rewrite 1/12 x^3 y + 5/12 xy^2 using a common factor
1/6 xy(2x2 + 5y)
1/6 x2y(2x + 5y)
1/12 xy(x2 + 5y)
1/12 x3y(y + 5)

The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Given :

The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .

From the table:

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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Answer:

14x+41

Step-by-step explanation:

Answer:

14x + 41

Step-by-step explanation:

4(2X - 1) + 3(2X + 15)  distribute the 4 and 3.

8x - 4 + 6x + 45  Combine like terms

14x + 41  This is your answer simplified.

We proved the expression rank(AB)=rank(B)  and  rank(BA)=rank(B),

where A and B are the two matrices of same order.

Given, A is a square matrix.

If  A  is invertible and a  n×n  square matrix of full rank.

Since both AB  and BA exist, where B is also a n×n square matrix.

rank(B)=rank(BT)

On using the rank–nullity theorem, we get

nullity of a matrix be n minus the rank of the matrix.

So let  U  be a matrix whose columns are a basis for the nullspace of  AB, so that  ABU = 0.

Pre-multiplying both sides by  A−1 , we obtain  BU=0,

As B and AB have the same rank.

Similarly, let  V  be a matrix whose columns are a basis for the null space of  ATBT, so that  ATBTV=0 .

Pre-multiplying both sides by (A−1)T , we get  

BTV=0.

Since  rank(BT)=rank(B)  and  rank(ATBT)=rank((BA)T)=rank(BA)

we get rank(AB)=rank(B)  and  rank(BA)=rank(B).

So, rank(AB)=rank(B)  and  rank(BA)=rank(B).

Hence, rank(AB)=rank(B)  and  rank(BA)=rank(B).

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Brittany Taylor employs some figurative language in her letter to the editor titled "I, Too, Have a Dream." She employed personification and metaphors. In order to persuade her audience to support the reinstatement of DACA, she makes her ideas by presenting a problem and a solution. According to Brittany Taylor's letter, she used personal experience and official government documents like the DACA to prove that deportation is cruel.

Brittany Taylor expresses the desire for DACA to continue so that the editor will permit its continuation in the United States. In order for her friend Areliss to continue living her dreams and remaining in the country, Brittany says she has a dream to keep DACA in the United States.

DACA recipients have a dream: they hope that one day their lifetime of service to the US will be acknowledged and they will be able to remain in the place they have always called home. An explanation of how the example achieves its objectives Brittany is attempting to persuade the editor that DACA has a dream to be acknowledged, remain operational, and not be terminated.

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Answer:

An idea to help: In “I, Too, Have A Dream”, Brittany Taylor, the author, uses a metaphor to help emphasize an objective in the minds of the audience

U KICKED ME OUT HOPE THIS HELPS KATEEEEE!

Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.

What is rewrite?

The term rewrite sentence refers to the sentence was the written in the sentence but in the different style. It was to describe the sentence meaning was the similar, but the wittering style was the different. The rewrite the sentence was the but not the copy to the sentence.

According to the given, the sentence are the rewrite. There was the sentence is the different but, the meaning was the same. The sentence was the "Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind."

As a result, the sentence was the Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.

Answer:

y > 5x + 14

Step-by-step explanation:

5x – y > –14

–y > –5x–14

divide both sides by (–)

–(–y) > –(–5x–14)

y > 5x + 14

if i deserve the right pls mark me as brainliest

Answer:

67.7215189873%

Step-by-step explanation:

The price of a desktop computer decreases from $3160 to $1020

Initial price of desktop =$3160

New Price= $1020

Change in price = 3160 - 1020 = 2140

Percentage decrease = [tex]\frac{2140}{3160}[/tex][tex]X[/tex][tex]100[/tex]=67.7215189873%

Hence , the answer is 67.7215189873%

Hope it helps u

Answer: I hope this is helpful

Step-by-step explanation:

The square root of 81 is 9 and you can say -9

We can find the square root of 81 using prime factorization method, or repeated subtraction method.

81 is a perfect square number and it is the fourth power of 3. we will calculate the square root of 81 by repeated subtraction method and solve a few interesting problems.Square Root of 81: √81 = 9

The square root of a number is the number that when multiplied to itself gives the original number as the product. Finding the square root of a number is the inverse of squaring a number. 81 = a × a = a2 Thus, a = √81= √(9 × 9)9 × 9 = 81 or -9 × -9 = 81. Therefore √81= ± 9This shows that 81 is a perfect square.

Answer:

I'm sorry but this question isnt do-able without the multiplechoice

Step-by-step explanation:

Step-by-step explanation:

since the fraction is a ratio, we know that the whole amount of $57 consists of 2+1 = 3 equally sized parts.

Ralf gets 2 of these parts, Susie one part.

each part is

57 / 3 = $19

so, Ralf gets

19×2 = $38

Susie gets

19×1 = $19

The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases.

| Roadway Area (x) | Chloride Concentration (y) |

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

| 10.7 | 28.2 |

| 11.3 | 28.3 |

| 11.7 | 28.4 |

| 11.8 | 28.5 |

| 12.6 | 28.8 |

| 13.2 | 29.2 |

The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases. Specifically, there was a statistically significant positive correlation between the two variables, with the chloride concentration increasing by an average of 0.3 mg/L for every 1% increase in the roadway area in the watershed.

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The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.

3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.

Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282

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The object is undergoing uniform circular motion. The radius of the circular path is equal to 0.50 meters. The centripetal force, F, acting on the object can be calculated using the equation F= mv^2/r in hporizontal circular path

m is the mass of the object, v is the velocity of the object and r is the radius of the circular path.

F = (1.0 kg) (5.0 m/s)^2 / 0.50 m

F = 50.0 kg m/s^2

The object is undergoing uniform circular motion, which means it is moving at a constant speed in a circular path with its center at point O. The radius of the circular path is equal to 0.50 meters. The force acting on the object is known as the centripetal force, and can be calculated by using the equation F= mv^2/r. This equation requires the mass of the object (m), its velocity (v), and the radius of the circular path (r). In this case, the mass is 1.0 kg, the velocity is 5.0 m/s, and the radius is 0.50 m. Plugging these values into the equation gives the centripetal force acting on the object as 50.0 kg m/s^2.

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Answer:

-13

Step-by-step explanation:

the pattern goes +7 - 14, so -20 + 7 = 13

Based on the data provided in the table, an inverse relationship exists between variables x and y. (Option A)

An inverse relationship refers to a relationship between two variables that changes in opposite directions. In other words, an increase in one variable results in a decrease in the other variable and vice versa. An inverse relationship is represented in the form of y = k/x, where x and y are two variables and k is the constant value. Based on the data provided in the table, as the value of x increases, the value of y decreases by a constant value. Hence, the relationship that exists between variable x and y is inverse.

Note: The question is incomplete as it is missing options which are A) inverse B) direct C) independent d) there is no relationship between variable x and y.

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Answer: 23.49

Step-by-step explanation:

Look at the thousandths place and the hundredths place.

92

Now we round 92.

1-4 it stays the same

5 or more you raise it

92 is about 90.

So you would get 23.490

You can eliminate the excess zero.

Your answer is 23.49

The length of the diagonal from point A to point G is √89.

Blank 1: Using the Pythagorean Theorem

Blank 2: Finding the AC.

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

In the given question, we have to find the length of the diagonal from point A to point G.

We would first use on the bottom of the box rectangle to find the diagonal AC.

Then we use CG as of the triangle ACG.

Blank 1: Using the Pythagorean Theorem

In this theorem; a^2+b^2=c^2

Where a=adjacent side, b=base, c=hypotenuse

Blank 2: Finding the AC.

Now in the triangle ABC, use Pythagorean Theorem

So AC = √(AB)^2+(BC)^2

AC = √(8)^2+(3)^2

AC = √64+9

AC = √73

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

Now in the triangle ACG, use Pythagorean Theorem

So AG = √(AC)^2+(CG)^2

AG = √(√73)^2+(4)^2

AG = √73+16

AG = √89

Hence, the length of the diagonal from point A to point G is √89.

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A farmer needs to construct two adjoining rectangular pens with each pen is to have an area of 1200 square feet. So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

For pictures of two rectangular pens, see the attachment.

Area of rectangle = length × width

A = x × y

1200 = xy

     y = 1200/x

The entire length of the fence

P = 3x + 4y

P = 3x + 4 (1200/x)

P = 3x + 4800/x

P = 3x + 4800x⁻¹

Find dimentions will minimize the length of fencing, if P' = 0.

P = 3x + 4800x⁻¹

P' = 3 - 1 × 4800x⁻¹⁻¹

0 = 3 - 4800x⁻²

4800x⁻² = 3

4800/x² = 3

4800 = 3x²

     x² = 4800/3

     x² = 1600

     x = 40

y = 1200/x

y = 1200/40

y = 30

So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

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As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.

What is standard deviation ?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.

The following null and alternative hypotheses need to be tested

H0 :  µ  = 16

Hα :  µ  < 16

This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28

The rejection region for this left-tailed test is R = {z : z < -1.282}

The z-statistics is computed as follow

[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]

   = (15.84 - 16) / (0.4 / √16)

   = -1.6

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The value of x such that no meterial left over after manufacturing the fertilizer is 1

The area of a place is the floor space occupied by an object.  we are to determine the value of x in the length and width of the floor to be used by the manufacturer

The givn parameters are the use of

2 units of potash and

3 units of urea.

Recall that the area of a rectangular floor space is (L*W).

This implies that (x+6)(x-2)=2

x²-2x+6x-12=2

x²+4x-10=0   ..........................  (1)

Also, for the urea

Area= (x-3)(x+1)=3

x²+x-2x-2=3

x²-x-2-3=0

This implies that

x²-x-5=0  .............................(2)

Assuming equal molar density in each product,

equations 1 and 2 are equal

x²+4x-10=x²-x-5

Collecting like terms

x²-x+4x+x-10+5=0

5x-5=0

5x=5

x=1

Therefore, assuming equal molar density in each product the value of x=1

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When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.

Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.

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Step 1

We are given a homogenous rod in a cubic curve shape having two free ends, upper end B

and lower end x

The distance of the upper end from x

axis is 1m

and from y axis is 2m.

The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by

[tex]y=2 x^3[/tex]

Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.

Step 3

The given equation of the homogenous rod is,

[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]

The given equation of the homogenous rod is,

\begin{aligned}

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]

[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]

[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]

Substituting the values in the above expression and solving,

[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]

Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,

[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]

Therefore, the center of gravity of the given homogeneous rod is

0.857 m above the horizontal axis

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The value of the other points in each of the number line is;

a) M = -2¹/₂; N = -1; R = 4

b) M = -1; P = 1; R = 1.6

c) M = -125; P = 125; N = -50

d) N = -6; P = 15; R = 24

a) The point P = 2¹/₂

The distance from point 0 of the number line to point P is 5 units and therefore;

Each unit = 2¹/₂/5 = ¹/₂

Thus;

M = -2¹/₂

N = -1

R = 4

b) The point N = -0.4

The distance from point 0 of the number line to point N is 2 units and therefore;

Each unit = 0.4/2 = 0.2

Thus;

M = -1

P = 1

R = 1.6

C) The point R = 200

The distance from point 0 of the number line to point R is 8 units and therefore;

Each unit = 200/8 = 25

Thus;

M = -125

P = 125

N = -50

D) The point M = -15

The distance from point 0 of the number line to point N is 5 units and therefore;

Each unit = 15/5 = 3

Thus;

N = -6

P = 15

R = 24

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consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36

The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.

To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.

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[tex]-4-4[/tex]

[tex]-4+(-4)[/tex]

[tex]=\fbox{-8}[/tex]

[tex]-4+(-4)[/tex] on a number line:

Answer:

y=-7(x+1)^2 +8

Step-by-step explanation:

Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.

y=-9(x+1)^2+8

start with the vertex form of a parabola:

y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.

1. plug in the vertex coordinates

y=a(x+1)^2+8

2. to find "a", plug in the point coordinates in the function from step 1 for x and y

-1=a(-2+1)^2+8

when you solve this equation, you will find that a=-9

3. substitute "a" value in the equation from step 1

Done

Answer:

TVM calculator: N = 40, PV = -1,075.25, PMT = 30.25, FV = 1,000; CPT I = 2.714% YTM = 2.714% × 2 = 5.43%

Step-by-step explanation:

The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft

According to the question,

A norman window has the shape of a rectangle surmounted by a semicircle.

Let The width of rectangle be x and height be y

It is given that  the diameter of the semicircle is equal to the width of the rectangle

Therefore , Diameter of circle = x

Radius = x/2

Perimeter of window  = 32 = Perimeter of rectangle + Perimeter of semi-circle

=> 32 = Width + 2height + πr

=> x + 2y + πx/2 = 32

=> 2x + 4y +  πx = 64

Solving for y,

=> 4y = 64 - 2x - πx

=> y = 64  - 2x - πx/ 4 ----------(1)

Area of the window = Area of rectangle + area of semi-circle

=> A = Width × hiegth +  πx²/8

=> A = xy + πx²/8

Substituting the value of y from equation (1)

=> A =  x (  64  - 2x - πx/ 4  ) + πx²/8

[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]

Differentiating A w.r.t x

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]

Now , To find a maximum area

dA/dx = 0

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]

Solving for x ,

64 - 4x - 2π + πx = 0

=> x = 64 / 4 + π ------(2)

Differentiating A again w.r.t x

=> d²A / dx² = -2(2 + π)/4 + π/4

=> -π+4 / 4 which is less than zero

Therefore,

Area is maximum when x = 64 / 4 + π

The exact value of x (in ft) so that the greatest possible amount of light is admitted is  8.96 ft

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Answer:4*3+70=840

Step-by-step explanation:

Perimeter = 2(Length + Width)

length = 4x ; width = 3x ; perimeter = 70

Perimeter = 2(Length + Width)

70 = 2(4x + 3x)

70 = 2(7x)

70 = 14x

x = 5

Perimeter = 2(Length + Width)

70 = 2(20 + 15)

70 = 2(35)

70 = 70

1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809

2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.

3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.

4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.

Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.

MINITAB procedure:

Choose Stat > Regression Regression

Step 2: In Responses, enter the column of Age (yrs)

Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901

The regression equation  Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)

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Answer:

Go and look up your tables and read below

Step-by-step explanation:

To solve the problem 5 x 4 using the multiplication table, you would look up the corresponding entries in the table for the numbers 5 and 4. In the row labeled 5 and the column labeled 4, you would find the product 20, which is the answer to the problem 5 x 4.

answer

Step-by-step explanation: