You have $4.75 in change in your pocket. You have a total of 34 nickels, dimes and quarters. If you have one more quarter than nickels how many of each kind of coin do you have? This is for matrics and solving systems.

Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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Answer: here’s the answer!

Step-by-step explanation: hope this helps!

Answer:

x=10

Step-by-step explanation:

3(x-2)+4=28

3x-6+4=28

3x-2=28

3x=30

x=10

The profit made from Thembile selling the second hand sewing machine if the cost price is R5700 and the selling price is R8850 is R3150.

Profit/loss refers to the difference between the cost price and selling price of an item. When the difference is positive; it is profit. When the difference is negative; it is loss.

Cost profit = R5700

Selling price = R8850

Profit = Selling price - Cost price

= R8850 - R5700

= R3150

Ultimately, Thembile made a profit of R3150 on the second hand sewing machine.

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

The greatest is 2,799

The lowest is 2,750

Step-by-step explanation:

Answer: The greatest whole number: 2799

The least whole number: 2750

Step-by-step explanation: I just went by the rule five or more round-up.

Answer: y = -x - 8

Step-by-step explanation: check the pic attached and lemme know if u dont get it :)

Calculate the slope of the line joining the points (1,1) and (-3,-1).

Use the equation m1m2=-1 to calculate the slope of the perpendicular line.

Given that, the line passes through the point (-3,4).

Use point slope form to calculate the equation of the line.

Therefore, the equation of the line is y=-2x-2.

Answer:

35&37

Step-by-step explanation:

Well 18% of 200 is 36 so...

Answer:13 x

Step-by-step explanation: bc i did the test

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

Answer:

Pull terms out from under the radical, assuming positive real numbers.

0

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

Possibly i'm not that great at math but this might be the answer.

The solution to the equation -2(x + 3) = -6 is x = 0.

To simplify the expression 5t + 7 + 8b, we can combine like terms.

There are two like terms in the expression: 5t and 8b.

Combining the like terms gives us:

5t + 8b + 7

Therefore, the simplified form of the expression 5t + 7 + 8b is 5t + 8b + 7.

Regarding the equation -2(x + 3) = -6:

To solve this equation, we can follow these steps:

Distribute the -2 to the terms inside the parentheses:

-2 * x + (-2) * 3 = -6

This simplifies to:

-2x - 6 = -6

Move the constant term to the right side by adding 6 to both sides of the equation:

-2x = 0

Divide both sides of the equation by -2 to isolate the variable x:

x = 0 / -2

Simplifying the right side of the equation gives us:

x = 0

The solution to the equation -2(x + 3) = -6 is x = 0.

The simplified expression 5t + 7 + 8b remains as 5t + 8b + 7, and the solution to the equation -2(x + 3) = -6 is x = 0.

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Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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The absolute value function that matches the graph is given as follows:

y = -|x + 1| + 1.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-1, 1).

Hence:

y = a|x + 1| + 1.

The function is reflected over the x-axis with a slope of -1, hence the leading coefficient a is given as follows:

a = -1.

Thus the function is:

y = -|x + 1| + 1.

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer: x = -2, \(\frac{2 }{3}\)

Step-by-step explanation:

     Given:

0 = –3x² – 4x + 4

    The quadratic formula:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

    Substitute known values:

* a = -3, b = -4, c = 4

\(\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-3)(4)} }{2(-3)}\)

    Simplify with multiplication:

\(\displaystyle x=\frac{4\pm\sqrt{16+48} }{-6}\)

    Simplify:

\(\displaystyle x=\frac{4\pm\sqrt{64} }{-6}\)

\(\displaystyle x=\frac{4+8 }{-6}\),    \(\displaystyle x=\frac{4-8 }{-6}\)

\(\displaystyle x=\frac{12 }{-6}\),    \(\displaystyle x=\frac{-4 }{-6}\)

Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

Answer:

a = 4.5

Step-by-step explanation:

In easy way you can understand by this simple way

if 4m half is 2m

so, 9m half is 4.5

in simple way answer

Answer:

21 inches

Step-by-step explanation:

If the boy is 25% smaller, that means his current height is 75% of his previous height. 75% of 28 is 0.75 * 28 which is 21.

Hope this helps :)

Answer:

35 inches tall. (This is assuming they want him to be 25% taller. Using the past tense of 28, I assume this is growth.)

Step-by-step explanation:

25% is 25/100 therefore we get 1/4 which gives us 28/4 = 7.

So this makes the boy 7 inches taller than 28.

28 + 7 = 35

Making him 35 inches tall.

9.

Q:-If the perimeter of an isosceles triangle is 83 cm. and its base is 23 cm. Find the measure of its equal sides.

Answer:- As we know that Perimeter is the sum of all sides.

Other two sides are 30 cm.

10.The perimeter of a rhombus is 5.6 cm. Find its side.

Answer:- As we know that

Side of Rhombus = Perimeter/4

11.The perimeter of a rectangle is equal to that of a square with side 17 m. If the length of the

The perimeter of a rectangle is equal to that of a square with side 17 m. If the length of therectangle is 26 m. What is its breadth ?

Answer:- Perimeter of square = 4 × s

Now,

12.What is the cost of fencing a rectangular field of length 16 m and breadth 11 m at the rate of 12 per m.

Answer:- Perimeter = 2(l + b)

Now,

\(\begin{gathered} \\ \end{gathered}\)

The probability P(not purple) is (a) 64%

From the question, we have the following parameters that can be used in our computation:

2 red, 4 green, 10 yellow, and 9 purple marbles.

This means that

P(not purple) = (not purple)/Total

Substitute the known values in the above equation, so, we have the following representation

P(not purple) = (2 + 4 + 10)/(2 + 4 + 10 + 9)

Evaluate

P(not purple) = 64%

Hence, the probability is 64%

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By dilation the square's new coordinates are W'(3, 2), X'(3, 4), Y'(1, 4), and Z' (1, 2).

Dilation is a transition in geometry that alters an object's size without altering its general shape. Given that it is a non-rigid transformation, the preimage and image are not congruent, and the distance between their points does not stay constant. Dilation can describe either a growth or a contraction in size1.

For instance, if we enlarge a square by a factor of 2, its area will increase by four times and each of its sides will be twice as long as before. A circle will have a radius that is three-fourths longer than previously and an area that is nine-sixteenths larger if we dilate it by a factor of 3/4.

In geometry, translation is a rigid transformation that maintains the size and shape of a figure while shifting each point by the same amount in a certain direction.

. To translate a square, we shift each corner to its new location by the specified distance.

Kevin translated the square in this instance by 3 units along the x-axis and -1 unit along the y-axis

. So, to obtain the new coordinates of the square W'X'Y'Z', we add 3 to each x-coordinate and remove 1 from each y-coordinate of the original square WXYZ.

- W'(3, 2) (3, 2)

- X'(3, 4) (3, 4)

- Y'(1, 4) (1, 4)

- Z'(1, 2) (1, 2)

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Answer:

For part D, x=5.217

Step-by-step explanation:

So essentially, all triangles have 180 degrees, so we an set up our equation as
55 + 8x + 15x + 5 = 180. We can simplify it to 60 + 23x = 180 by combining the like terms. Then we subtract 60 from both sides, getting us 23x = 120, and then we just divide 23 from both sides, and I just rounded the number to the thousandth place.

For part B, we an apply that same logic, and add 38 + 38 + 4x +... = 180. This gives us 76 + 4x+ ... = 180, and from there we just apply basic algebra. Hope this helps and lmk if you have and questions :D

Answer:

slope = \(-\frac{4}{3}\)  

Step-by-step explanation:

Use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\), to find the slope. \(m\) represents the slope. \(x_1\) and \(y_1\) represent the x and y values of one point, and \(x_2\) and \(y_2\) represent the x and y values of another point. So, substitute the x and y values of the points (-3, 4) and (0, 0) into the formula appropriately and solve:

\(m= \frac{(0)-(4)}{(0)-(-3)} \\m = \frac{0-4}{0+3} \\m = \frac{-4}{3}\)

Thus, the slope is \(-\frac{4}{3}\).

The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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