Let n, a, b, c be integer numbers. Prove that if n|a, n|b, and n|c, then n' a (b – 2c) + b(c - 2a) + c(a − 2b). ) + .
Answers
We can conclude that if n divides a, b, and c, then n also divides (a(b - 2c) + b(c - 2a) + c(a - 2b)).
To prove that if n divides a, n divides b, and n divides c, then n also divides (a(b - 2c) + b(c - 2a) + c(a - 2b)), we need to show that the given expression is divisible by n.
Given that n divides a, b, and c, we can express a, b, and c in terms of n as follows:
a = kn (where k is an integer)
b = ln (where l is an integer)
c = mn (where m is an integer)
Substituting these values into the expression (a(b - 2c) + b(c - 2a) + c(a - 2b)), we get:
(a(b - 2c) + b(c - 2a) + c(a - 2b)) = (kn(ln - 2mn) + ln(mn - 2kn) + mn(kn - 2ln))
Simplifying further:
= knln - 2kmn^2 + lnmn - 2lkn^2 + kmn^2 - 2ln^2 + kn^2 - 2lmn
= knln + lnmn + kmn^2 - 2kmn^2 - 2lkn^2 - 2ln^2 + kn^2
= (knln + lnmn + kn^2) + (kmn^2 - 2kmn^2 - 2lkn^2 - 2ln^2)
= n(kln + lmn + kn) + n(kmn^2 - 2kmn^2 - 2lkn^2 - 2ln^2)
= n(kln + lmn + kn + kmn^2 - 2kmn^2 - 2lkn^2 - 2ln^2)
= n(kln + lmn + kn + kmn^2 - 2kmn^2 - 2lkn^2 - 2ln^2)
= n(kln + lmn + kn + (k - 2k)mn^2 - (2l - 2l)kn^2 - (2l - 2k)ln^2)
= n(kln + lmn + kn + kmn^2 - kmn^2 - lkn^2 + lkn^2 - lln^2 + kln^2)
= n(kln + lmn + kn + kln^2)
= n(kln + kn + lmn + lln^2)
= n(k(ln + 1) + l(mn + ln^2))
Now, we can see that each term in the expression is divisible by n since k, l, m, and n are all integers. Therefore, we can conclude that if n divides a, b, and c, then n also divides (a(b - 2c) + b(c - 2a) + c(a - 2b)).
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Related Questions
Kristina walks from her house, around the park, to the store. She is interested in taking a shortcut through the park to save time. Approximately how far away from her house is the store, if she were to follow the path shown by the dotted line in the graphic below?* HOUSE PARK 80 m 100 m STOR O 134 m O 128 m O 180 m 200 m nal. If a 65 inch television has 1 point
Answers
If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.
How to calculate the distance between her house and the store?To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;
C² = a² + b²
where;
a= 80
b= 100
c= ?
That is;
c²= 80²+100²
= 6400+10000
= 16,400
c = √16400
= 128.1m
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(1 ÷ 2 3 ⁄ 4 ) + (1 ÷ 3 1 ⁄ 2 ) = _____.
Answers
Answer:
50/77
Step-by-step explanation:
(1÷2 3/4)+(1÷3 1/2)
2 3/4 is same as 11/44
1/2 is same as 7/2
so to divide fraction you have to flip the second number and multiply
so 1 times 4/11=4/11
and 1 times 2/7=2/7
4/11 +2/7=28/77+22/77=50/77
can someone adult or student is age 14 , more answer this worksheet plz
Answers
Answer:
I am 14 why are you asking
the levels of a(n) variable have meaning and order. a. prescriptive b. categorical c. analytical d. continuous
Answers
The correct answer is (c) analytical. Levels of a variable can have meaning and order when the variable is analytical variable.
Analytical variables are variables that have a meaningful order or ranking, such as height or weight. For example, height is an analytical variable because people can be ranked from shortest to tallest, and each height value is meaningful in relation to other height values.
Prescriptive variables describe the desired or prescribed behavior, such as in a set of rules or guidelines. Categorical variables divide data into categories or groups, such as gender or hair color. Continuous variables have an infinite number of values and can take on any value within a given range, such as temperature or time.
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HELP WILL MARK BRAINLIEST
Answers
Answer:
i think d
Step-by-step explanation:
im so sorry if this is wrong but im almost positive its d
please mark brainliest
If you take your pencil or your finger and hold it upright, parallel to the y axis, and move it from left to right your pencil or finger will thought the line in multiple places at the same time. This is the vertical line test and because it hits multiple places on the line at the same time it fails the test. This is telling you that an x value has more than one y value, so it is not a function.
Two angles that are located between two coplanar lines on the same side of the transversal.
Answers
what is the midpoint of AB
Answers
Answer:
Step-by-step explanation:
The midpoint of a segment connected by two points is the average of the coordinates. We have points (-3,3) and (-5,-4)
midpoint equals (x2+x1)/2, (y2+y1)/2 in this case
mp=(-3-5)/2, (3-4)/2
mp=(-4, -1/2)
Solve -\frac{1}{3}\left(9x+42\right)-5x=-70 please
Answers
The value of x after solving the fraction \(-\frac{1}{3}\left(9x+42\right)-5x=-70\) is 7.
Given fraction:
⇒ \(-\frac{1}{3}\left(9x+42\right)-5x=-70\)
⇒ -9x/3 - 42/3 - 5x = -70
⇒ -3x - 14 - 5x = -70
⇒ -8x -14 = -70
⇒ -8x = -70 + 14
⇒ -8x = -56
⇒ 8x = 56
divide by 8 on both sides
8x/8 = 56/8
x = 56/8
x = 7.
Therefore The value of x after solving the fraction \(-\frac{1}{3}\left(9x+42\right)-5x=-70\) is 7.
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Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?
constant
symmetric
positively skewed
negatively skewed
Answers
Answer:
B. Symmetric
Step-by-step explanation:
How do I find the volume?
Answers
Answer:
425 ft³
Step-by-step explanation
Find the volume of the entire figure, if the part wasn't cut out
It would be 11 x 8 x 5 = 440
Now do 5 x 1 x 3 = 15
440 - 15 = 425
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
how to find percentile with mean and standard deviation
Answers
Step-by-step explanation:
Step 1
Subtract the mean from your score. For example, if you scored 33 and the mean is 24, you would get a difference of 9.
Step 2
Divide the difference found in Step 1 by the standard deviation of the data to find the z-score, which is the number of standard deviations away from the mean that your score is. For example, if the standard deviation was 4.5, you would have a z-score of 2.
Step 3
Convert the z-score to a percentile using a z-score chart or converter available online (see Resources section). When converting, be sure to use a one-sided test. For example, a z-score of 2 would be in the 98th percentile.
1, What does the y_intercept mean2, What does the x_intercept mean3, identify the x intercept and the y intercept from. the equation y= 7/2x _ 2 x=_3
Answers
Y-intercept is the point where the line crosses the y-axis, at this point x=0.
X-intecept is the point where the line crosses the x-axis, at this point y=0.
To identify the x intercept and y intercept, we are going to substitute x=0 and y=0 in the function:
\(y=\frac{7}{2}x-2\)y=7/2(0)-2
y=-2 ---> y-intercept
0=7/2x-2
2=7/2x
2*2/7=x
x=4/7---> x-intercept
Which is the only solution to the equation log3(x2 6x) = log3(2x 12)?
Answers
Answer: x=2 on edg
Step-by-step explanation: i got it right :)
0, 3, 8, 15...
Generalize the pattern by finding the nth term.
Answers
The nth term of the pattern is (n²-1)
The nth term of a pattern:To find the nth term identify the patterns in a given sequence and use algebraic expressions to generalize the pattern and find the nth term.
By observing the given series we say that each number is one less than perfect Like 8 is one less than 9, 15 is one less than 16, etc. Use this condition to solve the problem.
Here we have
0, 3, 8, 15...
To find the nth terms identify the patterns in a given sequence
Here each term can be written as follows
1st term => 0 = (1)² - 1 = 0
2nd term => 3 = (2)² - 1 = 3
3rd term => 8 = (3)² - 1 = 8
4th term => 15 = (4)² - 1 = 15
Similarly
nth term = (n)² - 1 = (n²-1)
Therefore,
The nth term of the pattern is (n²-1)
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2.6.PS-
Amelia needs to buy some dog food. At the nearest store, 5 bags of dog food cost $12.50. How
much would Amelia spend on 3 bags of dog food?
Amelia would spend $__ on 3 bags of dog food.
Answers
Answer:
Step-by-step explanation:
5 bags= $12.50
1= ?
$12.50*1= 12.50
$12.50/5= $2.5
$2.5*5=$12.5
$2.5*3= $7.5
3 bags= $7.5
Helppppppp pleaseeee find the value of x. Step by step please
Answers
9x-58=180
9x= 180+58
9x= 238
X=26.4
What expression is equivalent to x2−x−6?
Answers
Answer:
\( - x + x 2 - 6\)
that's it hope its helpful
A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.
(A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs.
(B) Graph the total daily cost for 0≤x≤ 200.
(C) Interpret the slope and y intercept of the cost equation.
(A) C =
(Simplify your answer. Use integers or fractions for any numbers in the oxpropion
Answers
The function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.
Let's suppose x is the fixed cost and y is the variable cost.
4671 = 50y + x …(1)
5871 = 70y + x …(2)
1200 = 20y
y = 60
x = 1671
Total cost:
C(g) = 1671 + 60g
g is the number of golf per day.
Slope = 60
y- Intercept = 1671 (from the graph)
Thus, the function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g
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he defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3-sigma control chart limits are:
ucl = (enter your response as a number between 0 and 1, rounded to four decimal places).
Answers
The defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3-sigma The upper control limit (UCL) is approximately 0.0450.
The upper control limit (UCL) for a 3-sigma control chart is given by:
\(\[UCL\) = defect rate + 3 * sqrt((defect rate * (1 - defect rate)) / sample size)
Substituting the values, where the defect rate is 1.50% (0.015) and the sample size is 200, we get:
\(\[UCL = 0.015 + 3 \times \sqrt{\frac{0.015 \times (1 - 0.015)}{200}}\]\)
Calculating this expression, we find:
\(\[UCL \approx 0.0450\]\)
Therefore, the upper control limit (UCL) is approximately 0.0450.
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Find the minimum value of the function f (x) = 2x² + 11.4x + 18.5 to the
nearest hundredth.
Answers
Answer:
2\(x^{2}\) + 11.4x + 18.5 ---> No Like Terms
Step-by-step explanation:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is
defined as drawing a black tile from the bag on the first draw, and event B
is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without
replacement, what is P(A and B) expressed in simplest form?
2
OA)
O B)
21
5
O C)
OD)
14
+ |
45
4
15
Answers
Answer:
2/21
Step-by-step explanation:
The question is badly formatted so cannot match the answer choice
Total number of tiles = 4 + 5 + 6 = 15
P(A) = P(drawing a black tile from 15 tiles) = 4/15
After event A, there are 14 tiles left : 3 black, + 5 white + 6 blue
P(B/A) = P(drawing white tile after a black tile has been drawn) = 5/14
P(A and B) = P(A).P(B/A) = 4/15 x 5/14 = 2/21
Note that P(B) = 5/15 since we are talking about independently drawing a white tile from the original stack of tiles
Q1. [HW] A warehouse cold space is maintained at -18 °C by a large R-134a refrigeration cycle. In this cycle, R-134a leaves the evaporator as a saturated vapour at -24 °C. The refrigerant enters the condenser at 1 MPa and leaves at 950 kPa. The compressor has an isentropic efficiency of 82% and the refrigerant flowrate through the cycle is 1.2 kg/s. The temperature outside is 25 °C. Disregard any heat transfer and pressure drops in the connecting lines between the units. a) Sketch a flow diagram of the cycle, labelling each device, indicating where heat and work flows into, or out of, the system, and the direction of flow of the refrigerant. Number your streams, starting with 1 at outlet of the compressor and label with values given from the question description above. b) Show the cycle (approximately) on a T-s diagram with respect to saturation lines. Number points in the cycle the same as part (a), show the direction of the cycle and where energy transfers into, or out of, the cycle. c) What are three ways to reduce the energy consumption of an industrial freezer? These measures can be part of the design or the operation of the freezer. [Note: the freezer must operate at no higher temperature than -18 °C due to food regulations.] Q2. For the freezer system in Q1, determine the: a) compressor shaft work (in kW). b) rate of heat dumped into the surroundings (in kW). Q3. For the freezer system in Q1 and Q2, determine the: a) quality of the R-134a into the evaporator. b) rate of heat removal from the cold space by the refrigeration cycle (in kW) c) COP of the refrigeration cycle. d) second law efficiency of the refrigeration cycle.
Answers
In this refrigeration cycle problem, a warehouse cold space is maintained at -18 °C using an R-134a refrigeration cycle.
a) The flow diagram of the refrigeration cycle includes a compressor, condenser, expansion valve, and evaporator. The refrigerant flow is labeled starting with stream 1 at the outlet of the compressor and values are assigned based on the given description.
b) On a T-s diagram, the refrigeration cycle is approximately shown in relation to the saturation lines. Points in the cycle are numbered according to the flow diagram, and the direction of the cycle and energy transfers into or out of the cycle are indicated.
c) Three ways to reduce energy consumption in an industrial freezer include: 1) Improving insulation to minimize heat transfer from the surroundings. 2) Optimizing the compressor efficiency through proper maintenance and control. 3) Implementing energy-efficient evaporator and condenser designs to enhance heat transfer.
Q2: a) The compressor shaft work can be calculated using the isentropic efficiency and mass flow rate of the refrigerant. W_compressor = (h_2s - h_1) / η_isentropic.
b) The rate of heat dumped into the surroundings can be determined by the enthalpy change of the refrigerant during the condensation process. Q_out = m_dot * (h_2 - h_3).
Q3: a) The quality of the R-134a into the evaporator can be determined using the saturation temperature at -24 °C and the actual temperature at the evaporator inlet.
b) The rate of heat removal from the cold space can be calculated using the enthalpy change of the refrigerant in the evaporator. Q_in = m_dot * (h_1 - h_4).
c) The coefficient of performance (COP) of the refrigeration cycle is given by COP = Q_in / W_compressor.
d) The second law efficiency of the refrigeration cycle can be calculated as η_2nd_law = (Q_in - Q_out) / Q_in.
By performing the necessary calculations using the given information and thermodynamic properties of R-134a, the values for compressor shaft work, heat dumped into the surroundings, R-134a quality, heat removal rate, COP, and second law efficiency can be determined for the refrigeration cycle.
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Sarita showed the steps to solving the equation. 5 (x minus 3) + 7 (x + 4) = 73 Steps Sarita's Solution Sarita's Verification 1 5 x minus 15 + 7 x + 28 = 73 5 (5 minus 3) + 7 (5 + 4) = 73. 5 (negative 2) + 7 (9) = 73. Negative 10 + 63 = 73. 53 not-equal-to 73. 2 (5 + 7) x + (negative 15 + 28) = 73 3 12 x + 13 = 73 4 12 x + 60 5 x = 5 When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?
Answers
Answer:
Sarita’s solution is correct. She made an error in her verification. Sarita was supposed to add the 5 and 7 in the first step.
Step-by-step explanation:
Given the following equation:
The steps to solve it are:
5(x-3)+7(x+4)-73
1. Apply the Distributive property:
5x-15+7x+28=73
2. Add the like terms:
12x+13=73
3. Subtract5 13 from both sides of the equation:
12x+13-(13)=73-(13
12x=60
4. Divide both sides of the equation by 12:
12r/12 = 60/12
x = 5
To verify it, let's substitute into the equation:
5(5-3)+7(5+4)=73
Evaluating, we get:
5(2)+7(9)=73
10+63=73
73=73
Based on this, we can determine that Sarita's solution is correct, but she made an error in her verification (Observe that 5-3 is not equal to -2 )
Answer:
A. Sarita’s solution is correct. She made an error in her verification.
Step-by-step explanation:
EDGE 2020
Given sinx=2/3 find cosx
Answers
Answer:
\(\cos\theta=\frac{\sqrt{5}}{3}\)
Step-by-step explanation:
\(\sin\theta=\frac{2}{3}\\ \\\cos\theta=\frac{\sqrt{3^2-2^2}}{3}=\frac{\sqrt{9-4}}{3}=\frac{\sqrt{5}}{3}\)
Construct a right triangle with hypotenuse 3 and opposite side 2. The adjacent side used for cosine can easily be calculated using the Pythagorean Theorem.
What is (-11,,-27) reflected across the y-axis
Answers
Answer:
On the y- axis everything is postive so it would be (11,27)
I need help plz help me
Answers
Which one of the following would be most helpful in strengthening the content validity of a test?
A. Administering a new test and an established test to the same group of students.
B. Calculating the correlation coefficient.
C. Calculating the reliability index.
D. Asking subject matter experts to rate each item in a test.
Answers
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.
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a fair coin is tossed three times. the random variable x is defined to be 2ℎ , where h is the number of flips that come up heads. for example, x(hht)
Answers
The probability distribution for X is as follows: X=0 with probability 1/8, X=2 with probability 3/8, X=4 with probability 3/8, X=6 with probability 1/8.
The random variable X is defined as 2H, where H represents the number of flips that result in heads. For instance, if the outcomes are HHT, then X would be equal to 2.
To find the probability distribution of X, we need to determine the possible values of H and their respective probabilities. Since there are three coin tosses, H can take on values of 0, 1, 2, or 3.
To calculate the probabilities, we can use the binomial probability formula. The formula states that for n trials with probability p of success and x successes, the probability is given by P(x) = nCx * p^x * (1-p)^(n-x).
Applying this , since the coin is fair, the probability of getting a head on any given toss is 0.5. Plugging in the values, we find that P(0) = 1/8, P(1) = 3/8, P(2) = 3/8, and P(3) = 1/8.
Therefore, the probability distribution for X is as follows: X=0 with probability 1/8, X=2 with probability 3/8, X=4 with probability 3/8, X=6 with probability 1/8.
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Roland needs 8 sheets of fabric that are each 45 yard long.
Answers
Answer: 360 yards
(Assuming the question is "How many yards are needed."
Step-by-step explanation: (8 sheets)*(45 yards/sheet) = 360 yards
Answer:
Step-by-step explanation:
jigger boo jigger boo how can I say jigger boo
ΔΔΔ→ββ←⇵←→can you help me please?
Answers
Answer:
The correct answer should be 63°
Answer:
B
Step-by-step explanation: I took the test