Please help
Find the total area S₁ + S₂ under the normal distribution, where S, is the area to the left of z=-2.15
and S₂ is the area to the right of z =
= 1.62.

Answer:

Refers to the attachment given below!

Step-by-step explanation:

The Cauchy Integral Formula (Generalized version), we have: ∫C [tex]z^2[/tex] dz = ∫C[tex]z^2[/tex]/(z - 0) dz

To apply the Cauchy-Goursat Theorem, we need to check if the function f(z) is analytic inside the contour C, i.e., it should be differentiable everywhere inside C.

(a) Let f(z) =[tex]ze^(-z)[/tex]. Then, f(z) is entire, i.e., differentiable everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:

∮C f(z) dz = 0

(b) Let f(z) = 2. Since 2 is a constant, it is analytic everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:

∮C f(z) dz = f(0) × 2πi = 0 (since C does not enclose the origin)

(c) Let f(z) = z tan(2π/2). Since tan(2π/2) is not analytic at z = ±i, f(z) is not analytic inside the unit circle C. Hence, we cannot apply the Cauchy-Goursat Theorem directly to evaluate the integral ∮C f(z) dz.

To evaluate the integral ∮C f(z) dz, we can use the Cauchy Integral Formula (Generalized version) which states that for any analytic function f(z) and any closed contour C, we have:

∮C f(z)/(z - a) dz = 2πi f(a)

where a is any point inside the contour C.

For (a), let's use the Cauchy Integral Formula to evaluate the integral. We have:

f(z) = z[tex]e^{-z[/tex]

∮C f(z) dz = ∮C f(z)/(z - 0) dz (since f(0) = 0)

= 2πi f(0) = 0

For (b), we can use the Cauchy-Goursat Theorem as f(z) = 2 is analytic everywhere inside the circle |z| = 4. Hence, we have:

∮C2 dz = 2πi f(0) = 2πi × 2 = 4πi

For (c), we need to use the Cauchy Integral Formula to evaluate the integral. We have:

f(z) = z tan(π/2)

∮C f(z) dz = ∮C f(z)/(z - i) dz (since i is inside C)

= 2πi f(i) = 2πi × i × tan(π/2) = -2πi

Thus, we have:

∮C f(z) dz ≠ ∮C f(z) dz in general.

Now, let C be the positively oriented boundary of the square whose sides lie along x = ±2 and y = ±2.

(a) Using the Cauchy Integral Formula (Generalized version), we have:

∫C cos(z) dz = ∫C cos(z)/(z - π/2) dz

= 2πi cos(π/2) = 0

(b) Using the Cauchy Integral Formula (Generalized version), we have:

∫C cosh(z) dz = ∫C cosh(z)/(z - 0) dz

= 2πi cosh(0) = 2πi

(c) Using the Cauchy Integral Formula (Generalized version), we have:

∫C [tex]z^2[/tex]dz = ∫C [tex]z^2[/tex]/(z - 0) dz.

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The equation of the parabola in vertex form is: y = (1/4)x² - 5. We can calculate it in the following manner.

Since the parabola opens either up or down, its vertex form is given by:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the direction and shape of the parabola.

Using the given vertex (0, -5), we have:

h = 0 and k = -5

Substituting the vertex coordinates into the vertex form, we get:

y = a(x - 0)² - 5

y = ax² - 5

To determine the value of "a", we use the given point (–2, –4) on the parabola. Substituting these coordinates into the equation, we get:

-4 = a(-2)² - 5

-4 = 4a - 5

1 = 4a

a = 1/4

Substituting this value of "a" into the equation for the parabola, we get:

y = (1/4)x² - 5

Therefore, the equation of the parabola in vertex form is:

y = (1/4)x² - 5

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The distance between the Eiffel tower and the location where the observer is standing is 2869.2929 meters.

Therefore, you are 2869.2929 meters away from the Eiffel tower.

The Eiffel Tower is 300m tall. If a person is standing at a certain location in Paris, the tower subtends an angle of 6 degrees. To calculate the distance from the Eiffel tower, trigonometry is used. Here's how you can calculate the distance between the Eiffel tower and the location you are standing in Paris;

Let AB be the height of the Eiffel Tower, which is 300 m.
Let AC be the distance between the observer and the base of the Eiffel Tower.
Let the angle of elevation at A be θ = 6 degrees.
Now, from the diagram, it is clear that;
Tan θ = AB/AC
Therefore, AC = AB/Tan θ
Substituting values, we get:
AC = 300/Tan 6 degrees
AC = 300/0.104528
AC = 2869.2929 meters.

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Errors -in -variables bias represents the option c. arises from error in the measurement of the independent variable.

In a regression model Errors -in -variables bias is not only a problem in small samples.

It can affect large samples as well.

This can lead to biased estimates of the regression coefficients.

This can lead to biased and inconsistent estimates of the regression coefficients and standard errors.

Even if the error in the dependent variable is zero-mean.

Even if the measurement error in the dependent variable is negligible.

The problem is not limited to small samples.

And can be particularly severe when the measurement error in the independent variable is large.

Therefore, the errors -in - variables bias arises from the option c. arises from error in the measurement of the independent variable.

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The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. each regular pizza costs $41 and each deluxe pizza costs $22.

System of equations:

6r + 7d = 226

6r + 9d = 270

Solving:

6r + 7d = 226

6r + 9d = 270

-6r -6r

7d -9d = -44

d = -44/2

d = -22

6r + (-22) = 226

6r = 248

r = 248/6

r = 41

Each regular pizza costs $41, and each deluxe pizza costs $22.

The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. To solve this system of equations, we first subtracted 6r from both equations, leaving us with 7d and -9d on one side. We then divided both sides by -2, leaving us with d = -22. We then added 22 to the other equation, leaving us with 6r = 248. Finally, we divided both sides by 6, leaving us with r = 41. Thus, each regular pizza costs $41 and each deluxe pizza costs $22.

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Answer:

Step-by-step explanation:

To find the volume of a figure, you need to multiply the length, width, and height of the figure.

Answer:

Matrix B is a 3 × 7 matrix.

Answer:

  -1239/1961

Step-by-step explanation:

You want cos(A+B) given that tan(A) = 45/28 and cos(B) = 12/37.

Here, we'll use the tangent relations ...

The tangent of angle B can be found from ...

  tan(B)² = 1/cos(B)² -1

  tan(B)² = 1/(12/37)² -1 = 1225/144

  tan(B) = 35/12

Now the tangent of the angle sum is ...

  tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))

  = (45/28 +35/12)/(1 -(45/28)(35/12)) = (95/21)/(1 -75/16) = -1520/1239

Note that the tangent of this sum of two first-quadrant angles is negative. That means the result is a second-quadrant angle, so the cosine will also be negative.

  cos(A+B) = -1/√(tan(A+B)² +1)

  cos(A+B) = -1/√((1520/1239)² +1)

  cos(A+B) = -1239/1961

__

Additional comment

Some calculators maintain enough internal accuracy that you can obtain the answer directly from ...

  cos(arctan(45/28) +arccos(12/35))

The one shown in the attachment is not able to provide the ratio of integers equal to the floating point value it computes for this.

The value of [tex]$\tan A$[/tex] in its simplest radical form is [tex]8/3$.[/tex]

What is radical form?

Radical form refers to a mathematical expression that includes radicals, which are symbols that indicate a root of a number.

To find the value of [tex]$\tan A$[/tex], we first need to determine the value of [tex]\cos A$.[/tex]

Using the Pythagorean identity, we have:

[tex]$$\sin^2 A + \cos^2 A = 1$$[/tex]

Substituting the given value of [tex]$\sin A$[/tex], we get:

[tex]$$\left(\frac{8}{\sqrt{73}}\right)^2 + \cos^2 A = 1$$[/tex]

Simplifying the left-hand side, we get:

[tex]$\frac{64}{73} + \cos^2 A = 1$$$$\cos^2 A = \frac{9}{73}$$$$\cos A = \frac{3}{\sqrt{73}}$$[/tex]

Since angle [tex]$A$[/tex] is in the first quadrant, both [tex]$\sin A$[/tex] and [tex]$\cos A$[/tex] are positive.

Therefore, we have:

[tex]$$\tan A = \frac{\sin A}{\cos A} = \frac{8/\sqrt{73}}{3/\sqrt{73}} = \frac{8}{3}$$[/tex]

So the value of [tex]$\tan A$[/tex] in its simplest form is [tex]8/3$.[/tex]

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The cross product a ⨯b: A = 4, 5, 0 , b = 1, 0, 3

cross product {15, -12, -5}

dot products with 'a' and 'b': 0 and 0

For vectors a = {4, 5, 0} and b = {1, 0, 3}, you want the cross product and verification that the cross product is orthogonal to both 'a' and 'b'.

Cross product:

The cross product of 4i+5j+0k and 1i+0j+3k is the determinant :

  [tex]\left[\begin{array}{ccc}i&j&k\\4&5&0\\1&0&3\end{array}\right][/tex]

 = 15i - 12j -5k

As a list of coefficients, the cross product is c = {15, -12, -5}.

Orthogonal

Vectors are orthogonal if their dot product is 0.

a· c = {4, 5, 0}·{15, -12, -5} = (4·15) -(5·12) +(0·(-5)) = 60 -60 = 0

b· c = {1, 0, 3}·{15, -12, -5} = (1·15) +(0·(-12)) +(3·(-5)) = 15 -15 = 0

The dot products are both zero, so the cross product is orthogonal to both of the vectors that created it.

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Answer:   If x is less than -120, then x-120 will be less than zero, so we have:

|x-120| = -(x-120)

And since x is less than -120, we have:

|x-120| = -(x-120) = -x + 120

Therefore, the simplified expression for |x-120| when x<-120 is -x + 120.

Step-by-step explanation: I would reallyyyyyyyyyyyyyyyyy apreciate brainliest

Answer:

h=

[tex] \frac{15}{4} [/tex]

Step-by-step explanation:

Divide both sides by 8:

[tex]2 - 7 + 4h = \frac{80}{8} [/tex]

Divide 80 by 8 to get 10:

[tex]2 - 7 + 4h = 10[/tex]

subtract 7 from 2 to get -5:

[tex] - 5 + 4h = 10[/tex]

add 5 to both sides:

[tex]4h = 10 + 5[/tex]

Add 10 and 5 to get 15:

[tex]4h = 15[/tex]

divide both sides by 4.:

[tex]h = \frac{15}{4} [/tex]

Hopefully this helps! :)

If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.

The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.

And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.

Thus, the size of B is 3x7.

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Answer:

5/6π(4.25 in)^2

Step-by-step explanation:

Step 1: Calculate the full area of the disk using the formula for the area of a circle: A = π × r2

A = π × (4.25 inches)2

A = 56.41π inches2

Step 2: Calculate 5/6 of the full area.

A = (5/6) × 56.41π inches2

A = 47.01π inches2

Therefore, the area of 5/6 of the disk is 47.01π inches2.

Answer:

3

Step-by-step explanation:

The proof involves showing that the bisecting line QS and the parallel sides QR and PS create pairs of congruent angles, which then proves that opposite sides are parallel. Therefore, PQRS is a parallelogram.

Proof:

Since QS bisects PR at T, we know that PT = RT and QT = TS.

Also, QR is parallel to PS. Therefore, angle QTS is congruent to angle RPT (alternate interior angles).

Using the same reasoning, we can show that angle PST is congruent to angle QRP (alternate interior angles).

Now, we have two pairs of congruent angles in the quadrilateral PQRS, which means that the opposite sides are parallel.

Therefore, PQRS is a parallelogram.

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To make  a departure timetable:

The simplest: download a predefined template from Microsoft Excel.

To create a template: select A1:E2 > Merge and Center > click WEEKLY SCHEDULE > select Center Alignment.

Add borders and titles. Type the time in A3. In A4 and A5, enter time > fill cell > add days > save template.

1. Start Excel and open a new blank workbook.

2. Select the range A1:E2 and on the Home tab, select Merge and Center in the Alignment group.

3.

Type "WEEKLY SCHEDULE" in A1:E2, change the font size to 18, and select Center Alignment in the Alignment group.

4. Select cells F1:H2, on the Home tab, in the Font group, select the Border drop-down menu, and then select All Borders.

5. Enter “Daily Start Time” into F1, “Time Interval” into G1, and “Start Date” into H1.

Select the Select All icon (between 1 and A on the worksheet), then double-click the line dividing two columns to resize all cells to fit the contents.

6. Select cell A3 and enter "TIME".

7. Select cell A4 and enter the time you want the program to start.

To follow this example, enter "7:00".

8. In cell A5, enter the next interval to be listed in the plan. To follow this example, enter "7:30". Select A4:A5 and drag the fill handle down to fill the time increment for the rest of the day.

9. In cell B3, enter the day of the week you want the schedule to start. To follow this example, enter "SUNDAY".

10. Drag the fill handle to the right to automatically fill the calendar with the remaining days of the week.

11. Select row 3. Make the font bold and change the font size to 14.

12. Change the hour font size in column A to 12.

13. Choose the Select All icon or press Ctrl+A and choose Center from the Alignment group on the Home tab.

14. Select cells A1:H2. In the Font group on the Home tab, select the Fill Color drop-down list and choose a fill color for the selected cells.

15. Select the body of the program. Select the Border drop-down menu in the Font group and select All Borders.

16. Save the program that  we have made as time table.

Complete Question:

How can we help the park manager to draw a departure timetable in excel?

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A card is drawn from a standard deck of 52 playing cards. the probability that the card will be a spade or a jack is 17/52 or 0.3269 (rounded to four decimal places).

The total number of playing cards in a deck is 52. Out of these 52 playing cards, there are 4 suits, and each of these suits includes 13 cards.

Hence, there are 4 types of cards, and each of these types includes 13 cards. Therefore, there are 52/4 = 13 cards per type.A card is drawn from the deck of 52 playing cards.

The probability that it will be a spade or a jack is given below:

The probability of a spade card is 13/52 or 1/4, since there are 13 spade cards in the deck of 52 playing cards.

The probability of a jack card is 4/52 or 1/13, since there are 4 jacks in the deck of 52 playing cards.

Therefore, the probability that the card will be a spade or a jack is (13/52) + (4/52) = 17/52 or 0.3269 (rounded to four decimal places).

Thus, the probability that the card will be a spade or a jack is 17/52 or 0.3269 .

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In equation h=3.25w+19, the number 3.25 represents the rate of change in the height of the sunflower per week (w), and the constant term of 19 represents the initial height of the sunflower when it was first planted.

The equation h=3.25w+19 is in slope-intercept form, which means that it can be written as y=mx+b, where y represents the dependent variable (in this case, the height of the sunflower), x represents the independent variable (the number of weeks since the sunflower was planted), m represents the slope of the line, and b represents the y-intercept (the value of y when x=0).

In this equation, the slope is 3.25, which means that for each additional week that passes since the sunflower was planted, its height increases by an average of 3.25 inches. So, the number 3.25 represents the rate of change of the height of the sunflower with respect to time.

This means that for every additional week that passes since the sunflower was planted, the height of the sunflower increases by 3.25 inches on average.

The equation also includes a constant term of 19, which represents the initial height of the sunflower when it was first planted, before any weeks had passed.

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Answer:

Step-by-step explanation:

Line A passes through (5,1) and (0,-2). So

     gradient line A =[tex]=\frac{-2-1}{0-5} =\frac{3}{5}[/tex]

Since the lines are parallel they have equal gradients, so  [tex]m=\frac{3}{5}[/tex].

The line passes through point P and so has y-intercept = 3 (so c=3).

So the equation of the new line is:

                       [tex]y=\frac{3}{5} x+3[/tex]

This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.

If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula[tex]R125/(2^t)[/tex] = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula [tex]R125/(2^t)[/tex] for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.

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Answer:

B) x=12

Step-by-step explanation:

theres a 50/50 shot at getting heads, half of 24 is 12

Answer:

The secant function is defined as the reciprocal of the cosine function. So if `sec(theta) = √3`, then `cos(theta) = 1/√3`. Since `sin^2(theta) + cos^2(theta) = 1`, we can solve for `sin(theta)`:

`sin^2(theta) + cos^2(theta) = 1`

`sin^2(theta) + (1/√3)^2 = 1`

`sin^2(theta) + 1/3 = 1`

`sin^2(theta) = 2/3`

`sin(theta) = ±√(2/3)`.

Since it is given that `sin theta > 0`, we can conclude that `sin(theta) = √(2/3)`.

Now that we have the values of sine and cosine, we can find the remaining trigonometric functions:

`tan(theta) = sin(theta)/cos(theta)`

`= (√(2/3)) / (1/√3)`

`= √(6)/3`

`cot(theta) = cos(theta)/sin(theta)`

`= (1/√3)/(√(2/3))`

`= √6 / 6`

`csc theta = 1/sin theta`

`= 1/(√(2/3))`

`= √6 / √4`

So, in summary:

- sec theta = √3

- cos theta = 1 / √3

- sin theta = √(2 / 3)

- tan theta = √6 / 3

- cot theta = √6 / 6

- csc theta = √6 / √4

Is there anything else you would like to know?

The most expensive health insurance plan for someone who fills 7 prescriptions each month is Option B, which has a total monthly cost of $240.

To identify the most expensive health insurance plan, we need to calculate the total cost for each option per month. The total cost can be found by adding the monthly insurance premium to the product of the co-pay per prescription and the number of prescriptions per month.

From the calculations, Option B is the most expensive plan as it cost $240 per month.

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Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

The term "statistical data" refers to numerical data that is gathered from a sample or population in order to characterise or draw conclusions about a larger group. Observational studies, surveys, experiments, and other techniques can all be used to gather statistical data, as can data from already-existing records and databases. Many approaches and methodologies, including data visualisation, inferential statistics, and descriptive statistics, can be used to examine statistical data. Measures of central tendency (mean, median, mode), indicators of dispersion (standard deviation, range, interquartile range), and graphical representations are some examples of the key characteristics of a dataset that are summarised and described using descriptive statistics (histograms, box plots, scatter plots). A bigger population can be inferred from a sample of data using inferential statistics, on the other hand.

given

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 0 3

1 1 7 7 7 7

2 0 0 0 2 4 8 8

3 1 3

Key 1|1 = 11

This stem-and-leaf plot depicts the frequency distribution of the data set in an accurate manner.

Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

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Three-digit addition and subtraction with regrouping involves adding or subtracting numbers with three digits (numbers between 100 and 999) while carrying or borrowing values from one place value to another.

Addition is a basic arithmetic operation that involves combining two or more numbers or quantities to find the total amount or sum. It is often denoted by the symbol "+". For example, if we add 2 and 3, we get a sum of 5.

For example, let's say we want to add 357 and 468:

In this example, we first add the ones place (7 + 8 = 15), which gives us a sum of 5 and carry-over of 1. We then add the tens place (5 + 6 = 11) and add the carry-over from the ones place, which gives us a sum of 2 and carry-over of 1. Finally, we add the hundreds place (3 + 4 = 7) and add the carry-over from the tens place, which gives us a final sum of 825.

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Answer:

x = - 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

10(5x + 12) = 2(5x + 15)  Distribute the 10 and the 2

10(5x) + 10(12)  = 2(5x) + 2(15)

50x + 120 = 10x + 30  Subtract 10x from both sides

50x - 10x +120 = 10x - 10x + 30

40x + 120 = 30    Subtract 120 from both sides

40x + 120 - 120 = 30 - 120

40x = -90  Divide both sides by 40

[tex]\frac{40x}{40}[/tex] = [tex]\frac{-90}{40}[/tex]

x = [tex]\frac{-9}{4}[/tex] or - 2[tex]\frac{1}{4}[/tex]

Helping in the name of Jesus.

We can solve [tex]2^{a}[/tex] x[tex]2^{b}[/tex]  = [tex]2^{0}[/tex] by recognizing that [tex]2^{0}[/tex]equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1.

To solve [tex]2^{a}.2^{b}=2^{0}[/tex] for a and b, we must first recognize that 2^0 equals 1, which means that the equation can be rewritten as [tex]2^{a}.2^{b}=1[/tex]. Therefore, we can simplify the equation to [tex]2^{a+b}[/tex] = 1.

Since 2 raised to any negative power is a fraction, we need at least one of the exponents to be negative.

We could also choose other values that make either a or b negative, such as a = -2 and b = 2, or a = -3 and b = 3. The key is to have one negative exponent and one positive exponent so that their sum equals zero.

In summary, we can solve [tex]2^{a}.2^{b}=1[/tex]by recognizing that [tex]2^{0}[/tex] equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1. We must have at least one negative exponent to satisfy the equation, and we can choose various values for a and b as long as their sum equals zero.

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