suppose i work at a call center and i have to track the urgency of the incoming calls. in one day, i had 20 calls. 5 were classified as urgent and 15 were classified as no rush. what is the mode of this data?

Answer:

E[X|Y = y] = E[X] (by the definition of independence)

Step-by-step explanation:

To show that E[aX + bY + c] = aE[X] + bE[Y] + c, we can use the linearity of the expected value:

E[aX + bY + c] = E[aX] + E[bY] + E[c] (by linearity of E[ ])

= aE[X] + bE[Y] + c (since E[c] = c for any constant c)

To show that Var(aX + bY + c) = aVar(X) + 2abCov(X, Y) + b2Var(Y), we can use the definition of variance:

Var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]

= E[((aX - aE[X]) + (bY - bE[Y]) + c)^2]

= E[(aX - aE[X])^2] + E[(bY - bE[Y])^2] + E[c^2]

+ 2aE[(aX - aE[X])(bY - bE[Y])] + 2cE[aX - aE[X]] + 2cE[bY - bE[Y]]

= a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + c^2 + 2abE[(X - E[X])(Y - E[Y])]

+ 2ac(aE[X] - aE[X]) + 2bc(E[Y] - E[Y])

= aVar(X) + b^2Var(Y) + 2abCov(X, Y)

Finally, if X and Y are independent, then Cov(X, Y) = 0, so:

E[X|Y = y] = E[X] (by the definition of independence)

This means that the expected value of X given a particular value of Y is simply the expected value of X, regardless of the value of Y.

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The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model. The optimal number of notebooks to make in each order is 590 units. The annual ordering cost (AOC) is approximately $892.20. The Annual Holding Cost (AHC) is $3540. The annual product cost (APC) is $233,460. The annual total cost of managing inventory (ATC) is approximately $237,892.20. The total number of orders in the year (N) is 33. The estimated time between each order (T) is approximately 7.58 days. The daily demand is approximately 77.82 units. The reorder point (ROP) is approximately 311 units.

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model.

To find the optimal number of notebooks to make in each order, we can use the EOQ formula:

EOQ = √[(2 * Demand * Ordering Cost) / Holding Cost]

EOQ = √[(2 * 19455 * 27) / 6]

EOQ ≈ 589.96

Since the number of notebooks must be a whole number, the optimal number to order would be 590 notebooks.

The annual ordering cost (AOC) can be calculated by dividing the annual demand by the EOQ and multiplying it by the ordering cost:

AOC = (Demand / EOQ) * Ordering Cost

AOC = (19455 / 590) * 27

AOC ≈ $892.20

The Annual Holding Cost (AHC) is calculated by multiplying the EOQ by the holding cost per unit:

AHC = EOQ * Holding Cost

AHC = 590 * 6

AHC = $3540

The annual product cost (APC) is calculated by multiplying the annual demand by the cost per unit:

APC = Demand * Cost per unit

APC = 19455 * 12

APC = $233,460

The annual total cost of managing inventory (ATC) is the sum of the annual ordering cost, annual holding cost, and annual product cost:

ATC = AOC + AHC + APC

ATC = 892.20 + 3540 + 233460

ATC ≈ $237,892.20

The total number of orders in the year (N) can be calculated by dividing the annual demand by the EOQ:

N = Demand / EOQ

N = 19455 / 590

N ≈ 33

The estimated time between each order (T) can be calculated by dividing the number of working days in a year by the total number of orders:

T = Number of working days / N

T = 250 / 33

T ≈ 7.58 days

The daily demand is calculated by dividing the annual demand by the number of working days in a year:

Daily Demand = Demand / Number of working days

Daily Demand = 19455 / 250

Daily Demand ≈ 77.82 units/day

The reorder point (ROP) is the number of units at which a new order should be placed. It can be calculated by multiplying the daily demand by the lead time (time taken for the supplier to deliver the order):

ROP = Daily Demand * Lead Time

ROP = 77.82 * 4

ROP ≈ 311.28 units

Therefore, the reorder point would be approximately 311 units.

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Answer:

95°

Step-by-step explanation:

Here we have angles of 30° and 55°, so the remaining angle is:

The function c(t) = c(t) = c(t), left parenthesis, t, right parenthesis models the volume of the music (in dB) that Bulan hears t minutes after the ice cream truck arrives in her neighborhood. In this function, t is entered in radians.

The function c(t) represents how the volume of the music changes over time as t increases. The exact shape of the function depends on various factors like the distance between Bulan and the ice cream truck, the truck's speaker system, and any other interfering sounds in the neighborhood.

By analyzing the function c(t), one can determine the maximum and minimum volume levels Bulan experiences as the truck moves around her neighborhood. Additionally, the periodic nature of the function suggests that the music will repeat itself after a certain time interval.

In conclusion, the function c(t) = c(t) = c(t), left parenthesis, t, right parenthesis provides a mathematical representation of the volume of the music that Bulan hears as a function of time. This function helps us understand the changing volume levels and the periodicity of the ice cream truck's music in her neighborhood.

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An equation of the line that passes through the given point and is

(a) parallel to is y = -3x - 7

(b) perpendicular to is y = (1/3)x + 1/3.

a) Parallel line

The slope of the given line is -3. The slope of a parallel line is also -3. So, the equation of the parallel line will be of the form:

y = -3x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = -3(-2) + b

-1 = 6 + b

-7 = b

Therefore, the equation of the parallel line is:

y = -3x - 7

b) Perpendicular line

The slope of a perpendicular line is the negative reciprocal of the slope of the given line. The slope of the given line is -3, so the slope of the perpendicular line is 1/3. So, the equation of the perpendicular line will be of the form:

y = (1/3)x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = (1/3)(-2) + b

-1 = -2/3 + b

1/3 = b

Therefore, the equation of the perpendicular line is:

y = (1/3)x + 1/3

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The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

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Answer:

Equal to

Step-by-step explanation:

Answer:

27x ^6 y ^3

Step-by-step explanation:

Answer:

\(27x^{6} y^{3}\)

Step-by-step explanation:

\((3x^{2} y)^{3}\)

→ Write out as a multiplication

\(3x^{2} y*3x^{2} y*3x^{2} y\)

→ Simplify

\(27x^{6} y^{3}\)

Answer: 56.44 km/h

Step-by-step explanation:

Speed = Distance / Time

Time = 1950 - 1520 = 4 hours 30 minutes = 4.5 hours

Speed = 254/4.5

= 56.44 km/h

Answer:

The mistake is that 4x+x = 5x  not 4x

Step-by-step explanation:

4x + x = 30 –6

Combine like terms

5x = 24

Divide each side by 5

5x/5 = 24/5

x = 24/5

The mistake is that 4x+x = 5x  not 4x

The equation line of the of the road in slope-intercept form is; y = 2·x - 10

The standard form of the equation of a line is Ax + Bx + C, where A, B, and C are constants and A and B are nonzero numbers.

The parameters for the new road are;

The road will be parallel to village way with points (0, 5), and (-4, -3)

The road will pass through the intersection  of Gray Dr and Canon Rd., which is the point with coordinates (3, -4)

Required; The equation of the road

Since the new road is parallel to Village Way, which has slope;

m = (5 - (-3))/(0 - (-4)) = 8/4 = 2

The slope of the new road will also be 2.

Let the equation of the new road be y = m·x + c, where m = 2 is the slope we just found. To find c, we use the fact that the road passes through the point (3, -4);

y - (-4) = 2 × (x - 3)

y = 2·x - 6 - 4 = 2·x - 10

y = 2·x - 10

Therefore, c = -10

Therefore, the equation of the new road in slope-intercept form, therefore is; y = 2·x - 10

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To obtain the residuals from the fit in 8.4a and plot them against y and x, as well as prepare a normal plot, we need the specific details of the fit and the data used.

WE know that residuals represent the differences between the observed values and the predicted values from a statistical model or regression analysis.

Since the residuals against y and x can help identify patterns or trends in the data that may indicate issues with the model's fit.

A normal plot, known as a Q-Q plot, compares the distribution of the residuals to a theoretical normal distribution. If the residuals closely follow a straight line in the normal plot, the residuals are normally distributed, which is an assumption of many statistical models.

Interpreting these plots involves examining the patterns and deviations from expected behavior. If the residuals exhibit a consistent pattern, it might indicate that the model does not capture all the relevant information in the data.

Thus if the residuals appear randomly scattered around zero with no discernible pattern, it suggests that the model adequately explains the data. Deviations in the normal plot may indicate departures from the assumption of normality in the residuals, which could impact the reliability of statistical inferences.

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Answer:

1st one = 4th option

2nd one = 3rd option

Step-by-step explanation:

18. ∆PQR =~ ∆RPA ( by SAS )

19. ∆DQR =~ ∆PQR ( by AAS )

20. ∆ARO =~ ∆PQO ( by AAS )

Answer: y=mx+b

Step-by-step explanation:

The rate column will be:

A= 30

B= 20

C= x miles

D= x miles

It should be noted that rate simply means the measure, quantity, or frequency that one measure against another quantity or measure.

In this case, Jorden drives to the store at 30 miles per hour and on her way home she averages only 20 miles per hour.

Therefore, the rate column will be:

A= 30

B= 20

C= x miles

D= x miles

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Fill out the Rate column in the table below. Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour, how far does she live from the store? Fill out the Rate column in the table below. a = b =

Answer:

Step-by-step explanation:

Complete the following equation using , or = 3.20 ___ 3.02 A.

The following equation 3.20 > 3.02

Answer:

\(area = 4\pi {r}^{2} \\ = 4 \times 3.14 \times {7.5}^{2} \\ = 706.86 \: {cm}^{2} \)

The probability that Stephane wins 7 games out of 10 is 0.215 or about 21.5%.

We can model the number of games Stephane wins out of 10 as a binomial distribution with parameters n = 10 (number of trials) and p = 0.6 (probability of winning). The probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!) is the binomial coefficient.

To find the probability that Stephane wins 7 games out of 10, we can plug in k=7, n=10, and p=0.6 into the formula:

P(X=7) = (10 choose 7) * 0.6^7 * 0.4^3

= 120 * 0.0279936 * 0.064

= 0.215

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Answer:

h=3/4

Step-by-step explanation:

19=h4+16

19-16=h4+16-16

3=h4

3/4=h4/4

3/4=h

h=3/4

Answer:

h = 3/4 or as a decimal it would be 0.75

Step-by-step explanation:

19 = h × 4 + 16

Reorder the terms

Use the communative property to reorder the terms

19 = 4h + 16

19 = 4h + 16

Move the terms

Move the variable to the left - hand side and change its side

19 - 4h = 16

Move the constant to the right - hand side and change its sign

-4h = 16 - 19

-4h = 16 - 19

Calculate

calculate the difference of 16 minus 19

-4h = -3

-4h = -3

Divide both sides of the eqaution by -4

Therefore your answer is h = 3/4 or if you want a decimal simplify 3/4 by dividing 3 and 4, which gives you 0.75

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

The correct option is;

c. The horizontal axis labeled Hours Driven goes from 0 to 15 in increments of 1 and the vertical axis labeled Miles Remaining goes from 0 to 150 in increments of 10. The line starts at left parenthesis (0, 0), and passes through (1, 65) and (2, 130)

Step-by-step explanation:

The given parameters are;

The speed of the truck = 65 miles per hour

The length of the highway = 130 miles

Therefore, from the given information, we have;

The time, t, it will take the truck to arrive at the end of the highway is given as follows;

Time = Distance/speed = 130/65 = 2 hours

Therefore, if the truck timing starts from the point (0, 0), we have;

The points on the straight line (constant) speed graph are;

(0, 0), (1, 65), and (2, 130)

Answer:

C

Step-by-step explanation:

The equation of the ellipse with a center at (3, 1), a focus at (7, 1), and a vertex at (-2, 1) is given by \(\(\frac{{(x - 3)^2}}{{36}} + \frac{{(y - 1)^2}}{{25}} = 1\).\). In this equation, A = 6, B = 5, C = 3, and D = 1.

To find the equation of the ellipse, we need to determine the values of A, B, C, and D in the general form equation \(\[\frac{{(x - C)^2}}{{A^2}} + \frac{{(y - D)^2}}{{B^2}} = 1\]\)for an ellipse. The center of the ellipse is (C, D), so C = 3 and D = 1.

The distance between the center and each focus is given by the value of A, so we can calculate A as the distance between (3, 1) and (7, 1), which is 4. Therefore, A = 4.

The distance between the center and each vertex is given by the value of B, so we can calculate B as the distance between (3, 1) and (-2, 1), which is 5. Hence, B = 5. Plugging these values into the general form equation, we get \(\(\frac{{(x - 3)^2}}{{36}} + \frac{{(y - 1)^2}}{{25}} = 1\)\) as the equation of the ellipse.

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Answer: I would say 21 feet.

Step-by-step explanation:

Bernard is 12 feet ahead of Austin

So add 12 feet to get to Austin first

Then add the 9 feet that is apart from Austin and Bernard

12+9 = 21

21 feet would be the answer

Hope this helps ! ^^

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Answer:

48; 14.90 or 14.9

Step-by-step explanation:

First you have to take the mean of the data set.

In order to do this, we take the sum of all of the data points and then divide them by the number of values like so...

\(\frac{34+37+48+32+25+34+35+23+33+30}{10}\)

The answer to this is 33.1.

Now we have to find the value furthest from this value. In order to do this, we are going to take the highest (48) and the lowest value(23). Then we compare their distance from 33.1. After this, we can tell that 48 is further from 33.1 than 23 is.

Then for the second part, 48-33.1 = 14.90 and that is how far the value is from the mean.

Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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Answer:

Median, because the data are skewed and there is an outlier

Step-by-step explanation:

yo hoped it helped

Answer:

I honestly don't know

Step-by-step explanation:

8182i2o2o

828262781

Answer:kk

Step-by-step explanation: