The demand and supply curves are given by y=10-3x³ and y=4+x²+2x (y represents the price and x quantity). Find the equilibrium price and quantity

The area of the composite figures are:

1: 106.28 sq. yd.

2: 79.27 sq. in.

3: 64.28 sq. m.

4: 44.82 sq. ft.

5: 406 sq. cm.

6: 629.46 sq. km.

To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

No. 1

Area = area of semicircle + area of rectangle + area of semicircle

Area = (1/2 * πr²) + (L*W) + (1/2 * πr²)

r = 6/2 = 3 yd, L = 13 yd and W = 6 yd

Area = (1/2 * π*3²) + (13*6) + (1/2 * π*3²)

Area = 14.14 + 78 + 14.14

Area = 106.28 sq. yd.

No. 2

Area = area of semicircle + area of triangle

Area = (1/2 * πr²)  + (1/2 *base* height)

r = 10/2 = 5 in, base = 10 in and height = 8 in

Area = (1/2 * π * 5²)  + (1/2 * 10 * 8)

Area = 39.27 + 40

Area = 79.27 sq. in.

No. 3

Area = area of square + area of semicircle + area of semicircle

Area =  L² + (1/2 * πr²) +  (1/2 * πr²)

L = 6 m,  r = 6/2 = 3 m

Area =  6² + (1/2 * π * 3²) +  1/2 * π * 3²)

Area =  36 + 14.14 + 14.14

Area = 64.28 sq. m.

No. 4

Area = area of semicircle + area of rectangle

Area =  (1/2 * πr²) + (L * W)

r = 5/2 = 2.5 ft, L = 7 ft and W = 5 ft

Area =  (1/2 * π * 2.5²) + (7 * 5)

Area =  9.82 + 35

Area = 44.82 sq. ft.

No. 5

Area = area of triangle + area of rectangle

Area =  (1/2 * base * height) + (L * W)

base = 10cm, height = 14 cm, L = 24 cm and W = 14 cm

Area =   (1/2 * 10 * 14) + (24 * 14)

Area =  70 + 336

Area = 406 sq. cm.

No. 6

Area = area of semicircle + area of triangle

Area =   (1/2 * πr²) + (1/2 * base * height)

r = 26/2 = 13 km, base = 28 km and height = 26 km

Area =   (1/2 * π * 13²) + (1/2 * 28 * 26)

Area =  265.46 + 364

Area = 629.46 sq. km.

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The option B, 0.0625, is the correct answer.

The probability that all children are boys is 1/2 × 1/2 × 1/2 × 1/2 = 1/16. The probability of the event is 0.0625. The probability that all the children are boys is 0.0625.Therefore, option B, 0.0625, is the correct answer.

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Answer: x = 100

Step-by-step explanation:

Answer:

d=50.3

Step-by-step explanation:

cos(29)/1=44/d

cos29d/cos29=44/cos29

d=50.31

d=50.3

Answer:

£5329.51

Step-by-step explanation:

Knowing that £6502 is the price with 22% profit, we can understand that £6502 is 122% of the original price meaning that the individual would have had to multiply their original value by 1.22 to get £6502!

To find our answer we, therefore, have to do the inverse...

Turning the value into money we round to 2d.p leaving our answer as...

Hope this helps, have a lovely day! :)

There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

There are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.

We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.

For the chemistry group, there are 3 students who can be seated in any order.

For the business group, there are 2 students who can be seated in any order.

For the political science group, there are 3 students who can be seated in any order.

Finally, for the journalism group, there are 4 students who can be seated in any order.

Therefore, the total number of arrangements for the 12 students is:

3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728

Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

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Answer: first off i am not a nerd ur just a dummyboi second  this is simple math grade 4 really the answer is 24

Step-by-step explanation:

In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.

In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.

In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.

In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.

19+8=27 if ur making a 3x3 cube answer is 24

In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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The length of AC in this right-angled triangular prism is approximately 60.66 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Height²+Base²

However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.

If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:

AC² = AE²+ EC²

We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:

EC = 51 cm and ED = 45 cm

Substituting this into the equation above, we get:

AC² = 43² + 51²

AC² = 3680

AC ≈ 60.66 cm (to 1 decimal place)

Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.

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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.

Base is ED 51 cm and height is AE 43 cm of the prism."

The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.

A gardener will use up to 250 square feet for planting flowers and vegetables, hence:

x + y ≤ 250    (1)

She wants the area used for vegetables to be at least four times the area used for flowers. Hence:

y ≥ 4x     (2)

Plotting both equations using geogebra, the solution is the darker region.

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We οbtain JN  44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly  44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.

The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.

The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.

Law of sines

sin(∠A)/a = sin(∠B)/b = sin(∠C)/c

Therefore,

39/sin(53°) = JN/sin(65°)

JN = (39×sin(65°))/sin(53°)

JN = 44.3

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Answer:

a₉ = - 24

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁ = 8 and d = - 4 , then

a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24

Answer:

Tn = a + (n - 1)d

T9 = 8 + (9 - 1) × -4

T9 = (8 + 8) × -4

T9 = 16 × -4

T9 = -64

Tia's statement that the graph is a x^5 function is correct

The statements from the question are:

The zeros and the multiplicities in the format (zero, multiplicity) from the question are (-3, 1), (-1, 2), (2, 1) and (3, 1)

The equation of the polynomial can be expressed as

P(x) = (x - zero)^multiplicity

When the zeros and the multiplicities are substituted, we have

P(x) = (x + 3)(x - 3)(x - 2)(x + 1)^2

Expand

P(x) = (x^2 - 9)(x - 2)(x + 1)^2

When evaluated, we have

P(x) = x^5 - 12x^3 - 2x^2 + 27x + 18

The above is a x^5 function

Hence, Tia is correct

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The values of g(x) for the given values of x are g(0) = 4, g(-7) = 3, g(-4) = 0

Functions can be used to model a wide range of real-world phenomena, such as physical laws, economic relationships, or biological processes. They are a fundamental concept in mathematics and play a central role in many fields, including engineering, physics, computer science, and statistics.

Functions can be represented graphically, algebraically, or numerically, and can be manipulated and analyzed using a variety of mathematical tools and techniques. By understanding how functions work and how to use them, people can solve problems, make predictions, and gain insights into a wide range of mathematical and real-world phenomena.

To evaluate the piecewise function at each value of the independent variable, we need to substitute the given value of x into the appropriate expression for g(x):

a. To find g(0), we use the first expression since 0 is greater than or equal to -4:

g(0) = 0 + 4

g(0) = 4

b. To find g(-7), we use the second expression since -7 is less than -4:

g(-7) = -(-7 + 4)

g(-7) = -(-3)

g(-7) = 3

c. To find g(-4), we need to consider both expressions since -4 is exactly equal to -4:

g(-4) = -(-4 + 4) (using the second expression)

g(-4) = 0 (simplifying)

or

g(-4) = -4 + 4 (using the first expression)

g(-4) = 0 (simplifying)

So, g(-4) is equal to 0 using both expressions.

Therefore, the values of g(x) for the given values of x are:

g(0) = 4

g(-7) = 3

g(-4) = 0

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Answer:

17,20,23...

Step-by-step explanation:

you just have to add 3 that's how the pattern works.

The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

Calculating the likelihood that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all other outcomes when a specific event occurs.

The bar graph displays how many times a number cube was rolled along with the outcome. The graph shows that the number cube was rolled 300 times in total, yielding the number larger than 1 200 times.

Experimental probability is calculated as follows: 200/300 = 0.6667, or 66.67%, where experimental probability = (number of times greater than 1)/(total number of rolls)

Theoretical probability is calculated as follows: 5/6 = 0.8333 or 83.33% (number of possibilities greater than 1) / (total number of possible outcomes).

The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

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Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).

To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.

Let x be the length of the road connecting towns B and C. Then we have:

x^2 = 61^2 + 60^2

x^2 = 3721 + 3600

x^2 = 7321

x ≈ 85.6 km

Therefore, the length of the road connecting town B and C is approximately 85.6 km.

Step-by-step explanation:

A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.

A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:

1, 3, 5, 7, 9

3, 5, 1, 7, 9

The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.

Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each term in the sequence (starting with the third term) is the sum of the two preceding terms.

This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.

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What is the arrangement of objects in a definite order called?

a. The population in this question is all the Cheapo Coffee stores around the country.

b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.

In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.

However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.

The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.

We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.

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Answer:

Any line with a slope of -2/3 that doesnt have an intercept of -3

Step-by-step explanation:

y = − 2/3x − 3 is written in slope-intercept form y = mx + b, where m is the slope, and b is the y intercept

What your looking for is a line with the same -2/3 slope

Important! If a line has the same slope AND intercept, then they are identical, not parallel

x + 3x + 2x = 180°

Being straight angle...

6x = 180°

[tex]x = \frac{180}{6} \\ [/tex]

x = 30°

Answer:

If m = -7 and n = 4, then we can substitute these values into the expression:

5m + 9n = 5(-7) + 9(4)

= -35 + 36

= 1

Therefore, 5m + 9n simplifies to 1 when m = -7 and n = 4.

Step-by-step explanation:

Answer:

The correct probability is 16/100, or 4/25.

The null hypothesis is that the mean weight of women is 145 lbs.The P-value is 0.0145. At a 0.05 significance level, the null hypothesis can be rejected. This suggests that the mean weight of women is not 145 lbs.

The null hypothesis is that the mean weight of women is 145 lbs. To test the hypothesis, we need to calculate the P-value. The mean of the sample of 40 weights is 153.2 lbs, with a standard deviation of 30.86 lb. The P-value is calculated using a z-score formula which is (153.2-145)/(30.86/sqrt(40)) = 0.0145. Since the P-value is less than 0.05, this suggests that the mean weight of women is not 145 lbs. Therefore, at a 0.05 significance level, the null hypothesis can be rejected.

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The value of line segment AC is 8√2

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

If the other two sides of the right triangle are a and b and the hypotenuse is c, then mathematically l, Pythagoras theorem can be written as:

c² = a²+b²

If CD = 4 and AD = 12, then AC will be

12² = (AC)² +4²

(AC)² = 12² - 4²

(AC)² = 144-16

(AC)² = 128

AC = √128

AC = 8√2

therefore the value of the line segment AC is 8√2

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The cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

(a) 0.974

(b) 0.998

(c) 0.996

(d) 2.571

(a) To find the proportion of the area under the curve to the right of t = 2.015, we first calculate the cumulative probability of t = 2.015 from the t-distribution table. The cumulative probability of t = 2.015 is 0.974, which means that 0.974 or 97.4% of the area under the curve lies to the right of t = 2.015.

(b) To find the proportion of the area under the curve to the left of t = −3.365, we calculate the cumulative probability of t = −3.365 from the t-distribution table. The cumulative probability of t = −3.365 is 0.998, which means that 0.998 or 99.8% of the area under the curve lies to the left of t = −3.365.

(c) To find the proportion of the area under the curve between t = –4.032 and t = 4.032, we calculate the cumulative probability of t = 4.032 and subtract the cumulative probability of t = −4.032. The cumulative probability of t = 4.032 is 0.995 and the cumulative probability of t = −4.032 is 0.003. Subtracting the two gives us 0.996, which means that 0.996 or 99.6% of the area under the curve lies between t = –4.032 and t = 4.032.

(d) To find the value of t that cuts off the upper 2.5% of the distribution, we calculate the cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

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Using variation, the model for F = 42(m/p)

There is a direct variation between the two variables whenever one quantity directly influences the other, such as when one quantity increases relative to the other and vice versa. There is a connection between two variables when one of them is a constant multiple of the other. Because of their immediate connection, the two variables are referred to as directly proportional.

Inverse variation establishes a proportionality between two quantities that are inversely related. There are two separate proportionalities. They are the direct variation and inverse variation. The two quantities are said to be directly proportional if an increase or decrease in one generates an equal increase or decrease in the other. In an inverse variation, on the other hand, one quantity increases while the other falls.

Now as F is directly proportional to m and inversely to p, so we can form a model as:

F = 42(m/p)

So that F=36 when m =6 and p =7.

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The interest compounded equation to model the given situation is A(t) = 4000[tex]e^{0.05t}[/tex].

To model the given situation, the interest compounded can be written as the given equation of:

A(t) = A0e^(rt)

Where:

A(t) is the amount of money after t years

A0 is the initial amount of money, in this case,

r is the interest rate expressed as a decimal

t is the time in years that the money is invested.

From the case, we know that:

Initial deposit = $4,000

Interest rate = 5%

Time period = t (undetermined)

So, substituting the values given in the problem, the equation to model the given situation is:

A(t) = A0e^(rt)

A(t) = 4000e^(0.05t)

Therefore, A(t) = 4000e^(0.05t) is the required equation that models the given situation.

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Answer: Diego's playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.

Based on the number of songs Diego has and the proportion of the genres, Diego's song classification is:

The number of songs from a particular genre is:

[tex]= \text{Total number of songs}\times\text{Percentage of genre}[/tex]

Rock:

[tex]= 40\% \times 90[/tex]

[tex]\bold{= 36 \ songs}[/tex]

Country:

[tex]= 10\% \times 90[/tex]

[tex]\bold{= 9 \ songs}[/tex]

Hip hop:

[tex]= 30\% \times 90[/tex]

[tex]\bold{= 27 \ songs}[/tex]

Electronica:

[tex]= (100\% - 40\% - 10\% - 30\%) \times 90[/tex]

[tex]\bold{= 18 \ songs}[/tex]

In conclusion, there are various genres on Diego's phone.

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Complete Question:

Diego has 90 songs on his playlist. How many songs are there for hip-hop?

40% rock

10% country

30% hip-hop

The rest is electronica