Jasper claims that there exists a regular polygon for which the measure of each interior angle of the polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself.
For the case where Jasper's claim is true, complete the table by entering the correct information for such a regular polygon.
Answers
It is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.
What is the interior angle?
The inner of the two angles formed where two sides of a polygon come together. any of the four angles formed in the area between a pair of parallel lines when a third line cuts them.
Jasper's claim is not true. The minimum angle of rotation about the center of a regular polygon that carries the polygon onto itself is called the polygon's "order of rotational symmetry." This angle is always less than or equal to 180 degrees, and it is equal to 360 degrees divided by the number of sides in the polygon.
For example, a regular hexagon has an order of rotational symmetry of 60 degrees (360 degrees / 6 sides), and a regular octagon has an order of rotational symmetry of 45 degrees (360 degrees / 8 sides).
Therefore, if the measure of each interior angle of a regular polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself, then the measure of each interior angle would have to be at least 720 degrees. However, the sum of the interior angles of a regular polygon with n sides is 180(n-2) degrees, which is always less than 720 degrees for any value of n greater than 2.
Therefore, it is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.
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Related Questions
Analyze the graph of the function f(x) to complete the statement. On a coordinate plane, a curved line, labeled f of x, with a minimum value of (0, negative 3) and a maximum value of (negative 2.4, 17), crosses the x-axis at (negative 3, 0), (negative 1.1, 0), and (0.9, 0), and crosses the y-axis at (0, negative 3). f(x)<0 over and what other interval?
Answers
The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)
We have,
The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.
Therefore, we can say that:
f(x) < 0 for x < -3 and -1.1 < x < 0.9
And,
The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).
This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:
f(x) > 0 for x > -2.4
Now,
Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).
So,
The interval where f(x) is negative and greater than 0 is:
(-∞, -3) U (-1.1, 0)
Thus,
The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)
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Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 2 + sin(x), 0 ≤ x ≤ with n = 8.
Answers
The top and lower sums for n =2,4, and 8 and f(x) = 2 +sin(x),0 x are as follows:
n = 2: Upper Sum = 7.85398; Lower sum ≈ 7.85398
n = 4: Upper sum ≈ 6.43917; Lower sum ≈ 6.43917
n = 8: Upper sum ≈ 6.35258; Lower sum ≈ 6.352
It is necessary to first divide the range [0, ] into n subintervals of identical width x, where x = ( - 0)/n = /n, in order to calculate the upper and lower sums for the equations f(x) = 2 + sin(x), 0 x for n = 2, 4, and 8. The endpoints of these subintervals are:
x0 = 0, x1 = Δx, x2 = 2Δx, ..., xn-1 = (n-1)Δx, xn = π.
Then, for each subinterval [xi-1, xi], we can approximate the area under the curve by the area of a rectangle whose height is either the maximum or minimum value of f(x) on that interval. The sum of these areas' overall subintervals gives us the upper and lower sums.
For n = 2:
Subintervals: [0, π/2], [π/2, π]Width of subintervals: Δx = π/2Maximum values of f(x) on each subinterval:[0, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/2]: f(0) = 2 + sin(0) = 2
[π/2, π]: f(π/2) = 2 + sin(π/2) = 3
Upper sum: (3)(π/2) + (2)(π/2) = 5π/2 ≈ 7.85398Lower sum: (2)(π/2) + (3)(π/2) = 5π/2 ≈ 7.85398For n = 4:
Subintervals: [0, π/4], [π/4, π/2], [π/2, 3π/4], [3π/4, π]Width of subintervals: Δx = π/4Maximum values of f(x) on each subinterval:[0, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/4, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289
[3π/4, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/4]: f(0) = 2 + sin(0) = 2
[π/4, π/2]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/2, 3π/4]: f(π/2) = 2 + sin(π/2) = 3
[3π/4, π]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289
Upper sum: (2.70711 + 3 + 2.29289)(π/4) ≈ 6.43917Lower sum: (2 + 2.70711 + 3 + 2.29289)(π/4) ≈ 6.43917For n = 8:
Subintervals: [0, π/8], [π/8, π/4], [π/4, 3π/8], [3π/8, π/2], [π/2, 5π/8], [5π/8, 3π/4], [3π/4, 7π/8], [7π/8, π]Width of subintervals: Δx = π/8Maximum values of f(x) on each subinterval:[0, π/8]: f(π/8) = 2 + sin(π/8) ≈ 2.25882
[π/8, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/4, 3π/8]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593
[3π/8, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, 5π/8]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593
[5π/8, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711
[3π/4, 7π/8]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882
[7π/8, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/8]: f(0) = 2 + sin(0) = 2
[π/8, π/4]: f(π/8) = 2 + sin(π/8) ≈ 2.25882
[π/4, 3π/8]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[3π/8, π/2]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593
[π/2, 5π/8]: f(π/2) = 2 + sin(π/2) = 3
[5π/8, 3π/4]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593
[3π/4, 7π/8]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711
[7π/8, π]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882
Upper sum: (2.25882 + 2.70711 + 2.96593 + 3 + 2.96593 + 2.70711 + 2.25882 + 2)(π/8) ≈ 6.35258Lower sum: (2 + 2.25882 + 2.70711 + 2.96593 + 3 + 2.96593 + 2.70711 + 2.25882)(π/8) ≈ 6.352The complete question is:-
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 2 + sin(x),0 ≤ x ≤ π with n = 2, 4, and 8.
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What formula do I use for this? How do I get the points to graph?
Answers
The graph of the function y = 5|x - 4| is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 5|x - 4|
The above function is an absolute value function that has been transformed as follows
Vertically stretched by a factor of 5Shifted right by 4 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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Identifying Linear Equations Let x1, x2, ..., In be variables. Determine whether the following equations are linear or non-linear and explain why: (a) (x1 – 1)(x2 + 1) = 0 (b) 5x1 = 2x2 – 3x3 +4 (c) x1 + xż + x3 + ... + x n = 0 (d) sin(x3)x1 + x2 = 4 – cos^2(x3)21 (e) exı + e-x2 + ... +e" In = ln(5)
Answers
The following systems are :
a) Non-linear
b) Linear
c) Linear
d) Non-linear
e) Linear
a) Non-linear: The equation is non-linear because it contains a product of two variables (x1 - 1) and (x2 + 1). A linear equation only contains variables and their coefficients, not products of variables.
b) Linear: The equation is linear because it only contains variables and their coefficients.
c) Linear: The equation is linear because it only contains variables and their coefficients and the sum of variables.
d) Non-linear: The equation is non-linear because it contains the sine and cosine functions, which are non-linear.
e) Linear: The equation is linear because it only contains variables raised to a constant power (e raised to a constant power) and their coefficients.
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what is the slope of the line on the graph?
Answers
Answer:
1/6
Step-by-step explanation:
A (6,1)
B (12,2)
slope = (2-1)/(12-6)
1/6
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference? A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units. Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. The distance is exactly the difference. The distance is the absolute value of the difference. The distance is not related to difference.
Answers
Answer:
C) The distance is the absolute value of the differenceStep-by-step explanation:
We are interested in the last two columns.
If we compare them we see that each value of the distance column is the absolute value of corresponding value of difference:
a - b = 1, 5, - 3distance = 1, 5, 3Corect choice is C
Answer:
The distance is the absolute value of the difference.
Step-by-step explanation:
Given table:
\(\begin{array}{|c|c|c|c|c|}\cline{1-5} a & b & a+b & a-b & \sf distance\\\cline{1-5} 1 & 2 & 3 & -1 & 1 \sf \: unit\\\cline{1-5} 4 & -1 & 3 & 5 & 5 \sf \: units\\\cline{1-5} -6 & -3 & -9 & -3 & 3 \sf \: units\\\cline{1-5}\end{array}\)
The difference is column 4.
The distance is column 5.
The absolute value of a number is its positive numerical value. It is denoted by a vertical line either side of the real number.
For example, |5| means 'the absolute value of 5', and |-5| means 'the absolute value of -5'.
Taking the absolute values of the differences:
⇒ |-1| = 1
⇒ |5| = 5
⇒ |-3| = 3
Therefore, the distance is the absolute value of the difference.
Let the discrete random variable X have the geometric distribution with parameter p. (a) Give a real-life example in which the geometric distribution can be applied. (b) Use the definition of the expected value to show that: E[X] = 1/p. (c) Explain why it makes sense that the expected value of X is inversely proportional to p.
Answers
a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.
b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.
c) E(x) = 1/p
Discrete Random Variable:
A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.
Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...
Geometric Distribution :
The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.
The Geometric Random Variable can be written as X ~ G(p).
The probability mass function is P(X = x) = (1 - p)ˣ⁻¹ p
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Complete the following statement. 3(4 x 8) (3 x4) (_)
Answers
Answer:
8
Step-by-step explanation:
(8*4)3=96
3*4=12
12*8=96
hi can someone please help with this i’m confused by the graph. helpppp
Answers
Therefore , solving the provided question, we can say that the, probability P( 24 period hour) = 5/24
What is probability?The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 and 1, in which about 0 represents how likely the event should be to occur and 1 represents certainty. A probability is a quantitative illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set all equally likely options that lead to a specific occurrence.
Here,
=> E1 = stops at 5 clock
=> E2 = start at 24 hours
=> P( 24 period hour) = 5/24
=> the, probability P( 24 period hour) = 5/24
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John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and found a job that will allow him to purchase a car to finally catch Roadrunner. He can either buy a new car at a cost of $22,000, buy a used car for $12000 or lease a new car for one year at a cost of $8,500 (assume total cash purchase up front, no financing or monthly payments required). The new car has a 20% chance of a serious break down resulting in a permanent impairment to the trade-in value. The trade-in value for the new car without a serious break down after one year is $18,000 but only $10,000 if the break down occurs. On the other hand, the used car has a 40% chance of suffering a major break down with a $8,000 decrease in the resale value. However, if it does not break down, Wile can sell it to a friend one year from now for $9,000 cash (assume he can also sell it to the friend for $4,000 if the breakdown occurs). Finally, the leased car has a 10% chance of breaking down with a repair cost of only $2,000, and if it doesn’t, Wile will not gain or lose anything by returning the car at the end of a one year lease period. NOTE: For the new and used car purchases all related repair costs resulting from a breakdown have been netted against the trade-in / resale value.
a. Construct a decision tree for Wile
b. What is the expected value of the new car?
c. What is the expected value of the used car?
d. What is the expected value of leasing the car?
Answers
Answer: See explanation
Step-by-step explanation:
a. Construct a decision tree for Wile
The solution to the question has been attached.
b. What is the expected value of the new car?
= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000
= $2000 + $14400 - $22000
= $16400 - $22000
= -$5600
c. What is the expected value of the used car?
= [(0.4 × $4000) + (0.6 ×$9000] - $12000
= $1600 + 5400 - $12000
= $7000 - $12000
= -$5000
d. What is the expected value of leasing the car?
= [(0.1 × -$2000) + (0.9 ×0)] - $8500
= -$200 - $8500
= -$8700
Please Help!! The variables y and x have a proportional relationship, and y = 9 when x = 2. What is the value of y when x = 3? Enter your answer in the box.
Answers
Answer:
\(y=27/2\text{ or } 13.5\)
Step-by-step explanation:
If y and x have a proportional relationship, then they have the standard form:
\(y=kx\)
Where k is the constant of proportionality.
We know that y=9 when x=2. So, we can solve for our k. Substitute 9 for y and 2 for x. Hence:
\(9=2k\)
Divide both sides by 2:
\(\displaystyle k=\frac{9}{2}=4.5\)
So, our constant of proportionality is 9/2 or 4.5.
Therefore, our equation is:
\(\displaystyle y=\frac{9}{2}x\)
To find y when x=3, substitute 3 for x and evaluate. Hence:
\(\displaystyle y=\frac{9}{2}(3)\)
Evaluate:
\(\displaystyle y=\frac{27}{2}=13.5\)
So, when x=3, y=27/2 or 13.5
find the value of ...B
Answers
Answer:
b=–2
Step-by-step explanation:
we've got:
(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243
and we've also got the coefficient of x³ as –720
90b³=–720===> b³=–8===> b=–2
4. Juan cotiza un motor generador de ondas estacionarias para cuerdas en 50 almacenes
eléctricos. Obteniendo los siguientes datos:
300 mil pesos en un almacén y esta con el 10% de descuento; en el almacén dos, costaba 400
mil pesos con un 14% de descuento; en el almacén 3, tenía un costo de 500 mil pero le bajaban
el 20%, en el cuarto almacén, valía 700 mil pesos pero rebajan el 22%; en el almacén 5, costaba
750 mil pesos con un 12% de descuento; en el almacén 6, tenía un precio de 800 mil y le
bajaban el 10%; en el séptimo almacén, tiene un precio de 1000 y le hacen el descuento del 6%;
en almacén 8, cuesta 1200 y bajan el 4%; en el último almacén cobran 1500 y hacen el 2% de
rebaja.
Answers
De acuerdo con lo anterior, la respuesta correcta serían 270,000 es el precio más bajo que obtuvo para comprar un motor generador de ondas estacionarias para cuerdas en el primer almacén.
¿Cómo calcular cuál almacén le ofrece el precio más bajo a Juan?
Para calcular cuál es el almacén que le ofrece el precio más bajo a Juan debemos identificar a cuanto equivale el descuento y restarlo del precio total. Cuando sepamos el precio final comparamos para saber cuál de todos es el menor.
300,000 / 100 = 3,000
3,000 * 10 = 30,000
300,000 - 30,000 = 270,000
400,000 / 100 = 4,000
4,000 * 14 = 56,000
400,000 - 56,000 = 344,000
500,000 / 100 = 5,000
5,000 * 20 = 100,000
500,000 - 100,000 = 400,000
700,000 / 100 = 7,000
7,000 * 22 = 154,000
700,000 - 154,000 = 546,000
750,000 / 100 = 7,500
7,500 * 12 = 90,000
750,000 - 90,000 = 660,000
800,000 / 100 = 8,000
8,000 * 10 = 80,000
800,000 - 80,000 = 720,000
1'000.0000 / 100 = 10,000
10,000 * 6 = 60,000
1'000.000 - 60,000 = 940,000
1'200.000 / 100 = 12,000
12,000 * 4 = 48,000
1'200,000 - 48,000 = 1'152.000
1'500.000 / 100 = 15,000
15,000 * 2 = 30,000
1'500,000 - 30,000 = 1'270,000
De acuerdo a lo anterior, el precio más bajo para comprar un motor generador de ondas estacionarias para cuerdas es 270,000 en el primer almacén.
Nota: Esta pregunta está incompleta y tiene errores en los valores. A continuación esta la información completa y correcta.
Pregunta
¿Cuál tienda le ofrece el precio más bajo a Juan?
Precios
Almacén 1: 300 mil pesos con el 10% de descuento.
Almacén 2: 400 mil pesos con el 14% de descuento.
Almacén 3: 500 mil pero con el 20% de descuento.
Almacén 4: 700 mil pesos con el 22% de descuento.
Almacén 5: 750 mil pesos con el 12% de descuento.
Almacén 6: 800 mil pesos con el 10% de descuento.
Almacén 7: 1'000.000 de pesos con el 6% de descuento.
Almacén 8: 1'200.000 de pesos con el 4% de descuento.
Almacén 9: 1'500.000 de pesos con el 2% de descuento.
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Sean and his crew operate a fishing charter company. They caught a blue
marlin and an amberjack. The weight of the blue marlin was 12 times as
great as the weight of the amberjack. The combined weight of both fish was
1,014 pounds. How much did each fish weigh?
Answers
Given: a || b
Find the missing angle measures in the diagram. Explain how you find each angle measure. (please explain how you got the answer)
Answers
The angle measure explained in the solution.
Given that, a || b, we need to find the missing angles,
∠1 = 42° [vertically opposite angles]
∠3 = 62° [vertically opposite angles]
∠2 = 180°-(∠1+62°) [angle in a straight line]
∠2 = 76°
∠4 = ∠2 [vertically opposite angle]
∠4 = 76°
∠4 = ∠9 = 76° [alternate angles]
∠9 = ∠12 = 76° [vertically opposite angle]
∠3 = ∠ 6 = 62° [alternate angles]
∠ 6 = ∠7 = 62° [vertically opposite angle]
∠3 + ∠5 = 180° [consecutive angles]
∠5 = 118°
∠5 = ∠8 = 118° [vertically opposite angle]
∠4 + ∠10 = 180° [consecutive angles]
∠10 = 104°
∠10 = ∠11 [vertically opposite angle]
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Using the 95% confidence interval data below, what is the mean net profit/loss range when x1 = $5 million and x2 = $3.5 million and the standard error is 0.2144?
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.62113 0.02732 22.73849 0.00000 0.56691 0.67535
x1new 0.08746 0.01224 7.14528 0.00000 0.06317 0.11175
x2new 0.11226 0.01080 10.39308 0.00000 0.09082 0.13369
Multiple Choice
$340,000 to $1,190,000
$570,000 to $680,000
$190,000 to $1,050,000
$710,000 to $810,000
Answers
The mean net profit/loss range when x1 = $5 million and x2 = $3.5 million and the standard error is 0.2144, then the confidence interval is option (d) 1.18969 ± 0.4207, or $710,000 to $810,000.
In statistics, a confidence interval is a range of values that provides an estimate of the true population parameter with a certain degree of confidence. In this case, we will use the given data to determine the mean net profit/loss range with a 95% confidence interval.
To determine the mean net profit/loss range, we need to use the coefficients and standard errors provided in the data. The formula for a confidence interval is:
CI = point estimate ± (critical value) x (standard error)
Where the point estimate is the mean net profit/loss, the critical value is based on the level of confidence (95% in this case), and the standard error is given as 0.2144.
Using x₁ = $5 million and x₂ = $3.5 million, we can calculate the point estimate as follows:
Point estimate = Intercept + (x₁new coefficient) x (x₁) + (x₂new coefficient) x (x₂)
= 0.62113 + (0.08746) x (5) + (0.11226) x (3.5)
= 1.18969 million
Next, we need to calculate the critical value based on the level of confidence. Using a t-distribution with degrees of freedom (n-2), where n is the sample size (not provided), we can find the critical value as 1.96 (from a t-table).
Plugging in the values, we get:
CI = 1.18969 ± (1.96) x (0.2144)
= 1.18969 ± 0.4207
Therefore, the 95% confidence interval for the mean net profit/loss when x1 = $5 million and x2 = $3.5 million is:
1.18969 ± 0.4207, or $710,000 to $810,000.
Therefore, the correct option is (d).
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Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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HELP!!!
The image shown here is a floor-plan of a house.
Make a vertex-edge graph of this floor-plan, where each letter is a vertex and each doorway is an edge.
It is possible to take a tour of the house so that you walk through each doorway only once and finish at your starting point.
True
False
Answers
I Need help pls!
What is 75% of 800?
A; 9 3/8
B; 10.66
Answers
Answer:
it's 600
Step-by-step explanation:
that's not an option there but...
10% of 800 is 80
5% of 800 is 40
80 × 7 = 560
560 + 40 = 600
A wire is 71cm long . you wish to cut it into two pieces. One piece is bent into shape of triangle with legs of equal length .The piece is to be bent into shape of circle .
Answers
To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)
The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)
The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)
Solving for\(\(x\),\) we divide both sides of the equation by 3:
\(\(x = \frac{71}{3}\).\)
Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.
The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:
\(\(x = 2\pi r\).\)
Substituting the value of x we found earlier, we have:
\(\(\frac{71}{3} = 2\pi r\).\)
Solving for r, we divide both sides of the equation by \(\(2\pi\):\)
\(\(r = \frac{71}{6\pi}\).\)
Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.
In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.
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Terrence has a balance of $4000 on his credit cards with a 20% APR. he has decided that he will not make any other purchases on his card until he pays off the debt. he can pay $300 per month. after five months how much will he have paid in interest so far in how large will the remaining balance be?
Answers
The interest is $293.88 in interest
The remaining balance is approximately $2793.88.
How to solve for the interestMonthly Interest Rate = 0.2 / 12
Monthly Interest Rate ≈ 0.01667 (rounded)
Month 1:
Interest: $4000 * 0.01667 ≈ $66.68 (rounded)
New Balance: $4000 + $66.68 = $4066.68
Payment: $300
Remaining Balance: $4066.68 - $300 = $3766.68
Month 2:
Interest: $3766.68 * 0.01667 ≈ $62.82 (rounded)
New Balance: $3766.68 + $62.82 = $3829.50
Payment: $300
Remaining Balance: $3829.50 - $300 = $3529.50
Month 3:
Interest: $3529.50 * 0.01667 ≈ $58.86 (rounded)
New Balance: $3529.50 + $58.86 = $3588.36
Payment: $300
Remaining Balance: $3588.36 - $300 = $3288.36
Month 4:
Interest: $3288.36 * 0.01667 ≈ $54.80 (rounded)
New Balance: $3288.36 + $54.80 = $3343.16
Payment: $300
Remaining Balance: $3343.16 - $300 = $3043.16
Interest: $3043.16 * 0.01667 ≈ $50.72 (rounded)
New Balance: $3043.16 + $50.72 = $3093.88
Payment: $300
Remaining Balance: $3093.88 - $300 = $2793.88
Total = $66.68 + $62.82 + $58.86 + $54.80 + $50.72
≈ $293.88 in interest
The remaining balance is approximately $2793.88.
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Identify 2 congruent angles
Look at picture for reference
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In the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.
In the given diagram, we have ACDE as a quadrilateral, and we know that CD is congruent to CE. To identify two congruent angles, let's examine the properties of the quadrilateral.
Since ACDE is not specified to be a particular type of quadrilateral (such as a parallelogram or rectangle), we cannot directly infer congruent angles from its properties.
However, we can make use of some general properties of quadrilaterals to identify two congruent angles. One property is that the sum of the interior angles of a quadrilateral is always 360 degrees.
Let's consider angle C as one of the angles in ACDE. Since CD is congruent to CE, we can denote angle CDE as angle C' to represent the congruent angles.
Now, using the property that the sum of the interior angles of a quadrilateral is 360 degrees, we can express the relationship between the angles of ACDE as:
∠ACD + ∠CDE + ∠DEA + ∠EAC = 360 degrees
Since CD is congruent to CE, angles CDA and CEA are also congruent (opposite angles in a quadrilateral). So, we can rewrite the equation as:
∠ACD + ∠CDA + ∠C'EA + ∠EAC = 360 degrees
Since we want to identify two congruent angles, let's focus on angles CDA and C'EA. These two angles are formed by the intersection of the congruent sides CD and CE with different adjacent sides.
Therefore, we can conclude that angles CDA and C'EA are congruent in ACDE.
In summary, in the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.
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Please look at the photo for the question. Thank you!
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The function g(x) = x² + 4x has a: A. minimum.
The minimum value occur at x = -2.
The function's minimum value is -4.
How to determine the axis of symmetry and vertex of a quadratic function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:
Axis of symmetry = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function g(x) = x² + 4x, we have:
a = 1, b = 4, and c = 0
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(4)/2(1)
Axis of symmetry, Xmax = -2
Next, we would determine vertex as follows;
g(x) = x² + 4x
g(-2) = -(-2)² + 4(-2)
g(-2) = -4.
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Which one of the them please?
Answers
Answer:
Dog.
Step-by-step explanation:
Because:-
Tomato is much lighter.
Pineapple is not convincing
Dog is reliable.
Pencil is not correct.
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.
First randomization
group a
13.6
12.1
15.9
11.2
9.7
group b
9.2
8.2
11.5
13.8
14.6
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After the first randomization, μ₁ is 12.5, is μ₂ 11.46 and μ₁-μ₂ is 1.04. After the second randomization, μ₁ is 11.36, μ₂ is 12.6 and μ₁-μ₂ is -1.24. After the third randomization, μ₁ is 11.98, μ₂ is 11.98 and μ₁-μ₂ is 0.
Randomization is the process of placing a group of objects, persons, etc. in an unpredictable, illogical, or random order. The sum of all observations in a data set divided by the total number of observations is the data set's mean. The subtraction of two variables is the result of subtracting the means of the two variables. Each randomization in this problem consists of two sets of five observations.
For the first randomization:
μ₁= \(\frac{13.6+12.1+15.9+11.2+9.7}{5}\) = 12.5 [ μ₁ = Group A
μ₂=\(\frac{9.2+8.2+11.5+13.8+14.6}{5}\) = 11.46 μ₂ = Group B]
μ₁-μ₂ = 1.04
Similarly solve for the second and third randomizations
The complete question is:
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.
First randomization
group a
13.6
12.1
15.9
11.2
9.7
group b
9.2
8.2
11.5
13.8
14.6
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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
Midpoint (-15,2) endpoint (-12,11)
What is the other endpoint?
Answers
Answer:
The other endpoint of the segment is \((-18,-7)\).
Step-by-step explanation:
The midpoint of the points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the following formula:
\((x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\)
where \((x_m,y_m)\) = coordinates of the midpoint.
We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:
\((-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2} )\)
To find \(x_1\) we need to solve this equation:
\(-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18\)
and to find \(y_1\) we need to solve this equation:
\(2= \frac{y_1+11}{2} \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7\)
The other endpoint of the segment is \((x_1,y_1)=(-18,-7)\).
Which of the following statements about UK and UL is true?
O A. JL is longer than JK.
O B. UK and JL are the same length.
c. UK is 7 units long
D. UK is longer than UL
Answers
Answer:
B
Step-by-step explanation:
kim buys pet food in 1.5kg packs, het pet needs 0.8kg of food each week. She wants to have enough food for the next 14 weeks. She already has two 1.5kg packs. Work out the smallest number of packs she needs to buy.
Answers
========================================================
Explanation:
"She already has two 1.5kg packs" means she already has 2*1.5 = 3 kg of food.
The statements "her pet needs 0.8 kg of food each week" and "She wants to have enough food for the next 14 weeks" tell us that she needs 0.8*14 = 11.2 kg of food total.
--------------------------------
Let,
x = number of packs she needs to buy
1 pack = 1.5 kg of food
x packs = 1.5x kg of food
Add on the 3 kg of food she already has to get 1.5x+3
The expression 1.5x+3 represents how much food she'll have total after buying x packs.
Set this equal to 11.2 and solve for x
1.5x+3 = 11.2
1.5x+3-3 = 11.2-3 ... subtracting 3 from both sides
1.5x = 8.2
1.5x/(1.5) = 8.2/(1.5) .... dividing both sides by 1.5
x = 5.4667 approximately
x = 6 rounding up to the nearest whole number
We round up instead of down.
This is because if x = 5, then,
1.5*x+3 = 1.5*5+3 = 7.5+3 = 10.5, but this is less than 11.2
However, if x = 6, then,
1.5*x+3 = 1.5*6+3 = 9+3 = 12 which clears the hurdle of 11.2
So this means buying 6 packages of food is the smallest amount needed to ensure her pet has enough food for the next 14 weeks.
Kim needs to buy 6 packs of pet food.
What is Unitary Method?Unitary method is a mathematical technique used to solve problems involving proportions. It involves finding the value of one unit and then using that to find the value of other units. In other words, it is a method in which we find the value of one unit and then use it to calculate the value of a given number of units.
Kim already has 2 packs of 1.5 kg = 3 kg of pet food.
Kim needs 0.8 kg of pet food each week for 14 weeks
= 0.8 x 14
= 11.2 kg.
So, Kim needs to buy an additional
= 11.2 kg - 3 kg
= 8.2 kg of pet food.
Each pack of pet food is 1.5 kg, so Kim needs to buy 8.2 kg / 1.5 kg per pack = 5.47 packs.
Since Kim cannot buy a fraction of a pack, she needs to round up to the next whole number of packs.
Therefore, Kim needs to buy 6 packs of pet food.
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If a three-digit number is divided by 5 or by 6, remainder is 1 in each case. What is the least such three-digit number?
Answers
Answer:
The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.
Step-by-step explanation:
This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.
why mathematical induction is used ?(write a 100 words paragraph)
Answers
Answer:
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers ( non-negitive integers). The simplest and most common form of mathematical induction proves that a statement involving a natural number that holds for all values.