Find the general solution of the differential equation. (Enter your solution as an equation.)
y^3y’=6cos(pix)

the value of x in the isosceles triangle will be 36°.

What is an isosceles triangle ??

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

a) In the given triangle Δ the angles which are same given 72°

So the other angle will be 180 - 2(72) = 36°

Hence the value of x in the isosceles triangle will be 36°.

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The examination of the results of the two numerical articulations, 72 × 3 and 72 × 7, can be resolved utilizing the duplication administrator (×). 72 × 3 = 216 and 72 × 7 = 504.

While contrasting the results of these two expressions, we can see that 504 is more prominent than 216. This can be addressed as 504 > 216.

This implies that when 72 is duplicated by 7, the outcome is more prominent than when 72 is increased by 3.

This is on the grounds that 7 is a bigger number than 3, and thus, when it is increased by 72, the outcome will be bigger. All in all, the expression 72 × 7 delivers a more noteworthy worth than the expression 72 × 3.

All in all, the examination between 72 × 3 and 72 × 7 outcomes in 72 × 7 being more prominent than 72 × 3, or 504 > 216.

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The number of students who were wearing spirit wear at the assembly is = 120.

As given in Question that 3 out of 10 students were wearing spirit were.

if we have these type of Question then we will find the fraction part for 1 student as given 3 out of 10 then  the fraction part for 1 will be = 3/10 = 0.3

for 1 student there  is 0.3 fraction of students has wear spirit wear

so for 400 students were at the assembly

for 1 fraction is 0.3

for 400 = 400*(0.3 )= 120

Here 120 students were wear spirit wear in assembly

as like type we can solve for any number of students who were in assembly . like if there is 500 student the we can do like 500*.03 = 150 students.

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The statement "the two main methods used in inferential statistics is estimation and hypothesis testing." is True.

The two main methods used in inferential statistics are estimation and hypothesis testing.

Estimation involves using sample data to estimate the value of an unknown population parameter, such as the mean or standard deviation. The goal of estimation is to make inferences about a population based on a sample of data.

Hypothesis testing is a method used to make decisions about population parameters based on sample data. The goal of hypothesis testing is to determine whether a hypothesis about a population parameter is supported by the sample data, or whether there is enough evidence to reject the hypothesis.

In hypothesis testing, a null hypothesis is tested against an alternative hypothesis using a set of statistical tests and criteria. Both estimation and hypothesis testing play a crucial role in inferential statistics and are widely used in many fields, such as economics, psychology, biology, and others.

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The required ratio of the areas of the two similar figures is 16:9

What is the area?

The space found inside a 2D shape's perimeter is known as the area. It is expressed as square units like [tex]cm^2[/tex], [tex]m^2[/tex], etc. The area is the quantity of space an object takes up in a plane.

For the given similar figures,

The square of the ratio of the corresponding sides is equal to the ratio of the areas of two comparable figures.

The ratio of the areas of these rectangles would be

= [tex]\frac{(6+2)^2}{6^2} = \frac{64}{36} = \frac{16}{9}[/tex]

= 16:9

Hence, the required ratio is 16:9.

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The diagonal of a parallelogram bisects, so BE and DE are congruent, and AE is congruent with itself.

Assume that all four of it's angles at point E are 90°.

and Therefore, it is a congruence.

Triangles ABE and ADE are congruent through a side.

Therefore AB and AD are congruent.

Since opposite sides of a parallelogram are congruent, AD and BC are congruent and AB and CD are congruent.

Therefore all four sides are congruent. Therefore ABCD is a rhombus.

A parallelogram is a two-dimensional flat shape which is formed from two pairs of ribs and each of them is the same length and has two angles that are the same size in front of it.

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The correct answer is (a) Yes, because  we cannot use the binomial probability the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent

The probability of at least 30 adults out of 100 being left-handed can be calculated using the binomial probability formula with x counting the number who are left-handed. However, option (b) is not correct because the trials can still be considered independent even if the number of successes is greater than 5% of the sample size. The condition that the number of trials should be less than 5% of the population size is used to ensure that the sampling distribution can be approximated by a normal distribution.

Option (c) is also not correct because even though the sample was selected without replacement, the size of the population is much larger than the sample size, so the effect of the sampling without replacement is negligible.

Option (d) is not correct because we are interested in finding the probability of at least 30 left-handed adults, not the number of right-handed adults.

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Answer:

So the measure of angle Y is 50 degrees.

Step-by-step explanation:

By definition, complementary angles add up to 90 degrees. So we can set up the equation:

m∠S + m∠Y = 90

We also know that m∠S = 5(m∠Y) - 210. Substituting this into the first equation, we get:

5(m∠Y) - 210 + m∠Y = 90

Combining like terms, we get:

6(m∠Y) - 210 = 90

Adding 210 to both sides, we get:

6(m∠Y) = 300

Dividing both sides by 6, we get:

m∠Y = 50

So the measure of angle Y is 50 degrees.

The results of the multiplication of the binomials (x - 6)(x + 3) is x² - 3x - 28

The multiplication of binomials is the results of the products of two or more binomials.

(x - 6)(x + 3)

open parenthesis

= x² + 3x - 6x - 28

= x² - 3x - 28

Ultimately, the multiplication of the given binomials is x² - 3x - 28.

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The slope is 3/4.  It represent that for every 3 cup of brown sugar, 4 cup of butter is required

The y intercept is 0. This means that when no butter is used, no brown sugar is needed.

The equation is slope intercept form is y = (3/4)x

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

From the graph, using the point (4, 3) and (8, 6):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-3=\frac{6-3}{8-4}(x-4)\\ \\y=\frac{3}{4} x[/tex]

a) The slope is 3/4.  It represent that for every 3 cup of brown sugar, 4 cup of butter is required

b) The y intercept is 0. This means that when no butter is used, no brown sugar is needed.

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1. The value of h(1) is 24.5 m

2. The maximum height of the balloon is 39.59 m.

3. The balloon burst  after  5.5979 sec it hits the ground

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

h(t) = –4.9t² + 27t + 2.5.

1. For t= 1 hour

h(1) = –4.9(1)² + 27(1) + 2.5.

h(1) = 24.5m

2. Vertex formula (-b/2a, h(-b/2a))

Vertex = -27/ 2(4.9) = 2.755

So, h(2.755) = 39.59 m

3.–4.9t² + 27t + 2.5. = 0

solving the above equation for t we get

t= -0.877 sec

t = 5.5979 sec

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Answer:

The false statement is D) All kites are rectangles.

A kite is a quadrilateral with two pairs of adjacent sides that are congruent. A rectangle is a quadrilateral with four right angles and opposite sides that are parallel and congruent. While some kites can be rectangles (when the two pairs of congruent adjacent sides are also perpendicular), not all kites are rectangles. Therefore, statement D is false. Statements A, B, and C are true.

Step-by-step explanation:

The examples that represent the importance of determining the number of bacteria in a sample are determining the quality of milk, assessing the purity of food or water , testing to see if a patient has a bladder infection.

It is necessary to count the number of organisms present in a sample of a material, such as water, food, or a bacterial culture. Bacterial pathogens, for instance, can enter food at any point, including during growth/production at the farm, processing, handling, and packaging, as well as when the food is prepared in the kitchen . While pathogenic bacteria in tiny quantities are typically not harmful, poor storage and/or cooking practices can cause these germs to grow to dangerously high concentrations .Another method bacteria can be introduced into water is by faecal contamination . Gram-negative, non-spore-forming bacteria called coliforms can ferment lactose to create acid and gas. Fecal coliforms are a subset of these bacteria that are prevalent in both human and animal intestines. Other fecal coliform bacteria are frequently utilized as indicator species since they are rarely observed thriving in nature when there is no fecal pollution. The presence of E. coli signals the presence of feces, which raises the possibility of the presence of dangerous pathogens including Salmonella species and Campylobacter species.

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Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Given equation is ,

3^x - 3^{x-2} = 24

we can write it as,

3^x - (3^x/3^2) = 24

take out 3^x as common,

3^x ( 1 - 1/3^2) = 24

simplify,

3^x (1 -1/9)=24

3^x (9-1/9)=24

3^x * 8/9 = 24

3^x = 24 * 9/8

3^x = 27

3^x = 3^3

on comparing,

x = 3

and we are done!

Answer:

x = 3

Step-by-step explanation:

Given equation:

[tex]3^x-3^{x-2}=24[/tex]

Rewrite the exponent of the first term as (x - 2 + 2):

[tex]3^{x-2+2}-3^{x-2}=24[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]3^{(x-2)+2}-3^{x-2}=24[/tex]

[tex]3^{x-2}\cdot 3^2-3^{x-2}=24[/tex]

[tex]\textsf{Factor out the common term $3^{x-2}$}:[/tex]

[tex]3^{x-2}(3^2-1)=24[/tex]

Simplify the brackets:

[tex]3^{x-2}\cdot 8=24[/tex]

Divide both sides by 8:

[tex]3^{x-2}=3[/tex]

Apply the exponent rule a = a¹ :

[tex]3^{x-2}=3^1[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]x-2=1[/tex]

Add 2 to both sides of the equation:

[tex]x=3[/tex]

The minimum height of the cone is 17.87 in (approx)

In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.  

Total surface area, A = 2πr²+ 2πrh square units

The volume of the Cylinder, V = πr²h cubic units

Here we have

A cylindrical can with an open top is to be constructed so that

The volume of the cone is 167 in³  

As we know volume of cone = (1/3) πr²h

=> (1/3) πr²h = 167

=> h = 501/πr²  

As we know Surface Area of the cone = 2πrh + 2πr²  

Substitute h = 501/πr² in Surface Area of cone  

=> SA = 2πr(501)/πr² + 2πr²  

=> SA = 1002r⁻¹+ 2πr²        

Differentiate SA with respect to r

=> SA' = (-1) 1002r⁻²+ 4πr  

=> SA' = - 1002r⁻² + 4πr  

Here  - 1002r⁻² + 4πr = 0

=>  - 501r⁻² + 2πr = 0  

=>  - 501/r² + 2πr = 0  

=>  [-501 + 2πr³ ]/r² = 0

=>  [-501 + 2πr³ ] = 0  

=>  2πr³ = 501

=>  πr³ = 250.5

=>  r³ = 79.70

=>  r = 8.92  (approx)

Hence the height of the cone, h = 501/πr²    

= 501/π(8.92)

= 17.87 (approx)

Therefore,

The minimum height of the cone is 17.87 in (approx)  

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There is only one way to pick a president from 1000 number of professors, and that is to select one of the professors.

1. There are 1000 number of professors to choose from

2. The board of trustees can only pick one of the 1000 professors

3. Therefore, there is only one way to pick a president - select one of the professors.

The board of trustees can pick a president from the 1000 professors by considering their qualifications, experience, and other criteria. They can also take into account the opinion of the faculty and students of the college. If applicable, the board may also take into account any applicable legal requirements. Finally, they can make their selection by majority vote.

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The difference between the two diameters in meters for the red blood cells and the coarse grain of sand would be = 0.0000625meter

The diameter of red blood cell = 7.5 micrometers.

The diameter of coarse grain of sand = 70 micrometers.

The difference between the two = 70-7.5 = 62.5 micrometers.

To convert to micrometers to meters divide by 1000000;

That is 1 meter = 1000,000 micrometers

X meter = 62.5 micrometers

make X meters the subject of formula;

X = 62.5/1000000

X= 0.0000625 meter

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The probability of a randomly selected purchase having at most three tickets is  P(X ≤ 3). Option A

Probability is defined as a branch of mathematics that involves numerical descriptions of the likelihood of the occurance of an event, or how likely the possibility of the proposition.

The probability of an event is a number that is between 0 and 1.

Given that;

From the information given, we have that;

the probability of a randomly selected purchase having at most three tickets

This means that the probability is less than or equal to and not only less than ore greater than 3

Hence, the probability is P(X ≤ 3)

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Knowing the format of the series, such as the number of games and the requirements for series victory, is necessary to calculate the likelihood of winning the World Series (e.g., best-of-seven, first team to win four games, etc.).

Using the chance of winning any given game versus team B, which is given as 1/3, you would then need to compute the likelihood of winning each specific game.

The likelihood that team A will win the World Series may be computed as the total of the probabilities of winning each individual game, for instance, if the World Series is a best-of-seven series and team A wins each game with a probability of 1/3.

A binomial distribution, which simulates the number of successes in a certain number of Bernoulli trials with a fixed chance of success for each trial, can be used to do this.

It is impossible to calculate the likelihood that team A will win the World Series without further details about the World Series' structure and the results of each game.

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The first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.

Let's call the first of the three consecutive integers "x". The next two would then be "x + 1" and "x + 2".

According to the problem, the sum of the first two integers (x + (x + 1)) is 51 more than the third integer (x + 2), so we can write an equation:

x + (x + 1) = (x + 2) + 51

Expanding the left side and solving for x:

2x + 1 = x + 53

x = 52

So, the first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.

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Answer:

the second option

Step-by-step explanation:

the limit coming to x = 4 from the left (the '-' side) is -4.

the limit coming to x = 4 from the right (the '+' side) is 2.

it does not matter that the point itself is excluded. but the tendency of the function coming from the right is clear and defined.

the one-sided limit would not exist, if the function violently oscillates at the limit point.

or if the limit is infinite. then officially it does not exist, but we can write ±infinite.

for the case of the violent oscillation there is nothing else we can write but DNE.

No, they did not break the record. They were slower.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Barbara, Donna, Cindy, and Nicole ran in a relay race.

Their times are listed in the chart.

To break the school's record,

the girls' time had to be faster than 12[tex]\frac{2}{5}[/tex] minutes.

The time should be taken in the relay race,

33/10 + 14/5 + x + 21/10 = 62/60

x = 62/60 - 82/10

x = 43/6

Now,

43/6 + 33/10 + 14/5 + 21/10

= 15[tex]\frac{22}{60}[/tex]

Hence, they were slower.

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Answer:

  5, 7, 9

Step-by-step explanation:

You want three consecutive positive odd integers such that the square of the smallest exceeds twice the largest by 7.

Let x represent the middle of the integers. Then x-2 is the smallest, and x+2 is the largest. The given relation is ...

  (x -2)² -2(x +2) = 7

Eliminating parentheses gives ...

  x² -4x +4 -2x -4 = 7

  x² -6x -7 = 0 . . . . . . . . . subtract 7, simplify

  (x -7)(x +1) = 0 . . . . . . . factor

Values of x that make the factors zero are solutions to this equation:

  x -7 = 0   ⇒   x = 7

  x +1 = 0   ⇒   x = -1

The positive odd numbers are 5, 7, 9.

__

Check

5² -2(9) = 25 -18 = 7 . . . . as required

The values for each of the question is given below.

Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference, 'd'.

5. aₙ = 25.5 - 6.8n

a₁ = 25.5 - (6.8 * 1) = 18.7

a₂ = 25.5 - (6.8 * 2) = 11.9

a₃ = 25.5 - (6.8 * 3) = 5.1

a₄ = 25.5 - (6.8 * 4) = -1.7

a₁₀ = 25.5 - (6.8 * 10) = -42.5

6. aₙ = 25 - 10n

substituting the value of n and solving, we get,

a₁ = 15, a₂ = 5, a₃ = -5, a₄ = -15, a₅ = -25

7. aₙ = 11 + 9n

a₁ = 20, a₂ = 29, a₃ = 38, a₄ = 47, a₆ = 65

8. aₙ = 65 - 35n

a₁ = 30, a₂ = -5, a₃ = -40, a₄ = -75, a₉ = -250

The formula to find the nth terms of an arithmetic sequence is aₙ = a₁ + (n - 1)d

9. a₁ = 25, d = 100

aₙ = 25 + 100(n - 1)

a₂ = 125, a₃ = 225, a₄ = 325

10. a₁ = 5, d = 5

aₙ = 5 + 5(n - 1)

a₂ = 10, a₃ = 15, a₄ = 20

11. a₁ = 24, d = -15

aₙ = 24 - 15(n - 1)

a₂ = 9, a₃ = -6, a₄ = -21

12. a₁ = 9, d = -50

aₙ = 9 - 50(n - 1)

a₂ = -41, a₃ = -91, a₄ = -141

Hence each of the values are found.

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Answer: The perfect answer is 270x

Step-by-step explanation: I don’t really know but if I’d try I will say it’s:

For A: 10 x 12 x 9 x 6 x 15 = 97200

For B: 15 x 18 x ? x ? x X= 270x

97200 divided by 270x = 360x

Robert W. Fogel, in his famous article, used data from one year, 1890, to make inferences about a longer time period, 1850-1890. He did so through the use of statistical methods, including regression analysis and comparative economic growth analysis.

The basic idea behind this approach is to use the data from 1890 as a snapshot of the state of the economy at that time and to use this information to make inferences about the longer time period. The assumption behind this approach is that the data from 1890 is representative of the economy over the entire period 1850-1890, and that the underlying trends and patterns that existed in 1890 were also present in the earlier period.

Fogel used a combination of economic theory, demographic data, and historical information to validate his assumptions and to support his conclusions. He also conducted extensive sensitivity analysis to ensure that his results were robust to different assumptions and data sources.

In conclusion, while using data from one year to draw conclusions about a much longer time period might seem unconventional, it was a valid approach used by Robert W. Fogel in his research and allowed him to make important contributions to our understanding of the economic history of the United States.

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Answer:

Step-by-step explanation:

The semi-annual property tax bill is $2,987 and since it is semi-annual, he pays $2,987/2 = $1,493.5 each quarter.

So, each quarter he pays $1,493.5 + $334 = $1,827.5 for property taxes and homeowner's insurance.

And, each month he pays $1,827.5/3 = $609.17 for both property taxes and homeowner's insurance.

So, the total monthly payment he pays to North End Bank is $1,328 + $609.17 = $1,937.17.

a) The length of the rope left after tying the parcel is 260 cm

b) The original length of the rope was 305 cm.

The unitary method is a mathematical technique used to solve problems by breaking down the given information into smaller parts and finding the unknown value by using basic arithmetic operations.

(a) To find the length of the rope left after tying the parcel, we need to subtract the length of the rope used to tie the parcel from the original length of the rope.

Let's assume that the original length of the rope is x cm.

After Ravi tied the parcel, the remaining length of the rope is x - 45 cm.

(b) To find the original length of the rope, we need to use the information that the rope was cut into 4 pieces each 65 cm long.

Let's assume that the length of the rope left after tying the parcel is y cm.

Since the rope was cut into 4 pieces each 65 cm long, we have:

y = 65 x 4

y = 260 cm

And since the length of the rope left after tying the parcel is y cm, we have:

y = x - 45

So, the original length is

260 = x - 45

x = 305 cm

Complete Question:

Ravi had a rope. He used 45cm of the rope to tie a parcel. He then cut the remaining rope equally into 4 pieces. Each piece was 65cm long. (a) Find the length of the rope left after tying the parcel. (b) How long was the rope at first?

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The value of f(0) is 5.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given;

The graph

From the graph we can observe the value of function for various values.

When, x=0

y=5

Therefore, the answer of f(0) from the graph is 5.

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