Please help me solve this differential equation problem. Please show as many steps as you can.

Answer: 2(x-6) < -3(x-1) is x < 3.

Step-by-step explanation:
2(x-6) < -3(x-1)

Expanding the brackets, we get:

2x - 12 < -3x + 3

Adding 3x to both sides, we get:

5x - 12 < 3

Adding 12 to both sides, we get:

5x < 15

Dividing both sides by 5, we get:

x < 3

Answer:

x>12

Step-by-step explanation:

1/3(x-6)>2

distribute 1/3

1/3x-2>2

add 2 to both sides

1/3x>4

multiply both sides by 3

x>12

let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}} \implies \cfrac{1\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{ 7}{ 2} ~~}{\frac{5}{4}}\implies \cfrac{7}{2}\cdot \cfrac{4}{5}\implies \cfrac{7}{5}\cdot \cfrac{4}{2}\implies \cfrac{7}{5}\cdot 2\implies \cfrac{14}{5}\implies 2\frac{4}{5}\implies 2.8[/tex]

Using equations,

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15.

Many types of equations exist, including linear, quadratic, cubic, and others.

The quotient of 3 times a number and 7: 3n/7

5 less than a number is x:  x = n - 5

The sum of twice a number and 9: 2n + 9

Two times the sum of a number and 9: 2 (n+9)

The product of 3 times a number and 7: (3n) (7)

The difference between 5 and a number is x: 5 - n = x

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The inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

What is an inverse equation?

To find the inverse of the equation y = log(1/4)[tex]x^{5}[/tex], we can follow these steps:

Step 1: Interchange the x and y variables to obtain x = log(1/4)[tex]y^{5}[/tex].

Step 2: Solve for y in terms of x. To do this, we need to isolate the y term on one side of the equation. We can start by taking both sides of the equation to the power of 1/5:

[tex]x^{1/5}[/tex] = log(1/4)y

y = [tex](1/4)^{(1/log(x^(1/5)))}[/tex]

Step 3: Simplify the expression. Recall that [tex]a^b^{c}[/tex], so we can rewrite the exponent in the denominator as log([tex]x^{1/5}[/tex]) = (1/5)log(x). Substituting this into the expression for y, we get:

y = [tex](1/4)^{(1/(log(x^(1/5))))}[/tex]

 = [tex](1/4)^{(1/((1/5)log(x)))}[/tex]

 = [tex](1/4)^{(log(x)/5)}[/tex]

 = [tex]x^{(log(1/4)/5)}[/tex]

 = [tex]x^{(-log(4)/5)}[/tex]

 = 1/([tex]x^{(log(4)/5)}[/tex])

Therefore, the inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

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Complete question is: The inverse of the equation y = log(1/4)[tex]x^{5}[/tex] is x = 1/([tex]y^{(log(4)/5)}[/tex]).

The value of the angle m<C is 27 degrees. Option B

First, we need to know the different trigonometric identities and their ratios.

We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given in the diagram, we have;

Opposite side of angle C = 5

Adjacent side of angle C = 7.5

Hypotenuse side of angle C = 11

Using the sine identity

sin C = 5/11

sin C = 0. 4545

Take sine inverse

C = 27 degrees

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Answer:

1. The number of suite seats is 10% of the highest-priced seats, which is 10% of 92,000 = 9,200 seats.

2. The number of non-suite seats is 90% of the highest-priced seats, which is 90% of 92,000 = 82,800 seats.

3. The revenue generated from suite seats if all are purchased for one game is 9,200 x $200 = $1,840,000.

4. The revenue generated from non-suite seats if all are purchased for one game is 82,800 x $60 = $4,968,000.

5. The revenue earned at one sold-out game is the sum of the revenue from suite seats and non-suite seats: $1,840,000 + $4,968,000 = $6,808,000.

6. The net revenue of one sold-out game in which the nonconference team plays at the big stadium is the revenue earned at one sold-out game minus the payment to the nonconference team: $6,808,000 - $1,500,000 = $5,308,000.

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

When using multiple adjectives in a sentence, there is a general order that native English speakers tend to follow: opinion, size, age, shape, color, origin, material, purpose. This is known as the "OSASCOMP" order. However, this order is not always strictly followed, and there can be exceptions depending on the specific context or style of writing.

Answer:

It is False

Step-by-step explanation:

Answer: x= 24 and y= 73

Step-by-step explanation:

we know

The opposite interior angles are equal and

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
the sum of the interior angles of a parallelogram is 360 degrees.

So 107 + y = 180

180 - 107 = 73

Y = 73

y is equal to its opposite angle so

X can be found by 73 = 3x + 1

Subtract 1 from both sides

73 - 1 = 3x +1 -1

Simplify

72 = 3x

Divide both sides by 3 to solve for x

72/3 = 3/3x

x=24

Check your work by adding the 4 angles together to equal 360

107 + 107 + 73 + 73 = 360

360 = 360

They equal so your solution is correct

Answer: √698 or 26.42 (2 d.p.)

Step-by-step explanation:

Pythagoras' Threorem is a² + b² = c²

Substitute 13 for a and 23 for b

13² + 23² = x²

169 + 529 = x²

698 = x²

x = √698 = 26.42 (2 d.p.)

Answer:

The sonar station will not detect the submarine.

Step-by-step explanation:

The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.

The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:

[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]

[tex]\implies x^2+y^2=25[/tex]

To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.

[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]

Simplify:

[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]

[tex]\implies 9x^2+4x^2-104x+676=225[/tex]

[tex]\implies 13x^2-104x+451=0[/tex]

Solve the equation for x using the quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]

[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]

[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]

[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]

As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.

The area of the shaded region is 176 m² and area of compound shapes are 208 m² and 16 m².

What is rectangle?

A rectangle is a two-dimensional geometric shape with four straight sides and four right angles (90 degrees). It is a type of quadrilateral, which means it has four sides. The opposite sides of a rectangle are equal in length, and the adjacent sides are perpendicular to each other.

The formula for calculating the area of a rectangle is A = l x w, where "A" is the area, "l" is the length, and "w" is the width. The perimeter of a rectangle can be calculated by adding the lengths of all four sides, which is given by the formula P = 2(l + w).

Rectangles are commonly found in many aspects of everyday life, such as in buildings, furniture, electronic devices, and books. They can be used in architecture and engineering for creating stable and functional structures. In mathematics, rectangles are often used in geometry and algebraic expressions, as well as in statisticalanalysis and graphing.

Here we have a rectangle with length 16m and breadth 13 m.

Now, area of the rectangle is length × breath = 13×16 = 208 m².

And here we also have two square parts with side 4 m .

So, area of the square is side × side = 4×4 = 16 m².

Now, numbers of square are 2.

So, total area of two square is (2×16) = 32 m².

If we will subtract the total area of two square from area of the rectangle then we will get the area of shaded region .

So, area of the shaded region [tex] = 208 - 32 = 176 \: {m}^{2} [/tex]

Therefore, area of the shaded region is 176 m² .

Here compound shapes are one rectangle and two squares.

So, area of compound shapes are 208 m² and 16 m².

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Using the circumference formula the number of full revolutions the wheels need to make to travel 220 feet is obtained as 35.

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

The distance traveled by the car in one full revolution of the wheel is equal to the circumference of the wheel.

The circumference of a circle is given by the formula -

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Since the diameter of the wheel is 2 feet, the radius is half of that, or 1 foot.

Therefore, the circumference of the wheel is -

C = 2π(1 foot) = 2π feet

To find how many full revolutions the wheel needs to make to travel 220 feet, we can divide the distance traveled by the circumference of the wheel -

Number of revolutions = distance traveled / circumference of the wheel

Number of revolutions = 220 feet / (2π feet) ≈ 35.03

Therefore, the wheels need to make 35 full revolutions to travel 220 feet.

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Answer:

x = 24

Step-by-step explanation:

by the similarity theorem

the ratios of corresponding sides are in proportion , that is

[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{6}[/tex] ( cross- multiply )

6x = 9 × 16 = 144 ( divide both sides by 6 )

x = 24

The number is 300, as stated in the sentence. A histogram:

One common plotting instrument is the histogram. It is employed to present interval-scaled summaries of discontinuous or continuous data. It is commonly applied to easily represent the key features of the information's distribution.

To create a histogram of the weights of the miniature poodles, we would first divide the weight range into a series of intervals, or bins. The bin width should be chosen so that each bin has a similar number of observations.

According to the histogram and table: the height of a cell represents 10 15 ≤ x < 20: 120 ÷ 12=10

28 ≤ x <30 has 30 cells, so the frequency is 30 × 10=300

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We can use substitution to solve this system of equations. We can solve the first equation for y and get:

y = (2x + 12)/3

We can then substitute this expression for y into the second equation:

(2x + 12)/3 + 3x = -7

Multiplying both sides of this equation by 3 to eliminate the denominator, we get:

2x + 12 + 9x = -21

Simplifying this equation gives:

11x = -33

Dividing both sides by 11, we get:

x = -3

We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:

3y = 2(-3) + 12

3y = 6

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2.

To check the solution, we substitute these values back into both equations:

3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6

This equation is true, so the solution (x = -3, y = 2) checks out.

The equation for p is p + 6 = 14, which means that the number of pieces left is equal to the difference between the total number of pieces (14) and the number of pieces served (6).

Ron's mother bakes a pizza and divides it into 14 pieces. After serving 6 pieces to Ron and his friends, she has a certain number of pieces left. To determine this number, we can use the equation p + 6 = 14. This equation states that the number of pieces left (p) is equal to the difference between the total number of pieces (14) and the number of pieces served (6). Therefore, the equation for p is p + 6 = 14. By solving this equation, we can determine that the number of pieces left is 8. This means that Ron's mother has 8 pieces left after serving 6 pieces to Ron and his friends.

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Angle Y measures 125 degrees and angle Z measures 63 degrees.

what is a circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

Since quadrilateral WXYZ is inscribed in a circle, we know that opposite angles add up to 180 degrees. Therefore:

m∠Y + m∠W = 180 degrees ...(1)

m∠Z + m∠X = 180 degrees ...(2)

We are given that m∠W = 55 degrees and m∠X = 117 degrees, so we can substitute those values into equations (1) and (2):

m∠Y + 55 = 180 ...(1)

m∠Z + 117 = 180 ...(2)

Solving for m∠Y and m∠Z, we get:

m∠Y = 125 degrees

m∠Z = 63 degrees

Therefore, angle Y measures 125 degrees and angle Z measures 63 degrees.

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GCD (119, 378) = 7 and x = 25 and y = -6 is the value by using Euclidean alogorithm.

What does Euclidean algorithm mean?

By dividing the larger by the smaller, the smaller by the remainder, the first remainder by the second remainder, and so on, until an exact division is achieved, the greatest common divisor is the exact divisor. Euclid's algorithm is also known as.

by Euclidean division algorithm,

378 = 3 × 119 +21

119 = 5 × 21 + 14

21 = 1 × 14 + 7

14 = 2 × 7 + 0

Therefore 7 is GCD of 119 and 378.

so, GCD(119 , 378) = 119x + 378y = 7

now 7 = 119x + 378y

⇒7 = 7 × 13x + 7 × 54y

⇒1 = 13x + 54y

⇒13 × 25 + 54 × (-6) = 13x + 54y

on comparing we get, x = 25 and y = -6

Therefore GCD (119, 378) = 7 and x = 25 and y = -6

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Answer:

12.5

Step-by-step explanation:

9.6² + 2.8² = 10²

10² + 7.5² = 12.5²

Answer:

$38.40

Step-by-step explanation:

20% = 0.2

32 x 0.2 = $6.40

20% tip = $6.40

How much money should they leave for the bill and a 20% tip?

We take

32 + 6.40 = $38.40

So, they should leave $38.40 for the bill and a 20% tip.

The "loading" of the die makes P(1)=112, P(6)=312, and the following four outcomes equally likely. A roll with an even number larger than two has a 50% probability of occurring.

The probability of rolling an even number is 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes in total.

The probability of rolling a number greater than two is 5/6 since there are five outcomes (3, 4, 5, 6) greater than two and six possible outcomes in total.

To find the probability that the number rolled is both even and greater than two, we need to find the probability of rolling a 4 or a 6 since these are even numbers that are greater than two.

The probability of rolling a 4 is P(4) = 1/12 + 1/6 = 1/4 since the die is loaded to favour a 6 over the other numbers, but all other outcomes are equally likely.

The probability of rolling a 6 is P(6) = 3/12 = 1/4 since the probability of rolling a 6 is given as 3/12.

Therefore, the probability of rolling an even number that is greater than two is:

P(even and greater than two) = P(4 or 6) = P(4) + P(6) = 1/4 + 1/4 = 1/2.

So the probability of rolling an even number that is greater than two is 1/2.

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The probability of flipping heads is 1/2, and the probability of rolling an even number is 1/2 (since there are three even numbers and three odd numbers on the cube). To find the probability of both events happening (flipping heads and rolling an even number), we multiply the probabilities together:

1/2 x 1/2 = 1/4

So the probability that Olive flipped heads and rolled an even number is 1/4 or 25%.

Answer: 1/4

Step-by-step explanation:

10: Missing length, x = 16 cm

area of the composite figure = 240 cm²

perimeter = 72 cm

11: Missing length, x = 37 mm

area of the composite figure = 240 mm²

perimeter = 90 mm

To find the area and perimeter 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. 10

You will notice that the triangle is sharing one side with the square. And the length of the side is 12 cm. Thus:

x = √(20² - 12²)    (Pythagoras)

x = 16 cm

area of the figure = area of square + area of triangle

area of the figure =  L²  + (1/2 * base * height)

area of the figure =  12²  + (1/2 * 16 * 12)

area of the figure = 240 cm²

perimeter = 12 + 12 + 12 + 20 + 16 = 72 cm

No. 11

You will notice that the small triangle is sharing one side with the big triangle. And the length of the side is unknown. Let's call it y. Thus:

y = √(13² - 5²)    (Pythagoras)

y =  12 mm

x = √(35² + 12²)    (Pythagoras)

x = 37 mm

area of the figure = area of small triangle + area of big triangle

area of the figure =  (1/2 * base * height)   + (1/2 * base * height)

area of the figure =  (1/2 * 5 * 12) + (1/2 *  35 * 12)  

area of the figure = 240 mm²

perimeter = 5 + 13  + 37 + 35 = 90 mm

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The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.

According to the question:
The total number of balls in the bag is:

6 blue balls + 5 yellow balls + 4 green balls = 15 balls

The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:

P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)

P(blue or green) = (6 + 4) / 15

P(blue or green) = 10 / 15

P(blue or green) = 2/3

Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.


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Answer:

[tex]y=40\sqrt{\frac{6}{x} }[/tex]

[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]

Step-by-step explanation:

pls tell me if wrong have a good night/day

The confidence level is the probability that a confidence interval will contain the true population parameter in repeated sampling.

Confidence level is a statistical measure used to indicate the level of certainty or reliability in a statistical inference or estimate. In other words, it represents the success rate of the method used to construct a confidence interval. For example, a 95% confidence level indicates that if we were to repeat the same experiment many times and calculate the confidence interval for each trial, then we would expect 95% of these intervals to contain the true value.

The confidence level is typically chosen by the researcher based on the level of certainty they want to achieve. A higher confidence level corresponds to a wider confidence interval, which increases the likelihood of containing the true value, but reduces the precision of the estimate.

It is important to note that the confidence level does not guarantee that a particular confidence interval contains the true value, but rather it indicates the long-run success rate of the method used to construct the interval. Therefore, it is crucial to understand the underlying assumptions and limitations of the statistical method used to construct the confidence interval.

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The confidence level is a percentage between 0% and 100% that measures the success rate of the method used to construct the confidence interval. If we were to draw many samples and use each one to construct a confidence interval, then in the long run, the percentage of confidence intervals that cover the true value would be equal to the ________?