Lily measured the lengths of 16 fish.
Use the graph below to estimate the lower and upper quartiles of the fish

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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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity [tex](-32.2 ft/s^2)[/tex],

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters

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 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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To calculate the circumference of a circle, you can use the formula:

[tex]\displaystyle C=2\pi r[/tex]

Where [tex]\displaystyle C[/tex] represents the circumference and [tex]\displaystyle r[/tex] represents the radius of the circle.

Given that the radius [tex]\displaystyle r[/tex] is 8 inches, we can substitute this value into the formula:

[tex]\displaystyle C=2\pi (8)[/tex]

Simplifying the expression:

[tex]\displaystyle C=16\pi [/tex]

Thus, the circumference of a circle with a radius of 8 inches is [tex]\displaystyle 16\pi [/tex] inches.

Note: [tex]\displaystyle \pi [/tex] represents the mathematical constant pi, which is approximately equal to 3.14159.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Considering the definition of probability, the probability that the gumball machine dispenses 2 red gumballs in a row is 7/59.

Probability establishes a relationship between the number of favorable events and the total number of possible events.

The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)= number of favorable cases÷ number of posible cases

The conditional probability P(A|B) is the probability that event A occurs, given that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:

P(A|B) = P(A∩B)÷ P(B)

Expressed another way:

P(A∩B)= P(B)× P(A|B)

In this case, you know a gumball machine has:

Considering the definition of probability, since there are 21 red gumballs in a total of 60 gumballs, the probability of getting a red gumball on the first try is 21/60.

Now, the probability of getting a red gumball on the second try, given that you got a red gumball on the first try and now you have a 59 gumballs an 20 red gumballs on the machine, is 20/59.

So, the probability of getting 2 red gumballs in a row is calculated as:

P(A∩B)= P(B)× P(A|B)

P(A∩B)= 21/60× 20/59

P(A∩B)= 7/59

Finally, the probability that the gumball machine dispenses 2 red gumballs in a row is 7/59.

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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.

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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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

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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1. The fundamental undefined concepts in Geometry are point, line, and plane.

2. A line is formed by connecting at least two points.

3. Collinear points are three or more points that lie on the same line.

4. Concurrent lines are three or more lines that intersect at a common point.

5. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

6. An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side or its extension.

7. The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

8. The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

9.The incenter is the point where the angle bisectors of a triangle intersect.

10. The orthocenter is the point where the altitudes of a triangle intersect.

1. The three fundamental Undefined Concepts in Geometry are:

Point: A location in space that has no size or dimension.

Line: A straight path that extends infinitely in both directions.

Plane: A flat, two-dimensional surface that extends infinitely in all directions.

2. A Line consists of at least two points: A line is determined by two distinct points and extends infinitely in both directions.

3. A Plane consists of at least three non-collinear points: A plane is determined by three non-collinear points and extends indefinitely in all directions.

4. . Three or more points that lie on one line are called collinear: Collinear points are points that lie on the same straight line.

5. . Three or more lines that pass through one point are called concurrent: Concurrent lines are lines that intersect at a common point.

6.A line segment joining a vertex of a triangle to the mid-point of the opposite side is called a median: The median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

7. A line segment drawn from a vertex of a triangle perpendicular to the opposite side (or to the opposite side produced) is called an altitude: The altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side or its extension.

8. The perpendicular bisectors of the sides of any triangle are concurrent at a point which is equidistant from the vertices of the triangle: The point of concurrency of the perpendicular bisectors of the sides of a triangle is equidistant from the triangle's vertices.

9. The angle bisectors of any triangle are concurrent at a point which is equidistant from the sides of the triangle: The point of concurrency of the angle bisectors of a triangle is equidistant from the triangle's sides.

10. The point of intersection of the altitudes of a triangle is called the orthocenter: The orthocenter is the point of intersection of the altitudes of a triangle.

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Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Step-by-step explanation:

(i) The type of the given polynomial is a quadratic polynomial. It is a second-degree polynomial because the highest exponent of the variable x is 2.

(ii) To find the loss if no barrels are sold, we substitute x = 0 into the polynomial p(x):

p(0) = -(0)² + 350(0) - 6600

p(0) = -6600

Therefore, if no barrels are sold, the loss would be 6600 rupees.

(iii) To determine the minimum number of barrels required to have no profit or no loss, we need to find the x-value where the profit function p(x) equals zero.

p(x) = 0

Solving the quadratic equation:

-x² + 350x - 6600 = 0

We can factorize the equation:

-(x - 20)(x - 330) = 0

Setting each factor equal to zero:

x - 20 = 0  ->  x = 20

x - 330 = 0  ->  x = 330

So, the minimum number of barrels required to have no profit or no loss is either 20 barrels or 330 barrels.

Answer:

Step-by-step explanation:

[tex]\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)[/tex]

Lets look at the derivative part:

[tex]\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2][/tex]

[tex]=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)[/tex]

Substituting in eq(1), we have:

[tex]\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)][/tex]

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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the graph that best represents the solution to the given system of equations is Option 1. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

The given system of equations is:y = -2x + 14y = 2x + 2The equations represent two lines.

Let's solve them by substitution:y = -2x + 14Substitute this value of y into the second equation: y = 2x + 2

Therefore,-2x + 14 = 2x + 2Simplify and solve for x:-4x = -12x = 3Substitute this value of x into the first equation to find y:y = -2(3) + 14y = 8The solution is (3, 8).

The ordered pair (3, 8) represents the point where the two lines intersect. Let's now consider each option and determine which one best represents this point.

Option 1: A coordinate grid is shown from negative 10 to positive 10 on the x-axis and also on the y-axis.

Two lines are shown intersecting on the ordered pair 3, 8. This option represents the solution to the system of equations, therefore, it is the correct graph.

Option 2: A coordinate grid is shown from negative 10 to positive 10 on the x-axis and also on the y-axis. Two lines are shown intersecting on the ordered pair 8, 3. This point is not the solution to the system of equations.

Option 3: A coordinate grid is shown from negative 10 to positive 10 on the x-axis and also on the y-axis. Two lines are shown intersecting on the ordered pair negative 8, negative 3. This point is not the solution to the system of equations.

Option 4: A coordinate grid is shown from negative 10 to positive 10 on the x-axis and also on the y-axis. Two lines are shown intersecting on the ordered pair negative 3, 8.

This point is not the solution to the system of equations.

Therefore, the graph that best represents the solution to the given system of equations is Option 1.

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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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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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Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).

Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.

If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)

Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:

V = πr²lLet V = 100 cm³ and

r = 0.5 cm

(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:

l = 100 / (π(0.5)²)

l = 100 / (0.7854)l ≈ 127.32 cm

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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 three-digit number with the given conditions is 309.

Let's assume the hundreds digit of the three-digit number is "x". Since the tens digit is three less than the hundreds digit, the tens digit can be represented as "x - 3". Similarly, the unit digit is three times the hundreds digit, so it can be represented as "3x".

According to the given information, the sum of the digits of the three-digit number is 12. Therefore, we can write the equation:

x + (x - 3) + 3x = 12

Combining like terms:

5x - 3 = 12

Adding 3 to both sides:

5x = 15

Dividing both sides by 5:

x = 3

So, the hundreds digit of the number is 3. Substituting this value back into the expressions for the tens and unit digits:

Tens digit = x - 3 = 3 - 3 = 0

Unit digit = 3x = 3 * 3 = 9

Therefore, the three-digit number with the given conditions is 309.

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a) The price elasticity of demand is -2.

b) It  means that a decrease in price from 400 birr to 200 birr results in a relatively larger increase in the quantity demanded from 2000 to 4000.

To find the price elasticity of demand, we need to determine the percentage change in quantity demanded divided by the percentage change in price.

(a) Price elasticity of demand (ε) can be calculated using the following formula:

ε = (ΔQ/Q) / (ΔP/P)

Where:

ΔQ = Change in quantity demanded

Q = Initial quantity demanded

ΔP = Change in price

P = Initial price

In this case, when the price changes from 400 birr to 200 birr, the quantity demanded changes from 2000 to 4000. Let's calculate the percentage changes:

ΔQ/Q = (4000 - 2000)/2000 = 2000/2000 = 1

ΔP/P = (200 - 400)/400 = -200/400 = -0.5

Now we can substitute these values into the formula:

ε = (1)/(-0.5) = -2

The price elasticity of demand is -2.

(b) Based on the value of the price elasticity of demand (-2), we can determine the type of elasticity:

If the price elasticity of demand is greater than 1, it is considered elastic demand. This means that a small change in price will result in a relatively large change in quantity demanded. In this case, the demand is responsive to price changes.

Since the price elasticity of demand is -2, which is greater than 1, we can conclude that the demand for the concert tickets is elastic. This means that a decrease in price from 400 birr to 200 birr results in a relatively larger increase in the quantity demanded from 2000 to 4000.

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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 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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Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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