A first order linear differential equation is one that can be put in the form
dy/dx+P(x)y = Q(x) where
P and Q are continuous functions on a given interval. This form is called the standard form and is readily solved by multiplying both sides of the equation by an integrating factor

Answer:

A. x = 3

Hope this helps!! <3

Answer:

connotative meaning

Step-by-step explanation:

Answer:

connotative meaning

Step-by-step explanation:

I got ECHA... hope it's right:)

Rounding to 3 significant figures, we get DBC ≈ 338 degrees.

A triangle is a three-sided polygon with three vertices and three sides. It is one of the simplest and most fundamental shapes in geometry, and is used in many fields such as architecture, engineering, and physics. Triangles are named based on their sides and angles, and there are several types of triangles.

Types of Triangles:

Equilateral Triangle: A triangle with three equal sides and three equal angles, each measuring 60 degrees.

Acute Triangle: A triangle with three acute angles, meaning all angles are less than 90 degrees.

Obtuse Triangle: A triangle with one obtuse angle (greater than 90 degrees) and two acute angles.

The properties of triangles are important in geometry and trigonometry, where they are used to solve problems involving angles, sides, and area. The Pythagorean theorem, for example, relates the sides of a right triangle and is used to find the length of the hypotenuse (the longest side).

In addition, triangles have applications in fields such as engineering, architecture, and physics. The shape of a triangle is often used in the design of buildings and structures, such as bridges and roofs, because of its strength and stability.

In summary, a triangle is a three-sided polygon with three vertices and three sides. There are several types of triangles based on their sides and angles, and their properties are important in geometry, trigonometry, and other fields.

To find the size of angle DBC, we first need to find the size of angle BOC, since it is the central angle that intercepts arc BC.

Since the radius of the circle is 3.6 cm, the diameter is 2 times the radius, or 7.2 cm.

arc BC = (BC / diameter) x circumference of circle

arc BC = (4.1 / 7.2) x 2 x π x 3.6

arc BC ≈ 6.377 cm

Since BCD is 93 degrees, the size of arc BC is 360 - 93 = 267 degrees. Therefore, using the arc length formula, we can find the radius of the circle that subtends this arc as:

arc length = radius x angle in radians

6.377 = 3.6 x (267/360) x 2π

6.377 = 2.0996πr

r ≈ 1.920 cm

Now, we can find the size of angle BOC using the cosine rule, where a = b = 3.6 cm and c = 2r = 3.84 cm:

c^2 = a^2 + b^2 - 2ab cos(C)

(3.84)^2 = (3.6)^2 + (3.6)^2 - 2(3.6)(3.6) cos(93)

cos(93) ≈ -0.224951

(3.84)^2 = 2(3.6)^2 + 2(3.6)^2(0.224951)

cos(C) ≈ 0.3229

C ≈ 70.52 degrees

Since angle DBC is an exterior angle to triangle BOC, we know that:

DBC = BOC - BCD

DBC ≈ 70.52 - 93

DBC ≈ -22.48

Note that the negative answer indicates that angle DBC is actually a reflex angle, not an acute angle. To find the acute angle, we can add 360 degrees to the negative value:

DBC ≈ 337.52 degrees

Rounding to 3 significant figures, we get:

DBC ≈ 338 degrees.

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Answer:

Well there are 16 oz in every pound soooo the answer would be

4 pounds 3 ounces

Step-by-step explanation:

Answer: 11

Step-by-step explanation: Just took the test

The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here,
To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)
  = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

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Answer:70

Step-by-step explanation:

70 divided by 5 equals 14

We have,

= -6(3x - 2/3)

= -6(3x × 3 - 2)/3

= -6(9x - 2)/3

= -2(9x - 2)

= (-18x + 4)

Your answer will be option number 4.

Answer:

- 18x + 4

Step-by-step explanation:

\(-6(3x-\frac{2}{3})\)

- 18x + 4

Answer:

3.9

Step-by-step explanation:

pythagorean theorem states:

\(a^{2} +b^{2} =c^{2}\)

We know that a is the height of the triangle, 2.

We also know that b is the base of the triangle, 3.

So, solve for c:

2²+3²=c²

simplify

4+9=c²

15=c²

take the square root of both sides

c=3.9

So, the spider and the fly are 3.9 ft apart from each other

Hope this helps :)

Answer:

3.6 feet

Step-by-step explanation:

The Pythagorean theorem states that a^2+b^2=c^2, where c is the hypotenuse, or longest side of the triangle opposite to the right angle, and a and b are the two legs of the triangle (the other two sides.)

In the question, sides a and b are given as 2ft and 3ft long. Plugging 2 and 3 into the equation, we will get that 2^2+3^2=c^2. 2 x 2 = 4 and 3 x 3 = 9, so 4 + 9 = c^2, or, c^2 = 13.

However, this is still c^2, not c, so we must take the square root of both sides. This is because the equation is now essentially saying that c x c = 13, so if we find a number that when multiplied by itself equals 13, that number will be c. to do this, we must take the square root of 13. This will give us an irrational number- approximately 3.605551275. The question asks to round it to the nearest tenth though, so this will simply become 3.6.

In the context of this question, it means that the spider and the fly are 3.6ft apart.

Answer:

the answer is ç (3x+4)(x+7)

The area of the window is 49 10/12 square feet, which can be simplified to 49 5/6 square feet. The answer is (B) 49 5/6 ft2.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

The width of the window is 8 2/3 feet and the height is 5 3/4 feet. To find the area, we can simply multiply these two values:

Area = width × height

Area = (8 2/3 feet) × (5 3/4 feet)

First, we need to convert the mixed numbers to improper fractions:

8 2/3 = (8 × 3 + 2)/3 = 26/3

5 3/4 = (5 × 4 + 3)/4 = 23/4

Now, we can multiply the fractions:

Area = (26/3 feet) × (23/4 feet)

Area = (26 × 23)/(3 × 4) square feet

Area = 598/12 square feet

To simplify the mixed number, we can divide the numerator by the denominator:

598 ÷ 12 = 49 10/12

Therefore, the area of the window is 49 10/12 square feet, which can be simplified to 49 5/6 square feet. The answer is (B) 49 5/6 ft2.

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Answer:

half eaten pizza has greater circumference

Step-by-step explanation:

full eaten pizza's circumference = 2πr

= 2 * 3.14 * 7 = 43.96 inches

half eaten pizza's circumference = πd

= 3.14 * 20

=62.8 inches

Answer: The common factors for 30,70,60 30 , 70 , 60 are 1,2,5,10 1 , 2 , 5 , 10 . The GCF for the numerical part is 10 .

Step-by-step explanation:jfdcjtf

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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Maximum two hours of gaming a day is healthy.

What is meaning of healthy?

Not just the absence of illness or infirmity, but also a complete condition of physical, mental, and social well-being, is what is meant by "health."

Additionally, twice as many parents of teen boys than teen girls report that their son plays video games daily. Teenage guys are also more likely to play video games for three or more hours.

The American Academy of Pediatrics advises limiting screen-based entertainment to no more than two hours each day. According to Radesky, parents should make a "media plan" that specifies how much time a kid can spend playing video games without having an impact on their behavior or their schoolwork.

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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The average work of Mary per day for the whole week will be long 3.3 hours.

We have,

Total babysitting time during 5 days by Mary in past week = 16\(\frac{1}{2}\) hours,

i.e.

Total babysitting time during 5 days by Mary in past week = 16.5 hours ,

Now,

We know that,

Average is find out by dividing the sum of total numbers by the total numbers,

i.e.

Average = \(\frac{Total\ babysitting}{Total\ days}\)

So,

Now,

According to the question,

The average work per day of Mary  during past week = \(\frac{16.5 }{5}\) hours

On solving we get,

The average work per day of Mary  during past week  = 3.3 hours,

So,

Average work per day of Mary in the past week is 3.3 hours.

Hence we can say that the average work of Mary per day for the whole week will be long 3.3 hours.

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If the null hypothesis is true, we would expect approximately 156 of the 5200 test results to be statistically significant by chance alone.

If the null hypothesis is true, and we perform 5200 significance tests at a significance level of 3%, we can expect that 3% of these tests would result in statistically significant results by chance alone.

To calculate the expected number of statistically significant results, we can multiply the total number of tests (5200) by the significance level (3%).

Expected number of statistically significant results = 5200 * 0.03

Calculating this, we have:

Expected number of statistically significant results = 156

Therefore, if the null hypothesis is true, we would expect approximately 156 of the 5200 test results to be statistically significant by chance alone.

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Answer:

Multiply the two numbers and see what you get

Step-by-step explanation:

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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Answer:

9 inches

Step-by-step explanation:

(x + 2)² = 121

√(x + 2)² = √121

x + 2 = 11

x + 2 - 2 = 11 - 2

x = 9

Answer:

87

Step-by-step explanation:

common difference = d  = 2

an = a1 + (n-1)*d

a43 = 3 + 42*2  = 87

The $3 per unit subsidy will increase consumer surplus, decrease producer surplus, and increase total surplus. The $8 price floor will decrease consumer surplus, increase producer surplus, and decrease total surplus.

(a) To find the effect of a $3 per unit subsidy, we need to compare the equilibrium price and quantity before and after the subsidy. In the absence of the subsidy, the equilibrium price is determined by setting the demand equation equal to the supply equation:

7 - 0.5P = -2 + P

Solving for P, we find the equilibrium price P_eq = $5. The equilibrium quantity can be obtained by substituting this price back into either the supply or demand equation:

Q_eq = -2 + P_eq = -2 + 5 = 3 units

With the $3 per unit subsidy, the supply equation becomes Q = -2 + P - 3 = -5 + P. The new equilibrium price and quantity are determined by setting the demand equation equal to the new supply equation:

7 - 0.5P = -5 + P

Solving for P, we find P_subsidy = $6. The equilibrium quantity can be obtained by substituting this price back into the supply equation:

Q_subsidy = -5 + P_subsidy = -5 + 6 = 1 unit

To calculate the effects on consumer surplus (CS), producer surplus (PS), and total surplus (TS), we need to compare the areas of the relevant triangles. Before the subsidy, CS is the area above the demand curve and below the equilibrium price, PS is the area below the supply curve and above the equilibrium price, and TS is the sum of CS and PS. After the subsidy, CS expands, PS contracts, and TS increases.

(b) To find the effect of a $8 price floor, we need to compare the equilibrium price and quantity before and after the price floor. In the absence of the price floor, the equilibrium price and quantity remain the same as calculated in part (a): P_eq = $5 and Q_eq = 3 units.

With the $8 price floor, the market price cannot fall below $8. If the price floor is above the equilibrium price, it does not have any effect on the market. In this case, the price floor is below the equilibrium price, so it becomes binding. The new equilibrium price and quantity are determined by setting the supply equation equal to the price floor:

-2 + P_floor = 8

Solving for P_floor, we find P_floor = $10. The equilibrium quantity remains the same as Q_eq = 3 units.

To calculate the effects on CS, PS, and TS, we compare the areas of the relevant triangles. Before the price floor, CS is the area above the demand curve and below the equilibrium price, PS is zero because no units are being supplied, and TS is equal to CS. After the price floor, CS contracts, PS expands to include the entire area below the price floor and above the equilibrium quantity, and TS decreases.

In conclusion, the $3 per unit subsidy increases consumer surplus, decreases producer surplus, and increases total surplus. On the other hand, the $8 price floor decreases consumer surplus, increases producer surplus, and decreases total surplus. These effects can be visualized by comparing the areas of the relevant triangles in each scenario.

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the zeros of the quadratic function y = x² - 4x - 9 are x = 2 + √13 and x = 2 - √13.

ax²+bx+c=0, with a not equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, a quadratic equation  y = x² - 4x - 9

To find the zeros of the quadratic function y = x² - 4x - 9 by completing the square, we can follow these steps:

y = (x² - 4x) - 9

y = (x² - 4x + 4 - 4) - 9

y = (x - 2)² - 13

(x - 2)² - 13 = 0

(x - 2)² = 13

x - 2 = ±√13

x = 2 ± √13

Therefore, the zeros of the quadratic function y = x^2 - 4x - 9 are x = 2 + √13 and x = 2 - √13.

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Answer:

C

Step-by-step explanation:

The function \(f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}\) represents the stretch of an exponential decay function.

The process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula \(y = a(1-b)^{x}\)

where,

y is the final amount,

a is the original amount,

(1 -b) is the decay factor,

and x is the amount of time that has passed.

For a  exponential decay function (1-b) is always less than 1. If (1-b) < 1 it represents the exponential growth function.

And if a < 1, then it represents vertical compression and if a > 1, then it represents vertical stretch.

According to given question.

We have some functions in which we have to find the which one represents the decay function.

According to the function

\(f(x) = \frac{4}{5}(\frac{5}{4} )^{x} }\)

For the decay function, the decay factor will always less than 1. In the above function the decay factor \(\frac{5}{4}\) i.e. 1.25 is greater than 1.

Therefore, the above function doesn't represent decay function.

\(f(x) = \frac{4}{5}( \frac{4}{5} )^{x}\)

Here, a < 1 i.e.  \(\frac{4}{5}\) is less than 1 so the given function is not a stretch of an exponential decay function.

\(f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}\)

Here, b < 1 so it represents the exponential decay function. Also a > 1.

Therefore, the given function is the stretch of an exponential decay function.

\(f(x) = \frac{5}{4} (\frac{5}{4}) ^{x}\)

Here, a > 1 but b > 1. Therefore, the above function doesn't represent the exponential decay function. It represents the exponential growth function.

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Step-by-step explanation:

190 = 5

? = 30

30 / 5 = 6

190 x 6 = 1140

Answer:

B

Step-by-step explanation:

hope this helps with the work

Yes, if the bylaws of the corporation allow you to pool your votes and vote them all for a single candidate, you and your friends can ensure that your candidate for the board of directors wins, even with a minority of shares.

The bylaws of a corporation outline the rules and procedures governing its operations, including the election of directors. In some cases, the bylaws may allow shareholders to pool their votes and vote them all for a single candidate. This means that if you and your friends collectively own enough shares to secure a majority of the votes, you can consolidate your voting power and ensure the victory of your candidate.

By pooling your votes, you can leverage your collective shares to outweigh the votes of other shareholders and increase the chances of your preferred candidate winning. This strategy enables you to overcome the disadvantage of holding a minority of shares and still have a significant impact on the election outcome.

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Answer:

5/2.5

Step-by-step explanation:

Answer: -3/4 < -1/2 < 1/2 < 3/4

Step-by-step explanation: