Express cos a in terms of sin a

when the price is equal to the market equilibrium price, total surplus is maximized.

What is surplus?

Making the most of society's well-being is a desired goal for an economic system. Do free markets perform that? Buyers must profit from their purchases, and sellers must profit from their sales, in order to provide an answer. Consumer surplus is the difference between the price consumers are willing to pay and the price they actually pay for a commodity or service. When individuals buy something, they typically pay less than they would have otherwise. Similar to producers, sellers might command a higher price for a good than it costs them to make it; this is known as producer surplus because it occurs when the cost of production is less than the price at which the good is sold.

Consumer Surplus = Willingness to Pay Price − Market Price

Producer Surplus = Market Selling Price − Economic Cost

Total Surplus = Consumer Surplus + Producer Surplus

Only the most effective producers will be able to produce a product for less than the market price in highly competitive markets. Therefore, only those vendors will create a good.

Therefore, when the price is equal to the market equilibrium price, total surplus is maximized.

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Answer: the slope of line c is 7/9 because the slope of a line perpendicular is the opposite (reciprocal) of the slope of the original line.

Step-by-step explanation:

Yes, a plane figure can be transformed in various ways, including translations, rotations, reflections, and dilations.

A translation is a type of transformation that moves all the points in a figure through the same distance and in the same direction. The horizontal and vertical translations, denoted by h and v, respectively, specify the distance and direction of the movement.

For example, if h=2 and v=3, this would mean that the figure is moved 2 units to the right and 3 units up.

In general, the coordinates of a point (x, y) in the translated figure will be (x+h, y+v) in the new figure.

Hence , a plane figure can be transformed in various ways, including translations, rotations, reflections, and dilations.

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By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

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The amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.

The formula for finding the volume of a space is length x width x height. To find the cubic feet of sand needed to fill the space, we will need to calculate the volume of the space in cubic feet and then multiply it by the amount of sand needed to fill the space. To calculate the volume of the space, we will first convert the 6 inches to feet by dividing it by 12, which will give us 0.5 feet. We can then plug the numbers into the volume formula, which will look like this: 20 feet x 40 feet x 0.5 feet = 400 cubic feet. To find the amount of sand needed to fill the space, we will multiply the volume of the space by the amount of sand needed (which is usually 1.5 to 2 cubic feet per square foot). For this example, we will use 1.5 cubic feet. So to find  the amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.

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Answer:

Step-by-step explanation:

To keep the photo in proportion to its negative, you need to maintain the same aspect ratio, which is the ratio of the width to the height of the image. The aspect ratio of the negative is 5.4 cm / 1.35 cm = 4. To maintain this aspect ratio, the aspect ratio of the enlargement must also be 4.

The aspect ratio of the photo paper is 10.2 in / 2.4 in = 4.25. So, the largest length and width that you can use to keep the photo in proportion to its negative is 2.4 in * 4 = 9.6 in and 9.6 in / 4 = 2.4 in, respectively.

Answer:

Step-by-step explanation:

Conversion

First convert the dimensions of the photo paper to centimeters:

[tex]\implies \sf 10.2\;in=10.2 \times 2.54=25.908\;cm[/tex]

[tex]\implies \sf 2.4\;in=2.4 \times 2.54=6.096\;cm[/tex]

Therefore, the dimensions of the photo paper in centimeters are:

To determine the dimensions of the photo if the image is enlarged to fit on a 25.908 × 6.096 cm piece of photo paper, first calculate the scale factor by dividing the shortest side of the photo paper by the shortest side of the negative:

[tex]\sf Scale\;factor=\dfrac{6.096}{1.35}=4.51555...[/tex]

Multiply this scale factor by the longest side of the negative to determine the proportional length of the photo:

[tex]\implies \sf 4.51555...\times 5.4=24.384\;cm[/tex]

As 24.384 cm is less than the longest side of the photo paper, this scale factor will work to keep the photo in proportion to its negative.

Therefore, the largest length and width you can use to keep the photo in proportion to its negative is:

(a) The probability of having all six children be girls is (1/2)^6, or 1/64.
(b) The probability of having all six children be the same sex (either all boys or all girls) is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) The probability of having at least one boy is 1 - 1/64, or 63/64

The probability of having a child of a particular sex is 50%. Given a family with six children, we can calculate the probability of each event as follows:
(a) All the children being girls: the probability is (1/2)^6, or 1/64.
(b) All the children being the same sex (either all boys or all girls): the probability is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) At least one boy being in the family: the probability is 1 - (1/2)^6, or 63/64. This can be calculated by finding the probability of having no boys (all girls) and then subtracting it from 1.
In summary, the probability of having a particular outcome in a family with six children depends on the number of children of each sex and can be calculated using the formula (1/2)^n, where n is the number of children of a particular sex.


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Complete question:

Assume that the probability of the birth of a child of a particular sex is 50%. In a family with six children, find the probability of each event.

(a) All the children are girls.

(b) All the children are the same sex.

(c) There is at least one boy.

The estimate for the number of the paintings that are over 70 years old is given as follows:

56.

The histogram shows the number of observations that appear in each range of the data-set.

12 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

12/(3 x 2) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Hence the sum is given as follows:

22 + 22 + 12 = 56.

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The equation of a line is 3y + x - 15 = 0.

What is the equation of a line?

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.

Here, we have

Given: A(0,0), B(1,3)

The slope of AB = (3-0)/(1-0) = 3

The slope of a line perpendicular to AB = -1/3

y-intercept is 5

Equation of a line:

y - 5 = (-1/3)(x-0)

3y - 15 = -x

3y + x - 15 = 0

Hence, the equation of a line is 3y + x - 15 = 0.

Question: Given A(0,0) and B(1,3), find the equation of the line perpendicular to the y-intercept of 5

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The angle 1 and angle 2 are congruent by alternate interior angles.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

1. Angle1 and angle2 are complementary. angle2 and angle 3 are complementary.

= sum of these angles is 180 degree because they are linear angles

2. m angle1+ m angle2 = 90° m/2+m/3 = 90°

=There sum makes right angle

3. m angle1+ m angle2 = m angle2 + m angle3

= sum of both the sides is 180 degree

4. m angle2 = m angle2

= sum of both the sides is equal

5. m angle1= m angle3

= sum of both the sides is equal

6. angle1 congruent angle3

=They are alternate interior angles.

Therefore, by the triangles properties angle 1 and angle 3 are congruent.

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sum of the two polynomials is 5x^2 - 5x + 10. The two polynomials we are adding are:

− x 2 + 2 − x 2 + 2 and 3 x 2 − 7 x + 8

A polynomial is an expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication. The highest power of the variable in a polynomial is called its degree. In this case, both polynomials have degree 2, meaning the highest power of x is x^2.

When adding polynomials, we add the corresponding coefficients for each power of the variable. In this case, we have:

− x 2 + 2 + 3 x 2 = 2x^2

And:

− x 2 + 2 + 3 x 2 − 7 x + 8 = 2x^2 + 2 + 3x^2 - 7x + 8

= 5x^2 - 5x + 10

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Answer:

37/50

Step-by-step explanation:

Step 1) Multiply 7/10 by 5/5 to get 35/50

Step 2) Add 3/50 and 35/50

Step 3) 3/50+ 35/50= 37/50

The equivalent answer for the expression mentioned in question is 2x + 5y - 3.

Firstly we will solve the mentioned equation followed by checking each answer. Now, rewriting the equation provided in question -

3x + 5y - x + 2 - 5

Solving the values with x variable and without any variable. For this, we will perform subtraction of. the two pairs.

2x + 5y - 3

Now we see that second option is same as the solved part of the first answer. The first option has 3x and - 3x, which will eventually yield 0, further leaving the equation only with y variable. Therefore, it is the correct answer.

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Answer:-4/7y+4/7x

Step-by-step explanation:

Answer:

no they are not equal just look at the picture carefully and you will realise it's not equal

Answer:

y=1 1/2x

Step-by-step explanation:

y= mx+c

1st point : (2,3)

2nd point : (4,6)

m= 3-6/2-4

= -3/-2

= 1 1/2

y=1 1/2x

The variables t and d are best described by the speed S = d / t.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that During a road trip, Sterling keeps track of the time he spends driving, t, and the distance he drives, d.

The expression for the relation between the distance and the time will be calculated as:-

Speed = Distance / Time

Speed = d / t

Therefore, the speed S = d / t provides the best description of variables t and d.

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The solutions of the quadratic equation:

x^2 - 3x - 4 =0

are x = 4 and x = -1

Here we want to solve the quadratic equation:

x^2 - 3x - 4 =0

To do so, we just need to use the quadratic formula, remember that for:

a*x^2 + b*x + c = 0

The solutions are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Then in this case the solutions are:

[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4*1*-4} }{2*1}\\\\x = \frac{3 \pm 5 }{2}[/tex]

Then the two solutions are.

x = (3 +5)/2 = 4

x = (3 - 5)/2 = -1

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In many ways we can use the number -5.

-5 degrees Celsius or -5 degrees Fahrenheit can be used to represent temperatures below freezing. For example, if the outside temperature is -5 degrees Celsius, water will freeze.

Backward Counting: In mathematics, -5 can be used to count backwards from zero. For example, if we subtract 5 from 0, we get -5. This is frequently used when counting down from a starting number, such as in a countdown timer.

Credit Balance: A negative balance or debt owed in a financial account, such as a credit card or loan, can be represented by -5 in accounting. For example, if someone has a -5 dollar credit card balance, it means they owe the credit card company $5. it means they owe the credit card company $5 and have a negative balance on their account.

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Answer:

Parallel: m = -3/5
Perpendicular: m = 5/3

Step-by-step explanation:

First let's find the slope of the line.
To do so, we must make [tex]y[/tex] the subject of the line's equation. The slope would then be the coefficient of [tex]x[/tex].

[tex]3x + 5y = -1 \text{ // -3x} \\3x + 5y - 3x = -3x - 1\\\to 5y = -3x - 1 \text{ // :5}\\\\\frac{5y}5 = \frac{-3x - 1}5\\\\y = -\frac35x - \frac15[/tex]

Therefore, the slope of the line is [tex]m = -\frac35[/tex].

Parallel lines have similar slopes, therefore a line parallel to the line 3x + 5y = -1 would have a slope of -3/5.
If a line is perpendicular to our line, then its slope would be the negative invert of our line's slope. Therefore, its slope would be [tex]m = -\left(-\frac35\right)^{-1} \to -\left(-\frac53\right) \to \frac53[/tex]

Answer:

x = 49

Step-by-step explanation:

We can find the sum of the interior angles of a polygon using the formula

[tex]S_{n}=(n-2)*180[/tex], where n is the number of sides the polygon has.

Because the figure in the picture is a trapezoid and has four sides, we can find the sum of all the interior angles in the polygon by substituting 4 for n:

[tex]S_{4}=(4-2)*180\\ S_{4}=2*180\\S_{4}=360[/tex]

Since we know that the sum of all the angles in the trapezoid is 360, we can find x by subtracting the sum of the angles already given from 360:

[tex]x+118+104+89=360\\x+311=360\\x=49[/tex]

The probability that a randomly selected woman does not have red/green colorblindness is 99.08%.

The probability that a randomly selected woman does not have red/green colorblindness is calculated by subtracting the given rate of red/green colorblindness from 100%. The formula for this probability is P(not colorblind) = 100% - .92% = 99.08%. The calculation is 100% - .92% = 99.08%. Therefore, the probability that a randomly selected woman does not have red/green colorblindness is 99.08.

Therefore, The probability that a randomly selected woman does not have red/green colorblindness is 99.08%. This was calculated using the formula P(not colorblind) = 100% - .92%.

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The least positive integer we can get as the product is 2.

Here we have the following set of numbers:

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

And we want to take the product between 3 of them and find the least positive integer that we can get as the product.

So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)

Then we will get:

1*(-1)*(-2) = 2

That is the least positive integer we can get as the product.

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The probability of having an IQ score below the minimum Mensa IQ is 0.98, or the probability of having an IQ score above or equal to the minimum Mensa IQ is 0.02.

The features of the normal distribution can be used to determine the minimal IQ required to join Mensa if we assume that IQ scores follow a normal distribution. We can determine the IQ score that represents the 98th percentile of the IQ distribution because Mensa members make up the top 2% of all IQs.

We can determine the z-score for the 98th percentile using a typical normal distribution table, which is roughly 2.33. This indicates that the IQ score that is 2.33 standard deviations above the mean IQ is the minimal IQ required to join Mensa.

The formula: can be used if we are aware of the mean and standard deviation of the IQ distribution.

IQ equals (z-score) x standard deviation plus mean.

to determine the Mensa membership cutoff IQ. We are unable to determine the actual IQ score since the question does not include the mean or standard deviation of the IQ distribution.

The following is the probability statement for this issue:

P(IQ minimum Mensa IQ) = 0.02, or P(IQ minimum Mensa IQ) = 0.98, in other words. This indicates that the likelihood of having an IQ score below the minimum Mensa IQ is 0.98 and the likelihood of having an IQ score equal to or higher than the minimum Mensa IQ is 0.02.

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According to the values in the table, no, x and y does not have a proportional relationship. Therefore, the correct answer option is: B. no.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 93/1.1 ≠ 95/1.3 ≠ 98/1.6 ≠ 100/1.8

Since the constant of proportionality (k) for the relationship between the x-values and y-values are different, we can logically deduce that this is not a proportional relationship.

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Answer:

See table below.

Step-by-step explanation:

Enter each x value into the equation x^2+2x+5 to find the value of y.

For example, when x = -2:

x^2-2x+5

(-2)^-2(-2)+5  for x = -2  

4 + 4 + 5

y = 13

======

In the same manner:

x   y

-2  13

-1    8

0   5

1    4

2   5

3   8

Given the above values relative to the parallelogram, x = 2 and y = 1

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

Since the a parallelogram's diagonals are not all the same length, and they connect at the point of junction and have equal sides across the intersection, we can state that:
a

CG = EG and
FG = DG

Thus,
x+2y = 4; .........(1) and

3x-y = 5............(2)

Solving by substitution:

Let's make x the subject of the formula in (1)

x + 2y + (-2y) = 4 + (-2y)

x = -2y + 4 .......................................(3)

Substitute  (3) into (2)

Where (2)  is 3x-y = 5, thus;

3 (-2y + 4 )-y = 5.

-7y + 12 = 5

-7y + 12 -12 = 5 + -12
-7y = -1 (Divide both sides by -7)

y = 1    .............................(4)

Since y = 1, let's impute this in (1) x+2y = 4

x+2 (1) = 4
x = 4 -2

x = 2

Thus, x = 2, and y = 1

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Full Question;

Quadrilateral DEFC is parallelogram. Find x and y if CG = x + 2y, EG = 4, FG =3x-y, and DG = 5. Show your solution.​​

See attached image.

The Frequency table for grouped data using four classes are given in the table below.

The frequency table is to represent the data in the table form in which larger data are arranged according to their characteristics. In which frequency is the number which represents how many times the particular data occurs in it.

Here, there are 20 hours for each employee is given, we have to group into four classes.

Let us split the hours as,

0 - 5 ----this includes- 1,1,2,2,3,3,5(7 hours)

5 - 10---this includes - 8,10(2 hours)

10 - 15--this includes - 12,13,15,15(4 hours)

15 - 20-this includes - 17,18,18,19,19,20,20(7 hours)

(Note:This is exclusive classes i.e., upperlimit is not included)

Using this data the frequency table is constructed as shown below:

No. of hours              Frequency

     0 - 5                               7

     5 - 10                              2

    10 - 15                              4

    15 - 20                             7

Hence, the frequency table for the given data are grouped using four classes.

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Answer:

A. y = 1/2x + 3

Step-by-step explanation:

y = mx + b

m is the slope, b is the y-intercept

since 1/2 is the slope we now have

y = 1/2x + b

y-intercept is (0,3) which means b = 3 since 3 is the y value

y = 1/2x + 3