For the motion given by the equations x1 = X1 cosωt + X2 sinωt,
x2 = −X1 sinωt + X2 cosωt,
x3 = (1+kt) X3,
​
where ω and k are constants, determine the displacement field in Eulerian form.

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Problem 2.20: From the given statement:

1. If he was killed before noon, then his body temperature is at most 20°C.

We can conclude that if the person's body temperature is not at most 20°C, then he was not killed before noon.

Problem 2.17:

The truth table for (P∧(P→Q))→Q is as follows:

| P | Q | P→Q | P∧(P→Q) | (P∧(P→Q))→Q |

|---|---|-----|---------|-------------|

| T | T |  T  |    T    |      T      |

| T | F |  F  |    F    |      T      |

| F | T |  T  |    F    |      T      |

| F | F |  T  |    F    |      T      |

From the truth table, we can conclude that the statement (P∧(P→Q))→Q is always true regardless of the truth values of P and Q.

Problem 2.18:

(a) From the statements given, we can determine the following:

- If Alan is telling the truth, then Bernard didn't do it, and Charlotte is guilty.

- If Bernard is telling the truth, then Alan and Charlotte are guilty, or Charlotte acted alone.

- If Charlotte is telling the truth, then all three of them are guilty.

Since exactly one person is lying, and exactly one person committed the crime, we can conclude that Bernard is the guilty party.

(b) If exactly one person committed the crime and all the students are lying, it means that their statements are all false. In this case, we cannot determine the guilty party based on their statements alone.

Problem 2.19:

To show that if two statements, P and Q, are equivalent, then their negations, ¬P and ¬Q, are also equivalent, we need to prove that (P↔Q) implies (¬P↔¬Q).

We can prove this using the laws of logical equivalence:

(P↔Q) ≡ (¬P∨Q)∧(P∨¬Q) (equivalence of ↔)

Taking the negation of both sides:

¬(P↔Q) ≡ ¬((¬P∨Q)∧(P∨¬Q))

Using De Morgan's laws and double negation:

¬(P↔Q) ≡ (P∧¬Q)∨(¬P∧Q)

This is equivalent to (¬P↔¬Q), which shows that ¬P and ¬Q are also equivalent.

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Answer:

8

Step-by-step explanation:

Y) -8 x -4 = 32

X) -2 x -4 = 8

Answer:

X=8

hope this helps =3

sorry if im wrong

Answer:

8

Step-by-step explanation:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 64: 1, 2, 4, 8, 16, 32, 64

They share 1, 2, 4, and 8. 8 is the greatest digit in this case therefore it's your final answer.

The required greatest common factor of 24 and 64 is 8.

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include.

Here,
Factors of the number 24 and 64 is given as

24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24

64 ⇒ 1, 2, 4, 8, 16, 32, 64,

Pick the common factor,
= 1, 2, 4, 8,
Among the common factors, 8 is the greatest number,

Thus, the required greatest common factor of 24 and 64 is 8.

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Answer:

y = 2/3 x + 5/3.

Step-by-step explanation:

Slope m = (3-1)/(2-(-1)) = 2/3.

y - y1 = m(x - x1)

y - 1 = 2/3(x - (-1))

y - 1 = 2/3(x + 1)

y - 1 = 2/3 x+ 2/3

y = 2/3 x + 5/3.

There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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Ms. Adams did not invest any amount in the municipal bond or certificate of deposit. She placed the entire $15,000 in the money market account.

Let's break down the information given and solve the problem step by step: Let's assume:

Amount invested in the municipal bond = x

Amount invested in the certificate of deposit = 2x (twice the amount of the municipal bond)

Balance of the money invested in the money market account = Total amount invested - (amount in municipal bond + amount in certificate of deposit)

Interest from the municipal bond:

Interest = Principal (amount invested) × Rate × Time

Interest = x × 0.056 × 1 (assuming 1 year)

Interest from the municipal bond = 0.056x

Interest from the certificate of deposit:

Interest = Principal (amount invested) × Rate × Time

Interest = (2x) × 0.042 × 1 (assuming 1 year)

Interest from the certificate of deposit = 0.084x

Interest from the money market account:

Interest = Principal (amount invested) × Rate × Time

Interest = (Total amount invested - (amount in municipal bond + amount in certificate of deposit)) × 0.038 × 1 (assuming 1 year)

Interest from the money market account = (Total amount invested - 3x) × 0.038

Given that the total interest for one year is $635, we can set up the equation:

Interest from the municipal bond + Interest from the certificate of deposit + Interest from the money market account = Total interest

0.056x + 0.084x + (Total amount invested - 3x) × 0.038 = 635

Simplifying the equation:

0.056x + 0.084x + 0.038(Total amount invested - 3x) = 635

0.056x + 0.084x + 0.038Total amount invested - 0.038(3x) = 635

0.056x + 0.084x + 0.038Total amount invested - 0.114x = 635

0.056x + 0.084x - 0.114x + 0.038Total amount invested = 635

-0.026x + 0.038Total amount invested = 635

To solve for Total amount invested, we need the value of x. Let's rearrange the equation to solve for x:

0.038Total amount invested = 0.026x + 635

Total amount invested = (0.026x + 635) / 0.038

Substituting the value of Total amount invested in the equation:

0.056x + 0.084x - 0.114x + 0.038((0.026x + 635) / 0.038) = 635

Simplifying the equation further:

0.056x + 0.084x - 0.114x + 0.026x + 635 = 635

Combining like terms:

0.052x + 635 = 635

Subtracting 635 from both sides:

0.052x = 0

Solving for x:

x = 0 / 0.052

x = 0

Since x = 0, it means that Ms. Adams did not invest any amount in the municipal bond.

Now, to find the amounts invested in the certificate of deposit and money market account:

Amount invested in the certificate of deposit = 2x = 2 * 0 = 0

Amount invested in the money market account = Total amount invested - (amount in municipal bond + amount in certificate of deposit)

Amount invested in the money market account = Total amount invested - (0 + 0)

Amount invested in the money market account = Total amount invested

Therefore, all $15,000 was placed in the money market account.

In conclusion, Ms. Adams did not invest any amount in the municipal bond or certificate of deposit. She placed the entire $15,000 in the money market account.

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Micah's boxplot is incorrect because the statistical summary given by his boxplot is inaccurate.

The boxplot is a better at analysing the data as it gives more statistical output of the data than the histogram.

We need to write out the number of times taken by each student,

From the histogram; the data values are :

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 10, 10, 10

Using a boxplot maker or excel, we could create a boxplot of the data and compare with that given in the question.

5 number summary of Micah's boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 9 (Position of upper whisker)

Lower quartile = 3(starting point of box)

Upper quartile = 8 (endpoint of box)

Median = 5 (vertical line in between box)

Outlier = 10

5 number summary of correct or accurate boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 10 (Position of upper whisker)

Lower quartile = 2 (starting point of box)

Upper quartile = 8.2 (endpoint of box)

Median = 4.5 (vertical line in between box)

Outlier = None

Comparing the box plots, it can be concluded that Micah did not create the boxplot correctly.

The probability that the proportion of airborne viruses in a sample of 679 viruses would be greater than 8% is approximately 0.

To solve this problem,

Use the normal approximation to the binomial distribution.

We can assume that the sample proportion of airborne viruses follows a normal distribution with mean equal to the true proportion of 7% and standard deviation given by:

√(7%*(1-7%)/679) = 0.0155

Then, we want to calculate the probability that the sample proportion is greater than 8%.

Standardize the distribution as follows:

(z-score) = (sample proportion - true proportion) / std deviation (z-score)

              = (8% - 7%) / 0.0155

              = 64.52

Using a standard normal table, we can find the probability that a z-score is greater than 64.52, which is essentially 1.

Therefore, the probability of the sample proportion being greater than 8% is approximately 0.

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When x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

In the given question, we have to find what is remainder when x^3+2x^2+x+1 is divided by (x+1).

To find the remainder there are two ways. First we divide the x^3+2x^2+x+1 by (x+1). Second we find the value of from (x+1) by equating (x+1) equal to zero. The put the value of x in the expression x^3+2x^2+x+1.

In this we ca easily find the remainder.

Now we firstly find the value of x;

(x+1) = 0

Subtract 1 on both side we get;

x= −1

Now put x= -1 in the expression x^3+2x^2+x+1.

x^3+2x^2+x+1 = (−1)^3+2(−1)^2+(−1)+1

x^3+2x^2+x+1 = −1+2−1+1

x^3+2x^2+x+1 = 1

Hence, when x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

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The right question is:

What is remainder when x^3+2x^2+x+1 is divided by (x+1)?

Answer:

13•5ft

Step-by-step explanation:

1cm = 4.5ft

3cm = x

cross multiply

x= 3×4•5

:- x = 13•5ft

Answer:

x = - 1 or x = 5

Step-by-step explanation:

(x - 2)² = 9 ( take the square root of both sides )

x - 2 = ± \(\sqrt{9}\) = ± 3 ( add 2 to both sides )

x = 2 ± 3

Then

x = 2 - 3 = - 1 or x = 2 + 3 = 5

If the total value of his change is 620 cents, the man has 12 dimes and 20 quarters in his pocket.

Let's assume that the man has x dimes and y quarters in his pocket. We know that he has 32 coins in total,

x + y = 32.

We also know that the total value of his change is 620 cents, which can be expressed as

10x + 25y = 620.

To solve for x and y, we can use either substitution or elimination. Let's use substitution. Solving the first equation for x, we get

x = 32 - y.

Substituting this into the second equation, we get

10(32 - y) + 25y = 620

Simplifying this equation, we get

320 - 10y + 25y = 620

which yields

15y = 300.

Therefore, y = 20, and x = 32 - 20 = 12.

So the man has 12 dimes and 20 quarters in his pocket. We can check that this is correct by verifying that

12(10) + 20(25)

= 120 + 500

= 620.

In summary, we can solve the problem by setting up a system of equations, either using substitution or elimination to solve for the variables, and then checking our answer to make sure it is correct.

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Answer:

3 + 2k

Step-by-step explanation:

1/5(15+10k)

distribute

1/5 * 15 + 1/5 * 10k

3 + 2k

Answer:

3 + 2k

Step-by-step explanation:

First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:

a(b + c) = ab + ac

We can apply the distributive property to the expression 1/5(15 + 10k):

1/5(15 + 10k)

= (1/5)(15) + (1/5)(10k)

= 3 + 2k

By using the distributive property, we found the expression 3 + 2k.

I hope you find my answer helpful.

Answer:

Quiz - Quizizz

Q. In an exponential function, what does the 'a' represent? ... Q. What is a, the starting term, for the function: f(x) = 800(0.85)x? ... In the equation y=2(5)x , the a value (y-intercept) is.

Missing: r ‎| Must include: r

Answer:

V = Bh

Step-by-step explanation:

Answer:

v=lwh

v=bh

Step-by-step explanation:

edge2020

Over the course of 72 months, he will have paid back approximately $7,993.46 against the amount borrowed.

To calculate the total amount Pham will have paid back, we need to consider the principal amount, interest rate, and the duration of the loan.

The formula for compound interest is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, Pham borrowed $6,000 with a 6% interest rate compounded annually. The interest is compounded once a year, so n = 1. The loan duration is 72 months, which is equivalent to 6 years.

Plugging the values into the formula, we have A = 6000(1 + 0.06/1)^(1*6). Simplifying this equation, we get A = 6000(1.06)^6. Evaluating the expression, we find A ≈ $7,993.46.

Therefore, Pham will have paid back approximately $7,993.46 over the 72-month period to repay the loan.

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The particular solution or explicit general solution for y(1) = 4 is \(y = (6/5)(x - 1/25) + (356/125)e^(-5x)\)

To find the general solution of the differential equation xy' + 5y = 6x, we can use the method of integrating factors. First, we rearrange the equation to isolate the derivative term:

xy' = 6x - 5y

Now, we can see that the coefficient of y is 5. To make it easier to integrate, we multiply the entire equation by the integrating factor, which is e^(∫5dx) =\(e^(5x):\)

\(e^(5x)xy' + 5e^(5x)y = 6xe^(5x)\)

The left side of the equation can be simplified using the product rule:

(d/dx)(\(e^(5x)y) = 6xe^(5x)\)

Integrating both sides with respect to x, we get:

\(e^(5x)y\) = ∫6x\(e^(5x)dx\)

To find the integral on the right side, we can use integration by parts:

Let u = 6x (differential of u = 6dx)

Let dv =\(e^(5x)dx (v = (1/5)e^(5x))\)

Applying integration by parts, we have:

∫6\(xe^(5x)dx\)= uv - ∫vdu

= 6x(1/5)\(e^(5x)\) - ∫(1/5)\(e^(5x) * 6dx\)

= (6/5)\(xe^(5x)\) - (6/5)∫\(e^(5x)dx\)

\(= (6/5)xe^(5x) - (6/5)(1/5)e^(5x) + C\)

\(= (6/5)e^(5x)(x - 1/25) + C\)

Plugging this back into the equation, we have:

\(e^(5x)y = (6/5)e^(5x)(x - 1/25) + C\)

Dividing both sides by \(e^(5x),\) we get:

\(y = (6/5)(x - 1/25) + Ce^(-5x)\)

This is the general solution to the differential equation.

To find the particular solution for y(1) = 4, we substitute x = 1 and y = 4 into the equation:

\(4 = (6/5)(1 - 1/25) + Ce^(-5)\)

Simplifying the equation, we get:4 = \((6/5)(24/25) + Ce^(-5)\)

\(4 = 144/125 + Ce^(-5)\)

Subtracting 144/125 from both sides:

\(4 - 144/125 = Ce^(-5)\)

\(500/125 - 144/125 = Ce^(-5)356/125 = Ce^(-5)\)

Dividing both sides by \(e^(-5),\) we get:

\(356/125e^5 = C\)

Therefore, the particular solution for y(1) = 4 is:

\(y = (6/5)(x - 1/25) + (356/125)e^(-5x)\)

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Answer:

the third one

Step-by-step explanation:

3

Answer:

The third one

Step-by-step explanation:

3

Answer: answer for what?

Step-by-step explanation: oh I see it appeared iN wrong catogory I’m browsing History sorry

The sum of all the angles that are labeled in the given vertex is 294°

In a single vertex, the three angles around the vertex are given as 55°, 64°, and 175°

We have to find the sum of all the angles that are labeled in the given single vertex.

A vertex is a point two or more lines meets.

It is the corner of a geometrical shape.

Example:

A square has 4 corners so it has 4 vertexes.

A cube has 8 corners so it has 8 vertexes.

We will add all the different angles in the single vertex as shown in the figure below.

Let,

Angle A = 55°

Angle B = 64°

Angle C = 175°

The sum of all the angles that are labeled is:

= Angle A + Angle B + Angle C

= 55° + 64° + 175°

= 294°

The sum of all the angles that are labeled in the given vertex is 294°

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Answer:

(n-3) (n-1) :)

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

Answer:

1: (B)

2: (C)

3: (D)

4: (D)

5: (A)

Step-by-step explanation:

Question 1:

Answer choice B is the only set of ordered pairs where there is only possible ouput for each input.

Question 2:

The y-intercept represented on the graph is (0, -3) and only answer choice C & D have it. Next, we're going to find the slope by using the rise/run method. From point (0, -3) to point (2, 0), it rises 3 and runs 2, so the slope is 3/2. Answer choice C is the only one with a y-intercept of -3 and a slope of 3/2.

Question 3:

From point (0, 0) to point (1, 3), it rises 3 and runs 1, so the slope is 3/1 or 3.

Question 4:

It is nonlinear because linear functions increase/decrease at the same rate. In the question, it says that the function decreases quickly at first, but then decreases more slowly as time passes. This function is not decreasing at the same rate the entire time.

Question 5:

The $5 fee is the initial fee, or the y-intercept, and the $2.25 per pound is the rate, or slope, so answer choice A is correct.

Hope this helps (●'◡'●)

Answer:

slope -2

y int (0, 4)

Step-by-step explanation:

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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The fourth angle is also x degrees, or approximately 40.57 degrees. The closest answer choice to these measures is C. 100° and 80°.

To solve this problem, we need to remember that opposite angles in a parallelogram are congruent. Let's call the measure of the third angle x. Then, the fourth angle is also x degrees.
Using the given information, we can set up an equation:
3(2+10) + x + 4(x+10) = 360
Simplifying and solving for x, we get:
36 + 3x + 40 + 4x = 360
7x = 284
x ≈ 40.57
Therefore, the measures of the angles are:
3(2+10) = 36 degrees
4(x+10) = 163.43 degrees
x = 40.57 degrees
And the fourth angle is also x degrees, or approximately 40.57 degrees.
The closest answer choice to these measures is C. 100° and 80°.

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By what factor will the surface area of the bag increase: The increase in the surface area of the sack is by a factor of 20.

Scaling is the increase or lessening in the size of an item or figure by a factor k, to make a picture.

Considering that the pack size is increased in order to convey more food, thus:

Scale factor = 40 pounds/2 pounds = 20

The increase in surface area of the sack is by a factor of 20.

Scaling is a technique through which we draw an item that is relative to the genuine size of the item. Scaling in calculation implies that we are either enlarging or shrinking figures so they retain their essential shape.

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