intersects hence the two solutions. Note tht in the graph there ar etwo parabolas.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis. This is done in analytic geometry using the usual convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points fulfill x = 0 because of this.

Replace x in the equation with 0 and then solve for y, keeping in mind that the y-intercept always has an associated x-value of 0. Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

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After testing the hypothesis we can conclude that the evidence that the mean time to be cured is actually more than advertised.

To test the hypotheses and determine whether there is evidence that the mean time to be cured is actually more than advertised, we can use a one-sample t-test.

The null hypothesis is that the true mean time to be cured is equal to the advertised mean time, i.e., H0: µ = 5. The alternative hypothesis is that the true mean time to be cured is greater than the advertised mean time, i.e., Ha: µ > 5.

We are given that the sample size is n = 400, the sample mean is x = 5.2 days, and the standard deviation is σ = 1 day.

To conduct the one-sample t-test, we first calculate the test statistic t:

t = (x - µ) / (σ / sqrt(n))

t = (5.2 - 5) / (1 / sqrt(400))

t = 2

where µ = 5 is the hypothesized population mean.

The degrees of freedom for the t-distribution is n - 1 = 399.

Using a t-distribution table or an online calculator with df = 399, we can find the p-value associated with the test statistic t = 2 to be approximately 0.023.

Since the p-value (0.023) is less than the significance level α = 0.05, we reject the null hypothesis and conclude that there is evidence that the mean time to be cured is actually more than advertised.

Therefore, we can say that there is significant evidence that the mean time to be cured is greater than 5 days.

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The radius of this circle to the nearest tenth is equal to 1.3 units.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

By substituting the given parameters into the arc length formula, we have the following;

12.8 = r × 9.8

Radius, r = 12.8/9.8

Radius, r = 1.3 units.

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It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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The cube results in a square two-dimensional-plane section when slices horizontally or vertically.

The square right pyramid results in a square when sliced horizontally and a triangle when sliced vertically.

A cube has 6 faces which are all squares.

So when a cube is slice either parallel to the base or perpendicular to the base, the resulting section will be a square.

Whereas, a right square pyramid has a base square and 4 triangular faces joining at a common point.

So when the pyramid is cut vertically, it results in a triangle and when it cuts horizontally, it results in a square.

Hence the cube results in a square in either slices and right square pyramid results in a square or triangle.

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This statement is false. If K(t) = 0 for all t, it means that the curvature of the curve at any point is zero.

This does not necessarily imply that the curve is a straight line. A curve can have zero curvature at some or all points and still not be a straight line, for example, a circle. A straight line is characterized by having zero curvature everywhere, but having zero curvature does not necessarily mean that a curve is a straight line.

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Circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

Circular permutation refers to an ordering of elements in a circle. Factorial, on the other hand, is the product of all the natural numbers from an integer down to one. It is denoted by the exclamation mark (!). Series, on the other hand, refers to the indicated sum of the terms of an associated sequence. Finally, permutation is an order of elements of a set.

To summarize, circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

1. Circular permutation - an ordering of elements in a circle.
In a circular permutation, the arrangement of items is considered in a circular fashion rather than in a linear order. The number of circular permutations for 'n' elements can be calculated using the formula (n-1)!.

2. Factorial - the product of all the natural numbers from an integer down to one.
Factorial, denoted by the symbol '!', represents the product of all the positive integers from a given integer down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

3. Series - the indicated sum of the terms of an associated sequence.
A series is the sum of the terms in a given sequence, often represented by the summation symbol Σ. For example, the sum of the first 'n' natural numbers is represented as Σ(i=1 to n) i = n(n+1)/2.

4. Permutation - an order of elements of a set.
A permutation refers to the arrangement of elements in a specific order within a set. The number of possible permutations for a set of 'n' elements, taken 'r' at a time, can be calculated using the formula n!/(n-r)!.

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The requried solution of the given inequality is x > 5 and there is an open circle at 5  and a bold line starts at 5 and points to the right.

As mentioned in the question,

We have,

–3(2x – 5) < 5(2 – x)

Simplify the above inequality,

-6x+15 < 10-5x
x > 5

Since on the number line, there is an open circle at 5  and a bold line starts at 5 and points to the right.

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The equation of the parabola is

The equation of the parabola is solved using the equation

y = a(x - r1) (x - r2)

where r1 and r2 are the roots or x-intercept

The roots of the equation is given as -2 and 4.

hence we have that

y = a(x + 2) (x - 4)

Using (-1, -3) we solve for a

-3 = a(-1 + 2) (-1 - 4)

-3 = a(1) (-5)

-3 = -5a

a = 3/5

Plugging this figure back into the original equation,

y = 5/3(x + 2) (x - 4)

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So the vector  form of the equation is: y = -1(x - 2)² + 3.

To convert from standard form to vertex form, we complete the square by following these steps:

Factor out the coefficient of the x-squared term:

y = -x² + 4x - 1

= -1(x² - 4x) - 1

To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:

y = -1(x² - 4x + 4 - 4) - 1

Simplify the expression inside the parentheses by factoring a perfect square:

y = -1((x - 2)² - 4) - 1

Distribute the -1 and simplify:

y = -1(x - 2)² + 3

Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.

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The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)

Here, we have,

to determine the ordered pair that is a function

The list of options represents the given parameter

As a general rule, for an ordered pair to be a function;

The y values on the ordered pair must point to different x values

In (a) the y values 4, 5, 6 and 7 have the same x value of 3

So, it is not a function

In (b) the y values 5 and 8 have the same x value of 2

So, it is not a function

In (c) the y values -1 and 1 have the same x value of 1

So, it is not a function

In (d) all the y values have different x values

So, it is a function

Hence, the ordered pair that is a function is  (d)

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complete question:

The following sets of ordered pairs represent relations from the set X to the set Y. Which one is a function?

A (3, 4), (3, 5), (3, 6), (3, 7)

B (2, 5), (2, 8), (3, 7), (3, 9)

C (1, -1), (0, 0), (1, 1), (4, 2)

D (0, 0), (1, 1), (4, 2), (9, 3)

As the age of the bus increases, the annual maintenance cost generally increases as well. Therefore, the estimated regression model is: y = a + bx = 883.5 + 253.17x where y is the annual maintenance cost and x is the age of the bus.

(a) The correct scatter chart is (i) which has age of bus as the independent variable. The scatter chart indicates there may be a linear relationship between age of bus and annual maintenance cost.

(b) To develop an estimated regression equation, we can use the following steps:

X = (1+2+2+2+2+3+4+4+5+5)/10 = 3

Y = (350+370+480+520+590+550+750+800+790+950)/10

= 643

Calculate the deviations of age of bus (x) and annual maintenance cost (y) from their respective means (X and Y).

x - X: -2, -1, -1, -1, -1, 0, 1, 1, 2, 2

y - Y: -293, -273, -163, -123, -53, -93, 107, 157, 147, 307

Calculate the sum of the product of the deviations of x and y.

∑[(x - X)(y - Y)] = (-2)(-293) + (-1)(-273) + (-1)(-163) + (-1)(-123) + (-1)(-53) + (0)(-93) + (1)(107) + (1)(157) + (2)(147) + (2)(307)

= 4,557

Calculate the sum of the squared deviations of x.

∑[(x - X)²] = (-2)² + (-1)² + (-1)² + (-1)² + (-1)² + 0² + 1² + 1² + 2² + 2²

= 18

Calculate the estimated slope of the regression line, b.

b = ∑[(x - X)(y - Y)] / ∑[(x - X)²]

= 4,557 / 18

= 253.17

Calculate the estimated intercept of the regression line, a.

a = Y - bX

= 643 - (253.17)(3)

= 883.5

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The length of the segment VW, obtained using the relationship between similar triangles and Pythagorean Theorem is; VW = 5·√3

Similar triangles are triangles that have the same shape or in which in one of the triangles, two of the angles are congruent to two angles in the other triangle.

The common external tangent indicates that the radius WZ and XY are both perpendicular to the tangent [tex]\overline{VX}[/tex], therefore;

WZ and XY are parallel and triangles ΔVWZ and ΔVXY are similar triangles

VW/5 = VX/15

VW = 5 × (VX/15) = VX/3

ZY = 5 + 15 = 20

VY = VZ + ZY = VZ + 20

VZ = VY/3

VY = VY/3 + 20

VY - VY/3 = 20

(2/3) × VY = 20

VY = 20 × 3/2 = 30

Pythagorean Theorem indicates

VX = √(30² - 15²) = 15·√3

VX = 15·√3

VW = VX/3, therefore;

VW = 15·√3 ÷ 3 = 5·√3

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Answer:702

Step-by-step explanation:n*n-1

The perimeter of the rectangle is 16m

It is important that a rectangle has four sides, it also has four angles.

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter = 2(l + w)

Such that the parameters of the formula are;

From the information given, we have that;

Substitute the values

Perimeter, P = 2(4 + 4)

add the values

Perimeter = 2(8)

Expand the bracket

Perimeter = 16m

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The quadratic function with real coefficients and the given zeros of 5 and 4i is: f(x) = x^3 - 5x^2 + 16x - 80.

A quadratic function with real coefficients and the given zeros of 5 and 4i is:

f(x) = (x - 5)(x - 4i)(x + 4i)

Expanding this expression, we get:

f(x) = (x - 5)(x^2 - (4i)^2)

f(x) = (x - 5)(x^2 + 16)

f(x) = x^3 - 5x^2 + 16x - 80

Therefore, the quadratic function with real coefficients and the given zeros of 5 and 4i is:

f(x) = x^3 - 5x^2 + 16x - 80.
Hi! To write a quadratic function with real coefficients and the given zero 5 + 4i, you should also consider its complex conjugate, which is 5 - 4i. This is because complex roots of a quadratic equation with real coefficients always occur in conjugate pairs.

Let x = 5 + 4i and x = 5 - 4i be the zeros of the quadratic function. Using the factored form of a quadratic function, we can write it as:

f(x) = A(x - (5 + 4i))(x - (5 - 4i))

Now, expand the expression inside the parentheses:

f(x) = A((x - 5) - 4i)((x - 5) + 4i)

Multiply the two binomials using the difference of squares formula:

f(x) = A((x - 5)^2 - (4i)^2)

Simplify:

f(x) = A(x^2 - 10x + 25 + 16)

Combine the constant terms:

f(x) = A(x^2 - 10x + 41)

Since we want a quadratic function with real coefficients, A can be any real number. We can choose A = 1 to simplify the expression:

f(x) = x^2 - 10x + 41

So the quadratic function is f(x) = x^2 - 10x + 41.

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The solution to the equation 2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾ is m = -9.

Given the equation the question:

2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾

To solve the equation 2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾  using the equal base method, we can rewrite 16 as a power of 2:

2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾

2⁽ᵐ ⁺ ¹⁾ = 2⁴⁽ᵐ ⁺ ⁷⁾

2⁽ᵐ ⁺ ¹⁾ = 2⁽⁴ᵐ ⁺ ²⁸⁾

Now that both sides have the same base, we can equate their exponents and solve for m:

m + 1 = 4m + 28

4m - m = 1 - 28

3m = -27

m = -9

Therefore, the value of m is -9.

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The figures that have the same shaded area are Figure I and Figure IV. The correct option is A. Figure I and Figure IV

From the question we are to determine the figures that have the same area

Area of Figure I

Area = 12 m × 8 m

Area = 96 m²

Area of Figure II

Area = 1/2 × (12 m × 7.5 m)

Area = 45 m²

Area of Figure III

Area = π (12/2)²

Area = 3.14 × (6)²

Area = 3.14 × 36

Area = 113.04 m²

Area of Figure IV

Area = 1/2 × (6 m + 10 m) × 12m

Area = 1/2 × (16 m) × 12m

Area = 8 m × 12m

Area = 96 m²

Hence, Figure I and Figure IV have the same area

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The angle that is complementary to <BDC is <ADB. Option D

Complementary angles are simply described as pair of angles that sum up to give 90 degrees.

Some properties of complementary angles are;

From the information given, we have that;

The angles are;

<CDA

<CDB

<BDA

<ADB

The complementary angles are;

<BDC and <ADB

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