How many whole numbers lie between 237 and 143?​

Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.

To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.

Let's consider a cross section of the solid taken at a distance x from the center of the circle.

Since the cross section is an equilateral triangle, all its sides have the same length.

Let  this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:

\(height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}\)

Therefore, the area of the cross section at a distance x from the center of the circle is:

\(A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}\)

Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):

\(V = \int\ [-3,3]\sqrt{3/4*y^2} dx\)

To find the limits of integration for y, we need to consider the equation of the circle:

\(x^2 + y^2= 3^2\)

Solving for y, we get:

\(y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}\)

Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:

\(y = 3*\sqrt{3}\)

Substituting this into the integral, we get:

\(V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx\)

\(= \int\ [-3,3] 27/4*\sqrt{3} dx\)

Integrating, we get:

\(V = [27/4\sqrt{3x}]*[-3,3]\)

\(= 81/2*\sqrt{3}\)

Therefore, the volume of the solid is \(81/2*\sqrt3\)cubic units

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Answer:

(-2,-1)

Step-by-step explanation:

3-5=-2

-4+3=-1

The coordinate of the point S if the point is translated 5 units left and 3 units up are (-2,-1). The correct option is A.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Given the coordinate (3,-4) of the point S. Now, if the point is translated 5 units left and 3 units up, then the new coordinates of S are,

(3,-4) → (3-5 , -4+3) = (-2, -1)

Hence, the coordinate of the point S if the point is translated 5 units left and 3 units up are (-2,-1).

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Answer:

answer is D

Step-by-step explanation:

...........

Answer:

The total amount of money Mr. Wong received from dividends is $118 * 2 = $236.

The total value of Mr. Wong's shares before the bonus was 5,000 * $1.60 = $8,000.

The bonus he received was 3.3% of $8,000 = $264.

So, the total amount of money Mr. Wong received from the investment was $236 + $264 + $9,100 = $9,600.

The return on investment for Mr. Wong is the total amount of money he received from the investment divided by the amount of money he initially invested, expressed as a percentage.

So, the return on investment is ($9,600 / $8,000) * 100% = 120%.

Therefore, the return on investment for Mr. Wong is 120%.

To show explicitly that l[x−1] does not exist, we need to provide an explanation as to why this limit cannot be computed. One way to do this is to consider the behavior of the function as x approaches the point x=1 from both the left and the right.

If we approach x=1 from the left, we have x-1<0 and so l[x−1] becomes l[negative number]. However, the limit of a function as it approaches a value from the left and right must be the same in order for the limit to exist. Since l[x−1] becomes l[negative number] when approached from the left, and l[x−1] becomes l[positive number] when approached from the right, the limit does not exist.

In other words, we cannot define a unique value for l[x−1] as x approaches 1 because the function behaves differently on either side of 1. Therefore, l[x−1] does not exist.      

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Answer:

D

Step-by-step explanation:

The absolute value always gives a positive result. However the expression inside can be positive or negative , so

x + 2 - 1 > 3 or - (x + 2)  - 1 > 3

x + 1 > 3 ( subtract 1 from both sides )

x > 2

or

- (x + 2) - 1 > 3

- x - 2 - 1 > 3

- x - 3 > 3 ( add 3 to both sides )

- x > 6

Multiply both sides by - 1, reversing the symbol as a result of multiplying by a negative quantity.

x < - 6

solution is x < - 6 or x > 2

Answer: 5

Step-by-step explanation:

  8-2b=-2

8-2b-8=-2-8

    -2b=-10

-2b/-2=-10/-2

       b=5

The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.

How to solve and What is Probability?

The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.

Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.

It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.

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Answer: The second one

The type of sampling used in this scenario is B. Stratified sampling. Stratified sampling involves dividing the population into distinct subgroups or strata and then selecting samples from each subgroup.

In this case, Miranda divides her day into three parts: morning, afternoon, and evening. Each part of the day represents a stratum or subgroup.  Miranda measures her breathing rate at 4 randomly selected times during each part of the day. This means she is taking samples from each of the three strata (morning, afternoon, and evening) and collecting data from within those subgroups.

By using stratified sampling, Miranda ensures that her samples represent the different parts of her day in a proportional and systematic manner, allowing her to capture potential variations in her breathing rate throughout the day.

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In a rectangle WXYZ, if the measure of angle 1 is 30 degrees, then the measure of angle 8 can be determined.

A rectangle is a quadrilateral with four right angles. In a rectangle, opposite angles are congruent, meaning they have the same measure. Since angle 1 is given as 30 degrees, angle 3, which is opposite to angle 1, also measures 30 degrees.

In a rectangle, opposite angles are congruent. Since angle 1 and angle 8 are opposite angles in quadrilateral WXYZ, and angle 1 measures 30 degrees, we can conclude that angle 8 also measures 30 degrees. This is because opposite angles in a rectangle are congruent.
Since angle 3 and angle 8 are adjacent angles sharing a side, their measures should add up to 180 degrees, as they form a straight line. Therefore, the measure of angle 8 is 180 degrees minus the measure of angle 3, which is 180 - 30 = 150 degrees.

So, if angle 1 in rectangle WXYZ is 30 degrees, then angle 8 measures 150 degrees.

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If the median of a set of data is equal to the mean, then it implies that the data has a symmetric distribution. The correct answer is option d.

This is because the mean is sensitive to extreme values and tends to be pulled in the direction of the skewness of the distribution. On the other hand, the median is not sensitive to extreme values and only depends on the order of values in the data set.

Thus, if the median and mean are equal, it suggests that the distribution is symmetric and does not have any skewness. However, one cannot infer anything about whether the distribution is normal or approximately normal based solely on the equality of the median and mean.

The correct answer is option d.

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Step-by-step explanation:

x = number of sold sodas

y = number of sold hot dogs

x + y = 124

x = 3y

so,

3y + y = 124

4y = 124

y = 31

x = 3y = 3×31 = 93

there were 93 sodas and 31 hot dogs sold.

Answer:

the range value of x which satisfy inequality \((x + 2)^2 > 2x + 7\) is \(\mathbf{x>1 \ or \ x<-3}\)

Step-by-step explanation:

We need to find the range value of x which satisfy inequality \((x + 2)^2 > 2x + 7\)

Solving:

\((x + 2)^2 > 2x + 7\)

Using formula: \((a+b)^2=a^2+2ab+b^2\)

\(x^2+4x+4>2x+7\\x^2+4x+4-2x-7>0\\x^2+4x-2x+4-7>0\\x^2+2x-3>0\)

Now factoring the term: \(x^2+2x-3>0\)

Breaking the middle term: 2x= 3x-x

\(x^2+2x-3>0\\x^2+3x-x-3>0\\x(x+3)-1(x+3)>0\\(x-1)(x+3)>0\\x-1>0 \ or \ x+3>0\\x>1 \ or \ x<-3\)

So, the range value of x which satisfy inequality \((x + 2)^2 > 2x + 7\) is \(\mathbf{x>1 \ or \ x<-3}\)

Answer:

Step-by-step explanation:

240 has a reference angle of 60 in the third quadrant. The side across from 60 is going to be negative in this quadrant, measuring -√3; the side adjacent to the angle is also negative in this quadrant, measuring -1. The tangent ratio is the side opposite the angle over the side adjacent to the angle, so

tan(240) = √3

Answer:

-240

Step-by-step explanation:

The triangles AEB and DEC describes AA similarity .

What is AA Similarity ?

Two triangles are said to be congruent by AA Similarity when two angles in one triangle are congruent to two angles in another triangle .

In the question ,

a figure is given .

in triangle AEB and triangle DEC ,

we can see that ,

∠AEB ≅ ∠DEC    ,   because they are vertically opposite angles .

On rotating triangle CED by  180° around the point E, then the translate point D to point A confirms  ∠EAB ≅ ∠EDC.

Since two angles are Congruent

So , By AA Similarity , triangles AEB and DEC are Congruent .

Therefore , the triangles AEB and DEC are Congruent .

The given question is incomplete , the complete question is

Which of the following triangles in the given figure describes AA similarity ?

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Answer:

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

m<D + m<E + m<F = 180°

4x + 2x + m<F = 180

What is the measure of <F? It's not clear in the post.

Answer:

115 degrees.

Step-by-step explanation:

The sum of the angles, ∠1 and ∠4 is 250.

What is alternate exterior angles?

The pair of angles known as alternate external angles are those that are generated on the outer side of the parallel lines but on the transverse side.

As given, the diagram of airport runway intersections show two parallel runways. A taxiway crosses both runways.

After crossing runways by taxiway the angles, ∠8 and ∠1 becomes same.

Since, ∠8 = 125  so ∠1 = 125.

Now ∠1 and ∠4 are alternate exterior angles.

It becomes ∠4 is same as ∠1.

Therefore, ∠1 = ∠4 = 125.

So the sum of angles, ∠1 and ∠4 is

125 + 125 = 250.

Hence, the sum of angles ∠1 and ∠4 is 250.

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Answer:

Step-by-step explanation:

The correct expression is G: 5000(1.11)^10

This expression represents the value of the rare postage stamp after 10 years, given that its value has been increasing by 11% each year.

The value of the stamp after the first year would be 5000 * 1.11 = 5550.

The value of the stamp after the second year would be 5550 * 1.11 = 6160.5.

This process continues for 10 years, resulting in an overall increase in value of 5000 * 1.11^10 = 8261.3.

The other expressions are not correct because they do not accurately represent the value of the stamp after 10 years.

F: 5000(0.11)^10 represents the value of the stamp after 10 years, given that its value has been decreasing by 11% each year.

H: 5000(11)^10 represents the value of the stamp after 10 years, given that its value has increased by 1100% each year.

J: 5000(1.11)(10) represents the value of the stamp after 10 years, given that its value has increased by 11% for each of the 10 years. However, this expression does not take into account the compound interest that has accumulated over the 10 years.

Answer:

29

Step-by-step explanation:

If you calculate the difference with the 45 and percentage you will get 29 including with the X and - should be east

Answer:

y-1=-3(x+2)

Step-by-step explanation:

The claim that the population mean is less than 125 (Option E) would

the interval tends to refute.

The 90% confidence interval for the population mean is 135 to 160. This means that if we were to repeat the process of taking samples from the same population and constructing a 90% confidence interval, we would expect 90% of the intervals to contain the true population mean.

With this in mind, let's consider each claim:

A. The interval does not rule out the possibility that the population mean is more than 110, as 110 is less than the lower bound of the interval.

B. The interval does not rule out the possibility that the population mean is less than 150, as 150 is greater than the upper bound of the interval.

C. The interval does not rule out the possibility that the population mean is between 140 and 150, as both of these values fall within the interval.

D. The interval does not rule out the possibility that the population mean is more than 140, as 140 is less than the upper bound of the interval.

E. The interval refutes the claim that the population mean is less than 125, as 125 is less than the lower bound of the interval.

Therefore, the answer is (E) The population mean is less than than 125.

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The values of sine are positive in the first and second quadrants when moving counter-clockwise along the unit circle.

Moving counter-clockwise along the unit circle, the values of sine will be positive in the first and second quadrants.

In the first quadrant (0° to 90°), both the x-coordinate and y-coordinate of any point on the unit circle are positive. Therefore, the value of sine (which is the y-coordinate) will be positive in this quadrant.

In the second quadrant (90° to 180°), the x-coordinate is negative, but the y-coordinate is positive. Since sine is the ratio of the y-coordinate to the radius, it will still be positive in this quadrant.

In the third quadrant (180° to 270°), both the x-coordinate and y-coordinate are negative. Therefore, the value of sine will be negative in this quadrant.

In the fourth quadrant (270° to 360°), the x-coordinate is positive, but the y-coordinate is negative. Since sine is the ratio of the y-coordinate to the radius, it will be negative in this quadrant as well.

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The depreciation rate of a geometric sequence can be found by multiplying the difference of 1 and r by 100. The depreciation rate and the price after 6 years are given as 8% and $13,181.63 respectively.

In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.

The given geometric sequence is as below,

$20,000, $18,400,  $16,928 and  $15,573.

The common ratio is given as,

r = 18400/20000

 = 0.92

Since, r < 1, the sequence is decreasing.

Thus, the rate of depreciation can be found as,

Depreciation rate = (1 - 0.92) × 100%

                              = 8%.

The price after 6 years is given by finding the 6th term of the given  geometric sequence as,

a₆ = a × r⁵

   = 20000 × 0.92⁵

   = 13181.63

Hence, the depreciation rate is given as 8% and the price of the car after 6 years is $13,181.63.

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Answer:

-0.123

Step-by-step explanation:

...............

Answer:

23/99 or 0.22222222222222.

Step-by-step explanation:

Answer:

23/99

Step-by-step explanation: