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The expression (3a + 2b)^7 is a binomial expression;

The coefficient of the fourth term is 15120

The equation is given as:

(3a + 2b)^7

The above expression is a binomial expression;

Assume the expression is:

(x + y)^n

The equation of the expansion is:

[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]

When the expression is expanded, the parameters of the fourth term are

n = 7

r = 4

x = 3a

y = 2b

So, we have:

(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4

Evaluate each factor

(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4

Evaluate the powers

(3a + 2b)^7 = 35 * 27a^3 * 16b^4

Evaluate the product

(3a + 2b)^7 = 15120a^3b^4

The coefficient of the above expression is 15120

Hence, the coefficient of the fourth term is 15120

Read more about binomial expressions at:

https://brainly.com/question/13602562

Answer:

10

Step-by-step explanation:

The Interquartile Range (IQR) is the difference between Q3 and Q1.

From the diagram we see that Q1 = 40, and Q3 = 50

IQR = Q3-Q1 = 50 - 40 = 10

Answer:

1/7 and 1/2

Step-by-step explanation:

The probability of orange marble is 1/7

Probability of tails is 1/2

If you need to add this, then it'll be 1/14

7 x 2 = 14

1 x 1 = 1

Answer:

I believe a is equal to -54

Answer:

9

Step-by-step explanation:

Add all numbers together: 36

divide by the amount of numbers in the list: 9

                                      :)

Answer:

the answer without rounding is 147 but with its 100

Step-by-step explanation:

firsts you add up both sides of the triangle and then you subtract by 180 and now that you your answer but you had to round AN anyting above 150 you would have to run to 200 but you had one 47 so it's 100

Artificial selection picks previously existing qualities by breeding individuals with favourable traits, whereas genetic engineering affects the genetic composition of plants or animals by adding new genes or silencing genes.

Answer: 377.36cm^2

Step-by-step explanation:

1. find proper equation. to find the volume of any three dimensional cube or box, use: length * width * height

2. plug in given numbers into the equation: 8.9cm * 4cm * 10.6* which gives us our answer, 377.36cm^2

hoped this helped! ♡

The question asked by Troy is a statistical question because there would be variability in the answers he get fro the 12 maths teachers.

A statisical question is a question that can only be answered through the collection of data. Thhere would be variablility in the results gotten from the data.

A non- statistical question is a question that has only one answer. For example, how old are you? is a non-statistical question.

To learn more about a statisitcal question, please check: https://brainly.com/question/21508412

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

Volume is the amount of space occupied by a three dimensional shape or object.

Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:

Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³

Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

Find out more on volume at: https://brainly.com/question/12410983

Answer:

182 m

Step-by-step explanation:

The shape is a trapezoid. The area of the trapezoid formula is [tex]\frac{a + b}{2}h[/tex].

The two bases (AKA a and b) are 8 + 18.

The height is 14.

[tex]\frac{18+8}{2} 14[/tex], Add 18 + 8

[tex]\frac{26}{2}14[/tex], Divide 26 by 2

[tex]13 *14[/tex], 182

Answer:

x = 110

y = 23

Step-by-step explanation:

For X :

100 = x -10

110 = x

Corresponding angles are equal

For Y :

180 - 110 = 70

(2y + 24) = 70

2y = 46

y = 23

Adjacent Angles on a straight line add up to 180 Degrees

Step-by-step explanation:

120 in sq.  ,   260 in sq.Step-by-step explanation:question 1.area of a parralelogram = perperndicular height x basetherefore area = 8in x 15 inarea is 120in sq.question 2.the second parallelogram dimensions are as followsheight = 8 in +5 in = 13 inbase = 15in + 5in = 20therefore area = 13x20area = 260 in sq.

Answer:

Yes.

Step-by-step explanation:

because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.

Answer:

Mary has $1120

Step-by-step explanation:

money mary has at first : x

money jane has at first : y

Mary brought twice as much money as Jane : x=2y

Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240

=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]

=> x=1120

y=560

Answer:

Step-by-step explanation:

Let the amount mary and jane had be 2x and x respectively.

Let the equal amount be y:

[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]

Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:

[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]

Subtract the second equation from the first equation:

[tex] - y = - 320 \\ y = 320[/tex]

$320 was their equal amount.

Substitute 320 for y in any equation:

[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]

Therefore, Jane had $560 at first and Mary had $1120 at first.

Answer:

$168

Step-by-step explanation:

x + 3x = 672

4x = 672

x = 672 / 4

x = 168

Farah has $168

Answer:

y = 60 :)

Step-by-step explanation:

Triangle angle total measure: 180

We need to add upp the angles we know and subtract from the total 180, so we can figure out y.

60 + 60 + y = 180

120 + y = 180

180 - 120 = 60

y = 60

Now you know how to solve this type of problem!

Have a great day!!

Please rate and mark brainliest!!

Answer:

The value of y should be 60

Step-by-step explanation:

Tell me if its not right

[tex]\boxed{\bold{x = 2, 3}}[/tex]

Stepwise Solving:

[tex]\rightarrow \sf x^2-5x + 6 = 0[/tex]

[tex]\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

Identify the coefficients:

Solve for x:

[tex]\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}[/tex]

[tex]\dashrightarrow \ \sf x= 3, \ 2[/tex]

Answer:

83

Step-by-step explanation:

first add whatever is in the 1's place so for 38, 8 is in the 1's place and for 45, 5 is in the 1's place

so first it will be 8+5 which is 13 so you are going to carry the 1 over to the tens place so now it will be 30 + 40 + 10 and that equals 80 so you add 80 and 3 which looks like 80+3 and that equals 83

Answer:

I have no idea ask 567 9922 mathe teacher

Hey there!

[tex] \rm{\frac{5}{x} = \frac{7}{x + 2} }[/tex]

Solve:--

[tex] \sf\rightarrow \: (7)(x) = (5)(x + 2)[/tex]

[tex] \sf\rightarrow \: 7x = 5(x + 2)[/tex]

[tex] \sf\rightarrow \: 7x = 5x + 10[/tex]

[tex] \sf\rightarrow \: 7x - 5x= 5x + 10 - 5x[/tex]

[tex] \sf\rightarrow \: 2x= 10 [/tex]

[tex] \sf\rightarrow \: \frac{ 2x}{2}= \frac{10 }{2}[/tex]

[tex] \sf\rightarrow \: x= 5[/tex]

~Done~

Answer:

=1/6

Step-by-step explanation:

thats the answer

follow

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brainlest

pleassseee

Step-by-step explanation:

I hope its helped ! studied well.

Answer:

a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.

B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.

Step-by-step explanation:

b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.

Answer:

706.5m^2

Step-by-step explanation:

The sign is a circle

Area of a circle is (pi)r^2

d = 30 in -> r = d/2  = 30/2 = 15

Area = 3.14 x (15)^2 = 706.5m^2

Answer:

about 706.5 or 706.86

Step-by-step explanation:

to find this answer we need to use the area formula of a circle which is A = πr ^2

we know the diameter is 30, and the radius is half the of diameter, so we take 30 and divide it by 2, which should give us 15 for the radius. ( 30/2 = 15, so r = 15)

depending on how your teacher wants u to answer this you can use π on a calculator or use 3.14

now just plug in your numbers to formula

A = 3.14 * 15^2 or A = π * 15^2

and should equal about 706.5 or 706.86 (depending on if you use 3.14 or π)

Answer:

132

Step-by-step explanation:

since they are 180 degrees subtract

Answer:

132

Step-by-step explanation:

since this is a 180 degree angle ABC will be

180-48

132

Answers:

Angle T = 79 degrees

Angle V = 14 degrees

=========================================================

Work Shown:

T + V = 93

(2x+85) + (5x+29) = 93

7x+114 = 93

7x = 93-114

7x = -21

x = -21/7

x = -3

This x value is used to find each angle mentioned.

As a check, T+V = 79+14 = 93 which confirms our answers.

Answer:

An alternate interior angle, c, 180 degrees

Step-by-step explanation:

did it

Answer: 30 units^2

Step-by-step explanation:

[tex]\mathrm{From \ the \ figure \ we \ know \ this \ is \ a \ right \ triangle. \ The \ area \ of \ the \ triangle}:[/tex]

[tex]A = \frac{1}{2}bh \\= \frac{1}{2} \times 6 \times 10\\= 30 \ units^2[/tex]

(Formula for area of right triangle: Half of the product of two right edges)

Therefore, the area of the triangle is 30 units^2