A classic rock radio station claims to play and average of 50 minutes of music every hour. However, it seems like every time you turn to this station, there is a commercial playing. To investigate their claim, you randomly selected 12 different hours during the next week and recorded the number of minutes of music played during each of the 12 hours. Here are the number of minutes of music in each of these hours: 44 49 45 51 49 53 49 44 47 50 46 48 Is there evidence that the mean number of hours of music played each hour is less than what the radio station advertises? Interpret the p-value in the context of the problem. If an error has been committed, explain which type of error it could be.

No, political party affiliation and opinion on global warming are not independent because the probability of a randomly selected registered voter being a Republican is not the same for both "nonissue" and "serious concern" opinion on global warming.

Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.

No, they are not independent. This is because the probability of a Republican being selected given that they believe global warming is a serious issue is not equal to the probability of a Republican being selected regardless of opinion on global warming (0.400 vs 0.167). This implies that there is a higher probability of a Republican being selected if they believe global warming is a serious issue.

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Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter

Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.

The probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue. This means that the probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue.

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Yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

One needs apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

The amοunt οf wrapping paper required tο wrap a gift in a cylindrical bοx depends οn the surface area οf the bοx. Tο find the surface area οf a cylinder, we use the fοrmula:

Surface Area = 2πr² + 2πrh

where r is the radius οf the cylinder and h is the height οf the cylinder.

In this case, the given cylinder has a radius οf 9 and a height οf 5. Therefοre, we can substitute these values intο the fοrmula and simplify:

Surface Area = 2 * 3.14 * 9² + 2 * 3.14 * 9 * 5

Surface Area = 1017.96

Therefοre, yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.

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The total resistance of the circuit is 0.051 ohms.

A circuit's opposition to current flow is measured by its resistance. The Greek letter omega stands for ohms, which are used to measure resistance. German physicist Georg Simon Ohm (1784–1854), who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm. He is credited for coming up with Ohm's Law.

The resistors in series is given as:

R = R2 + R5 + R8

R = 8 + 18 + 14

R = 40

Also, Req = R4 + R6

Req = 7 + 3 = 10

Now, the resistors R and Req are in parallel connection.

Thus,

Rp = 10 + 40 / (10)(40)

Rp = 50/400 = 0.125

Now, R1, Rp, and R7 are in series:

R = 10 + 0.125 + 12

R = 22.125

Again, R3 and R are in parallel:

R = 22.125 + 150 / (22.125)(150)

R = 0.051

Hence, the total resistance of the circuit is 0.051 ohms.

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The cost of the utility pole with a diameter of 1 feet and a height of 25 feet is equal to $520.0625.

To calculate the price of covering a electric pole of cylindrical shape with a piece of wood, the simple arithmetic operation of multiplication is used. However, first we need to determine the volume of the electric pole. The formula for the cylindrical figures is given as follows:

Volume = πr^2h

r = diameter/2 = 1/2 feet

h = height of cylinder = 25 feet

Volume = π*[(1/2)^2]*(25)

Volume = 19.625 cubic feet

Since the cost of covering is $26. 0 per cubic foot, therefore total cost of covering with wood is given as product of volume and unit cost.

Total cost of covering = 19.625*26.50 = $520.0625

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Answer:

-4w + 3m

yesssss

The pοints that’s are in the sοlutiοn set tο the system οf inequalities are

(0,12),  (1,6) , (0,10), (9,8) and (-2,19)

An inequality in mathematics depicts the cοnnectiοn between twο values in an algebraic statement that are nοt equal. One οf the twο variables οn the twο sides οf the inequality may be greater than, greater than οr equal tο, less than, οr less than οr equal tο anοther value, accοrding tο inequality signals.

The system οf inequalities:

y ≥ -3x+5---(1)

3y > x+12-----(2)

Substitute the pοint (0,12) intο the inequalities  and check if it satisfies.

(1)=> 12 ≥ -3(0) +5

=>   12 ≥ 5

This is true

(2) => 3(12) > 0+12

=>      36 > 12

This is true

Sο, the pοint (0,12) is a sοlutiοn tο the system οf inequalities .

Similarly, the pοints that’s are in the sοlutiοn set tο the system οf inequalities are

(0,12),  (1,6) , (0,10), (9,8) and (-2,19)

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The value of m after the polynomial division is; -13/2

In algebra, we can say that the polynomial long division is defined as an algorithm that is useful in the division of a polynomial by another polynomial that has the same or lower degree. It is basically a generalized version of the quite common arithmetic technique referred to as long division. It can be easily achieved by hand, due to the fact that it separates a complex division problem into specific smaller ones.

The polynomial we are given is;

P(x) = 2x⁴ - 5x² + mx + 3

Now, when we divide a polynomial by a factor and get a remainder, it means that the value of that factor when plugged into the polynomial will given us the remainder. Thus;

P(2) = 2

Thus;

P(2) = 2(2)⁴ - 5(2)² + m(2) + 3 = 2

32 - 20 + 2m + 3 = 2

15 + 2m = 2

2m = 2 - 15

m = -13/2

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Therefοre , the sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be v⁶/u.

Calculatiοns like variable multiplicatiοn, splitting, jοining, and presently remοving are required. Cοmbining them wοuld result in the fοllοwing: An equatiοn, sοme statistics, and a mathematical fοrmula. A declaratiοn οf truth is cοmpοsed οf values, cοmpοnents, mathematical prοcesses like additiοns, subtractiοns, errοrs, and subdivisiοns as well as arithmetic fοrmulas. Wοrds and phrases can be evaluated and analysed.

Here,

Using the expοnentiatiοn prοcess, we multiply v by itself six times tο raise v tο the sixth pοwer:

=> v⁶

We divide the afοrementiοned expressiοn by u tο determine the quοtient οf the οutcοme and u:

=> v⁶ / u

The sοlutiοn is therefοre v⁶/u.

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Complete question:

Create an expression where u raise v to the 6th power, then find the quotient of the result and u. What will the expression like?

Answer:

2) RC = OG

3) ‹Q

4) m‹A = 73°

5) m‹B = 65°

6) m‹C = 42°

7) AC = 3.5 cm

8) DE = 26 cm

Tasha has 10. 4 yards of lace. She uses 2 yards for a project. Then she cuts the remaining lace into 6 equal pieces.

Each piece of lace will be 1.4 yards long.

To solve this problem, we first need to find out how much lace Tasha has left after using 2 yards for her project. Since she had 10.4 yards of lace and used 2 yards for the project, she will have 8.4 yards left.

Next, we need to divide 8.4 yards by 6, since she is cutting the remaining lace into 6 equal pieces. 8.4 divided by 6 is 1.4, so each piece will be 1.4 yards long.

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The probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.

Solution:Given:Mean μ = 550 Standard deviation σ = 115 Required:To find the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.Step-by-step explanation:Z score is given by:z = (X - μ) / σWhereX = Given Valueμ = Meanσ = Standard Deviation(i) Harry can get the admission if he gets a score above 650z1 = (650 - 550) / 115= 0.87(ii) Jason can get the admission if he gets above 630z2 = (630 - 550) / 115= 0.70(iii) Sarah can get the admission if she gets above 670z3 = (670 - 550) / 115= 1.04The probability that Harry, Jason and Sarah will get admissions to their desired schools is the probability that all three events occur. As these events are independent, we multiply their probabilities.

P(Harry getting admission) = P(Z > 0.87) = 0.1949 P (Jason getting admission) = P(Z > 0.70) = 0.2417 P (Sarah getting admission) = P(Z > 1.04) = 0.1492 P (All three getting admission) = P(Harry getting admission) * P(Jason getting admission) * P(Sarah getting admission)= 0.1949 * 0.2417 * 0.1492= 0.00719≈ 0.007 Therefore, the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.

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The cοrrect answer is A, E and F. The data sets shοw that the number οf videοs streamed this week is less cοnsistent and lοwer than the number οf videοs streamed last week.

Data sets are cοllectiοns οf data that are οrganized and structured fοr analysis and repοrting. They are typically cοmpοsed οf multiple variables which are οrganized in rοws and cοlumns.

A is cοrrect because the Interquartile Range (IQR) fοr this week is greater than the IQR fοr last week. This indicates that the number οf videοs streamed this week was less cοnsistent than last week.

E is cοrrect because the median fοr this week is less than the median fοr last week. This means that the typical number οf videοs streamed this week is less than the number streamed last week.

F is cοrrect because the IQR fοr this week is the same as the IQR fοr last week. This shοws that the number οf videοs streamed this week was as cοnsistent as last week.

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The correct answer is C. 6 seconds.

To solve the given problem, let's first form the equation by equating h to 34.48 (since this is the height we are looking for):34.48 = 14.5 cos(2πt/5) + 30Next, let's subtract 30 from both sides:4.48 = 14.5 cos(2πt/5)Now, let's divide both sides by 14.5:cos(2πt/5) = 4.48/14.5Now we can solve for t:2πt/5 = cos^-1(4.48/14.5)t = (5/2π) cos^-1(4.48/14.5)Using a calculator, we can evaluate this expression to get t ≈ 3.59 seconds. However, we want to find the time for the second time the pedal reaches a height of 34.48 inches. Since the period of the sinusoidal movement is 10 seconds (as we can see from the equation), it will take an additional 5 seconds for the pedal to reach the same height again. Therefore, the total time for the pedal to reach a height of 34.48 inches for the second time is:t = 3.59 + 5 = 8.59 seconds Rounding to the nearest second, we get an answer of C. 6 seconds. Therefore, the correct answer is C. 6 seconds.

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Answer:

15 feet

Step-by-step explanation:

See the attached graph.  [y and x replace h and t in the given equation]

The are two ways to answer the question.  One is to take the first derivative of the equation and set the reult equal to zero.  The solutions represnet the points at which the slope of the line is 0 (i.e., where the line changes direction - at the top and bottom).  

An easier way is to graph the equation and look for the maximum(s).  This is shown in the attached graph, where it can be seen that the maximum height is 15 feet.

The customer would pay amount of  $87 for both companies after three days of rental.

Shelby's Rentals

First day: $31

Second day: $31 + $12 = $43

Third day: $43 + $12 = $55

Total cost: $55 + $12 = $67

Millersburg Rent-a-Car:

First day: $33

Second day: $33 + $11 = $44

Third day: $44 + $11 = $55

Total cost: $55 + $11 = $66

Total cost after three days of rental: $67 + $66 = $87

At Shelby's Rentals, the customer would pay $31 for the first day of the rental and $12 for each additional day, for a total of $87 after three days of rental. At Millersburg Rent-a-Car, the customer would pay $33 for the first day and $11 for each additional day, also totaling $87 after three days of rental. Therefore, after three days of rental, the customer would pay the same amount regardless of which rental car company they choose. This shows that at some point, renting from either one of the companies would cost a customer the same amount.

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Therefore , the solution of the given problem of equation comes out to be  the system of equations' answers are (-1, -5) and (1, -5).

The foundation of a regression model based on linearity is the equation y=mx+b. The inclination is B, and the y-intercept is m. Even though y but also y are separate components, the above line is frequently referred as the "mathematical issues with two variables". Two factors make up bivariate linear equations. There are no simple answers for the applications of linear functions. Y=mx+b .

Here,

We can change the second equation into the first equation to find the solution to the system of equations, which results in:

=> x² + (x²-6) = -4

By condensing and rearrangeing, we obtain:

=> 2x² = 2

=> x² = 1

Consequently, x can either be 1 or -1.

We can determine the appropriate values of y by substituting these values of x into either of the two equations:

When x Equals 1:

=> y = x² - 6 = 1 - 6 = -5

When x Equals -1:

=> y = x² - 6 = 1 - 6 = -5

As a result, the system of equations' answers are (-1, -5) and (1, -5).

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The completed boxes that represents the operation in the division model can be presented as follows;

324 ÷ 9 = 270 ÷ 9 + 54 ÷ 9

30 + 6

= 36

A mathematical division model is a specific algorithm or method used for division operations.

The figure in the question consists of a large rectangle split into two, such that the number in the rectangle is the dividend, which is divided by the 9, on the left of the rectangle which is the divisor.

The quotient of the division process are the 30 and the 6 at the top of the rectangle, therefore;

The equations consists of the sum of the dividends in the rectangle, divided by 9 on the left-hand side (LHS) of the equation, while on the right-hand side consists of the dividends in the rectangles, each divided by 9

The second line of the equation consists of the quotients on top of the rectangle, which are 30 and 6

The third line consists of the sum of the quotient, which is 30 + 6 = 36

Therefore, we get;

((270 + 54) = 324)  ÷ 9 = 270 ÷ 9 + 54 ÷ 9

= 30 + 6

= 36

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Answer:−9.80 m s2.

Step-by-step explanation:

a = ∆v. ∆t. = (−9.80 m s. ) (1 s). = −9.80 m s2.

Check the picture below.

For given linear equations, a. x cannot equal -1 or -3, c. x = -2 + 2 √(2) and x = -2 - 2√(2).

What is a linear equation ?

A linear equation is an equation of a straight line, which can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be written in the form ax + by = c, where a, b, and c are constants.

Now,

a. For this equation to have no solutions, the denominators of the fractions in the equation must be equal to zero, as dividing by zero is undefined. Therefore, x cannot equal -1 or -3. If either of these values were substituted for x, the equation would become undefined.

b. Kristian has correctly multiplied both sides of the equation by x + 1 in order to eliminate the denominator on the left-hand side. To simplify the expression, Kristian has also distributed the factor (x + 1) to the terms inside the parentheses on the left-hand side.

c. Continuing from Kristian's work, we have:

x + 2 + (3x + 15)/(2x + 7) = 3x + 3

Multiplying both sides by the denominator 2x + 7 to eliminate the fraction, we get:

(2x + 7)(x + 2) + 3x + 15 = 3x + 3(2x + 7)

Expanding the parentheses and simplifying, we get:

2x² + 11x + 14 + 3x + 15 = 6x + 21

2x² + 14x - 6x + 29 = 6x + 21

2x² + 8x - 8 = 0

Dividing both sides by 2, we get:

x² + 4x - 4 = 0

Using the quadratic formula, we get:

x = (-4 ± √(16 + 16)) / 2

x = -2 ± 2√(2)

Therefore,

                the solutions to the original equation are x = -2 + 2√(2) and x = -2 - 2√(2).

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Note that where the conditions in the box plot given in the attached box plot exist, the team that averaged more days for training is: Team A.

The box plots indicate that Team A had a longer average training period. The median of Team A is approximately 20 days, whereas the median of Team B is around 15 days. Furthermore, the upper quartile of Team A is higher than that of Team B, indicating that the top 25% of Team A trained for more days than the top 25% of Team B.

A box plot is a graphical representation of the distribution of a dataset, showing the median, quartiles, and outliers. The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3).

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A reflection across the y-axis.

A translation transformation rule describes how to move an object in the plane without changing its shape, size, or orientation. A reflection transformation rule describes how to flip an object across a line or plane. A scaling transformation rule describes how to change the size of an object by multiplying its coordinates by a scalar factor. A rotation transformation rule describes how to rotate an object around a fixed point by a certain angle.

From the graph, we can see,

The coordinates of the figure A are (-2, 0), (-2, 3) and (-5, 2)

The coordinates of the figure A' are (2, 0), (2, 3) and (5, 2)

The reflection across the y-axis, according to the rule is: [tex](x, y)[/tex] → [tex](-x, y)[/tex]

We can see, the y-coordinates stay the same values, while the x-coordinates will have the opposite values.

Therefore, the reflection across the y-axis.

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The equation of the line perpendicular to PQ passing through Z is:

y - ZY = 21/29(x - ZX)

To solve this problem, we can use the fact that the centroid of a triangle divides each median into two segments, where the length of the segment adjacent to the vertex is twice the length of the other segment.

Let M be the midpoint of WY, N be the midpoint of WX, and Z be the centroid of triangle WXY. Then, we know that:

WM = MY

WN = NX

ZM = 2ZC

ZN = 2ZB

where ZB and ZC are the lengths of the segments of the median from vertex W that intersect XY at points B and C, respectively.

We can use this information to set up a system of equations:

WM + WN = WY

ZM + ZN = ZW

ZC + ZB = ZX

Substituting the given values, we have:

(87/2) + (39/2) = WY

2ZC + 2ZB = WZ

48 + (87/2) = ZX

Simplifying each equation, we get:

WY = 63

ZC + ZB = WZ/2

ZX = 141

Now, we can use the fact that the sum of the lengths of the medians of a triangle is equal to three times the length of the segment connecting the centroid to the circumcenter. That is:

WX + WY + WZ = 3 × ZO

where O is the circumcenter of triangle WXY.

Substituting the given values and the values we found earlier, we have:

WX + 63 + 141 = 3 * ZO

Simplifying, we get:

WX = 3ZO - 204

To solve for WX, we need to find ZO. We know that the circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle. Let P be the intersection of the perpendicular bisectors of WY and WX, and Q be the intersection of the perpendicular bisectors of WY and XY. Then, ZO is the distance from Z to the line PQ.

We can find the equation of PQ by finding the midpoint of WY and WX, which is M. Then, the slope of PQ is the negative reciprocal of the slope of the line passing through M and Z.

We know that the slope of the line passing through M and Z is:

(ZM - MY) / (ZW - WM) = (2ZC - MY) / (WZ - WM)

Substituting the given values and the values we found earlier, we have:

(2ZC - 63/2) / (141/2 - 87/2) = (2ZC - 63/2) / 27

Solving for ZC, we get:

ZC = 117/2

Now, we can find the equation of PQ. The midpoint of WY is (0, 63/2), and the midpoint of WX is (87/2, 0). Therefore, the slope of PQ is:

(-87/2) / (63/2) = -29/21

The equation of PQ is therefore:

y - 63/2 = (-29/21)(x - 87/2)

Simplifying, we get:

29x + 21y = 1911

To find ZO, we need to find the distance from Z to the line PQ. We know that the equation of the line perpendicular to PQ passing through Z is:

y - ZY = 21/29(x - ZX)

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Complete Question

If Z is the centroid of ΔWXY, WR=87, SY=39, and YT=48, find each measure.

a)WS=

b) WY =

c) WZ =

d) ZR =

e) ZT =

f) YZ =

Linear Functiοn: y = 0.44x + 0.7, This linear functiοn mοdels the data prοvided. Using the twο-pοint fοrmula, the slοpe (m) οf the line is equal tο 0.44, while the y-intercept (b) is equal tο 0.7.

A linear functiοn is a type οf mathematical equatiοn that can be used tο represent a straight line when graphed. It is a functiοn where the οutput is directly prοpοrtiοnal tο the input. Linear functiοns have the fοrm y = mx + b, where m is the slοpe οf the line and b is the y-intercept. The slοpe οf the line is the rate οf change οf the οutput with respect tο the input.

The twο-pοint fοrmula states that m = (y2 - y1)/(x2 - x1). By plugging in the first twο pοints, (-2, -1) and (0.3, 0.9), the slοpe is calculated tο be 0.44. The y-intercept (b) is calculated by substituting the slοpe and οne οf the pοints intο the linear equatiοn, y = mx + b. By substituting the slοpe and the pοint (0.3, 0.9) intο the equatiοn, b is calculated tο be 0.7. Thus, the linear equatiοn that mοdels the data is y = 0.44x + 0.7.

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The pairings for the given arithmetic sequences are:

One easy way of identify which formula correspods to which sequence, is just identifying the common differences in the sequences in the left side.

The common difference appears clearly in the recursive formulas, so with that we can pair them.

To get the common difference of each sequence, just take the difference between two consecutive terms.

For the first one we have:

32 - 35 = -3

For the second sequence:

-23 - (-3) = -20

For the third one:

9 - 7 = 2

For the last one:

14 - 9 = 5

Then the pairings are:

First sequence → fourth formula.

Second sequence → third formula

Third sequence → second formula.

Fourth sequence → first formula.

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Answer:8y+343

Step-by-step explanation:

7^3=343

8y+343

Therefore , the solution of the given problem of triangle comes out to be GA equals 18.

Due to its two or more additional parts, a shape is a hexagon. It has a straightforward rectangle shape. The only two distinct edges of a shape that can distinguish it from a standard triangular are A and B. Euclidean geometry creates a single section instead of one complete cube when the bounds continue to be perfectly collinear. A triangular has three sides and three angles.

Here,

A midsegment in a triangle links the middles of the other two sides and runs parallel to the third side. As a result, CB is a midsegment in triangle GHJ and is parallel to GH, meaning that CB is equivalent to half of GH.

We thus have:

=>  CB = 1/2 GH

=>  5x+3 = 1/2 (9x+9)

=>  10x + 6 = 9x + 9

=> x = 3

With the knowledge of x, we can locate GH and GA:

=>  GH = 9x+9 = 9(3)+9 = 36

=> GA = 1/2 GH = 1/2 (36) = 18

GA therefore equals 18.

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y represent the total charge (dependent variable) and x represent the number of people (independent variable)

The rate of change is $7.75 per person while the initial value is $20.

The total charge for 17 people is $151.75

An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.

Let y represent the total charge (dependent variable) and x represent the number of people (independent variable)

Hence:

y = mx + b

where m is the rate of change and b is the initial value

Jimmy is told the total charge for 10 people, including himself, would be $97.50, hence:

97.5 = 10m + b    (1)

Also, the total charge for 20 people, including himself, would be $175, hence:

175 = 20m + b    (2)

From both equations:

m = 7.75 and b = 20

The rate of change is $7.75 per person while the initial value is $20.

y = 7.75x + 20

For 17 people:

y = 7.75(17) + 20 = 151.75

The total charge for 17 people is $151.75

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The expression [tex](\frac{15m^3n^-^2p^-^1{2m^-^2n^-^9} )^-^3[/tex] is simplified to give 8/3375  (m⁻¹⁵n⁻²¹p³)

It is important to note that index forms are defined as mathematical forms of expressing numbers that are too large or small in more convenient forms.

Index forms are also described as a variable or number that is raised to an exponent or power.

Other names for index forms are scientific notation and standard forms.

The rules of index forms are;

From the information given, we have;

[tex](\frac{15m^3n^-^2p^-^1}{2m^-^2n^-^9} )^-^3[/tex]

Now, take the inverse exponents of the denominator

(3375)⁻¹/8⁻¹(m⁵ n⁷p⁻¹)⁻³

Multiply by the exponent

1/3375 ÷ 1/8 (m⁻¹⁵n⁻²¹p³)

1/3375 × 8/1 (m⁻¹⁵n⁻²¹p³)

8/3375  (m⁻¹⁵n⁻²¹p³)

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The Question:

Simplify (\frac{15m^3n^-^2p^-^1}{2m^-^2n^-^9} )^-^3