Last month, sales were £180 000.

This month, sales reached £196 200.

What percentage increase is this?

The producer's surplus is 258.84.

Producer's surplus is a measure of the profit earned by a producer in a market. It is calculated as the difference between the price at which a producer is willing to supply a good and the actual market price. The formula for producer's surplus is PS = (P_e - MC) × Q_e, where P_e is the equilibrium price, MC is the marginal cost, and Q_e is the equilibrium quantity.

In this problem, the supply function is given by S(x) = √x+5, where x is the quantity of the item produced. The equilibrium point (x_e, P_e) is given as (40, 6.71). To find the producer's surplus, we need to first find the marginal cost.

The marginal cost is the additional cost incurred by producing one more unit of the good. In this case, it is the derivative of the supply function with respect to x, which is MC = S'(x) = 1/(2√x+5). Substituting x = 40, we get MC = 0.0905.

Now, substituting the values of P_e, Q_e, and MC in the formula for producer's surplus, we get PS = (6.71 - 0.0905 × 40) × 40 = 258.84. Therefore, the producer's surplus is 258.84.

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To calculate the percent of Container A that is empty after the pumping is complete, we need to calculate the volume of water in Container B and compare it to the volume of Container A.

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height.

Container A:

Diameter = 24 feet

Radius = Diameter / 2 = 24 / 2 = 12 feet

Height = 15 feet

Container B:

Diameter = 18 feet

Radius = Diameter / 2 = 18 / 2 = 9 feet

Height = 19 feet

Now let's calculate the volumes:

Volume of Container A = π * (12^2) * 15 ≈ 6785.4 cubic feet

Volume of Container B = π * (9^2) * 19 ≈ 4848.5 cubic feet

To find the percent of Container A that is empty, we can calculate the ratio of the empty space to the total volume:

Empty space in Container A = Volume of Container A - Volume of Container B

= 6785.4 - 4848.5

= 1936.9 cubic feet

Percent of Container A that is empty = (Empty space / Volume of Container A) * 100

= (1936.9 / 6785.4) * 100

≈ 28.5%

Therefore, to the nearest tenth, approximately 28.5% of Container A is empty after the pumping is complete.[tex][/tex]

Answer:

I think its 6.4 if you evaluate.

Step-by-step explanation:

Part A = Teddy did not properly arrange the words and fractions as it should be

Part B: Teddy can make 53 1/3 ornaments with 20 pounds of clay

To determine the value, we have that;

From the information given

Teddy has 20 pounds of clay

But to make an ornament, we have;

3/8 pound of clay  1 ornament

Then, using the law of proportion, we get;

If 1 ornament = 3/8 pound of clay

Then x = 20 pounds of clay

cross multiply the values

x = 20 ×8/3

x = 53 1/3 ornaments

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Answer:

3 or 4, im not 100% sure which one

Step-by-step explanation:

Answer:

----------------------------

Plot the points and connect.

See attached

As we can see this is a right isosceles triangle.

Prove by finding lengths and slopes:

Proved, as the slopes are negative reciprocals and distances are equal.

The triangle formed by the given vertices be acute angle triangle

The given vertices of triangle,

A(-3, -2), B(-1, 3), and C(2, -4)

We know that,

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ [(x₂ - x₁)² + (y₂ - y₁)²]

Now calculate the length of each side using the distance formula:

AB = √[(3 - (-2))² + (-1 - (-3))²]

     = √(29)

AC = √[(-4 - (-2))² + (2 - (-3))²]

     = √(29)  

BC = √[(-4 - 3)² + (2 - 1)²]

     = √(50)

     = 5√2

Now use the Law of Cosines to find the measure of each angle,

cos(A) = (BC² + AB² - AC²) / (2 BC AB)

cos(B) = (AC² + AB² - BC²) / (2 AC AB)

cos(C) = (BC² + AC² - AB²) / (2 BC AC)

Plugging in the values we calculated, we get:

cos(A) =  5√(2) / 58

cos(B) =  1 / √(58)

cos(C) = 5√(2) / 58

Now we can find the measure of each angle using the inverse cosine function:

A = [tex]cos^{-1}[/tex](5√(2) / 58) = 70.53 degrees

B = [tex]cos^{-1}[/tex](1 / √(58)) = 56.31 degrees

C = [tex]cos^{-1}[/tex](5√(2) / 58) = 70.53 degrees

Since all three angles are less than 90 degrees,

Hence, triangle ABC is an acute angle triangle.

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Using the confidence interval formula for the mean of normally-distributed data, the amount that a typical parent would spend on their child's birthday gift at a 98% confidence level is between $31.6 and $44.4.

The confidence interval formula is given as follows:

Formula

CI = xˉ ± z √(σ/ₙ)

Where

CI = confidence interval

xˉ = sample mean

z = confidence level value

σ = sample standard deviation

{n} = sample size

The number of survey participants, n = 19

The sample mean, xˉ = $38

Standard deviation, σ = $12

Confidence level = 98% = 2.33

Confidence Interval = 38 ± 2.33 √​12​/19

= 38 ± 6.42

= (31.58, 44.42)

= 31.6, 44.4

Thus, at 98% confidence level, we can conclude that a typical parent would spend between $31.6 and $44.4 on their child's birthday gift.

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The experimental probability that only 2 of the 4 children in the family are boys, from the number or desired outcomes is; P(Only 2 boys) = 0.45

Experimental probability is the computation of estimate of an event occurring based on actual experiments.

The number of outcomes that have exactly two heads = 9, which are;

HTTH, HTHT, HHTT, THHT, HTTH, HTHT, TTHH, THTH, HTHT

The total number of outcomes = 20

Therefore, the experimental probability of having only two boys is; 9/20 = 0.45

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The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer[tex]x = (739 - 625) / 3 = 38[/tex] surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

[tex]CS = \int_0^{38} [D(x) - 25] dx[/tex]

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

[tex]CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83[/tex]

Therefore, the consumer surplus is approximately $145.83.

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The zeros, their multiplicities and effects on the graph of the function f(x) = 2x(x+4)⁶(3x-2)³ are:

Zero      Multiplicity         Effect

x = 0            1                 Intersects

x = -4           6                 Bounces

x = 2/3         3                Intersects

To identify the zeros, their multiplicity, and the effect on the graph of the function f(x) = 2x(x+4)⁶(3x-2)³, we need to determine where the function equals zero and the multiplicity of each zero.

First, we set each factor equal to zero and solve for x:

2x = 0

Zero:

x = 0

Multiplicity: 1

(x+4)⁶ = 0

Zero:

x = -4

Multiplicity: 6

(3x-2)³ = 0

Zero:

x = 2/3

Multiplicity:

3

Now, let's analyze the effect (bounces or intersects) of each zero on the graph:

Zero:

x = 0

Multiplicity:

1

Effect:

The graph intersects the x-axis at x = 0.

Zero:

x = -4

Multiplicity:

6

Effect:

The graph bounces off the x-axis at x = -4 since the multiplicity is even.

Zero:

x = 2/3

Multiplicity:

3

Effect:

The graph intersects the x-axis at x = 2/3.

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Answer:

y= -2

Step-by-step explanation: x-10=0 move the - 10 to the other side it will be +10 s0 x=10

then use that value to solve the second equation

3*10 +5y=20

30 +5y=20

remember: anything that moves to the other side of the equation always invert its sign so +30 will be -30

5y= 20-30

5y= -10

y= -10/5

y= -2

the assumption being that he'll be deferring taxes on $2500 bucks, so is saving is that Da Tax Man is not going to bite him by 25% of that much.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 2500}}{\left( \cfrac{25}{100} \right)2500}\implies \text{\LARGE 625}[/tex]

Answer: the total length of sides 1 and 2 of the triangle is 2x² + 4.

Step-by-step explanation:

To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of the two sides together.

Given:

Side 1: 3x² - 4x - 1

Side 2: 4x - x² + 5

To find the total length, we add the lengths of Side 1 and Side 2:

Total length = Side 1 + Side 2

Total length = (3x² - 4x - 1) + (4x - x² + 5)

We can combine like terms:

Total length = 3x² - 4x - 1 + 4x - x² + 5

Combining like terms gives:

Total length = (3x² - x²) + (-4x + 4x) + (-1 + 5)

Simplifying further:

Total length = 2x² + 4

Therefore, the total length of sides 1 and 2 of the triangle is 2x² + 4.

Answer:

B. Angle 7 is an exterior angle.

Answer:

P(divisor of 20) = 2/3

Step-by-step explanation:

4 and 5 are both a divisor of 20. The numbers 4 and 5 make up 2/3 of the spinner, therefore the probability of spinning a divisor of 20 is 2/3.

Answer:

please see answers below

Step-by-step explanation:

Area of circle = π r ²

Circumference = π X D (D = diameter = 2 X radius)

Volume of sphere = (4/3) X π X r ³

Volume of prism = area of cross-section X length

Volume of cylinder (questions 6 and 7 are cylinders) = π r ² h

In a right-angled triangle, a ² + b ² = c ²

6) π (16) ² X 14 = 11259.47 in³

7) Diameter² = 40² - 32²

Diameter = √(40² - 32²) = 24. Radius = 12.

Volume = π (12)² X 32 = 14476.46 mm³

8) volume = 8 X 12 X 39 = 3744 ft³

9) cross-section (triangle) = 1/2 X 5.4 X 11 = 29.7

Volume = 29.7 X 16 = 473.6mm³

10) radius = 33/2 = 16.5

volume = (4/3) π (16.5)³ = 18816.57cm³

11) volume = (4/3) π (2.8)³ = 91.95m³

The mean absolute deviation of given data set is 1.11.

Mean = (4 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 9

Mean = 63 / 9

Mean = 7

The absolute deviations from the mean are:

|4 - 7| = 3

|6 - 7| = 1

|6 - 7| = 1

|7 - 7| = 0

|7 - 7| = 0

|8 - 7| = 1

|8 - 7| = 1

|8 - 7| = 1

|9 - 7| = 2

The sum of absolute deviations is:

= 3 + 1 + 1 + 0 + 0 + 1 + 1 + 1 + 2

= 10

The mean absolute deviation will be:

= Sum of absolute deviations / Number of data points

= 10 / 9

= 1.11.

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Answer: 1.true 2.false 3.alpha 4.greater

Step-by-step explanation:

Step-by-step explanation:

Greater than 4 means  it lands 5 or 6  or  1/3 of the possible rolls

  1/3 * 45 = 15 times

The ratio of the area of the circle to the area of the triangle is 2 : 1

Let

Area of Triangle = t

Area of Triangle Shaded = 2/3t

Area of Triangle not shaded = t - 2/3t

= 1/3t

Area of Circle = C

Area of Circle shaded = 5/6c

Area of Circle not shaded = C - 5/6c

= 1/6c

Area of Circle not shaded = Area of Triangle not shaded

1/6c = 1/3t

c/t = 1/3 ÷ 1/6

= 1/3 × 6/1

= 6/3

= 2/1

Hence, ratio of the area of the circle to the area of the triangle is 2 : 1

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The function f(x) = x + cos x on the interval [0.5π, 1.5π] fulfills Mean Value theorem.

In this problem we must check if a given function satisfy all conditions of Mean Value theorem. This theorem indicates that there is at least an x-value c such that f'(c) = [f(b) - f(a)] / (b - a).

First, determine the value of the first derivative of the function:

f(0.5π) = 0.5π + cos 0.5π

f(0.5π) = 0.5π

f(1.5π) = 1.5π + cos 1.5π

f(1.5π) = 1.5π

f'(c) =  (1.5π - 0.5π) / (1.5π - 0.5π)

f'(c) = 1

Second, find the x-values such that f'(c) = 1:

f'(c) = 1 - sin c

1 = 1 - sin c

sin c = 0

c = π · i, where i is a whole number.

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The function f(x) = x + cos x on the interval [[tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]]  has been found to fulfill the Mean Value theorem.

The mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

We from the scenario shown above check if a given function satisfy all conditions of Mean Value theorem .

This theorem indicates that there is at least an x-value c such that f'(c) = [f(b) - f(a)] / (b - a).

The first step is to determine the value of the first derivative of the function:

f(0[tex]\frac{\pi }{2}[/tex]) = [tex]\frac{\pi }{2}[/tex] + cos [tex]\frac{\pi }{2}[/tex]

f([tex]\frac{\pi }{2}[/tex]) = [tex]\frac{\pi }{2}[/tex]

f([tex]\frac{3\pi }{2}[/tex]) = [tex]\frac{3\pi }{2}[/tex] + cos [tex]\frac{3\pi }{2}[/tex]

f([tex]\frac{3\pi }{2}[/tex]) = [tex]\frac{3\pi }{2}[/tex]

f'(c) =  ([tex]\frac{3\pi }{2}[/tex] -  [tex]\frac{\pi }{2}[/tex]  ) / ([tex]\frac{3\pi }{2}[/tex] - [tex]\frac{\pi }{2}[/tex]  )

f'(c) = 1

Next, we find the x-values such that f'(c) = 1:

f'(c) = 1 - sin c

1 = 1 - sin c

sin c = 0

c = π .  i, where i is a whole number.

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Answer:

Here is the expected value for each type of ticket:

Regular ticket:

$20 \cdot 0.73 + $5 \cdot 0.27 = $16.60

Standby ticket:

$40 \cdot 0.27 + $15 \cdot 0.73 = $22.10

Therefore, Enzo should purchase standby tickets to maximize his expected value.

Here is the math behind the expected value calculation:

Regular ticket:

$20 \cdot 0.73 + $5 \cdot 0.27 = ($20 \cdot \frac{146}{200}) + ($5 \cdot \frac{54}{200}) = $16.60

Standby ticket:

$40 \cdot 0.27 + $15 \cdot 0.73 = ($40 \cdot \frac{54}{200}) + ($15 \cdot \frac{146}{200}) = $22.10

Step-by-step explanation:

The expression without the absolute value is x + 12.

Given expression with absolute value = |x + 12| if x>-11

Given expression has a condition which is the expression is having absolute condition only when the 'x' value is greater than -11.

So, the expression is x+12 is valid for the above expression without the absolute value because even if we substitute the x value as -11 in the equation the value of the equation will be still positive value only.

So, from the above analysis, the expression without the absolute value is x+12.

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The formula provides insights into the relationship between price and demand for Papa's Fried Chicken, indicating how changes in price affect the number of buckets of chicken sold.

From the formula b = 100 - 5p, we can infer the following:

The formula represents a linear relationship between the number of buckets of chicken sold (b) and the price per bucket (p).

The coefficient of p, which is -5, indicates that for every increase of 1 unit in the price, the number of buckets sold decreases by 5 units. Conversely, for every decrease of 1 unit in the price, the number of buckets sold increases by 5 units.

The intercept term of 100 represents the maximum number of buckets that can be sold at a price of 0. This suggests that there is a limit to the number of buckets that customers are willing to purchase, regardless of the price.

The formula assumes a downward-sloping demand curve, indicating that as the price increases, the quantity demanded decreases. This aligns with the typical behavior of most goods or services.

The formula implies that there may be an optimal price point where the number of buckets sold is maximized. Finding this price point would involve finding the value of p that maximizes the expression 100 - 5p.

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Answer:

Mario: Start at 6 and add x (x represents the number of miles walked by Mario).

Lila: Start at 12 and add y (y represents the number of miles walked by Lila).

Please note that the specific values to add for each student (x and y) are not provided in the question.

Step-by-step explanation:

To provide an accurate answer on how many minutes each group takes to tell a story, we would need specific information about the groups, the nature of their stories, and any predetermined time limits or guidelines for their storytelling sessions.

To determine the number of minutes each group takes to tell a story, we need additional information about the groups and the specific details of their storytelling. Without this information, it is not possible to provide an accurate answer.

The time taken to tell a story can vary greatly depending on various factors, including the length and complexity of the story, the style of storytelling, the pace of delivery, and individual or group dynamics. Additionally, the specific purpose or context of the storytelling can also influence the duration.

For example, a group of professional storytellers may have well-rehearsed and structured performances that adhere to specific time limits, such as 10 minutes or 20 minutes. On the other hand, a group of children sharing stories in a casual setting may take varying amounts of time, with some stories being shorter and others longer.

Furthermore, the storytelling format can also affect the duration. Some stories may be told orally, while others may include visual aids, props, or interactive elements that can extend the time required.

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note :

This is a english question

Step-by-step explanation:

y=kx

25= k(-5)

k= -5

y= -5x

y = -5 ×3 = -15