Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²

Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

Given that,

In Clark's backyard, a sizable gazebo is being constructed. It has a typical hexagonal form. The gazebo has 12 feet on each side. 10.4 feet tall is the apothem. He must get stones for the flooring. The price of a particular kind of interlocking stone is $9.50 per square foot.

We have to identify the gazebo's floor's cost.

We know that,

The distance from the center of the regular polygon to the mid point of the side. Here, AB is the chord and AM =BM. O is the center of the circumcircle.

Segments joining the center of a circle to the midpoint of the chord is perpendicular to the chord.

So, OM ⊥AB

In ΔOAB,

AB is the base and OM is the height.

AB = 12 feet

OM = 10.4 feet.

The area of the triangle OAB =1/2×base×height

= 1/2×12×10.4

=62.4 square feet.

A regular hexagon is divided into 6 equilateral triangle having each side  12 feet.

Area of the regular hexagon = 6× area of the one triangle

=6×62.4=374.4 square feet

Cost of inter locking stones = $9.50 per square feet.

Total cost of gazebo's floor = 374.4× 9.50 =$3556.8

Therefore, Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

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On solving the provided question, we can say that - by doing the equation, we have -12 +18 = p + 7 => 6 = p + 7 => p = -1

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

-12 +18 = p + 7

6 = p + 7

p = -1

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The probability Richard marker is 11.The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

According to question:-

11/1 = 11

11/1 = 11

The probability Richard marker is 11.The probability of anything occurring is known as probability.

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Answer:

Yes, it is possible

Step-by-step explanation:

Answer:

dunno la saya , gak bisa bahasa ingeris

Answer:

-sqrt(2)/2 , the last option of your document.

Step-by-step explanation:

sin(7pi/4) = -sin(7pi/4 - pi)

                = -sin(7pi/4 - 4pi/4)

                 = - sin(3pi/4)

sin(3pi/4) is a special angle , which is sqrt(2)/2

Hence, sin(7pi/4) = -sin(3pi/4)

                             = -sqrt(2)/2

Answer:

-sqrt(2)/2

Step-by-step explanation:

did the test

First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.

Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:

time = distance/rate

time = 26/6

time = 4.33 hours

Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:

time = 26/7.5

time = 3.47 hours

Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:

time = 2 + (36/60)

time = 2 + 0.6

time = 2.6 hours

In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.

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The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.

The midpoint formula is expressed as;

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1(-3,10)

Point 2( 15,-2 )

Plug the given values into the midpoint formula and simplify.

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]

[ ( 12)/2, ( 10 - 2 )/2 ]

[ ( 12)/2, ( 8 )/2 ]

( 12/2, 8/2 )

( 6,4 )

Therefore, the midpoint is (6,4).

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 15 - (-3)  )² + ( -2 - 10 )² )

D = √( ( 15 + 3  )² + ( -2 - 10 )² )

D = √( ( 18  )² + ( -12 )² )

D = √( 324 + 144 )

D = √( 468 )

D = 6√13

Therefore, the distance between the points is 6√13.

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Answer:

The answer is D (2 1/2)

Hope u helped

Answer:

Step-by-step explanation:

Dans le calcul d'une somme, ou d'un produit, de deux nombres, on peut échanger la place de deux nombres. Dans le calcul d’une somme, ou d'un produit, de trois nombres (ou plus), on peut associer de différentes façons les nombres deux par deux. Pour calculer le produit d’une somme par un nombre, on peut calculer le produit de chacun des termes par ce nombre, puis calculer la somme des résultats obtenus.

The complete table is given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

Time after         change in water     expression      water in tank  

sensor starts

0                              0                        770 + (0)(-14)        770

1                             -14                        770 + (1)(-14)         756

5                            -70                       770 + (5)(-14)        700

10                          -140                      770 + (10)(-14)       630

2)

Time after         change in water     expression      water in tank  

sensor starts

1                           -14                          770 + (1)(-14)         756

0                          0                           770 + (0)(-14)        770

-1                           14                          770 + (-1)(-14)        784

-2                          28                         770 + (-2)(14)        798
-3                          42                         770 + (-3)(14)         812

-4                          56                         770 + (-4)(14)         826

-5                          70                          770 + (-5)(-14)       840

Thus,

The complete table is given above.

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The complete question is given below.

a). The number of scores which are expected to be lower than 18.31 is; 16 scores.

b). The number of scorers that are expected to be below 32.38 is; 98 scores.

As evident in the task content; the 100 ACT scores in discuss are normally distributed, hence, all peculiar characteristics of a normal distribution apply.

First, since the mean is given as; 23 and the standard deviation is; 4.69.

By observation; 23 - 4.69 = 18.31 and

23 + 4.69 + 4.69 = 32.38.

a). Since the percentage of data values which fall below one standard deviation below the mean is; 15.9% which is approximately; 16%.

Therefore, the number of scores below the 18.31 score is; 16% of 100 = 16 scores.

b). Also, since the score; 32.38 is 2 standard deviations above the mean, and it follows from a normal distribution that the percentage of data values below such data value is; 97.7% which is approximately 98%.

Therefore, the number of scores which are expected to be below 32.38 is; 98% of 100 = 98.

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Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]

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The number in the replacement set that will make the equation true is (c) 112

From the question, we have the following parameters that can be used in our computation:

x ÷ 2 = 56

Rewrite the expression properly

so, we have the following representation

x/2 = 56

Also, we have the replacement set to be

{28, 56, 112}

In the given equation, we have the variable to be

The variable is x

Multiply 2 to both sides of the expression

So, we have the following representation

2  * x/2 = 56 * 2

Evaluate the products on both sides of the equation

x = 112

Hence, the solution is x = 112

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Answer:

y=-3.5

Step-by-step explanation:

substitute -4 for x

add 4 on both sides to get rid of the -4

divide -2 on both sides to isolate y

and you get 3.5 for y

The value of y that will satisfy the equation given is -3.5.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,

To find the same, just replace the value of x by -4,

-4-2y = 3

-2y = 7

y = -3.5

Hence, the value of y that will satisfy the equation given is -3.5.

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Answer:

90 degree

Step-by-step explanation:

since the original angle BAC is 90 degree, no matter the triangle is rotated or translated, the angle remain unchanged

Answer: x is -2 and y is 4 if needed (-2,4) is the origin form

Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of  y=-x+2 to y=-(-2)+2 mult  -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4

Please review the analysis for the dependent and independent variables. Equation: The total probability for the number w=160 m on the chart is 160 m.

Equation w=160 m.w (words) equals 160 words in the first minute and 320 words in the next two minutes. 800 words in five minutes, 480 words in three minutes, and 640 words in four minutes. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B).

The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. A probability is a number that expresses the possibility or likelihood that a specific event will take place.

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The half life of the iodine is obtained as 6.2 s.

Let us recall that the half  life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.

Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;

Half life = 0.693/K

Half life = 0.693/0.1113

Half life = 6.2 s

It would have the half life about 6.2 s.

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Answer:

-3

Step-by-step explanation:

i hope this helps

The test statistic from the factory population is 2.12. The p value is given as .017003.

We have the following values to solve the problem with

n = 58

sample mean x = 12.07

standard deviation = 0.25 meters

u = length = 12

The formula is given by

[tex]z= \frac{x-u}{sd/\sqrt{n} }[/tex]

when we insert the values we would have:

[tex]z= \frac{12.07-12}{0.25/\sqrt{58} }[/tex]

z = 0.07 / 0.033

z = 2.12

we have to find the p value when z = 2.12

The p value is 0.017003 using a statistical calculator

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Answer:

if the scale used 1/4 inch = 3 feet, then what is the perimeter of the actual garden? AI Recommended Answer: The perimeter of the actual garden is 144 feet.

Step-by-step explanation:

The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.

The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.

The present value is higher when the discount rate is lower, and vice versa.

The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.

In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).

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Answer:

The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.

To find the magnification, we can divide the size of the image by the size of the object:

Magnification = size of image / size of object

Plugging in the values, we have:

Magnification = 85mm / 23mm

Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.

Step-by-step explanation:

The table is completed as shown below and total earnings of Lori is found.

What exactly is total earnings of a person?

The wages paid for both regular working hours and other working hours, including extra work or tips are referred to as total earnings.

Consider Tuesday

Hours worked = 4

Base salary = 4 × 7 ( $7 per hour given)

                     = $28

Tips = 18% of food sales = 0.18 × 300 = $54

Total earnings on Tuesday = 28 + 54 = $82

In the similar way the table can be completed as below.

1) The total earnings of Lori for the week = 82+138.9+218.5+173 = $612.4

2) Total earnings in a year = 52 × 612.4 = $31844.8

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The number of yards of rope she can make for the step is 3 yards

From the question, we have the following parameters that can be used in our computation:

Yards of rope per step = 1/2 yards per step

Total number of steps = 6 steps

The number of yards of rope she can make for the step can then be calculated using the following equation

The number of yards of rope = Total number of steps * Yards of rope per step

Substitute the known values in the above equation, so, we have the following representation

The number of yards of rope = 1/2 * 6

Evaluate

The number of yards of rope = 3

Hence, the number of yards of rope is 3

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Complete question

Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?

The equation of p(x) in vertex form is p(x) = 3(x - 1)² - 2.

Option C is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

From the table,

From p(x) = 10 to p(x) = -2 the value of p(x) is decreasing and from p(x) = -2 to p(x) = 46 it is increasing.

So,

The vertex is (1, -2).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(1, -2) = (h, k)

Make (0, 1) = (x, p(x))

1 = a (0 - 1)² + (-2)

1 = a - 2

a = 1 + 2

a = 3

Thus,

The vertex equation of p(x).

p(x) = 3(x - 1)² - 2

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