Find the unit rate :


Running 2. 3km in 7 minutes

If a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then

a) p(no events for 3 min) - 0.0498

b) p(1 event in 1 min) - 0.3347

c) p(>= 1 event in 1 min) - 0.7769

d) uncertainty for a, b, c - For a), σ = 1.732 and for b) and c), σ = 1.225

A Poisson process is a stochastic process that counts the number of events in a given time interval. It is characterized by two parameters: the rate, λ, which is the average number of events in a given time interval, and the mean, μ, which is the average number of events in the entire process.

a) The probability of no events in 3 minutes is given by the Poisson probability mass function:

P(X = 0) = (λt)^0 * e^(-λt) / 0! = e^(-λt)

Where t is the time interval (3 minutes), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 0) = e^(-1.5 * 3) = 0.0498

b) The probability of 1 event in 1 minute is given by the Poisson probability mass function:

P(X = 1) = (λt)^1 * e^(-λt) / 1! = λt * e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 1) = 1.5 * e^(-1.5) = 0.3347

c) The probability of at least 1 event in 1 minute is given by the complement of the probability of no events:

P(X >= 1) = 1 - P(X = 0) = 1 - e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X >= 1) = 1 - e^(-1.5) = 0.7769

d) The uncertainty for each of the probabilities is given by the standard deviation of the Poisson distribution:

σ = sqrt(λt)

For a), the standard deviation is:

σ = sqrt(1.5 * 3) = 1.732

For b) and c), the standard deviation is:

σ = sqrt(1.5 * 1) = 1.225

Therefore, the uncertainty for each of the probabilities is given by the standard deviation.

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The cost of one rose shrub costs $12 and one pot of ivy costs $24, respectively.

It takes two equations with two variables to solve a system of equations. The variables can then be solved for using algebraic techniques like substitution or elimination.

Let x be the cost of one rose bush and y be the cost of one pot of ivy.

From Mei's purchase, we have:

3x + y = 36

From Ming's purchase, we have:

9x + 8y = 168

Use the first equation to solve for y:

y = 36 - 3x

Substituting this into the second equation, we get:

9x + 8(36 - 3x) = 168

9x + 288 - 24x = 168

-15x = -120

x = 8

Substituting x = 8 into equation of y, we get:

y = 24

Hence, the cost of one rose bush is $8, and the cost of one pot of ivy is $24.

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Answer: 0.72

Step-by-step explanation:

0.62 + 0.10 = 0.72

The volume of the rectangular prism is 11.28 feet³.

In terms of geometry, a rectangular prism is a polyhedron having two parallel, congruent bases. It also goes by the name cuboid. A rectangular prism is made up of six rectangles, each with twelve edges.

We are given that a rectangular prism has the following dimensions:

Length (l) = 4.7 feet

Width (w) = 1.5 feet

Height (h) = 1.6 feet

We know that

Volume (V) = [tex]l \times w \times h[/tex]

From this, we get

⇒V = [tex]4.7 \times 1.5 \times 1.6[/tex]

⇒V = 11.28 feet³

Hence, the volume of the rectangular prism is 11.28 feet³.

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Answer: Your answer is 11.28 ft³

Step-by-step explanation: 4.7 x 1.5 x 1.6 = 11.28 you have to do it in this order also I did the k12 quiz here's proof.

Hope it helped :D

In a right-angled triangle, the sum of two acute angles is equal to 90°.

So if α and β are the two acute angles of a right-angled triangle, then α + β = 90°.Using the formula for sin of the difference of two angles, we can write:sin2α = sin(90° − β) = sin90°cosβ − cos90°sinβ = cosβsin2β = sin(90° − α) = sin90°cosα − cos90°sinα = cosαSince sin2α = cosβ and sin2β = cosα, we can conclude that sin2α = sin2β.Now, let's write 3sinx − 5cosx in the form kcos(x+a). Using the formula for cos of the sum of two angles, we can write:3sinx − 5cosx = kcos(x+a) = k(cosxcos a − sinxsin a)Equating the coefficients of sinx and cosx, we get:−5 = kcos a3 = −ksin aSquaring and adding these equations, we get:25 + 9 = k^2(cos^2a + sin^2a) = k^2So k = √34.Taking the ratio of the two equations, we get:−5/3 = cos a/sin a = 1/tan aSo tan a = −3/5.Using the inverse tangent function, we get:a = tan^−1(−3/5)So the final answer is:kcos(x+a) = √34cos(x + tan^−1(−3/5)).

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The measure of the 2 angle in the triangle is 55 degrees.

In geometry, a kite is a quadrilateral with two pairs of adjacent sides that are equal in length. This means that a kite is a special type of quadrilateral called a "tangential quadrilateral" because its sides can be inscribed in a circle.

If one angle of a triangle is a right angle (90 degrees) and another angle is 35 degrees, then the sum of the three angles in the triangle is 180 degrees.

Therefore, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees:

Third angle = 180 degrees - 90 degrees - 35 degrees

Third angle = 55 degrees

So the measure of the 2 angle in the triangle is 55 degrees.

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Among Jack, Pandu and  Sam, Pandu scored the best as his marks scored percentage is 60%.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'. 

Solution according to the information given:

Jack's percentage = (5/10)×100

                               = 50%

Sam's percentage = (22/40)×100

                               = (11/20)×100

                               = 55%

Pandu's percentage = (12/20)×100

                                  = 60%

Thus, Pandu scored the best marks by scoring 60%.

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The diagonals are 17.4 inches

From the question, we have the following parameters that can be used in our computation:

DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8

Given that DHB is a right triangle, we have

DB² = HB² + DH²

So, we have

DB² = (8.2 + 6)² + 10²

DB² = 301.64

Take the square root

DB = 17.4

The triangles DBY and RYB are congruent triangles

So, we have

RY = 17.4

The figure is an isosceles triangle, and the length does not meet the regulation

This is so because the length is less than the required 20 inches

The two non-parallel sides of an isosceles triangle are of equal length

So, we have

1/2x + 5 = 2x - 4

Evaluate the like terms

3/2x = 9

This gives

x = 9 * 2/3

x = 6

So, we have

KR = 1/2x + 5

This gives

KR = 1/2 * 6 + 5

KR = 8

So, the value of KR is 8 units

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Answer:

she added the denominator

Step-by-step explanation:

Answer:

She added the numerators and denominators. This is not correct.

Step-by-step explanation:

[tex]x(\frac{2}{3} +\frac{1}{4} )=x(\frac{8+3}{12} )[/tex]

[tex]=\frac{11}{12} x[/tex]

Hope this helps.

The length of segment CB in trapezoid CBAD is 11.

In a trapezoid, the midsegment is the line segment that joins the midpoints of the two non-parallel sides. In this case, KJ is the midsegment of trapezoid CBAD, which means that it is parallel to both CB and AD, and its length is equal to the average of the lengths of CB and AD.

We are given that;

CB=4x-13

KJ=6x-18

DA=25

we can use the formula for the midsegment of a trapezoid to set up an equation and solve for x:

KJ = (CB + AD) / 2

6x - 18 = (4x - 13 + 25) / 2

6x - 18 = (4x + 12) / 2

6x - 18 = 2x + 6

4x = 24

x = 6

Now that we have found the value of x, we can substitute it back into the expression for CB to find its length:

CB = 4x - 13 = 4(6) - 13 = 11

Therefore, the answer of the given trapezoid will be 11.

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Answer:

29 months

Step-by-step explanation:
if the trumpet is 360 and he has 285, we need to find out how much he needs to gain to get the trumpet.

360-285=80

If the Intrest is 1% per month, he’s gaining $2.85 per month.
So we divide 80 by 2.85, and get 28.07.

We have to go to the next number because it gets the money at the end of the month.
29 months

Answer:

d>500

t>130

Step-by-step explanation:

For the first problem:

we must set up an inequality to answer :D soooo:

d>500

the same thing goes for the second one:

t>130

Hope this is right!

1.  A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.

2. The value of x2 =  [128,295, 44,557]T.

3. The value of x = [0.701, 0.299, 0]T .

1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.

2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T

3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue

1. We can do this by finding the null space of (P - I), where I is the identity matrix:

(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.

To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T

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The camp charge per week = slope = $25 per week.

The slope is also referred to as the unit rate which is given as: m = change in y / change in x.

From the given scenario, let:

x = number of weeks

y = camp charges

We will therefore have these two points:

(6, 190) and (9, 265)

Use the two points to find the slope, which is the swimming camp charge per week:

Camp charge per week (m) = change in y / change in x = 265 - 190 / 9 - 6

= 75/3

= $25 per week.

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The graph and the solution to the system of inequalities are added as attachments

System 1

From the question, we have the following parameters that can be usedin our computation:

x ≤ -3

y < 5/3x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is (-4, -5)

System 2

Here, we have the following system

y ≤ -5/2x - 2

y < -1/2x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (-4, -5)

System 3

Here, we have the following system

y ≥ 2/3x + 3

y > -4/3x - 3

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (4, 7)

See attachment for the graph of the inequalities

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Answer: Hayley is hosting a party. She has 50 pieces of candy she wants to give to her 10 friends. How many pieces should each friend get so everyone receives the same amount?

The value of x = 44.

Interior angles are those found within a polygon. For instance, a triangle has three interior angles. The phrase "angles limited in the interior area of two parallel lines when intersected by a transversal are known as interior angles" is the third definition of internal angles.

We must use the congruence of the alternate interior angles created by transversal t and parallel lines p and q in order to determine the value of x. Hence, we can construct the equation shown below:

180 - 2x = 3x - 40

When we simplify this equation, we obtain:

5x = 220

x thus equals 44.

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The length of the segment indicated is 8.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Here, two right-angled triangles are given. In a right-angled triangle, the sides are the same, and it can be proved by congruence triangle rules.

The two angles are congruent if they are complements of the same angle (also known as congruent angles). Congruent angles are all just angles.

So, the sides' hypotenuse is 8 which is equal to x. So the value of x is 8.

Thus, the length of the segment indicated is 8.

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40000000

Step-by-step explanation:

ezy Peasy lemon squeeze

Answer:40,000,000

Step-by-step explanation:

its just like 2 divided by 8 which is 4 then just add all your zeros

Assuming a constant rate of production, 360 workers can produce approximately 7200 widgets in 20 hours.

The problem asks how many widgets can be produced by 360 workers in 20 hours. To solve this problem, we need to use the formula:

widgets = rate x time x workers

We know the time is 20 hours and the number of workers is 360. We need to find the rate at which the workers can produce widgets. Let's assume that each worker can produce one widget in one hour, so the rate is 1 widget per worker-hour.

Substituting the values, we get:

widgets = 1 x 20 x 360

widgets = 7200

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The constant of proportionality for the relationship between number of laps (x) and minutes swimming (y) is 5x-2y = 0.

A proportionality graph, also known as a direct proportionality graph, is a graph that represents the relationship between two variables that are directly proportional to each other.

In a proportionality graph, the x-axis represents the independent variable, while the y-axis represents the dependent variable. When the two variables are directly proportional, the graph will form a straight line passing through the origin (0,0). This means that as the independent variable increases, the dependent variable also increases in proportion to it.

Here we by using the graph the relationship is 5x = 2y

Let x is a number of laps and y is the minutes swimming then the constant of proportionality is 5x-2y = 0.

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Answer:

[tex]x = \frac{y}{3} - 1[/tex]

Step-by-step explanation:

[tex]1. \: 4y - 8 - 4 = 12x \\ 2. \: 4y - 12 = 12x \\ 3. \: \frac{4y - 12}{12} = x \\ 4. \: \frac{4(y - 3)}{12} = x \\ 5. \: \frac{y - 3}{3} = x \\ 6. \: - 1 + \frac{y}{3} = x \\ 7. \: \frac{y}{3} -1 = x \\ 8. \: x = \frac{y}{3}-1[/tex]

The correlation coefficient relating is 0.76 thath mean  the accompaniment rates for wives and sons is the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

To find the correlation coefficient relating the accompaniment rates for wives and sons, we can use the formula:

r = (nΣxy - (Σx)(Σy)) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Where:
- r is the correlation coefficient
- n is the number of observations (in this case, 9)
- x and y are the accompaniment rates for wives and sons, respectively
- Σxy is the sum of the products of x and y
- Σx and Σy are the sums of x and y, respectively
- Σx^2 and Σy^2 are the sums of x squared and y squared, respectively

Using the data from the table, we can calculate the following:

Σx = 27.2 + 40.1 + 35.7 + 37.8 + 38 + 38.4 + 38.7 + 29.8 + 23.8 = 309.5
Σy = 2.2 + 1.5 + 0.3 + 3.5 + 5.4 + 11 + 11.9 + 8.6 + 7.4 = 51.8
Σxy = (27.2)(2.2) + (40.1)(1.5) + (35.7)(0.3) + (37.8)(3.5) + (38)(5.4) + (38.4)(11) + (38.7)(11.9) + (29.8)(8.6) + (23.8)(7.4) = 1164.41
Σx^2 = 27.2^2 + 40.1^2 + 35.7^2 + 37.8^2 + 38^2 + 38.4^2 + 38.7^2 + 29.8^2 + 23.8^2 = 11491.89
Σy^2 = 2.2^2 + 1.5^2 + 0.3^2 + 3.5^2 + 5.4^2 + 11^2 + 11.9^2 + 8.6^2 + 7.4^2 = 349.98

Plugging these values into the formula, we get:

r = (9)(1164.41) - (309.5)(51.8) / √[(9)(11491.89) - (309.5)^2][(9)(349.98) - (51.8)^2] = 0.76

This value of r indicates a strong positive correlation between the accompaniment rates for wives and sons. This means that as the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

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The volume of the oblique cone is  5887.5 ft³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

We know, The volume of an oblique cone is, (1/3)×B×h.

Where h = height and B = area of the base.

Here the area of the base is, π(15)² = 706.5 ft², and the height is 25 feet.

Therefore, The volume is,

= (1/3)×706.5×25.

= 5887.5 ft³

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(a) After 2 seconds, the ant's position in the  (Euclidean) coordinates is (4,0)

(b) To pass the point (0.999, 0), the ant needs 0.4995 seconds.

The ant is traveling along the positive x-axis at a speed of 2 Poincare units of length per second. This means that its position at any given time can be determined using the equation:

x = 2t

where x is the ant's position along the x-axis, and t is the time in seconds.

(a) To find the ant's position after 2 seconds, we can simply plug in t = 2 into the equation:

x = 2(2) = 4

So the ant's position after 2 seconds is (4, 0).

(b) To find how long it will take the ant to pass the point (0.999, 0), we can set x = 0.999 and solve for t:

0.999 = 2t

t = 0.999/2 = 0.4995

So it will take the ant 0.4995 seconds to pass the point (0.999, 0).

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Answer: 0.125 and 12.5%

Step-by-step explanation:

To convert any fraction to decimal form, we just need to divide its numerator by the denominator.

Here, the fraction is 1/8 which means we need to perform 1 ÷ 8.

This gives the answer as 0.125. So, 1/8 as a decimal is 0.125

To get its percentage form, you simply multiply the obtained decimal value by 100:

0.125 x 100 = 12.5

Answer:

x > 5

Step-by-step explanation:

-2x - 2 < 8

-2x < 10

x > 5

So, the answer is x > 5

The required length of side CD is 22 units.

Since the perimeter of the rectangle is 80 units, we can use the formula for the perimeter of a rectangle, which is:

perimeter = 2(length + width)

In this case, we know that the perimeter is 80 units, so we can write:

80 = 2(length + width)

We also know that CD is a side of the rectangle, so it must be either the length or the width. Let's assume that CD is the length, so we can write:

CD = 4z + 2

Substituting this expression for the length into the formula for the perimeter, we get:

80 = 2(4z + 2 + width)

Simplifying the right-hand side, we get:

80 = 8z + 4 + 2width

Subtracting 4 from both sides, we get:

76 = 8z + 2width

Dividing both sides by 2, we get:

38 = 4z + width

Now we can use the fact that CD is a side of the rectangle to substitute for width. Since the opposite side of the rectangle must also have length 4z + 2, we can write:

width = 3z + 3

Substituting this into the previous equation, we get:

38 = 4z + 3z + 3

Simplifying the right-hand side, we get:

38 = 7z + 3

Subtracting 3 from both sides, we get:

35 = 7z

Dividing both sides by 7, we get:

5 = z

Now we can substitute this value of z into the expression for CD:

CD = 4z + 2 = 4(5) + 2 = 22

Therefore, the length of side CD is 22 units.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \implies y +4= \cfrac{1}{2} (x +2) \\\\\\ y+4=\cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x-3 \end{array}}[/tex]