Suppose promoters of xyz music concerts knows that if they charge 400 birr per ticket, 2000 people would buy the tickets for concerts and if charge 200 birr per ticket 4000 people would by tickets over this price range; a. Find price elasticity of demand b. What types of price elasticity of demand "​

Using angle rules, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

Angle 1 + 69 + 47 = 180 (sum of angles on a straight line)

Angle 1 = 180 - (69+47)

Angle 1 = 64°

Angle 2 + 64 + 63 = 180 (sum of angles in a triangle)

Angle 2 = 180 - (64+63)

Angle 2 = 53°

Angle 1 + Angle 3 = 180 (sum of angles in a triangle)

Angle 3 = 180 - 64

Angle 3 = 116°

Angle 6 + 136 = 180 (sum of angles on a straight line)

Angle 6 = 180 - 136

Angle 6 = 44°

Angle 5 + Angle 3 + 32 = 180 (sum of angles in a triangle)

Angle 5 + 116 + 32 = 180

Angle 5 = 180 - (116 + 32)

Angle 5 = 32°

47 + Angle 6 + Angle 4 = 180

47 + 44 + Angle 4 = 180

Angle 4 = 180 - 91

Angle 4 = 89°

Therefore, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

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The length of portion BC of the cloth is approximately 5.8709 inches.

To find the length of portion BC of the cloth, we need to use trigonometric functions.

In this case, we can use the cosine function.

Given that the adjacent side to angle B is labeled BC and the hypotenuse is labeled 7 in, we can apply the cosine function, which is defined as the adjacent side divided by the hypotenuse:

cos(angle) = adjacent / hypotenuse

In this scenario, the angle we are considering is 33 degrees.

Therefore, we have:

cos(33°) = BC / 7 in

To isolate BC, we can rearrange the equation:

BC = 7 in [tex]\times[/tex] cos(33°)

Calculating this expression, we find:

BC ≈ 7 in [tex]\times[/tex] 0.8387 (rounded to four decimal places)

BC ≈ 5.8709 in.

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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The size of the exterior angle in the given 7-sided shape, as shown in the image attached below is: x = 46°.

To calculate the size of the exterior angle in a polygon when the interior angle is known, we can use the following relationship:

Interior angle + Exterior angle = 180°

Given that the interior angle measures 134°, as shown in the image below, we can substitute it into the equation:

134° + Exterior angle = 180°

To isolate the exterior angle, we subtract 134° from both sides of the equation:

Exterior angle = 180° - 134°

Simplifying further:

Exterior angle = 46°

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Based on the given information and adjustments, the adjusted bank balance for ABC Company on July 31 would be Br. 5,169.42.

Based on the provided information, let's analyze the various transactions and their impact on the bank reconciliation for ABC Company:

1. The deposit of Br. 410.90 made after banking hours: This deposit does not appear in the bank statement, so it should be added to the bank balance. After including this deposit, the adjusted bank balance would be Br. 5,375.37 (Br. 4,964.47 + Br. 410.90).

2. The erroneously charged check of Br. 79: This check should be deducted from the bank balance as it was charged in error by the bank. After deducting this amount, the adjusted bank balance would be Br. 5,296.37 (Br. 5,375.37 - Br. 79).

3. Outstanding checks: The outstanding checks that haven't been paid by the bank need to be deducted from the adjusted bank balance. The total amount of outstanding checks is Br. 610.75 (Br. 100 + Br. 10.25 + Br. 294.50 + Br. 205). After deducting this amount, the adjusted bank balance would be Br. 4,685.62 (Br. 5,296.37 - Br. 610.75).

4. Incorrectly charged check of Br. 210 as Br. 120: This error made by the bank needs to be corrected. The bank balance should be increased by the difference, which is Br. 90. Therefore, the adjusted bank balance would be Br. 4,775.62 (Br. 4,685.62 + Br. 90).

5. Proceeds from collection of an interest-bearing note receivable: The face amount of the note was Br. 500. Since the note was left with the bank's collection department, the amount collected should be added to the bank balance. Therefore, the adjusted bank balance would be Br. 5,275.62 (Br. 4,775.62 + Br. 500).

6. Interest earned on the average account balance: The interest earned of Br. 24.75 should be added to the bank balance. After including this amount, the adjusted bank balance would be Br. 5,300.37 (Br. 5,275.62 + Br. 24.75).

7. The returned check of Br. 10: This check was recorded in the check register as Br. 100 but was returned for Br. 10. The difference of Br. 90 should be deducted from the bank balance. Therefore, the adjusted bank balance would be Br. 5,210.37 (Br. 5,300.37 - Br. 90).

8. Fee charged by the bank for handling the collection of the note receivable: The fee of Br. 5.00 should be deducted from the bank balance. After deducting this fee, the adjusted bank balance would be Br. 5,205.37 (Br. 5,210.37 - Br. 5.00).

9. Check from customer John charged as Non-sufficient funds (NSF): The check of Br. 50.25 should be deducted from the bank balance. After deducting this amount, the adjusted bank balance would be Br. 5,155.12 (Br. 5,205.37 - Br. 50.25).

10. Service charge by the bank for the month of July: The service charge of Br. 12.70 should be deducted from the bank balance. After deducting this charge, the adjusted bank balance would be Br. 5,142.42 (Br. 5,155.12 - Br. 12.70).

11. Erroneously recorded check of Br. 85 as Br. 58: This error in the cash payment journal needs to be corrected. The bank balance should be increased by the difference, which is Br. 27. Therefore, the adjusted bank balance would be Br. 5,169.42 (Br. 5,142.42 + Br. 27).

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To write an equation for the cubic polynomial function with zeroes at 2, 3, and 5, we can use the factored form of a polynomial.

The factored form is given by (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.

So, for this problem, the equation would be (x - 2)(x - 3)(x - 5).

Regarding the multiplicity of the roots, in this case, none of the roots have multiplicity. Each root appears once in the equation.

To find a function with these roots, you can use the factored form of the polynomial and substitute different values for the coefficients to get different functions.

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The area of the composite figure is 800m²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

Composite geometric figures are made from two or more geometric figures.

The figure consist of a rectangle , a semi circle and a triangle.

Area of the semicircle = 1/2 πr²

= 1/2 × 3.14 × 10²

= 314/2 = 157 m²

Area of the rectangle = l × w

= 25 × 20

= 500m²

area of the triangle = 1/2bh

= 1/2 × 10 × 25

= 25 × 5

= 125 m²

Therefore the area of the composite figure

= 125 + 500 + 175

= 800m²

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The height of the canvas is approximately 11.5 inches.

To find the height of the canvas, we can use trigonometry and the given angle. Let's denote the height as 'h' inches.

We know that the width of the canvas is 20 inches, and it forms a 35° angle with the diagonal. Since a rectangle has 90° angles, the diagonal forms a right triangle with the width and height of the canvas.

The diagonal can be found using the Pythagorean theorem: diagonal^2 = width^2 + height^2.

In this case, diagonal^2 = 20^2 + h^2.

Since the angle between the width and the diagonal is given as 35°, we can use the sine function: sin(35°) = opposite/hypotenuse = h/diagonal.

Rearranging the equation, we have h = diagonal * sin(35°).

Substituting the value of diagonal^2 from the Pythagorean theorem, we get h = sqrt(20^2 + h^2) * sin(35°).

Solving this equation, we find that h ≈ 11.5 inches.

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Yes, we would have reason to believe that the proportion of rats developing tumors when subjected to this diet has increased if the experiment were repeated and 16 of 48 rats developed tumors.

To determine whether there is an increase in the proportion of rats developing tumors when subjected to a coffee bean diet, we can conduct a hypothesis test using the 0.05 level of significance.

1. State the hypotheses:

  - Null hypothesis (H0): The proportion of rats developing tumors remains the same.

  - Alternative hypothesis (Ha): The proportion of rats developing tumors has increased.

2. Identify the test statistic:

  We will use a z-test to compare the observed proportion of rats developing tumors with the expected proportion.

3. Set the significance level:

  The significance level (α) is given as 0.05.

4. Collect data:

  In the original experiment, 25% of rats developed tumors. In the repeated experiment, 16 out of 48 rats developed tumors.

5. Compute the test statistic:

  The test statistic formula for comparing proportions is:

  z = (p - P) / sqrt(P(1-P)/n)

  where p is the observed proportion, P is the hypothesized proportion, and n is the sample size.

  Using the observed proportion (16/48 = 0.333), the hypothesized proportion (0.25), and the sample size (48), we can calculate the test statistic.

6. Determine the critical value:

  Since we are using a 0.05 level of significance and conducting a one-tailed test (Ha: >), we can find the critical value from the standard normal distribution table. The critical value for a 0.05 significance level is 1.645.

7. Make a decision:

  If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the proportion of rats developing tumors has increased.

8. Calculate the test statistic:

  Plugging in the values into the formula, we calculate the test statistic:

  z = (0.333 - 0.25) / sqrt(0.25 * 0.75 / 48) = 1.404

9. Compare the test statistic and critical value:

  The test statistic (1.404) is less than the critical value (1.645).

10. Make a decision:

   Since the test statistic is not greater than the critical value, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion of rats developing tumors has increased when subjected to this diet.

In summary, based on the given data and conducting a hypothesis test, we do not have reason to believe that the proportion of rats developing tumors has increased if the experiment were repeated and 16 of 48 rats developed tumors.

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Answer:

a) All the students in Nadia's year are the population

b) All the students in Nadia's class are the sample

Step-by-step explanation:

She wants to find out if students in her year like the school lunches.

So, this is the population.

i.e All the students in Nadia's year

She asks her class to complete a survey,

So, this is the sample of the population (Her classmates are in the same year as her and so on)

i.e All the students in Nadia's class

It would cost 2025p to send one parcel weighing 170g and two parcels weighing 320g each.

In order to find out how much it will cost to send one parcel weighing 170g and two parcels weighing 320g each, we can use the information given to us in the question: it costs 50p to post a parcel that weighs 20g. Using this information, we can create a proportion. We know that 50p is the cost to send a parcel weighing 20g, so if we multiply the weight of the parcel by 2.5, we can find out how much it would cost to send that parcel.

For example, a parcel weighing 50g would cost 125p (50 x 2.5 = 125). To find out how much it would cost to send a parcel weighing 170g, we can use this porpotion: 50p/20g = x/170g

Multiplying both sides by 170g, we get:

x = (50p/20g) * 170gx = 425p

So, it would cost 425p to send a parcel weighing 170g.To find out how much it would cost to send two parcels weighing 320g each, we can use the same proportion:

50p/20g = x/320g

Multiplying both sides by 320g, we get:

x = (50p/20g) * 320gx = 800p

So, it would cost 800p to send two parcels weighing 320g each.

To find out the total cost to send all three parcels, we simply add up the costs:

425p + 800p + 800p = 2025p.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

To find the measures of angles ABD and DBC in the right triangle ABC, we considered two cases: when point D lies on segment AB and when point D lies on segment BC. In both cases, the measures of the angles were determined based on the given ratio of 3:2.

In the given problem, we have a right triangle ABC, and we need to find the measures of angle ABD (mABD) and angle DBC (mDBC) based on the ratio of the measures of angle A and angle B.

Let's consider the different cases for the location of point D:

Case 1: Point D lies on segment AB.

In this case, angle ABD and angle DBC will be acute angles. Let's assume that angle ABD has a measure of 3x and angle DBC has a measure of 2x. Since angle ABD and angle DBC are acute angles, the sum of their measures should be less than 90 degrees.

Therefore, we have the inequality: 3x + 2x < 90. Solving this inequality, we get 5x < 90, which gives x < 18. So, the measure of angle ABD (mABD) will be 3x, and the measure of angle DBC (mDBC) will be 2x.

Case 2: Point D lies on segment BC.

In this case, angle ABD and angle DBC will be obtuse angles. Let's assume that angle ABD has a measure of 3x and angle DBC has a measure of 2x. Since angle ABD and angle DBC are obtuse angles, the sum of their measures should be greater than 90 degrees.

Therefore, we have the inequality: 3x + 2x > 90. Solving this inequality, we get 5x > 90, which gives x > 18. So, the measure of angle ABD (mABD) will be 3x, and the measure of angle DBC (mDBC) will be 2x.

By investigating these two cases, we can find the measures of angle ABD (mABD) and angle DBC (mDBC) based on the given ratio of 3:2. The specific values of mABD and mDBC will depend on the exact location of point D within the triangle ABC.

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates ([tex]x_{mid, y_{mid[/tex]) can be found using the midpoint formula:

    [tex]x_{mid[/tex] = (x1 + x2) / 2 and [tex]y_mid[/tex] = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates ([tex]x_{mid[/tex], [tex]y_{mid[/tex]), write the equation of the perpendicular bisector in point-slope form: y - [tex]y_{mid[/tex] = [tex]m_{perp[/tex] * (x - [tex]x_{mid[/tex]), where [tex]m_{perp[/tex] is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + [tex]\frac{r}{2}[/tex] - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

Answer:

1.50 rand

Step-by-step explanation:

divide 18 by 12

= 1.5

therefore each egg costs 1 rand 50

Answer:

2/3

Step-by-step explanation:

if a dozen of eggs costs 18 rupees, what is the cost of each egg?

to get this we have to divide the cost of 12 eggs to 18 rupees

12/18

2/3 that's all

The missing parts of the proof of supplementary angles are:

Supplementary; ∠2 and ∠3; substitution; 2.

Supplementary angles are defined as angles whose measures sum to 180°.  Thus this is the first answer.  

Since we are told that ∠2 and ∠3 are supplementary, their measures sum to 180° and they are the second answer.

We know that m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.  We can substitute "m∠2 + m∠3" for 180° in the first equation; this is the substitution property.

To isolate m∠1 on the right, we will subtract m∠2 from each side, and get that m∠1 = m∠3 and the angles are congruent.

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Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

Answer:

The lower quartile of the fish lengths is 15 inches

The upper quartile of the fish lengths is 30 inches

Step-by-step explanation:

(the cumulative frequency gives how much of the observations/measurements are under a certain value e.g, in our case, for lengths of 40 inches, all 16 of the fish have length in that range (less than or equal to 40) so, the cumulative frequency is 16 and so on)

We need to find the lower and upper quartiles of the fish lengths,

Now, the lower quartile contains 25% (or 1/4) of the values

in our case, since there are 16 fish,

25% of 16 is 4

So, for the lower quartile, the cumulative frequency should be 4.

For which the length is 15 inches,

So, the lower quartile of the fish lengths is 15 inches

The upper quartile contains 75% (or 3/4) of the values,

Now, 3/4 of 16 is 12.

So, for the upper quartile, the cumulative frequency should be 12.

For which the length is 30 inches

So, the upper quartile of the fish lengths is 30 inches

To find the dimensions of the rectangle, we need to determine the length of the base (or width) and the length of the height.

Given the upper-left coordinates (-1, 7) and upper-right coordinates (4, 7), we can see that the base of the rectangle runs horizontally along the x-axis. Therefore, the length of the base is the difference between the x-coordinates of the upper-right and upper-left corners:

Length of base = 4 - (-1) = 4 + 1 = 5 units

Next, we can determine the height of the rectangle. Since the upper-left and upper-right corners have the same y-coordinate (7), we know that the height runs vertically along the y-axis. However, the given information does not provide the coordinates of the lower-left or lower-right corners, so we don't have enough information to determine the exact height of the rectangle.

Therefore, we cannot determine the dimensions of the rectangle with the given information.

The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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