Find a synchronous solution of the form A cos Qt+ B sin Qt to the given forced oscillator equation using the method of insertion, collecting terms, and matching coefficients to solve for A and B.
y"+2y' +4y = 4 sin 3t, Ω-3
A solution is y(t) =

The inequality which represents the possible values for the number of peaches and mangos purchased will be;

⇒ $0.75p + $1.75m = $15

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Avni and her children went into a grocery store and will buy peaches and mangos.

Each peach costs $0.75 and each mango costs $1.75.

And, Avni has a total of $15 to spend on peaches and mangos.

Now,

Let number of peaches purchased = p

And, Number of Mangos purchased = m

Since, Each peach costs $0.75.

Hence, Total cost of peaches purchased = $0.75p

And, Each mango costs $1.75.

Hence, Total cost of mangos purchased = $1.75m

Since, Avani has a total of $15 to spend on peaches and mangos.

So, An inequality that would represent the possible values of peaches and mangos will be;

⇒ $0.75p + $1.75m = $15

Thus, The inequality which represents the possible values for the number of peaches and mangos purchased will be;

⇒ $0.75p + $1.75m = $15

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C .2/3

Step 1: Subtract 4/3 from both sides.

x+4/3-4/3=2-4/3

x=2/3

Answer:

0.290

Step-by-step explanation:

You just have to divide 3.49/12

If the outlier is removed, the following measures will change:

mean

range

a) Mean: Mean is the average of a set of numerical values. It is calculated by summing up all the values in the set and then dividing the sum by the number of values. The mean is a measure of central tendency and represents the typical value of a set of data.

b) Range: Range is a measure of dispersion and represents the difference between the largest and smallest values in a set of numerical data. It provides a quick and simple way to understand the spread of the data, and the difference between the extreme values. The range is calculated by subtracting the smallest value in the set from the largest value.

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Answer:

corresponding angles, alternate exterior angles

Step-by-step explanation:

when you have to parallel lines cut be a transversal, you get different pairs of angles that are either equal or supplementary (add to 180).

For example, corresponding angles are congruent, and alternate exterior angles are congruent.

The sum of angles in a 14 sided polygon is 2160°.

The sum of angles in a dodecagon is 1800°.

The sum of angles in a 16 sided polygon is 2520°.

The sum of angles in an equilateral triangle is 180°.

To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

Therefore, it can be represented as follows:

sum of interior angles = (n - 2)180

Hence,

sum of angles in 14 sided polygon = (14 - 2)180

sum of angles in 14 sided polygon = 180 × 12

sum of angles in 14 sided polygon = 2160 degrees

sum of angles in dodecagon polygon = (12 - 2)180

sum of angles in dodecagon polygon = 10 × 180

sum of angles in dodecagon polygon = 1800 degrees

sum of angles in 16 sided polygon = (16 - 2)180

sum of angles in 16 sided polygon = 14(180)

sum of angles in 16 sided polygon = 2520 degrees

sum of angles in equilateral triangle = 180 degrees

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Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

What is construction?

In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.

To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:

Step 1: Draw a circle with center C and point D on it.

Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.

Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.

Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.

Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.

Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.

To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.

Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

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The correct probability that Juan's bus is going to be late every week next week is 20 percent.

We have the total number in the stimulation on to be from 0 to 9

On the fact that it would be late, the number ranges from 2 to 9

Hence the fact that it would be late would be

2/10

= 0.2

0.2 is also the same as 20 percent.

Juan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:

• Let 0 and 1 = bus is on time

• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late

The table shows the results of the simulation.

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Answer:1/2

Step-by-step explanation:

2 heads

2 tails

2 + 2 = 4

heads - 2/4 - total

1/2

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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There is not enough evidence to conclude that the average time spent on leisure activities by American adults has changed. Sample standard deviation (s) is 8.984 hours. Sample mean (x') is 19.9 hours per week

To test whether the claim that American adults spend an average of 18 hours per week on leisure activities is true or false, we can conduct a hypothesis test.

First, we need to define the null and alternative hypotheses. Let µ be the population mean time spent on leisure activities by American adults.

Null hypothesis: µ = 18 hours per week

Alternative hypothesis: µ ≠ 18 hours per week

We can then calculate the sample mean and standard deviation from the data given as follows:

Sample mean (x') = (13+4+15+9+21+42+15+34+20+6) / 10 = 19.9 hours per week

Sample standard deviation (s) = 8.984 hours

Next, we can calculate the test statistic (t-value) using the formula:

t = (x' - µ) / (s / √(n))

where n is the sample size (10).

Using a t-distribution with 9 degrees of freedom (n-1), we can find the critical t-value at a 5% significance level to be ±2.306.

We calculate the t-value as:

t = (19.9 - 18) / (8.984 / √(10)) = 0.911

Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis.

In other words, the claim that American adults spend an average of 18 hours per week on leisure activities is not contradicted by the sample data.

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Answer:

y-3=-12(x-5)

Step-by-step explanation:

y-y1=m(x-x1)

y-3=-12(x-5)

Answer:

I hope this helps.

Step-by-step explanation:

Answer: its (4f 5) ^3

Step-by-step explanation:

As per the given equation, the cost for one hot dog and one drink is $2.75.

Let's begin by setting up some equations. Let H be the cost of one hot dog and D be the cost of one drink. We can use the information given in the problem to create two equations:

2H + 4D = 8 (equation 1)

3H + 2D = 7 (equation 2)

Equation 1 represents the cost of 2 hot dogs and 4 drinks, which is equal to $8. Equation 2 represents the cost of 3 hot dogs and 2 drinks, which is equal to $7.

To solve for H and D, we can use algebraic techniques such as substitution or elimination. Let's use substitution by solving equation 2 for D in terms of H:

2D = 7 - 3H

D = (7/2) - (3/2)H

Now we can substitute this expression for D into equation 1 and solve for H:

2H + 4[(7/2) - (3/2)H] = 8

2H + 14 - 6H = 8

-4H = -6

H = 3/2

We have found that one hot dog costs $1.50. To find the cost of one drink, we can substitute H = 3/2 into equation 2 and solve for D:

3(3/2) + 2D = 7

9/2 + 2D = 7

2D = 5/2

D = 5/4

We have found that one drink costs $1.25.

Then the cost for one hot dog and one drink is calculated as,

=> $1.50 + $1.25 = $2.75.

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Answer:

2x–5y = 12

2(–9)–5y = 12

–18–5y=12

–5y=12+18

–5y=30

y= –30/5

y= – 6

(x,y) —> (–9,–6)

Answer:

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  ( − 2 , − 1 )

Focus:  ( − 2 , − 3/ 4 )

Axis of Symmetry:  x = − 2

Directrix:  y = − 5 /4

x-intercept is -1

y-intercept is 3

vertex is (-2, -1)

axis of symmetry is x = -2

One of the most intriguing ideas in mathematics is called coordinate geometry.

As per the given data:

We have to find out the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function g(x) = x² + 4x + 3

For finding the graph of the given function, we must know its zeroes.

x² + 4x + 3 = 0

x² + 3x + x + 3 = 0

x(x+3) + 1(x+3) = 0

(x + 1)(x+3) = 0

The zeroes are -1 and -3.

The graph will be parabola in shape, as it is a quadratic equation.

From the graph:

x-intercept is -1

y-intercept is 3

vertex is (-2, -1)

axis of symmetry is x = -2

Hence, the values are as follows:

x-intercept is -1

y-intercept is 3

vertex is (-2, -1)

axis of symmetry is x = -2

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Answer:

26.0

Step-by-step explanation:

87.2-61.2= something

something is= 26

The multiplication equation which can be used to solve 1/6 divided by 5 is 1/30.

Reciprocal, represented by 1/x, is a number which when multiplied by x gives the result 1.

The reciprocal of 5 is 1/5.

We know that dividing a function is the same as multiplying by its reciprocal.

So, 1/6 divided by 5 is,

1/6 x 1/5 = 1/30

Hence, the multiplication equation which can be used to solve 1/6 divided by 5 is 1/30.

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Answer:

D) 40 degrees

Step-by-step explanation:

If ray BD bisects <ABC, then we have <ABD and <DBC. Both angles would be the same because the angle bisector theorem states an angle bisector is a ray in the interior of an angle forming two congruent angles. So, the answer is D) 40 degrees.

Answer:

?

Step-by-step explanation:

???????????????

Answer:

You just multiply what x was by 4 to get 4x

The side of the base of the rectangular box is √(100/5) cm.

Let's consider a rectangular box with a square base. We need to find the length of a side of the base, represented by the variable x.

The total surface area of the box is given as 100 cm². This includes the area of the base, which is a square with side length x, and the area of the four sides of the box.

The formula for the total surface area of a rectangular box is:

Total Surface Area = 2(base area) + 4(side area)

Given that the base area is a square with side length x, its area is x². The side area of the box is determined by the product of the length and width of the rectangle formed by the sides. Since the base is a square, the width is also x, and the length is represented by a different variable, which we'll denote as y.

Using the formula for the total surface area and substituting the known values, we have:

100 = 2(x²) + 4(xy)

Simplifying the equation, we get:

100 = 2x² + 4xy

Now, since the base is a square, its side length is equal to x. Therefore, the length and width of the rectangle formed by the sides are x and y, respectively. Since the opposite sides of a rectangle are equal, we have y = x.

Substituting y with x in the equation, we get:

100 = 2x² + 4x²

100 = 6x²

Dividing both sides of the equation by 6, we have:

16.67 = x²

Taking the square root of both sides, we get:

x ≈ √(16.67)

Therefore, the side of the base of the rectangular box is approximately √(16.67) cm, which simplifies to approximately √(100/5) cm.

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Answer:

(2,5)

Step-by-step explanation:

Coordinates means where the numbers line up to the point.

So first you go to the x-axis and look for te number that leads to the point and you do that with the y-axis too and you get (2,5) as the coordinates.

(a) Opposite sides of a rectangle are equal, that is, AD = BC and AB = CD.

(b) The diagonals of a rectangle are equal, that is, AC = BD.

Let's consider a rectangle ABCD, where AB || DC and AB ⊥ AD. We know that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well. Therefore, AD ⊥ AB and AD ⊥ BC. Similarly, BC ⊥ AB and BC ⊥ AD.

So, we have two pairs of perpendicular sides, and from the Pythagorean theorem, we can calculate their lengths as follows:

AD² = AB² + BD² and BC² = AB² + CD²

Since AB = CD (opposite sides of a rectangle), we can substitute AB for CD and simplify:

AD² = AB² + BD² and BC² = AB² + AD²

Taking the square root of both sides of each equation, we get:

AD = √(AB² + BD²) and BC = √(AB² + AD²)

Since AB = CD and AD = BC, we can conclude that opposite sides of a rectangle are equal.

Let's continue with rectangle ABCD from part (a) and draw its diagonals AC and BD. We can use the Pythagorean theorem again to calculate their lengths:

AC² = AD² + DC² and BD² = AB² + BC²

Since AB = CD and AD = BC (opposite sides of a rectangle), we can substitute and simplify:

AC² = AD² + AB² and BD² = AD² + AB²

Taking the square root of both sides of each equation, we get:

AC = √(AD² + AB²) and BD = √(AD² + AB²)

Since both equations simplify to the same expression, we can conclude that the diagonals of a rectangle are equal.

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The equation is \(y=-87(x-1)^{2} (x-3)^{3}\).

What is meant by zeroes of polynomials?

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.

It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.

So, the equation is \(y=a(x-1)^{2} (x-3)^{3}\).

We will substitute x=2 and y= 87 in the above equation.

\(87=a(2-3)^{3} \\a=-87\)

Therefore now the equation will be:

\(y=-87(x-1)^{2} (x-3)^{3}\).

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The statement that is TRUE based on the given facts is that the customer's fixed income portfolio has experienced a greater decline in value than the decrease in the Consumer Price Index (CPI).

To elaborate, the customer's fixed income portfolio has dropped by 5% over the past 4 years. This means that the value of their portfolio has decreased by 5% compared to its initial value. On the other hand, the Consumer Price Index (CPI) has dropped by 2% during the same period. The CPI is a measure of inflation and represents the average change in prices of goods and services.

Since the customer's portfolio has experienced a decline of 5%, which is larger than the 2% drop in the CPI, it indicates that the value of their portfolio has decreased at a higher rate than the general decrease in prices. In other words, the purchasing power of their portfolio has been eroded to a greater extent than the overall decrease in the cost of goods and services measured by the CPI.

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The series ∑(k=1 to infinity) k ln(k) / (k^2 + 3) diverges.

To test for convergence or divergence, we can use the comparison test or the limit comparison test. Let's use the limit comparison test.

First, note that k ln(k) is a positive, increasing function for k > 1. Therefore, we can write:

k ln(k) / (k^2 + 3) >= ln(k) / (k^2 + 3)

Now, let's consider the series ∑(k=1 to infinity) ln(k) / (k^2 + 3). This series is also positive for k > 1.

To apply the limit comparison test, we need to find a positive series ∑b_n such that lim(k->∞) a_n / b_n = L, where L is a finite positive number. Then, if ∑b_n converges, so does ∑a_n, and if ∑b_n diverges, so does ∑a_n.

Let b_n = 1/n^2. Then, we have:

lim(k->∞) ln(k) / (k^2 + 3) / (1/k^2) = lim(k->∞) k^2 ln(k) / (k^2 + 3) = 1

Since the limit is a finite positive number, and ∑b_n = π^2/6 converges, we can conclude that ∑a_n also diverges.

Therefore, the series ∑(k=1 to infinity) k ln(k) / (k^2 + 3) diverges

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Answer:

5

This is essentially the third identical question that you posted with the same

type of solution ... if you look at the previous question you asked and the explanation.. you will see that the red line crosses a corner of a box at (4,20)

4 cups =  20 pralines thus the number you are looking for is 20/4 = 5

Step-by-step explanation:

lets try this "story" to explain...

assume that you can walk 3 miles in 1 hour

this means that at 0 hr you go 0 miles , 1 hr you go 3 miles etc

0,0

1,3

2,6

3,9

etc.

if you graph that you will have the red line in you graph, and the x values would be 0,1,2,3 with the y values being 0,3,6,9....

if you DIVIDE any of those points

3/1 ,6/2, 9,3 the result is always a "3" that is the speed that you are walking at

it is a CONSTANT (in this problem) ... note: if the speed is NOT constant then this basically becomes a calculus problem, ant an algebra one.