Consider the function represented by the graph. On a coordinate plane, a straight line with a negative slope begins on the y-axis at (0, 9) and exits the plane at (8, 1). What is the domain of this function?

the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

How to solve?

To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.

Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:

P(X ≥ 7 | X ~ ∝(λ×3))

= 1 - P(X ≤ 6 | X ~ ∝(λ×3))

= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)

where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.

To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.

Substituting lambda = 2 into the formula, we get:

P(X ≥ 7 | X ~ ∝(2×3))

= 1 - P(X ≤ 6 | X ~ ∝(6))

= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)

Using a calculator or computer software, we can evaluate this expression to get:

P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081

Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

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Distance 1 = 1662 km

Time T= 3 hours

Distance 2= 2142 km

Time T=3 hours

Also

V1 = Plane velocity

V2= Air velocity

Then

Distance1/T = V1 - V2

and

Distance2/T= V1 + V2

1662/3= 554 = V1 - V2

2142/3= 706= V1 + V2

Now solve this 2x2 system, by substitution

then

V1= (554+ 706)/2= 1260/2= 630

V2= 706 - 630= 76

Then answer is

Velocity of plane= 630 km/h

Velocity of air= 76 km/h

By using the concept of mean and standard deviation, it can be inferred that

The the drug stays in the system for more than 397 minutes

What is mean and Standard Deviation?

Suppose there is a data set and the average of the data set has to be calculated. To calculate the average of the data set, mean is used

To know about Standard Deviation, it is important to know about Variance

Variance is the sum of the square of deviation from mean.

Square root of the variance gives the standard deviation

Given n = 35,

\(\bar{x} = 403,\)

Population mean \(\\ (\mu)\) = 397

Population Standard Deviation \(\\(\sigma)\) = 18

Here the sample size is large. So the distribution is approximately normal

To test :

\(H_ 0 = \mu \leq 397\\H_1 = \mu > 397\)

Test statistic t = \(\frac{403 - 397}{\frac{18}{\sqrt{35}}}\)

                       = 1.97

p value at \(\alpha = 0.05\) = 0.0244

Since 0.0244 < 0.05, the null hypothesis is rejected

So the the drug stays in the system for more than 397 minutes

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Answer:

18x - 36

Step-by-step explanation:

In an equilateral triangle the 3 sides are congruent, then

perimeter = 6x - 12 + 6x - 12 + 6x - 12 ← collect like terms

                = 18x - 36

The required expression would be 18x - 36 for the perimeter of the triangle in simplest form.

The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

As we know in an equilateral triangle the 3 sides are congruent.

The perimeter of the triangle = 6x - 12 + 6x - 12 + 6x - 12

Combine the likewise terms and we get

The perimeter of the triangle =  18x - 36

Therefore, the required expression would be 18x - 36 for the perimeter of the triangle in simplest form.

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Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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Answer:

C. -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Pre-Calculus

Calculus

Step-by-step explanation:

Step 1: Define

g(x) = cot(x)

g'(π/4) is x = π/4

Step 2: Differentiate

Step 3: Evaluate

The empirical method is the right answer.

Empirical probability is calculated by dividing the number of times an event was seen in your data by the entire sample size. An event's relative frequency is strongly connected to an empirical probability, also known as an experimental probability.

Empirical probability bases its estimation of the likelihood that a specific result will recur on the number of instances of that outcome within a sample set. In short, the empirical method uses relative frequencies to determine probabilities.

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Answer:

-5x+9y=-18

Dividing both sides by -18

-5x/-18+9y/-18=-18/-18

5x/18-y/2=1

x/(18/5)-y/2=1. eqn(i)

eqn (i) is comparing with x/a+y/b=1, we get

x - intercept (a) =18/5

y-intercept (b) = -2

Answer:   go to quizlet it will most likely have the answers

Step-by-step explanation:

The  solution of the initial value problem dx/dt = 10x - 5y dy/dt = 8x - 12y x(0) = 2, y(0) = 1 is option (c) x = (35e^8t + e^(-10t))/18, y = (7e^8t + 2e^(-1)t).

To solve the given initial value problem, we need to find the values of x and y that satisfy the given differential equations and initial conditions.

We can start by solving the system of differential equations:

dx/dt = 10x - 5y

dy/dt = 8x - 12y

We can rearrange the first equation as follows:

dx/dt + 5y = 10x

This is a linear first-order differential equation, which we can solve using an integrating factor. The integrating factor is e^(∫5dt) = e^(5t), so we multiply both sides of the equation by e^(5t):

e^(5t)dx/dt + 5e^(5t)y = 10e^(5t)x

The left-hand side is the derivative of the product e^(5t)x with respect to t, so we can rewrite the equation as:

d/dt (e^(5t)x) = 10e^(5t)x

We can integrate both sides with respect to t to obtain:

e^(5t)x = (1/2)10e^(5t)^2 + C1

where C1 is a constant of integration. Simplifying the right-hand side, we get:

e^(5t)x = 5e^(10t) + C1

Dividing both sides by e^(5t), we get:

x = (5e^(5t) + C1e^(-5t))

Next, we can rearrange the second equation as follows:

dy/dt + 12y = 8x

This is another linear first-order differential equation, which we can solve using an integrating factor. The integrating factor is e^(∫12dt) = e^(12t), so we multiply both sides of the equation by e^(12t):

e^(12t)dy/dt + 12e^(12t)y = 8e^(12t)x

The left-hand side is the derivative of the product e^(12t)y with respect to t, so we can rewrite the equation as:

d/dt (e^(12t)y) = 8e^(12t)x

We can integrate both sides with respect to t to obtain:

e^(12t)y = (1/2)8e^(12t)^2 + C2

where C2 is a constant of integration. Simplifying the right-hand side, we get:

e^(12t)y = 4e^(24t) + C2

Dividing both sides by e^(12t), we get:

y = (4e^(12t) + C2e^(-12t))

Now we can use the initial conditions x(0) = 2 and y(0) = 1 to find the values of C1 and C2:

x(0) = 5(1) + C1(1) = 2

C1 = (2-5)/1*(-1) = 3

y(0) = 4(1) + C2(1) = 1

C2 = (1-4)/1*(-1) = 3

Substituting these values of C1 and C2 into the expressions we derived for x and y, we get:

x = (5e^(5t) + 3e^(-5t))

y = (4e^(12t) + 3e^(-12t))

Therefore, the correct option is (C) x = (35e^8t + e^(-10t))/18, y = (7e^8t + 2e^(-1)t).

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Answer:

C. y ≤ −3x + 2 . Not sure, but I'm kind of confident in my answer.

Answer:

k=3 (3)x2+5=11

Hope this helps you and good luck :)

Step-by-step explanation:

The vertices of the dilated polygon A'B'C'D' are A'(-2, 3), B'(-1, 1), C'(2, -1), D'(2, 2).

What is the scale factor?

A scale factor is a number that represents the amount of magnification or reduction applied to an object, image, or geometrical shape.

To dilate a polygon by a scale factor of 1/2, each of its vertices needs to be multiplied by the factor of 1/2. This can be done by multiplying the x-coordinate and the y-coordinate of each vertex by 1/2.

So, for polygon ABCD, the coordinates of the dilated polygon A'B'C'D' can be found as follows:

Vertex A:

x-coordinate: -4 * 1/2 = -2

y-coordinate: 6 * 1/2 = 3

So, A' is located at (-2, 3).

Vertex B:

x-coordinate: -2 * 1/2 = -1

y-coordinate: 2 * 1/2 = 1

So, B' is located at (-1, 1).

Vertex C:

x-coordinate: 4 * 1/2 = 2

y-coordinate: -2 * 1/2 = -1

So, C' is located at (2, -1).

Vertex D:

x-coordinate: 4 * 1/2 = 2

y-coordinate: 4 * 1/2 = 2

So, D' is located at (2, 2).

Therefore, the vertices of the dilated polygon A'B'C'D' are:

A'(-2, 3), B'(-1, 1), C'(2, -1), D'(2, 2).

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Answer:

See the diagram below:

                             Red  3/8  -----------------> Red-Red  = 4/9*3/8 = 1/6

Red 4/9            <

                            Orange 5/8 --------------> Red-Orange = 4/9*5/8 = 5/18

                            Red 4/8 --------------------> Orange-Red = 5/9*4/8 = 5/18

Orange 5/9      <

                           Orange 4/8 ----------------> Orange-Orange = 5/9*4/8 = 5/18

The length of the other side of the rectangle playground is 12/7 kilometers.

To find the length of the other side of the rectangle playground, we can use the formula for the area of a rectangle which is length multiplied by width.
Given that the area of the playground is 2 2/5 square kilometers, we can write this as a mixed number fraction:
2 2/5 = (5 x 2 + 2)/5 = 12/5
Let's assume that the side of the playground that we know the length of is the width. So, we have:
width = 1 2/5 km = (5 x 1 + 2)/5 km = 7/5 km
Now, we can substitute the area and width values into the formula for the area of a rectangle:
length x width = area
length x (7/5 km) = (12/5) km^2
Multiplying both sides by the reciprocal of 7/5, we get:
length = (12/5) km^2 ÷ (7/5) km
Simplifying, we get:
length = 12/7 km

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9514 1404 393

Answer:

  D.  37.5 square units

Step-by-step explanation:

There are a couple of ways to figure this.

1. The altitude KM is the geometric mean of the segment lengths ML and MJ

  KM = √(ML·MJ)

  ML = KM²/MJ = 36/8 = 4.5

Then LJ = 4.5 +8 = 12.5, and the area of the triangle is ...

  A = (1/2)bh

  A = (1/2)(12.5)(6) = 37.5 . . . square units

__

2. Triangle LKM is similar to triangle KJM. The scale factor is ...

  KM/JM = 6/8 = 3/4

Then the area of triangle LKM is (3/4)² = 9/16 of the area of triangle KJM.

The total area is ...

  Area of LJK = (area of KJM)×(1 + 9/16)

  = (1/2)(8)(6)(25/16) = 75/2 = 37.5 . . . square units

Answer:

1. Change the mixed number to an improper fraction; 1 1/2 as 3/1

2. Multiply both sides with the reciprocal of the improper fraction

3. Simplifly your answer if possible

Answer:

D. It represents .90 cents, which is $5.40 divided by 6

Scale factor is given by the formula below:

Using the right-hand side

new length = 1

old length= 3

substitute the values into the formular

Answer:

1/6p + 1/5

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The equation of the given line is expressed as

3x - 6y = 30

Rearranging it so that it will look like the slope intercept form, it becomes

6y = 3x - 30

Dividing both sides by 6, it becomes

6y/6 = 3x/6 - 30/6

y = x/2 - 5

Looking at the equation, slope, m = 1/2

If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2

To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute

x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes

- 9 = 1/2 * 4 + c

- 9 = 2 + c

c = - 9 - 2

c = - 11

By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be

y = x/2 - 11

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

y=mx+b

b is the y intercept

b=0, so 0 is the y intercept

Step-by-step explanation:

The significance level chosen for the tests with total number of test performed as 1000 for given p-value is equal to 0.87 or 87%.

Total number of test performed = 1000

p-value is equal to 0.00013

The Bonferroni correction involves ,

Adjusting the significance level for multiple comparisons by dividing it by the number of comparisons performed.

Here, 1000 tests were performed and the resulting p-value is 0.00013.

The significance level that was chosen for the tests,

Reverse the Bonferroni correction by multiplying the p-value by the number of comparisons,

adjusted p-value = p-value / number of comparisons

number of comparisons = 1000

adjusted p-value = 0.00013

p-value = adjusted p-value x number of comparisons

⇒p-value = 0.00013 x 1000

⇒p-value = 0.13

So the original p-value before the Bonferroni correction was 0.13.

The significance level, we subtract the p-value from 1,

significance level = 1 - p-value

⇒significance level = 1 - 0.13

⇒significance level = 0.87

Therefore, the significance level chosen for the tests was 0.87 or 87%

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Answer:Therefore, the range is 32 and the standard deviation is approximately 10.523 for the given data set.

Step-by-step explanation:To calculate the range and standard deviation for the given data set {40, 65, 33, 46, 55, 50, 61}, we can follow these steps:

Step 1: Find the range.

The range is calculated by subtracting the minimum value from the maximum value in the data set.

Range = Maximum value - Minimum value

Range = 65 - 33

Range = 32

Step 2: Calculate the mean.

The mean is calculated by summing up all the values in the data set and dividing by the total number of values.

Mean = (40 + 65 + 33 + 46 + 55 + 50 + 61) / 7

Mean = 350 / 7

Mean = 50

Step 3: Calculate the deviation for each value.

Deviation is calculated by subtracting the mean from each value in the data set.

Deviation for 40 = 40 - 50 = -10

Deviation for 65 = 65 - 50 = 15

Deviation for 33 = 33 - 50 = -17

Deviation for 46 = 46 - 50 = -4

Deviation for 55 = 55 - 50 = 5

Deviation for 50 = 50 - 50 = 0

Deviation for 61 = 61 - 50 = 11

Step 4: Square each deviation.

Squared deviation for -10 = (-10)^2 = 100

Squared deviation for 15 = 15^2 = 225

Squared deviation for -17 = (-17)^2 = 289

Squared deviation for -4 = (-4)^2 = 16

Squared deviation for 5 = 5^2 = 25

Squared deviation for 0 = 0^2 = 0

Squared deviation for 11 = 11^2 = 121

Step 5: Calculate the variance.

Variance is calculated by summing up all the squared deviations and dividing by the total number of values.

Variance = (100 + 225 + 289 + 16 + 25 + 0 + 121) / 7

Variance = 776 / 7

Variance ≈ 110.857

Step 6: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation ≈ √110.857

Standard Deviation ≈ 10.523

By calculating, The value of x from the given right angled triangle is 26.4

What is Tanx ?

Tanx can be defined as the ratio of sinx and cosx and it is also defined as the ratio of opposide side and hypothenuse in a given right angled triangle.

26.4° (nearest tenth)

sinx = opp/hyp

Put the given values opp = 4 and hyp=9

we get,

sinx = 4/9

x = sin^-1 ( 4/9)

So, by Taking the inverse of sine on both sides

we get,

x= 26.4° (nearest tenth)

Therefore, By calculating, The value of x from the given right angled triangle is 26.4

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The trajectory of your message illustrates a quadratic function

The equation of the trajectory of the message is \(y = -\frac 15(x - 17)^2 + 20\)

The trajectory graph (see attachment) is a quadratic function that passes through the following points:

(x,y) = (7,0) and (27,0)

And the vertex is:

(h,b) = (17,20)

A quadratic function is represented as:

\(y = a(x - h)^2 + b\)

So, we have:

\(y = a(x - 17)^2 + 20\)

Substitute (7,0) for (x,y)

\(0 = a(7 - 17)^2 + 20\)

Evaluate

\(0 = 100a + 20\)

Collect like terms

\(100a = -20\)

Divide both sides by 100

\(a = -\frac 15\)

Recall that:

\(y = a(x - 17)^2 + 20\)

So, we have:

\(y = -\frac 15(x - 17)^2 + 20\)

Hence, the equation of the trajectory of the message is \(y = -\frac 15(x - 17)^2 + 20\)

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Step-by-step explanation:

Firstly take the unknown angle be x

now x + 138° = 180° {: linear pair}

x = 180-138

x = 42

now , angle 1+ angle x + 18 = 180 { because of angle sum property }

=> angle 1 +42 +18 = 180

=> angle 1 +60 = 180

=> angle 1 = 180-60

=> angle 1 = 120

(a) Interval: [1, 3] ∪ (1.5, 2.5)

(b) Inequality: 1 ≤ x ≤ 3 or 1.5 < x < 2.5

Number line:

```

               1          1.5         2          2.5          3

----------------|-----------|-----------|-----------|---------------------

```

The interval [1, 3] ∪ (1.5, 2.5) consists of all real numbers greater than or equal to 1 and less than or equal to 3, including both endpoints, along with all real numbers greater than 1.5 and less than 2.5, excluding both endpoints.

In the inequality notation, 1 ≤ x ≤ 3 represents all numbers between 1 and 3, including 1 and 3 themselves. The inequality 1.5 < x < 2.5 represents all numbers between 1.5 and 2.5, excluding both 1.5 and 2.5.

On the number line, the interval is represented by a closed circle at 1 and 3, indicating that they are included, and an open circle at 1.5 and 2.5, indicating that they are not included in the interval. The line segments between the circles represent the interval itself, including all the real numbers within the specified range.

The interval [1, 3] ∪ (1.5, 2.5) includes all real numbers between 1 and 3, including 1 and 3 themselves, as well as all real numbers between 1.5 and 2.5, excluding both 1.5 and 2.5.

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