Determine the value of x and y in the following systems of equations. 3x+y=9 x-y=-1

The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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sin alpha= a/c

sin 23° = x/13

x= sin 23° ×13

x≈ 5.08

I hope this helps you

Hey there :)

Answer:

y = 4/5x - 2

Step-by-step explanation:

Begin by using the slope formula to calculate the slope:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in the coordinates into the equation:

\(m = \frac{6 - 2}{10 - 5}\)

Simplify:

\(m= \frac{4}{5}\)

Plug in the slope, as well as the x and y values of a point into the equation

y = mx + b to solve for the b value:

2 = 4/5(5) + b

2 = 4 + b

2 - 4 = b

b = -2.

Therefore, the equation of this line is:

y = 4/5x - 2

the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%

The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.

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Two fair dice are tossed, and the up face on each die is recorded.

The probability of observing each of the given events: are

P(A) = 1/3

P(B) = 5/18

P(C) = 1/2

A: The difference of the numbers is 2 or less.

The favorable outcomes for event A are when the difference between the numbers on the dice is 2 or less. We can have the following outcomes:

(1,1), (1,2), (2,1), (2,2), (1,3), (3,1), (2,3), (3,2), (3,3), (4,4), (5,5), (6,6)

So, there are 12 favorable outcomes for event A.

The total number of possible outcomes when two dice are tossed is 6 * 6 = 36.

Therefore, the probability of event A, P(A), is 12/36 = 1/3.

B: A 6 appears on exactly one of the dice.

The favorable outcomes for event B are when a 6 appears on exactly one of the dice. We can have the following outcomes:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6)

So, there are 10 favorable outcomes for event B.

Again, the total number of possible outcomes is 6 * 6 = 36.

P(B), is 10/36 = 5/18.

Therefore, the probability of event B,

C: The sum of the numbers is even.

The favorable outcomes for event C are when the sum of the numbers on the dice is even. We can have the following outcomes:

(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

So, there are 18 favorable outcomes for event C.

Once again, the total number of possible outcomes is 6 * 6 = 36.

Therefore, the probability of event C, P(C), is 18/36 = 1/2.

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Answer:

f in chat

Step-by-step explanation:

11

12

90

8

8

0

Answer:

19 minutes

Step-by-step explanation:

simply add the 2 highest years of experience and divide by 2 to obtain the average.

Bank B offers a higher return after 8 years. This is because compounding interest more often (daily in Bank B's case) will result in a higher total return. With Bank A, you would have earned $6,921.36 after 8 years, while with Bank B, you would have earned $6,964.76.

Interest is a fee paid by a borrower of money to a lender. It is most commonly calculated as a percentage of the principal loan amount, and is usually paid periodically at intervals, such as monthly or semi-annually. Interest can also be paid at the end of the loan period. Interest helps to compensate the lender for the time value of money and the risk associated with lending out funds. It is also a source of income for banks and other financial institutions. The interest rate on a loan is determined by the risk associated with the loan, the amount of money being borrowed, the creditworthiness of the borrower, and the current market interest rates.

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Bank A would provide a higher return of $3498.76 after 8 years as it has a higher rate 5.2% when compounded monthly and Bank B provides less return of $3183.22 after 8 years as it has a low rate of 4.8% when compounded daily.

Compound interest is actually interest on interest.

Compound interest(CI) annually = \(P(1+\frac{r}{100} )^n-P\)

To find compound interest monthly, rate is divided by 12 and time is multiplied by 12.

\(CI=P(\frac{1+r}{1200} )^{12t}-P\)

Similarly ,to find compound interest daily, the rate is divided by 365 and time is multiplied by 365 as 1 year consists of 365 days

\(CI=P(\frac{1+r}{36500} )^{365t}-P\)

Here the principal amount P=$6800

CI of Bank A at 5.2% interest and time 8 years compounded monthly

\(CI=P(1+\frac{5.2}{1200} )^{12\times 8}-6800\)

Simplify the equation,

\(=6800(1+\frac{5.2}{1200} )^{12\times 8}-6800\\\\=6800(1+\frac{1200+5.2}{1200} )^{12\times 8}-6800\\\\=6800(1+\frac{1205.2}{1200} )^{12\times 8}-6800\\\\=6800(1.00433)^{12\times 8}-6800\\\\=6800(1.51452)-6800\\\\=10,298.760-6800\\\\=3498.76\)

Compound interest from this bank A would be $3495.48

Now,CI of Bank B at 4.8% interest and time 8 years compounded monthly

\(CI=P(\frac{1+r}{36500} )^{365\times t}-P\)

Simplify the above equation,

\(=6800(1+\frac{4.8}{36500} )^{365\times 8}-6800\\\\=6800(1.00013151)^{365\times 8}-6800\\\\=6800(1.468)-6800\\\\=9983.22-6800\\\\=3183.22\)

Compound interest from this bank B would be $3183.22

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Answer:

coefficients- 3  2  -1

constant terms-  -1

like terms- 3r & 2r

Step-by-step explanation:

:)

Answer:

The slope is 2

Step-by-step explanation:

Every time the x unit goes up one the y unit is going up 2

Answer:

the amount of force is zero newton

Step-by-step explanation:

Given that

Mass of an object = 2kg

Constant speed of the object = 8m/s

We need to find out the amount of the force

As in the question it is mentioned that the speed is constant so there would be no change in the velocity due to this acceleration would be zero

Now following formula should be used to find out the force

Force = ma

As a = 0

f = 0

Therefore, the amount of force is zero newton

The probability of x being greater than 18 (p(x > 18)) is equal to the probability of x being less than 18 (p(x < 18)) in a normal distribution.

In a normal distribution, the probability of an event happening to the left of the mean (μ) is equal to the probability of the event happening to the right of the mean. This means that if we know the probability of x being less than 18 (p(x < 18)), we can use the property of symmetry to determine the probability of x being greater than 18 (p(x > 18)).

Since the probability distribution of x is symmetric around the mean, the area under the probability density function (PDF) to the left of the mean is the same as the area to the right of the mean. Therefore, we can say:

p(x > 18) = p(x < 18)

In other words, the probability of x being greater than 18 is equal to the probability of x being less than 18 in a normal distribution.

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Step-by-step explanation:

all can come

better to take 1,2,3

because triangle is of only three sides and we can construct a triangle according to the angle which we want

Answer:

7,24,25

Step-by-step explanation:

i got it right. i may be a little too late. but thats the answer

Answer:

i think 10 or 5

Step-by-step explanation:

To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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Answer:

Mark forgot to multiply 5 · 5, so he ended up with 5 in the denominator instead of 5 · 5 = 25

Step-by-step explanation:

Answer:

33.94 cms of ribbon

Step-by-step explanation:

Because you need two diagonals to form the x, therefore the amount  of ribbon needed is the sum of the distance of both diagonals.

When crossing the diagonal, a rectangular angle is formed, where the diagonal would be the hypotenuse, we know that the distance of the hypotenuse can be calculated by means of the legs, which we know its value (12):

d ^ 2 = a ^ 2 + b ^ 2

a = b = 12

d ^ 2 = 12 ^ 2 + 12 ^ 2

d ^ 2 = 288

d = 288 ^ (1/2)

d = 16.97

16.97 cm is what it measures, a diagonal, therefore tape is needed:

16.97 * 2 = 33.94

A total of 33.94 cms of ribbon is needed

Answer:

Answer is 34

Step-by-step explanation: Took the quiz and got it right.

The diagonals are 17.4 inches

From the question, we have the following parameters that can be used in our computation:

DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8

Given that DHB is a right triangle, we have

DB² = HB² + DH²

So, we have

DB² = (8.2 + 6)² + 10²

DB² = 301.64

Take the square root

DB = 17.4

The triangles DBY and RYB are congruent triangles

So, we have

RY = 17.4

The figure is an isosceles triangle, and the length does not meet the regulation

This is so because the length is less than the required 20 inches

The two non-parallel sides of an isosceles triangle are of equal length

So, we have

1/2x + 5 = 2x - 4

Evaluate the like terms

3/2x = 9

This gives

x = 9 * 2/3

x = 6

So, we have

KR = 1/2x + 5

This gives

KR = 1/2 * 6 + 5

KR = 8

So, the value of KR is 8 units

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First, we must find the total of females, it will be

Now we must look at the table how many females prefer suspense movies, it's

Now we do the quotient between the females that prefer suspense by the total of females:

Rounding it, we can say that approximately,

Or 20% of the females prefer suspense movies

Answer:

d

Step-by-step explanation:

The function is nonlinear. Linear is a straigt line and this function has a curve. You can find that by thinking of the story or placing it on a graph.

Answer:

d

Step-by-step explanation:

the answer is non-linear because a linear function  would only have the first part not 9x+4  

Answer:

false, we loose to much insight,it's in the tens I guess, good trade off between smoothing and insight

The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.

To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.

The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.

Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.

By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.

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To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

4,-4 I think

Step-by-step explanation:

My brain is off right now so might be wrong

The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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Answer:

13 (i think)

Step-by-step explanation:

Answer:

P = 17

Step-by-step explanation:

3y – 2 = y + 4

3y -2 (+2) = y + 4 (+2)

3y = y + 6

3y (-y) = y (-y) + 6

2y = 6

2y / 2 = 6 / 2

Y = 3

PR = 3y – 2

PR = 3(3) – 2

PR = 9 – 2

PR = 7

P of PQR = 4 + 6 + 7

P of PQR = 17

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Answer:

x=-17

Step-by-step explanation:

Answer:

\(3x - 17 = 4x \\ \\ 3x - 4x = 17 \\ \\ x = - 17\)

Answer:

6x6x55x5x5x2

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

According to the statement

we have to find that the rational numbers.

So, For this purpose, we know that the

Rational number, a number that can be represented as the quotient p/q of two integers such that q ≠ 0.

From the given information:

The given numbers are between -1/2 and 4/7

Then to find the numbers then

Rational numbers = (-1/2 +4/7) /2

Rational numbers = (-1 +2/7)

Rational numbers = -5/7.

And then the number becomes -6/7, 2/7,3/7.

Now, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

So, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

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