Four particles are located at points (1,3), (2,1), (3,2), (4,3). Find the moments Mr and My and the center of mass of the system, assuming that the particles have equal mass m.
Mx = 10
My= 11
xCM = 7.5
усм = 2.75
Find the center of mass of the system, assuming the particles have mass 3, 2, 5, and 7, respectively.
xCM = 50/17
усм = 40/17

Answer:

f= -4x-7/x

Step-by-step explanation:

This leads to a contradiction, proving that the equation has no solutions.

To prove that the equation\(x^4 + 4y = z^2\) has no solutions, let's consider the reduced case where x > 0, y > 0, z > 0, (x, y) = 1, and x is odd.

Assume there exists a solution to the equation. Since x is odd, we can write it as x = 2k + 1 for some integer k. Substituting this into the equation, we have\((2k + 1)^4 + 4y = z^2.\)

Expanding the left side, we get\(16k^4 + 32k^3 + 24k^2 + 8k + 1 + 4y = z^2.\)

Rearranging, we have\(4(4k^4 + 8k^3 + 6k^2 + 2k + y) = z^2 - 1.\)

Since\(z^2 - 1\) is odd, the left side must also be odd. However, \(4k^4 + 8k^3 + 6k^2 + 2k + y\) is even since it is divisible by 2. This leads to a contradiction, proving that the equation has no solutions.

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The perimeter of the triangle XYZ according to the midsegment theorem is 37

The midsegment theorem states that the segment that is obtained by joining the midpoints of two sides of a triangle is parallel to the third side and it is half the length of the third side of the triangle.

The specified parameters are;

The midpoint of \(\overline{XY}\) = A

The midpoint of \(\overline{YZ}\) = B

The midpoint of \(\overline{XZ}\) = C

The length of segment AC = 5

The length of segment BC = 6

The length of side XZ = 15

The segments AC, BC, and AB are midsegments of the triangle XYZ

According to the midsegment theorem, we get

AC = 0.5 × \(\overline{YZ}\)

BC = 0.5 × \(\overline{XY}\)

AB = 0.5 × \(\overline{XZ}\)

Therefore;

2 × AC = \(\overline{YZ}\)

2 × BC = \(\overline{XY}\)

2 × AB = \(\overline{XZ}\)

\(\overline{YZ}\) = 2 × 5 = 10 (substitution property)

\(\overline{XY}\) = 2 × 6 = 12 (substitution property)

The perimeter of the triangle = \(\overline{YZ}\) + \(\overline{XY}\) + \(\overline{XZ}\)
Plugging in the values, of \(\overline{YZ}\), \(\overline{XY}\), and \(\overline{XZ}\)  we get;

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Answer:

How much does it cost per pound because if it’s just $3.99 per pound then it’ll cost $3.99

Step-by-step explanation:

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Answer:

A. 30°, 70° and 80°

B. 10cm

Step-by-step explanation:

A. the two triangle have same angles so the angles of triangle 2 are 30°, 70° and 80°

B. the perimeter of triangle, is twice as long as the perimeter of triangle 2 so the perimeter of triangle 2 is 20÷2 = 10 cm

Answer:

The speed of Sara is 78.4 km/h.

Step- by-step explanation:

Manuel and Sara travel a certain distance, and the times they use are in the ratio 21/15. Manuel's speed is 56km / h. What is Sara's speed?

Let the distance is d.

speed of Manuel = 56 km/h

time taken by Manuel = 21 t

time taken by Sara =  15 t

Let the speed of Sara is v.

Distance = speed x time

For Manuel:

d = 56 x 21 t ..... (1)

For Sara:

d = v x 15 t ..... (2)

From (1) and (2)

56 x 21 t = v x 15 t

v = 78.4 km/h

The third term is 245 and the first term is 5 -> To get from the first term to the third term, we multiply it by 49.

Since in a geometric sequence, the difference between each term has to be a constant multiplier or a sequence of multipliers -> We can find the second number to be 5 x 7 = 35

So, this geometric sequence is 5 ; 35 ; 245 and so on.

-> The common ratio of this sequence is 7. (and sorry if the things above don't make sense)

Answer:

7

Step-by-step explanation:

Given:

Let the second term be "x".

⇒ 5, x, 245...

Thus, the following equations:

To find the common ratio between the three terms, we need to find the value of "x". Simplify both the equations to obtain the values of (something). Then compare both the values.

⇒ [5 × (something)] = x

⇒ [5 × (something)]/5 = x/5

⇒ (something) = x/5

⇒ x × (something) = 245

⇒ [x × (something)]/x = 245/x

⇒ (something) = 245/x

Now, let's compare both the results of (something).

⇒ x/5 = 245/x

⇒ x² = 5 x 245

⇒ x² = 1225

⇒ x = √1225 = 35

Substitute the second term into the sequence.

⇒ 5, x, 245 = 5, 35, 245

Looking at the sequence formed, we can tell that 7 is being multiplied to each term. Thus, 7 is the common ratio.

The average time allowed the 15 selected students to be 3.06hours

What is Average?

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

With a sample size of 15 and a p value of 0.04

From binomial probability, (nCx)px(1p) is where the application of binomial probability originates from (n-x)

1 - p = 0.96

a) P(x=1) is the probability that precisely 1 received a special accommodation.

= 15C1 x (0.04)^1 x (0.96) ^14 = 0.3388

b) P(x >=1) = 1 - P(x = 0) is the likelihood that at least 1 person received a special accommodation.

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 = 0.4579

c) the likelihood that two people at least obtained special accommodations

= [P(x = 0) + P(x = 1)] - [P(x>=2) = P(x>=2)

= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 + 15C1 x (0.04)^1 x (0.96)^14]

= 1 - [0.5420 + 0.3388] .3388]

= 0.1192

d) likelihood that the proportion of the 15 who received a special accommodation is within two standard deviations of the proportion you would anticipate receiving one;

= P( x<=1) = P( x= 0) = 0.5429

e) expected average time = 0.04 x 4.5 + 0.96 x 3 = 3.06hours

Hence, The average time allowed the 15 selected students to be 3.06hours

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Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

The down payment is $450.

The total dollar amount of the monthly installment payments is $4,860.

The Loan amount Jeanie contracted was $4,050.

The total interest Jeanie paid was $810.

The down payment is the cash payment made upfront when an asset is bought on credit.

The down payment represents a percent of the total price, indicating the buyer's willingness and capacity to enter the contract.

The price of the snowmobile = $4,500

Down payment = 10% = $450 ($4,500 x 10%)

Loan amount = $4,050 ($4,500 - $450)

Installment periods = 18 months

Monthly payments = $270 ($4,050/18)

Total installment payments = $4,860 ($270 x 18)

The total interest = $810 ($4,860 - $4,050)

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Answer:

8

Step-by-step explanation:

Do the equation backwards.

25 - 17 = 8

Given,

The initial balance in the checkbook is $463.18.

The deposite money is $265.

The amount of check is $198.73.

The charge paid for bank is $2.50.

The ending balance at the month end is,

Hence, option b ($526.95) is correct.

Answer:

7x²y⁴

Explanation:

Given the expanded expression:

We have two x(s) and 4 y(s), thus:

The formula for the general term, a_n, of the given sequence {6, 3, 0, -3, -6, ...} is a_n = 9 - 3n, where n represents the position of the term in the sequence.

In the given sequence, each term is decreasing by 3 compared to the previous term. This indicates a common difference of -3. To find the general term, we need to determine the relationship between the position of a term (n) and the value of the term (a_n).

We observe that the first term, a_1, is 6, and the second term, a_2, is 3. This suggests that as the position of a term increases by 1, the value of the term decreases by 3. We can express this relationship as a_n = a_1 - 3(n - 1). Simplifying further, we get a_n = 6 - 3(n - 1).

To eliminate the constant term 6, we rewrite the formula as a_n = 9 - 3n, which represents the general term of the sequence. This formula allows us to find the value of any term in the sequence by substituting its position, n, into the formula.

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There will be 30 yards of extra string. To start, let's calculate the length of string in inches on the spool: 1800 inches are equal to 50 yards multiplied by the yard length of 36 inches.

Let's now determine how many inches of string will be required: 24 pupils times 30 inches each = 720 inches.

Let's finally calculate how many inches remain: 180 inches - 720 inches = 1080 inches.

The remaining length of string may now be converted to yards using the formula: 1080 inches / 36 inches per yard = 30 yards.

Unit conversion is the process of converting a quantity between different units of measurement. We convert the string's length in this issue from yards to inches and back to yards.

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Answer:

The speed is: 0.0142MHz

Step-by-step explanation:

Given

\(C(s) = 1234s^2 - 35s + 1900\)

Required

The processor speed when the cost is at minimum

First, differentiate C(s) with respect to s

\(C(s) = 1234s^2 - 35s + 1900\)

\(C'(s) = 2468s - 35\)

The cost is at minimum when \(C'(s) = 0\)

So, we have:

\(C' = 2468s - 35 = 0\)

\(2468s - 35 = 0\)

Solve for s

\(2468s = 35\)

\(s=\frac{35}{2468}\)

\(s\approx0.0142\)

Answer:

1. 537.1

2. 8.15

3. 9.77

4. 26.75

Step-by-step explanation:

The percentage of the sixth graders at this middle school write left-handed is 8%.

Since there are there are 90 girls and 60 boys in the sixth grade at kimbrough middle school. The total number will be:

= 90 + 60

= 150 students

Since 9 girls and 3 boys write left-handed, this will give a total of 9 + 3 = 12

Therefore the percentage for left handed people will be:

= Number of left handed people / Total students × 100

= 12 / 150 × 100

= 8%

The percentage is 8%.

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The number of silver coins Lily initially had is 28.

A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.

Now according to the question;

Let 'x' be the share of silver coin of Lily.

Let 'y' be the share of silver coin of Nada.

Lily and Nada share silver coins in the ratio 7:3

Thus, x/y = 7/3

Cross-multiplying

3x = 7y (equation 1)

Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.

(x - 3)/(y + 3) = 5/3

cross multiplying;

3x - 9 = 5y + 15

Simplifying;

3x  = 5y + 24 (equation 2)

Comparing equation 1 and 2.

7y = 5y + 24

2y = 24

y = 12 (Nada's share)

Substitute the value of y in equation 1;

3x = 7y

3x = 7×12

x = 28

Therefore, the initial share if Lily was 28.

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The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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\(\cfrac{~~ \frac{ x }{x+4 } ~~}{\frac{1}{x}+\frac{1}{x+4}}\implies \cfrac{~~ \frac{ x }{x+4 } ~~}{\frac{x+4~~ + ~~x}{x(x+4)}}\implies \cfrac{~~ \frac{ x }{x+4 } ~~}{\frac{2x+4}{x(x+4)}}\implies \cfrac{x}{x+4}\cdot \cfrac{x(x+4)}{2x+4}\implies \cfrac{x^2}{2x+4}\)

Answer:

A: 4

B: -2

Step-by-step explanation:

calculate dy/dx:

A: 1 to the right and 4 up: gradient is 4/1 = 4

B: 2 to the right and 4 down: gradient is 4/-2 = -2

Answer:

Basically if you know side-angle-anlge, you can determine the third angle by

3rd angle = 180 - angle 1 - angle2

In this way, you are using the Angle-Side-Angle method of congruence.

Step-by-step explanation:

Answer:

In this case SAA is a valid means for establishing triangle congruence. You can see in the following image. The triangles are the same, in other words congruent. How I figured it out was by making a random triangle (ABC) then finding the lengths and angles.  From there, I picked a random side (AB) and angles (A) and (B) after I transferred the information I had and put it into a new triangle. Using this formula to determine the third angle: 3rd angle (C = 45*) = 180* - angle A (45*) - angle B (90*). From there, I looked for where line (BC) and (CA) would connect. Leaving me with two congruent triangles.

Answer:

She drinks 6L of water during the 12 days

Step-by-step explanation:

500×12=6000ml

convert 6000ml into liters= 6 liters

Answer:

Leave it the same, it still works for the equation.

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Answer:

I would leave it the same because if it were a proper fraction it would much harder to graph.

The best-fitting line through a scatterplot is known as the linear regression line.

The linear regression line is a statistical method used to model the relationship between two variables by fitting a straight line that minimizes the overall distance between the observed data points and the line.

The linear regression line is often used to determine the strength and direction of the linear relationship between two variables. It provides an estimate of the average relationship between the independent variable (x) and the dependent variable (y) in the form of a linear equation (y = mx + b), where "m" represents the slope of the line and "b" represents the y-intercept.

The goal of the linear regression line is to find the line that best represents the pattern of the data points. It minimizes the sum of the squared differences between the observed y-values and the predicted y-values based on the line. By finding the best-fitting line, we can make predictions or infer the relationship between the variables beyond the observed data points.

Therefore, the best-fitting line through a scatterplot is known as the linear regression line.

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